American Practical Navigator

GE EH

9 Kë

Digitized by the Internet Archive
in 2025

https://archive.org/details/bwb_S0-CBU-308

H.O. Pub. No. 9

AMERICAN
PRACTICAL NAVIGATOR

AN EPITOME OF NAVIGATION

ORIGINALLY BY
NATHANIEL BOWDITCH, LL.D.

1966— Corrected Print

PUBLISHED BY THE
U.S. NAVAL OCEANOGRAPHIC OFFICE
UNDER THE AUTHORITY OF THE

SECRETARY OF THE NAVY

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON : 1966

For sale by authorized Sales Agents of the U.S. Naval Oceanographic Office, also the
Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Price $7.

Last painting by Gilbert Stuart (1828). Considered by the family of

Bowditch to be the best of various paintings made, although it was unfinished
when the artist died.

NATHANIEL BOWDITCH
(1773-1838)

Nathaniel Bowditch was born on March 26, 1773, at Salem, Mass., fourth of the
seven children of shipmaster Habakkuk Bowditch and his wife, Mary. j

Since the migration of William Bowditch from England to the Colonies in the
17th century, the family had resided at Salem. Most of its sons, like those of other
families in this New England seaport, had gone to sea, and many of them became
shipmasters. Nathaniel Bowditch himself sailed as master on his last voyage, and
two of his brothers met untimely deaths while pursuing careers at sea.

It is reported that Nathaniel Bowditch's father lost two ships at sea, and by late
Revolutionary days he returned to the trade of cooper, which he had learned in his
youth. This provided insufficient income to properly supply the needs of his growing
family, and hunger and cold were often experienced. For many years the nearly
destitute family received an annual grant of fifteen to twenty dollars from the Salem
Marine Society. By the time Nathaniel had reached the age of ten, the family's poverty
necessitated his leaving school and joining his father in the cooper's trade.

Nathaniel was unsuccessful as a cooper, and when he was about 12 years of age,
he entered the first of two ship-chandlery firms by which he was employed. It was
during the nearly ten years he was so employed that his great mind first attracted public
attention. From the time he began school Bowditch had an all-consuming interest in
learning, particularly mathematics. By his middle teens he was recognized in Salem
as an authority on that subject. Salem being primarily a shipping town, most of the
inhabitants sooner or later found their way to the ship chandler, and news of the bril-
liant young clerk spread until eventually it came to the attention of the learned men
of his day. Impressed by his desire to educate himself, they supplied him with books
that he might learn of the discoveries of other men. Since many of the best books
were written by Europeans, Bowditch first taught himself their languages. French,
Spanish, Latin, Greek, and German were among the two dozen or more languages
and dialects he studied during his life. At the age of 16 he began the study of Newton’s
Principia, translating parts of it from the Latin. He even found an error in that classic,
and though lacking the confidence to announce it at the time, he later published his
findings and had them accepted.

During the Revolutionary War a privateer out of Beverly, a neighboring town to
Salem, had taken as one of its prizes an English vessel which was carrying the phil-
osophical library of a famed Irish scholar, Dr. Richard Kirwan. The books were
brought to the Colonies and there bought by a group of educated Salem men who used
them to found the Philosophical Library Company, reputed to have been the best
library north of Philadelphia at the time. In 1791, when Bowditch was 18, two
Harvard-educated ministers, Rev. John Prince and Rev. William Bentley, persuaded
the Company to allow Bowditch the use of its library. Encouraged by these two men
and a third—Nathan Read, an apothecary and also a Harvard man—Bowditch studied
the works of the great men who had preceded him, especially the mathematicians and
the astronomers. By the time he became of age, this knowledge, acquired before and
after his long working hours and in his spare time, had made young Bowditch the out-

standing mathematician in the Commonwealth, and perhaps in the country.
3

4 NATHANIEL BOWDITCH

In the seafaring town of Salem, Bowditch was drawn to navigation early, learning
the subject at the age of 13 from an old British sailor. A year later he began studying
surveying, and in 1794 he assisted in a survey of the town. At 15 he devised an almanac
reputed to have been of great accuracy. His other youthful accomplishments included
the construction of a crude barometer and a sundial.

When Bowditch went to sea at the age of 21, it was as captain’s writer and nominal
second mate, the officer’s berth being offered him because of his reputation as a scholar.
Under Captain Henry Prince, the ship Henry sailed from Salem in the winter of 1795
on what was to be a year-long voyage to the Ile de Bourbon (now called Īle de la
Réunion) in the Indian Ocean. |

Bowditch began his seagoing career when accurate time was not available to the
average naval or merchant ship. A reliable marine chronometer had been invented
some 60 years before, but the prohibitive cost, plus the long voyages without opportunity
to check the error of the timepiece, made the large investment an impractical one. A
system of determining longitude by “lunar distance,” a method which did not require
an accurate timepiece, was known, but this product of the minds of mathematicians
and astronomers was so involved as to be beyond the capabilities of the uneducated
seamen of that day. Consequently, ships navigated by a combination of dead reckon-
ing and parallel sailing (a system of sailing north or south to the latitude of the destina-
tion and then east or west to the destination).

To Bowditch, the mathematical genius, computation of lunar distances was no
mystery, of course, but he recognized the need for an easier method of working them
in order to navigate ships more safely and efficiently. Through analysis and observa-
tion, he derived a new and simplified formula during his first trip, a formula which was
to open the book of celestial navigation to all seamen.

John Hamilton Moore's The Practical Navigator was the leading navigational
text when Bowditch first went to sea, and had been for many years. Early in his
first voyage, however, the captain's writer-second mate began turning up errors in
Moore's book, and before long he found it necessary to recompute some of the tables
he most often used in working his sights. Bowditch recorded the errors he found,
and by the end of his second voyage, made in the higher capacity of supercargo, the
news of his findings in The Practical Navigator had reached Edmund Blunt, a publisher
at Newburyport, Mass. At Blunt's request, Bowditch agreed to correct Moore's
book. The first edition of The New Practical Navigator was published in 1799, with
correction of the errors Bowditch had found to that time, and with some additional
information. The following year a second edition was published with additional
corrections. Bowditch eventually found more than 8,000 errors in the work, however,
and it was finally decided to completely rewrite the book and to publish it under his
own name. In 1802 the first edition of The New American Practical Navigator by
Nathaniel Bowditch was published, and his vow to put nothing in the book he could
not teach every member of his crew served to keep the work within the understanding
of the average seaman. In addition to the improved method of determining longitude,
Bowditch’s book gave the ship’s officer information on winds, currents, and tides;
directions for surveying; statistics on marine insurance; a glossary of sea terms;
instruction in mathematics; and numerous tables of navigational data. His simplified
methods, easily grasped by the intelligent seaman willing to learn, paved the way for
"Yankee" supremacy of the seas during the clipper ship era.

Two months before sailing for Cadiz on his third voyage, in 1798, Bowditch married
Elizabeth Boardman, daughter of a shipmaster. While he was away, his wife died at

NATHANIEL BOWDITCH 5

the age of 18. Two years later, on October 28, 1800, he married his cousin, Mary
Ingersoll, she, too, the daughter of a shipmaster. They had eight children.

Bowditch made a total of five trips to sea, over a period of about nine years, his last
as master and part owner of the three-masted Putnam. Homeward bound from a 13-
month voyage to Sumatra and the Ile de France (now called Mauritius) the Putnam
approached Salem harbor on December 25, 1803, during a thick fog without having
had a celestial observation since noon on the 24th. Relying upon his dead reckoning,
Bowditch conned his wooden-hulled ship to the entrance of the rocky harbor, where he
had the good fortune to get a momentary glimpse of Eastern Point, Cape Ann, enough
to confirm his position. The Putnam proceeded in, past such hazards as “Bowditch's
Ledge” (named after a great-grandfather who had wrecked his ship on the rock more
than a century before) and anchored safely at 1900 that evening. Word of the daring
feat, performed when other masters were hove-to outside the harbor, spread along the
coast and added greatly to Bowditch’s reputation. He was, indeed, the “practical
navigator.”

His standing as a mathematician and successful shipmaster earned him a lucrative
(for those times) position ashore within a matter of weeks after his last voyage. He
was installed as president of a Salem fire and marine insurance company, at the age
of 30, and during the 20 years he held tbat position the company prospered. In 1823
he left Salem to take a similar position with a Boston insurance firm, serving that
company with equal success until his death.

From the time he finished the “Navigator” until 1814, Bowditch's mathematical
and scientific pursuits consisted of studies and papers on the orbits of comets, applica-
tions of Napier’s rules, magnetic variation, eclipses, calculations on tides, and the chart-
ing of Salem harbor. In that year, however, he turned to what he considered the
greatest work of his life, the translation into English of Mécanique Céleste, by Pierre
Laplace. Mécanique Céleste was a summary of all the then known facts about the
workings of the heavens. Bowditch translated four of the five volumes before his
death, and published them at his own expense. He gave many formula derivations
which Laplace had not shown, and also included further discoveries following the
time of publication. His work made this information available to American astronomers
and enabled them to pursue their studies on the basis of that which was already known.
Continuing his style of writing for the learner, Bowditch presented his English version
of Mécanique Céleste in such a manner that the student of mathematics could easily
trace the steps involved in reaching the most complicated conclusions.

Shortly after the publication of The New American Practical Navigator, Harvard
College honored its author with the presentation of the honorary degree of Master
of Arts, and in 1816 the college made him an honorary Doctor of Laws. From the
time the Harvard graduates of Salem first assisted him in his studies, Bowditch had a
great interest in that college, and in 1810 he was elected one of its Overseers, a position
he held until 1826, when he was elected to the Corporation. During 1826-27 he was
the leader of a small group of men who saved the school from financial disaster by
forcing necessary economies on the college’s reluctant president. At one time Bow-
ditch was offered a Professorship in Mathematics at Harvard but this, as well as
similar offers from West Point and the University of Virginia, he declined. In all his
life he was never known to have made a public speech or to have addressed any large
group of people.

Many other honors came to Bowditch in recognition of his astronomical, math-
ematical, and marine accomplishments. He became a member of the American

6 NATHANIEL BOWDITCH

Academy of Arts and Sciences, the East India Marine Society, the Royal Academy of
Edinburgh, the Royal Society of London, the Royal Irish Academy, the American
Philosophical Society, the Connecticut Academy of Arts and Sciences, the Boston
Marine Society, the Royal Astronomical Society, the Palermo Academy of Science,
and the Royal Academy of Berlin.

Nathaniel Bowditch outlived all of his brothers and sisters by nearly 30 years.
Death came to him on March 16, 1838, in his sixty-fifth year. The following eulogy
by the Salem Marine Society indicates the regard in which this distinguished American
was held by his contemporaries:

“In bis death a public, a national, a human benefactor has departed. Not this
community, nor our country only, but the whole world, has reason to do honor to his
memory. When the voice of Eulogy shall be still, when the tear of Sorrow shall cease
to flow, no monument will be needed to keep alive his memory among men; but as long
as ships shall sail, the needle point to the north, and the stars go through their wonted
courses in the heavens, the name of Dr. Bowditch will be revered as of one who helped
his fellow-men in a time of need, who was and is a guide to them over the pathless
ocean, and of one who forwarded the great interests of mankind.”

The New American Practical Navigator was revised by Nathaniel Bowditch several
times after 1802 for subsequent editions of the book. After his death, Jonathan
Ingersoll Bowditch, a son who made several voyages, took up the work and his name
appeared on the title page from the eleventh edition through the thirty-fifth, in 1867.
In 1868 the newly organized U. S. Navy Hydrographic Office bought the copyright
and has published the book since that time, revisions being made from time to time
to keep the work in step with navigational improvements. The name has been
altered to the American Practical Navigator, Hydrographic Office Publication No. 9,
but the book is still commonly known as “Bowditch.” A total of more than 700,000
copies has been printed in about 70 editions during the more than a century and a
half since the book was first published in 1802. It has lived because it has combined
the best thoughts of each generation of navigators, who have looked to it as their final
authority.

PREFACE

This epitome of navigation has been maintained since its initial publication in
1802. The account of its origin, immediate success, and perpetuation appears so
inseparable from the accomplishments of its original author, Nathaniel Bowditch,
that it has been included in the life résumé of this illustrious navigator and author.

In this extensively revised edition, the U. S. Navy Hydrographic Office has included
timely information consistent with modern practices and techniques. The text has
been completely rewritten. Since a primary objective has been to provide a reference
publication, some duplication exists, cross-referencing is extensive, and the index is
detailed. All illustrations are new. Color has been added where it serves a useful
purpose. Practice problems have been included with some chapters. Selected
references have been given where complete coverage would be inappropriate.

The appendix has been enlarged, and the table arrangement improved. Certain
tables of previous editions have been omitted, some of those retained have been altered,
and new ones have been added.

The intent of the original author to provide a compendium of navigational material
understandable to the mariner has been consistently followed. However, navigation
is not presented as a mechanical process to be followed blindly. Rather, emphasis
has been given to the fact that the aids provided by science can be used effectively to
improve the art of navigation only if a well-informed person of mature judgment and
experience is on hand to interpret information as it becomes available. Thus, the facts
needed to perform the mechanics of navigation have been supplemented with addi-
tional material intended to help the navigator acquire perspective in meeting the
various needs that arise.

Many institutions, organizations, groups, and individuals have assisted in the
preparation of this publication, but all of the material has been edited by one individual
to assure continuity and consistency. Particular acknowledgment is given the follow-
ing: Mr. Charles L. Petze, Jr. for assistance in preparation of chapter I; the U. S.
Navy Bureau of Ships for information relating to chapters VI and VII; the U. S. Naval
Research Laboratory for review of part three; the U. S. Naval Observatory for infor-
mation relating to chapter XIV and for suggestions relating to appendices F, H, I, and
X; the Corps of Engineers of the U. S. Army for assistance in preparation of chapter
XXVII; the U. S. Coast and Geodetic Survey of the Department of Commerce for
preparation of chapter XXXI, and for providing information on geomagnetism and
data for appendix M and most of table 5; the U. S. Weather Bureau for assistance in
preparation of part seven and tables 16 and 17; the National Bureau of Standards of the
Department of Commerce for assistance in preparation of appendix D; the U. S. Naval
Institute for permission to use modified versions of work forms published in Dutton's
Navigation and Nautical Astronomy (copyrighted 1943, 1948, 1951); the U. S. Power
Squadrons for suggestions relating to the graph of article 924 for height of tide determi-
nation, navigation of small craft (art. 2310), and table 3; and many individuals, espe-
cially experienced practicing navigators, who have offered constructive suggestions or

directed attention to errors in previous editions.
7

PREFACE TO THE 1962 REPRINT

This 1962 corrected reprint has presented the opportunity to incorporate new and
timely information. Adoption by the United States of new equivalents for length and
mass and of new values for absolute zero necessitated a major revision of Appendix D.
Minor corrections to tables 6,11,17,20,21,and the text, resulting from these changes, have
been made. Hydrographic Office publication numbers now conform to the numbering
system in use since 1960. The sections relating to air navigation publications and
space navigation have been rewritten. The revised Loran-A coverage diagram includes
all rates operational in 1961. Appendix S, Maritime Positions, now includes revised
material for Africa as well as several new ports.

In addition to the correction of errors published in errata sheets for the 1958 edition,
other minor unpublished ones have been corrected. Editorial changes have provided
clarification of certain parts of the text and some illustrations have been modified to
present information more clearly. All appendices now carry their numerical or al-
phabetical designation at the top of each page. A list of contents now immediately
precedes each part of the volume.

For practical navigation, the additions, corrections, and revisions incorporated in
this reprint are not considered to be of sufficient scope and magnitude to necessitate
replacement of the 1958 printing.

H.O. Pub. No. 9—Tables, including 1 through 34, is now available as a separate
volume entitled “Tables from the American Practical Navigator—Bowditch."

PREFACE TO THE 1966 CORRECTED PRINT

This printing includes modifications and minor corrections to the previous 1962
printing. Appendix K has been revised so that it conforms to the nautical chart
symbols listed in the September 1963 edition of Chart No. 1. The text, references,

appendices, and index have been modified to reflect recent changes in United States
Government publications.

The change in the name of the U.S. Navy Hydrographie Office to U.S. Naval
Oceanographic Office has not been indicated in this print.
The modifications and corrections incorporated in this 1966 print are not considered

sufficient to warrant replacement of either the 1958 edition or the 1962 corrected print
for ordinary purposes of navigation.

CONTENTS

UNT P
` anre TT TA E Wa
K Rūniel Bowditch Hee 22.2220ibratvn1⁄ bool LEY ZY nama
IE E TAIANA 7

PART ONE

FUNDAMENTALS

CHAPTER I. History of Navigation___________- MESA LA US 15
CAPTER ABA Definitions ArT Pale M ma A 62
pre is Charalrojections O Pan sr ee 69
Kipere iw Charts and Publications ae Nuu S E 93
era VT Des NauticālkOhbartft Bele Ma Sey o E 103

PART TWO

PILOTING AND DEAD RECKONING

CHAPTER VI. Instruments for Piloting and Dead Reckange 121
GEVI kGConpasssError C eo ss ave pee See ee eee 158
Weeer VI Dead Reckoning Mesto Beep D as Mss ME. SE E ous 213
CHAPTER IX. Piloting_ _----- E A ARM E LEA) a cm de ee 240

PART THREE

ELECTRONIC NAVIGATION

A A A EE E R AN MASA ds S 289
@eerrer AI M Electronics. and Navigation Me 270 DO S00 Siete LE a. 304
CuHapTer XII. Direction and Distance by Electronics__-_-.----.---------- A UE
GEHXPPER-XIIIAHyperbolic Systems. S == Ee 2 = ee ina») dk re ss DOS

PART FOUR

CELESTIAL NAVIGATION

Greng XIV. Navigational Astronomy. -See =ausLuzaadd.. dd 351
CHAPTER XV. Instruments for Celestial Navigation __-.---.---------------- 398
Omarrek X VI. Sextant Altitude Corrections 2.202 ae Ed -- 2 acte 421
CHAPTER XVII. Lines of Position from Celestial Observations. - - ------------ 449
a norm XVIII The Almanacs ds Haces anat) ap 2 Jas 466
Gnarr X Aseme ea m4. A < ass ss AERE + ge 482
CHAPTER XX. Sight Reduction --..+-.---+-----------+-+++-+-----+------- 502
CuarreR XXI. Comparison of Various Methods of Sight Reduction.......... 517
Gnaprez X XII. Identification of Celestial Bodies. .. -..-2----.-224------.-- 575

10 CONTENTS

PART FIVE
THE PRACTICE OF NAVIGATION E
CHaPTER XXIII. The Practice of Marine Navigation.........-...--.------- 595
CHAPTER XXIV. Submarine Nāvigātione ss r S 607
GCuaPTER AA V. Polar Navigation ...- sa S» 612
GuarrER XXVI. lifeboat Navigation <=. 2... o... 645
CHAPTER XXVII. Land Navigation. ` < ` «Siri E ae 664
CHAPTER XXVIII. Aw Navigation uec xen 670
CHAPTER XXX NavigationaHrrors- EE 678

PART SIX
OCEANOGRAPHY

CHAPTER XXX. The Oceans. oc =: + on. ot ee A 691
(CHAPTER XXXI Tides and ‘Tidal Currents -e pss ee 703
GHAPTER AA XII. Ocean Currents. 30 sea tr ea E 718
(CHAPTER AS A TH. Ocean Waves. J e= E Pame E LE EE 727
CHAPTER XXXIV. Amphibious Operations... S SS GER
CHAPTER X.XX V. Sound m the Eege 742
CmiprER CX XVLEIcednsbhe Sea ee e xac ME 746

PART SEVEN

WEATHER
CHAPTER XXXVII. Weather Observations--- OAINNT Pe eee 765
CHAPTER XXXVIII. Weather and Weather Rorecasts TT 793
CHAPTER XXXIX Tropical’ Gy clones M co" "T" 819

PART EIGHT

HYDROGRAPH Y
CHAPTER XL. Instruments for Hydrographic Surveying... 2 222 837
CHAPTER XLI. Hydrographic Surveying. yd ae beta Tp TIPS 848
CHAPTER XLII. Oceanic Soundings. <. «AS 868
Cuaprer ALIS Photogrammetry Jaa 874
CuaPrER XLIV. Production of Nautical Oharts a 886
APPENDICES

APPENDIX A. Abbreviations and Symbols. www. IA 903
APPENDIX D. Greek Alphabet... emra E 908
APPENDIX C. Glossary.........2... ego) SL, OE 909
APPENDIX D. Miscellaneous Datād V 0 MMT AS 954
APPENDIX E. Navigational Coordinātes EM PS 963
APPENDIX F. Planeís............. ee 964
APPENDIX G. Identification of Navigational Star 2 2 965
APPENDIX H. Navigational Stars and the Planets- 0 7 7 973
APPENDIX I. Constellations....... Að 974
APPENDIX J. Buoyage Systems NE 976

APPENDIX K. Chart Symbols

APPENDIX L. Units of Depth Measurement on Charts of Various Nations
APPENDIX M. Tidal Datums in Use in Various Areas
APPENDIX N. Sources of Charts and Publications
APPENDIX O. Mathematics
APPENDIX P. Interpolation
APPENDIX Q. Work Forms
APPENDIX R. Beaufort Scale
APPENDIX S. Maritime Positions
APPENDIX T. Extracts from Tide Tables
APPENDIX U. Extracts from Tidal Current Tables

CONTENTS

APPENDIX V. Extracts from Nautical Almanac________-__-___-___---------
merenorxs W Extracts from Air Almanac 2 econo ssem EE
DEPENDIS « Long-term Almanac sk 2 2 css as ods sea oe o ee
Ee Estractstfron EC bub, No. 260.2 ee
IPOD EE iron H.OSPub*No.201:-: 5:599 BO S
EPDPENDIXEA A. RExtracta irom,.H.0..PubR@Nosi4e_... cro e
EE A frons IO. Pub NO.221. 25: 29 A
APPENDIX CO Extracts fromyH.Oc Pub. Ņot249% rs =. lll. E

AA Ee oe Er as ag ds A da E

TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE

TABLE
TABLE
TABLE
TABLE
TABLE

TABLE

TABLE

COM orion Anele a pm E
. Conversion of Compass Points to Degrees_-_-_----------_---------
TAN Y a PN
ZOouvepasen Table for Meridional! Parts ls eer
"Exi udenmaParis SSS see re Ae Spite A RUE dde
. Length of a Degree of Latitude and Longitude. .................-
SDistance of an Object by lwo Bearings: ree --
NEDisanceotihe Horizon x eee 0 ee UM ee oes
WM DistancoibyaVerticalAngle re c o
. Direction and Speed of True Wind in Units of Ship's Speed. ......
. Correction of Barometer Reading for Height Above Sea Level. - - --
^ Correction of Barometer Reading for Gravity m m
. Correction of Barometer Reading for Temperature. ............--
. Conversion Table for Millibars, Inches of Mercury, and Millimeters

Of Mercure s <. 9 e a Í `` `

"Conversion Table for Thermometer Scales._....-_-..--:....-----
Selvindi y EE
. Zënse eerie Ru Ss LPA AS as ee
. Speed Table for Measured Mile. -------------------------------
19.
TABLE 20.
TABLE 21.
D
TABLE 23.
TABLE 24.
TABLE 25.
26.
TABLE 24.
TABLE 28.

Speed, Time, and Distance. e oome
Conversion Table for Nautical and Statute Miles_-__---.----------
Conversion Table for Meters, Feet, and Fathoms. ---------.-------
Dip of the Sea Short of the Horizon. --------------------------
Altitude Correction for Air Temperature. ........--.-.----------
Altitude Correction for Atmospheric Pressure. .......-.-..-------
Meridian Angle and Altitude of a Body on the Prime Vertical Circle. . -
Latitude and Longitude Factors____.--.--.------=---~---------

Ain em 3 oe o -- >= SEE
Correction of Amplitude as Observed on the Visible Horizon... - --

11

Pago

999
1000
1002
1005
1045
1052
1059
1060
1129
1132
1136

12

TABLE 29.
TABLE 30.
TABLE 31.
TABLE 32.
'T ABLE 33.
TABLE 34.

CONTENTS

Page
Altitude: Factor 4.4041 ra 1apureyess 1d Ap oue T. ae 1298
Change of Altitude in Given Time from Meridian Transit_-------- 1308
Natural Trigonometric Functions 21 Loc Miri cene C7 OS 1312
Logarithms. of: Numbers... ..--<-2.----- men - SES 1357
Logarithms of Trigonometric Functions. .....---------2...-----2 1376
Haversines ee coo coe o AVE eee ee IN 1421

1457

PART ONE
FUNDAMENTALS

PART ONE

FUNDAMENTALS
CHAPTER I. History of Navigation. EE 15
CHAPTER II. Basic Definitions... e 62
CHAPTER lil ChartProjections =... - ae Cp 69
CHARTER IV: Charts and Publications ES ÓN 93

CHAPTER V. The Nautical Chart... Loca ee I 103

CHAPTER I
HISTORY OF NAVIGATION

Introduction

101. Background.—Navigation began with the first man. One of his first con-
scious acts probably was to home on some object that caught his eye, and thus land
navigation was undoubtedly the earliest form. His first venture upon the waters
may have come shortly after he observed that some objects float, and through curiosity
or an attempt at self-preservation he learned that a larger object, perhaps a log, would
support him. Marine navigation was born when he attempted to guide his craft.
Air navigation by men, of course, came much later.

The earliest marine navigation was a form of piloting, which came into being as
man became familiar with landmarks and used them as guides. Dead reckoning
probably came next as he sought to predict his future positions, or perhaps as he
bravely ventured farther from landmarks. Celestial navigation, as it is known today,
had to await acquisition of information regarding the motions of the heavenly bodies,
although these bodies were used to steer by almost from the beginning. Electronic
navigation is the modern application of a different form of energy to solve an old
problem, its principal use being to extend the range of piloting.

102. From art to science.—Navigation is the process of directing the movements
of a craft from one point to another. To do this safely is an art. In perhaps 6,000
years—some writers make it 8,000—man has transformed this art almost into a science,
and navigation today is so nearly a science that the inclination is to forget that it was
ever anything else. It is commonly thought that to navigate a ship one must have a
chart to determine the course and distance, a compass to steer by, and a means of
determining the positions of the ship during the passage. Must have? The word
“must” betrays how dependent the modern navigator has become upon the tools
now in his hands. Many of the great voyages of history —voyages that made known
much of the world—were made without one or more of these "essentials."

103. Epic voyages.—History records a number of great voyages of varying navi-
gational significance. Little or nothing is known of the navigational accomplishments
of the ancient mariners, but the record of the knowledge and equipment used during
later voyages serves to illustrate periodic developments in the field.

104. Pre-Christian navigation Down through the stream of time a number of
voyages have occurred without navigational significance. Noah’s experience in the
ark is of little interest navigationally, except for his use of a dove to locate land. There
is evidence to support the view that at least some American Indians reached these
shores by sea, the earliest of several groups probably having come about 2200 BC,
the approximate time that a general exodus seems to have occurred from a center in
southwestern Asia. This is about the time the Tower of Babel is believed to have been
built. It is noteworthy that almost every land reached by the great European explorers
was already inhabited.

It is not difficult to understand how a people not accustomed to the sea might make
a single great voyage without contributing anything of significance to the advancement

of navigation. Not so clear, however, is the fact that the Norsemen and the Poly-
15

16 HISTORY OF NAVIGATION

nesians, great seafaring people, left nothing more than conflicting traditions of their
methods. The reputed length of the voyages made by these people suggests more
advanced navigational methods than their records indicate, although the explanation
may be that they left few written accounts of any kind. Or perhaps they developed
their powers of perception to such an extent that navigation, to them, was a highly
advanced art. In this respect their navigation may not have differed greatly from that
of some birds, insects, fishes, and animals.

One of the earliest well-recorded voyages is known today through the book of ob-
servations written by Pytheas of Massalia, a Greek astronomer and navigator. Some-
time between the years 350 BC and 300 BC he sailed from a Mediterranean port
and followed an established trade route to England. From there he ventured north
to Scotland and Thule, the legendary land of the midnight sun. He went on to
explore Norwegian fiords, and rivers in northwest Germany. He may have made
his way into the Baltic.

Pytheas’ voyage, and others of his time, were significant in that they were the
work of men who had no compasses, no sextants, no chronometers, no electronic devices
such as are commonplace today. The explanation of how they did it is not what
some historians have said, that before seafaring men had adequate equipment, the
compass especially, they hugged the shore and sailed only by daylight in fair weather.
Many undoubtedly did use this practice. But the more intrepid did not creep along
the coast, venturing nothing more daring than sailing from headland to headland.
They were often out of sight of land, and yet knew sufficiently well where they were
and how to get home again. They were able to use the sun, the stars, and the winds
without the aid of mechanical devices.

Pytheas had none of the equipment considered essential by the modern navigator—
none, at least, as it is thought of today. It would be incorrect, however, to say
that he had no navigational aids whatever. He was not the first to venture upon the
sea, and even in his time man was the inheritor of his predecessors’ knowledge.

He must have known what the mariners of his time, Phoenician and Greek, knew
about navigation. There was a fair store of knowledge about the movements of the
stars, for example, which all seafaring men shared. They had a practical grasp of
some part of what is now called celestial navigation, for the moving celestial bodies
were their compasses. Pytheas may not have been acquainted with the Periplus of
Scylax, the earliest known sailing directions, but it is reasonable to suppose that he had
similar information.

If there were sailing directions, there may well have been charts of a sort, even
though no record of them exists.

Even if Pytheas and his contemporaries had sailing directions and charts, these
must have been far from comprehensive, and they undoubtedly did not cover the
areas north of Britain. But these early seamen knew direction by day or night if the
sky was clear, and they could judge it reasonably well when the sky was overcast, using
the wind and the sea. They knew the hot Libyan wind from the desert—today called
the sirocco—and the northern wind, the mistral.

They could estimate distance. Their ships must have carried some means of
measuring time—the sand glass was known to the ancients—and they could estimate
speed by counting the strokes of the oars, a common practice from galley to modern
college racing shell. Mariners who spent their lives traveling the Mediterranean knew
what their ships could do, even if today itis not known what they meant by “a day’s
sail” —whether 35 miles, or 50, or 100.

105. Sixteenth century navigation.—Progress in the art of navigation came slowly
during the early centuries of the Christian era, all but stopped during the Dark Ages,

HISTORY OF NAVIGATION 17

and then spurted forward when Europe entered a golden age of discovery. The
circumnavigation of the globe by the expedition organized by Ferdinand Magellan,
a disgraced Portuguese nobleman who sailed under the flag of Spain, was a voyage
which illustrates the advances made during the 1,800 years following Pytheas.

Magellan was able to find justification for his belief that a navigable pass to the
Pacific Ocean existed in high southern latitudes, in Martin Behaim's globe or chart of
the world, in the globe constructed by Johann Schoner of N uremberg in 1515, and in
Leonardo da Vinci's map of the world drawn in the same year. He obtained further
information for his voyage from Ruy Faleiro, an astronomer and cartographer whose
charts, sailing directions, nautical tables, and instructions for use of the astrolabe and
cross-staff were considered to be among the best available. Faleiro was also an advocate
of the fallacious methods of determining longitude by variation.

When Magellan sailed in 1519, his equipment included sea charts, parchment skins
to be made into charts en route, a terrestrial globe, wooden and metal theodolites,
wooden and wood-and-bronze quadrants, compasses, magnetic needles, hour glasses
and “timepieces,” and a log to be towed astern.

So the 16th century navigator had crude charts of the known world, a compass to
steer by, instruments with which he could determine his latitude, a log to estimate speed,
certain sailing directions, and solar and traverse tables. The huge obstacle yet to be
overcome was an accurate method of determining longitude.

106. Eighteenth century navigation.—Little is known today of the “timepieces”
carried by Magellan, but surely they were not used to determine longitude. Two hun-
dred years later, however, the chronometer began to emerge. With it, the navigator, for
the first time, was able to determine his longitude accurately and fix his position at sea.

The three voyages of discovery made by James Cook of the Royal Navy in the
Pacific Ocean between 1768 and 1779 may be said to mark the dawn of modern nav-
igation. Cook's expedition had the full backing of England's scientific organiza-
tions, and he was the first captain to undertake extended explorations at sea with
navigational equipment, techniques, and knowledge that might be considered modern.

On his first voyage Cook was provided with an astronomical clock, a “journeyman”
clock, and a watch lent by the Astronomer Royal. With these he could determine,
longitude, using the long and tedious lunar distance method. On his second voyage
four chronometers were provided. These instruments, added to those already pos-
sessed by the mariner, enabled Cook to navigate his vessels with a precision undreamed
of by Pytheas and Magellan.

By the time Cook began his explorations, astronomers had made great contribu-
tions to navigational advancement, and the acceptance of the heliocentric theory
of the universe had led to the publication of the first official nautical almanac. Charts
had progressed steadily, and adequate projections were available. With increased
understanding of variation, the compass had become reliable. Good schools of
navigation existed, and textbooks which reduced the mathematics of navigation to
the essentials had been published. Speed through the water could be determined with
reasonable accuracy by the logs then in use. Most important, the first chronometers
were being produced.

107. Twentieth century navigation.—The maiden voyage of the SS United States
in July 1952 served to illustrate the progress made in navigation during the 175 years
since Cook's voyages. Outstanding because of its record trans-Atlantic passage,
the vessel is of interest navigationally in that it carried the most modern equipment
available and exemplified the fact that navigation had become nearly a science.

Each of the deck officers owned a sextant with which he could make observations
more accurately than did Cook. Reliable chronometers, the product of hundreds of

18 HISTORY OF NAVIGATION

years of experimental work, were available to determine the time of each observation.
The gyro compass indicated true north regardless of variation and deviation.

Modern, convenient almanacs were used to obtain the coordinates of various
celestial bodies, to an accuracy greater than needed. Easily used altitude and azimuth
tables gave the navigator data for determining his Sumner (celestial) line of position
by the method of Marcq St.-Hilaire. Accurate charts were available for the waters
plied, sailing directions for coasts and ports visited, light lists giving the characteristics
of the various aids to navigation along these coasts, and pilot charts and navigational
texts for reference purposes.

Electronics served the navigator in a number of ways. Radio time signals and
weather reports enabled him to check his chronometers and avoid foul weather. A
radio direction finder was available to obtain bearings, and a radio telephone was used
to communicate with persons on land and sea. The electrically operated echo sounder
indicated the depth of water under the keel, radar the distances and bearings of objects
within range, even in the densest fog. Using loran, the navigator could fix the position
of his ship a thousand miles and more from transmitting stations.

Piloting and Dead Reckoning

108. Background.—The history of piloting and dead reckoning extends from man’s
earliest use of landmarks to the latest model of the gyro compass. In the thousands
of years between, navigation by these methods has progressed from short passages
along known coast lines to transoceanic voyages during which celestial observations
cannot be, or are not, made.

109. Charts.—A form of sailing directions was written several hundred years
before Christ. Although charts cannot be traced back that far, they may have existed
during the same time. From earliest times men have undoubtedly known that it is
more difficult to explain how to get to a place than it is to draw a diagram, and since the
first charts known are comparatively accurate and cover large areas, it seems logical
that earlier charts served as guides for the cartographers.

Undoubtedly, the first charts were not made on any “projection” (ch. III) but
were simple diagrams which took no notice of the shape of the earth. In fact, these
"plane" charts were used for many centuries after chart projections were available.

The gnomonic projection (art. 317) is believed to have been developed by Thales
of Miletus (640-546 BC), who was chief of the Seven Wise Men of ancient Greece;
founder of Greek geometry, astronomy, and philosophy; and a navigator and cartog-
rapher.

The size of the earth was measured at least as early as the third century BC, by
Eratosthenes. He observed that at noon on the day of the summer solstice, a certain
well at Syene (Assuan) on the tropic of Cancer was lighted throughout its depth by the
light of the sun as it crossed the meridian; but that at Alexandria, about 500 miles to
the north, shadows were cast by the sun at high noon. He reasoned that this was due
to curvature of the earth, which must be spherical. By means of the shadow of an
object of known height at Alexandria, Eratosthenes determined the zenith distance to
be about 7:5, or 1⁄4 of the earth's circumference. The earth must therefore be 48X
500=24,000 (statute) miles. The correct value is about 24,900 statute miles.

Eratosthenes is believed to have been the first person to measure latitude, using
the degree for this purpose. He constructed a 16-point wind rose, prepared a table of
winds, and recognized local and prevailing winds. From his own discoveries and from
information gleaned from the manuscripts of mariners, explorers, land travelers,
historians, and philosophers, he wrote an outstanding description of the known world,
which helped elevate geography to the status of a science.

HISTORY OF NAVIGATION 19

Stereographic (art. 318) and orthographic (art. 319) projections were originated
by Hipparchus in the second century BC.

Ptolemy's World Map. The Egyptian Claudius Ptolemy was a second century
AD astronomer, writer, geographer, and mathematician who had no equal in astron-
omy until the arrival of Copernicus in the 16th century. An outstanding cartographer,
for his time, Ptolemy constructed many charts and listed the latitudes and longitudes,
as determined by celestial. observations, of the places shown. As a geographer, how-
ever, he made his most serious mistake. Though Eratosthenes’ calculations on the
circumference of the earth were available to him, he took the estimate of the Stoic
philosopher, Posidonius (circa 130-51 BC), who calculated the earth to be 18,000
miles in circumference. The result was that those who accepted his work—and for
many hundreds of years few thought to question it—had to deal with a concept that
was far too small. In 1409 the Greek original of Ptolemy’s Cosmographia, a book in
which he declared this doctrine, was discovered and translated into Latin. It served
as the basis for future cartographic work, and so it was that Columbus died convinced
that he had found a shorter route to the East Indies. Not until 1669, when Jean
Picard computed the circumference of the earth to be 24,500 miles, was a more accurate
figure generally used.

Ptolemy’s map of the world (fig. 109a) was a great achievement, however. It was
the original conic projection, and on it he located some 8,000 places by latitude and
longitude. It was he who fixed the convention that the top of the map is north.

Asian Charts. Through the Dark Ages some progress was made. Moslem
cartographers as well as astronomers took inspiration from Ptolemy. However, they
knew that Ptolemy had overestimated the length of the Mediterranean by some 20°.
Charts of the Indian Ocean, bearing horizontal lines indicating parallels of latitude,

ic ence
iem

Courtesy of the Map Division of the Library of Congress.

isi it IS 7 d in
3 9a.—The world, as envisioned by Ptolemy about AD 150. This chart was prepare
Mini 1482 by Nicolaus Germanus for a translation of Cosmographia.

20 HISTORY OF NAVIGATION

Courtesy of the Map Division of the Library of Congress.
FiGURE 109b.—A 14th-century Portolan chart.

and vertical lines dividing the seas according to the direction of the wind, were drawn
by Persian and Arabian navigators. The prime meridian separated a windward from
a leeward region and other meridians were drawn at intervals indicating “three hours
sail.” This information, though far from exact, was helpful to the sailing ship masters.

Portolan Charts. The'mariners of Venezia (Venice), Livorno (Leghorn), and Genova
(Genoa) must have had charts when they competed for Mediterranean trade before,
during, and after the Crusades. Venice at one time had 300 ships, a navy of 45 galleys,
and 11,000 men engaged in her maritime industry. But perhaps the rivalry was too
keen for masters carelessly to leave charts lying about. At any rate, the earliest useful
charts of the Middle Ages that are known today were drawn by seamen of Catalonia
(now part of Spain).

The Portolan charts were constructed from the knowledge acquired by seamen
during their voyages about the Mediterranean. The actual courses and dead reckon-
ing distances between land points were used as a skeleton for the charts, and the coasts
between were usually filled in from data obtained in land surveys. After the compass
came into use, these charts became quite accurate. Some, for example, indicated the
distance between Gibraltar and Bayrüt (Beirut) to be 3,000 Portolan miles, or 4025
of longitude. The actual difference of longitude is 4098.

These charts were distinguished by a group of long rhumb lines intersecting at a
common point, surrounded by eight or 16 similar groups of shorter lines. Later Porto-
lanis had a rose dei venti (rose of the winds), the forerunner of the compass rose, super-
imposed over the center (fig. 109b). They carried a scale of miles, located nearly all
the known hazards to navigation, and had numerous notes of interest to the pilot.
They were not marked with parallels of latitude or meridians of longitude, but present-
day harbor and coastal charts trace their ancestry directly to them.

Padrón Real. The growing habit of assembling information for charts took
concrete form in the Padrén Real. This was the pattern, or master, map kept after
1508 by the Casa de Contratación at Seville. It was intended to contain everything
known about the world, and it was constructed from facts brought back by mariners
from voyages to newly discovered lands. From it were drawn the charts upon which
the explorers of the Age of Discovery most depended.

World maps of the Middle Ages. In 1515 Leonardo da Vinci drew his famous map
of the world. On it, America is represented as extending more to the east and west

HISTORY OF NAVIGATION 21

YPVS ORBIS TERRARV
LAIA = tm

/ Xy ERICK VIVA Lë
DIA NÓ VA ey
"as 7 berne me vc

QVID EI POTEST VIDERI MAGNVM IN REBVS HVMANIS, CVI AETERNI TA
OMNIS TOI IVSQVE M VNDI NOTA SIT MAGNITVDO. CICERO

TU QRS

3 pa AA S ETA eee ——— an

Courtesy of the New York Public Library.

FiGuRE 109c.—Ortelius’ world map, from his atlas Theatrum Orbis Terra, published at Antwerp in
1570.

than to the north and south, with only a chain of islands, the largest named Florida,
between it and South America. A wide stretch of ocean is shown between South
America and Terra Australis Nondum Cognita, the mythical south-seas continent
whose existence in the position shown was not disproved until 250 years later.

Ortelius’ atlas Theatrum Orbis Terra was published at Antwerp in 1570. One of
the most magnificent ever produced, it illustrates Europe, Africa, and Asia with com-
parative accuracy. North and South America are poorly depicted, but Magellan's
Strait is shown. All land to the south of it, as well as Australia, is considered part of
Terra Australis Nondum Cognita (fig. 109c).

The Mercator projection (art. 305). For hundreds, perhaps thousands, of years
cartographers drew their charts as “plane” projections, making no use of the discoveries
of Ptolemy and Hipparchus. As the area of the known world increased, however, the
attempt to depict that larger area on the flat surface of the plane chart brought map
makers to the realization that allowance would have to be made for the curvature of
the earth.

Gerardus Mercator (Latinized form of Gerhard Kremer) was a brilliant Flemish
geographer who recognized the need for a better method of chart projection. In
1569 he published a world chart which he had constructed on the principle since known
by his name. The theory of his work was correct, but Mercator made errors in his
computation, and because he never published a complete description of the mathe-
matics involved, mariners were deprived of the full advantages of the projection for
another 30 years.

Then Edward Wright published the results of his own independent study in the
matter, explaining the Mercator projection fully and providing the table of meridional
parts which enabled all cartographers to make use of the principle.

22 HISTORY OF NAVIGATION

Wright was a mathematician at Caius College who developed the method and
table and gave them to certain navigators for testing. After these proved their use-
fulness, Wright decided upon publication, and in 1599 Certaine Errors in Navigation
Detected and Corrected was printed.

The Lambert projections. Johann Heinrich Lambert, 1728-1777, self-educated
son of an Alsace tailor, designed a number of map projections. Some of these are still
widely used, the most renowned being the Lambert conformal (art. 314).

110. Sailing directions.—From earliest times there has been a demand for knowl-
edge of what lay ahead, and this gave rise to the early development of sailing directions
(art. 420). Ë

The Periplus of Scylax, written sometime between the sixth and fourth centuries
BC, is the earliest known book of this type. Surprisingly similar to modern sailing
directions, it provided the mariner with information on distances between ports, alds and
dangers, port facilities, and other pertinent matters. The following excerpt is typical:

“Libya begins beyond the Canopic mouth of the Nile. . . . The first people in
Libya are the Adrymachidae. From Thonis the voyage to Pharos, a desert island
(good harbourage but no drinking water), is 150 stadia. In Pharos are many harbors.
But ships water at the Marian Mere, for it is drinkable. . . . The mouth of the bay
of Plinthine to Leuce Acte (the white beach) is a day and night’s sail; but sailing
round by the head of the bay of Plinthine is twice as long. . . ."

Parts Around the World, Pytheas’ book of observations made during his epic voy-
age in the fourth century BC, was another early volume of sailing directions. His
rough estimates of distances and descriptions of coast lines would be considered crude
today, but they served as an invaluable aid to navigators who followed him into these
otherwise unknown waters.

Sailing directions during the Renaissance. No particularly noteworthy improve-
ments were made in sailing directions during the Middle Ages, but in 1490 the Portolano
Rizo was published, the first of a series of improved design. Other early volumes of
this kind appeared in France and were called "routiers"—the rutters of the English
sailor. In 1557 the Italian pilot Battista Testa Rossa published Brieve Compendio del
Arte del Navigar, which was designed to serve the mariner on soundings and off. It
forecast the single, all-inclusive volume that was soon to come, the Waggoner.

About 1584 the Dutch pilot Lucas Jans Zoon Waghenaer published a volume of
navigational principles, tables, charts, and sailing directions which served as a guide
for such books for the next 200 years. In Spieghel der Zeevaerdt (The Mariner’s Mir-
ror), Waghenaer gave directions and charts for sailing the waters of the Low Countries
and later a second volume was published covering waters of the North and Baltic seas.

These “Waggoners” met with great success and in 1588 an English translation of the
original book was made by Anthony Ashley. During the next 30 years, 24 editions of
the book were published in Dutch, German, Latin, and English. Other authors
followed the profitable example set by Waghenaer, and American, British, and French
navigators soon had “Waggoners” for most of the waters they sailed.

The success of these books and the resulting competition among authors were
responsible for their eventual discontinuance. Each writer attempted to make his
work more inclusive than any other (the 1780 Atlantic Neptune contained 257 charts
of North America alone) and the result was a tremendous book difficult to handle.
They were too bulky, the sailing directions were unnecessarily detailed, and the charts
too large. In 1795 the British Hydrographic Department was established, and charts
and sailing directions were issued separately. The latter, issued for specific waters,
were returned to the form of the original Periplus.

HISTORY OF NAVIGATION 23

Modern sailing directions. The publication of modern sailing directions by the
U. S. Navy Hydrographic Office is one of the achievements properly attributed to
Matthew Fontaine Maury. During the two decades he headed the institution, Maury
gathered data that led directly to the publication of eight volumes of sailing directions.
Today there are more than 65 volumes providing the mariner with detailed informa-
tion on almost all foreign coasts, in addition to eight volumes of coast pilots of the
United States and its possessions, published by the U. S. Coast and Geodetic Survey.

111. The compass.—Early in the history of navigation man noted that the pole
star (it may have been a Draconis then) remained close to one point in the northern
sky. This served as his compass. When it was not visible, he used other stars, the
sun and moon, winds, clouds, and waves. The development of the magnetic compass,
perhaps a thousand years ago, and the 20th century development of the gyro compass,
offer today’s navigator a method of steering his course with an accuracy as great as
he is capable of using.

The magnetic compass (art. 623) is one of the oldest of the navigator’s instruments.
Its origin is not known. In 203 BC, when Hannibal set sail from Italy, his pilot was
said to be one Pelorus. Perhaps the compass was in use then; no one can say for
certain that it was not. There is little to substantiate the story that the Chinese
invented it, and the legend that Marco Polo introduced it into Italy in the 13th century
is almost certainly false. It is sometimes stated that the Arabs brought it to Europe,
but this, too, is unlikely. Probably it was known first in the west. The Norsemen
of the 11th century were familiar with it, and about 1200 a compass used by mariners
when the pole star was hidden was described by a French poet, Guyot de Provins.

A needle thrust through a straw and floated in water in a container comprised the
earliest compass known. A 1248 writer, Hugo de Bercy, spoke of a new compass con-
struction, the needle “now” being supported on two floats. Petrus Peregrinus de
Maricourt, in his Epistola de Magnete of 1269, wrote of a pivoted floating compass
with a lubber’s line, and said that it was equipped with sights for taking bearings.

The reliability of the magnetic compass of today is a comparatively recent achieve-
ment. As late as 1820 Peter Barlow reported to the British Admiralty “half of the
compasses in the Royal Navy were mere lumber, and ought to be destroyed." Some
75 years ago, Lord Kelvin developed the Admiralty type compass used today.

The compass card, according to tradition, originated about the beginning of the
14th century, when Flavio Gioja of Amalfi attached a sliver of lodestone or a mag-
netized needle to a card. But the rose on the compass card is probably older than the
needle. It is the wind rose of the ancients. Primitive man naturally named directions
by the winds. The prophet Jeremiah speaks of the winds from the four quarters of
heaven (Jer. 49:36) and Homer named four winds—Boreas, Eurus, Notus, and Lephy-
rus. Aristotle is said to have suggested a circle of 12 winds, and Eratosthenes, who
measured the world correctly, reduced the number to eight about 200 BC. The
“Tower of Winds” at Athens, built about 100 BC, had eight sides. The Latin rose
of 12 points was common on most compasses used in the Middle Ages.

Variation (art. 709) was well understood 200 years ago, and navigators made
allowance for it, but earliest recognition of its existence is not known. Columbus and
even the 11th century Chinese have been given credit for its discovery, but little proof
can be offered for either claim.

The secular change in variation was determined by a series of magnetic observa-
tions made at Limehouse, England. In 1580 William Borough fixed the variation in
that area at approximately 11°25’ east. Thirty-two years later Edmund Gunter,
professor of astronomy at Gresham College, determined it to be 6°13’ east. At first

24 HISTORY OF NAVIGATION

it was believed that Borough had made an error in his work, but in 1633 a further de-
crease was found, and the earth's changing magnetic field was established.

A South Atlantic expedition was led by Edmond Halley at the close of the 17th
century to gather data and to map, for the first time, lines of variation. In 1724
George Graham published his observations in proof of the diurnal change in variation.
Canton determined that the change was considerably less in winter than in summer,
and about 1785 the strength of the magnetic force was shown by Paul de Lamanon to
vary in different places.

The existence of deviation (art. 709) was known to John Smith in 1627 when he
wrote of the “bittacle” as being a “square box nailed together with wooden pinnes,
because iron nails would attract the Compasse.” But no one knew how to correct a
compass for deviation until Captain Matthew Flinders, while on a voyage to Australia
in HMS Investigator in 1801-02, discovered a method of doing so. Flinders did not
understand deviation completely, but the vertical bar he erected to correct for it was
part of the solution, and the Flinders bar (art. 720) used today is a memorial to its
discoverer. Between 1839 and 1855 Sir George Airy, then Astronomer Royal, studied
the matter further and developed combinations of permanent magnets and soft iron
masses for adjusting the compass. The introduction, by Lord Kelvin, of short needles
as compass magnets made adjustment more precise.

The gyro compass (art. 631). The age of iron ships demanded a compass which
could be relied upon to indicate true north at all times, free from disturbing forces of
variation and deviation.

In 1851, at the Pantheon in Paris, Leon Foucault performed his famous pendulum
experiment to demonstrate the rotation of the earth. Foucault’s realization that the
swinging pendulum would maintain the plane of its motion led him, the following year,
to develop and name the first gyroscope, using the principle of a common toy called a
“rotascope.” Handicapped by the lack of a source of power to maintain the spin of
his gyroscope, Foucault used a microscope to observe the indication of the earth’s
rotation during the short period in which his manually operated gyroscope remained in
rotation. A gyro compass was not practical until electric power became available,
more than 50 years later, to maintain the spin of the gyroscope.

Elmer A. Sperry, an American, and Anschutz-Kampfe, a German, independently
invented gyro compasses during the first decade of the 20th century. Tested first in
1911 on a freighter operating off the East Coast of the United States and then on Ameri-
can warships, Sperry’s compass was found adequate, and in the years following World
War I gyro compasses became standard equipment on all large naval and merchant
ships.

Gyro compass auxiliaries commonly used today were added later. These include
gyro repeaters, to indicate the vessel’s heading at various locations; gyro pilots, to steer
vessels automatically; course recorders, to provide a graphic record of courses steered ;
gyro-magnetic compasses, to repeat headings of magnetic compasses so located as to
be least affected by deviation; and others in the fields of fire control, aviation, and
guided missiles.

112. The log.—Since virtually the beginning of navigation, the mariner has
attempted to determine his speed in traveling from one point to another. The earliest
method was probably by estimate.

The oldest speed measuring device known is the Dutchman’s log. Originally,
any object which would float was thrown overboard on the lee side, from a point well
forward, and the time required for it to pass between two points on the deck was noted.
The time, as determined by sand glass, was compared with the known distance along
the deck between the two points to determine the speed.

HISTORY OF NAVIGATION 25

Near the end of the 16th century a line was attached to the log, and as the line was
paid out a sailor recited certain sentences. The length of line which was paid out during
the recitation was used to determine the speed. There is record of this method having
been used as recently as the early 17th century. In its final form this chip log, ship log,
or common log consisted of the log chip (or log ship), log line, log reel, and log glass.
The chip was a quadrant-shaped piece of wood weighted along its cireumference to keep
it upright in the water (fig. 112). The log line was made fast to the log chip by means
of a bridle, in such manner that a sharp pull on the log line dislodged a wooden peg and
permitted the log chip to be towed horizontally through the water, and hauled aboard.
Sometimes a stray line was attached to the log to veer it clear of the ship's wake. In
determining speed, the observer counted the knots in the log line which was paid out
during a certain time. The length of line between knots and the number of seconds
required for the sand to run out were changed from time to time as the accepted length
of the mile was altered.

The chip log has been superseded by patent logs that register on dials. However,
the common log has left its mark on modern navigation, as the use of the term knot
to indicate a speed of one nauti-
cal mile per hour dates from this
device. There is evidence to
support the opinion that the
expression “dead reckoning”
had its origin in this same de-
vice, or perhaps in the earlier
Dutchman's log. There is logic
in attributing “dead” reckon-
ing to a reckoning relative to
an object “dead” in the water.

Courtesy of “Motor Boating.”

: Figure 112.—The common or chip log, showing the log
Mechanical logs first apa reel, the log line, the log chip, and the log glass.

peared about the middle of the

17th century. By the beginning of the 19th century, the forerunners of modern
mechanical logs were used by some navigators, although many years were to pass
before they became generally accepted.

In 1773 logs on which the distance run was recorded on dials secured to the
taffrail were tested on board a British warship and found reasonably adequate, although
the comparative delicateness of the mechanism led to speculation about their long-
term worth. Another type in existence at the time consisted of a wheel arrangement
made fast on the underside of the keel, which transmitted readings to a dial inside the
vessel as the wheel rotated.

An improved log was introduced by Edward Massey in 1802. This log gave
considerably greater accuracy by means of a more sensitive rotator attached by a
short length of line to a geared recording instrument. The difficulty with this log
was that it had to be hauled aboard to take each reading. Various improvements
were made, notably by Alexander Bain in 1846 and Thomas Walker in 1861, but it
was not until 1878 that a log was developed in which the rotator could be used in
conjunction with a dial secured to the after rail of the ship, and although refinements
and improvements have been made, the patent log used today is essentially the same
as that developed in 1878.

Engine revolution counters (art. 615) had their origin with the observations of
the captains of the first paddle steamers, who discovered that by counting the paddle
revolutions, they could, with practice, estimate their runs in thick weather as accurately
as they could by streaming the log. Later developments led to the modern revolution

26 HISTORY OF NAVIGATION

counter on screw-type vessels, which can be used with reasonable accuracy if the
propeller is submerged and an accurate estimate of slip is made.

Pitot-static and impeller-type logs (arts. 613, 614) are recent mechanical develop:
ments in the field of speed measurement. Each utilizes a retractable rodmeter' which
projects through the hull of the ship into the water. In the Pitot-static log, static and
dynamic pressures on the rodmeter transmit readings to the master speed indicator.
In the impeller-type log an electrical means of transmitting speed indications is used.

113. Units of distance and depth.—The modern navigator is concerned principally
with three units of linear measure: the nautical mile, the fathom, and the foot (some-
times also the meter). Primitive man, however, used such natural units as the width of a
finger, the span of his hand, the length of his foot, the distance from elbow to the tip
of the middle finger (the cubit of biblical renown), or the pace (sometimes one but
usually a double step) to measure short distances.

These ancient measurements varied from place to place, and from person to
person. One of the first recorded attempts to establish a tangible standard length
was made by the Greeks, who used the length of the Olympic stadium as a unit called
a stadium. This was set at 600 Greek feet (607.9 modern U. S. feet), or almost exactly
one-tenth of a modern nautical mile. The Romans adopted this unit and extended its
use to nautical and even astronomical measurements. The Roman stadium was 625
Roman feet, or 606.3 U.S. feet, in length. This approximates the modern British Navy
cable of 608 feet. The U.S. Navy cable is 720 feet.

The origin of the Mediterranean mile of 4,035.43 U.S. feet is attributed to the
Greeks. The Roman mile of 4,858.60 U.S. feet gradually replaced the shorter Greek
unit, and was probably the value in use in Palestine when Christ in his Sermon on the
Mount spoke of the “second mile” (Matt. 5:41). It is probable that the mile was
given its name by the Romans, since the word is derived from the Latin mille (thou-
sand). This unit was defined as a thousand paces. However, the Greek unit was
similarly defined, as was the Arabian mille or mil of 6,000 Arabian feet, equal to 1.03
nautical miles.

The nautical mile bears little relation to these land measures, which were not
associated with the size of the earth. With the emergence of the nautical chart, it
became customary to show a scale of miles on the chart, and the accepted value of this
unit varied over the centuries with the changing estimates of the size of the earth.
These estimates varied widely, ranging from about 44.5 to 87.5 modern nautical miles
per degree of latitude, although generally they were too small. Columbus and Magellan
used the value 45.3. Actually, the earth is about 32 percent larger. The Almagest of
Ptolemy considered 62 Roman miles equivalent to one degree, but a 1466 edition of
this book contained a chart of southern Asia drawn by Nicolaus Germanus on which 60
miles were shown to a degree. Whether the change was considered a correction or
an adaptation to provide a more convenient relationship between the mile and the
degree is not clear, but this is the earliest known use of this ratio.

Later, when the size of the earth was determined by measurement, the relation-
ship of 60 Roman miles of 4,858.60 U.S. feet to a degree of latitude was seen to be
in error. Both possible solutions to the problem—changing the ratio of miles to a
degree, or changing the length of the mile—had their supporters, and neither group
was able to convince the other. As a result, the shorter mile remained as the land or
statute mile (now established as 5,280 feet in the United States), and the longer
nautical mile gradually became established at sea. The earliest known reference to
it by this name occurred in 1730.

Finer instruments and new methods make increasingly more accurate determina-
tions of the size of the earth an ever-present possibility. Hence, a unit of length

HISTORY OF NAVIGATION 27

defined in terms of the size of the earth is undesirable. Recognition of this led, in
1875, to a change in the definition of the meter from one ten-millionth of the distance
from the pole to the equator of the earth to the distance between two marks (approxi-
mately 39.37 U. S. inches) on a standard platinum-iridium bar kept at the Pavillon de
Breteuill at Sevres, near Paris, France, by the International Commission of Weights
and Measures. In further recognition of this principle, the International Hydrographic
Bureau in 1929 recommended adoption of a standard value for the nautical mile, and
proposed 1852 international meters. The length of 1852 meters has not changed, but
in 1959, U. S. measurements were redefined; the length of one nautical mile was estab-
lished at 6,076.11549 U. S. feet (approximately). Most major maritime nations now
use the international value.

The fathom as a unit of length or depth is of obscure origin, but primitive man
considered it a measure of the outstretched arms, and the modern seaman still es-
timates the length of a line in this manner. That the unit was used in early times
is indicated by reference to it in the detailed account given of the Apostle Paul's
voyage to Rome, as recorded in the 27th chapter of the Acts of the Apostles. Posidonius
reported a sounding of more than 1,000 fathoms in the second century BC. How
old the unit was at that time is unknown.

114. Soundings.—Probably the most dangerous phase of navigation occurs when
the vessel is “on soundings.” Since man first began navigating the waters, the possi-
bility of grounding his vessel has been a major concern, and frequent soundings have
been the most highly valued safeguard against that experience. Undoubtedly used long
before the Christian era, the lead line is perhaps the oldest instrument of navigation.

The lead line. The hand lead (art. 617), consisting of a lead weight attached to a
line usually marked in fathoms, has been known since antiquity and, with the exception
of the markings, is probably the same today as it was 2,000 or more years ago. The deep
sea lead, a heavier weight with a longer line, was a natural outrowgth of the hand lead.
A 1585 navigator speaks of soundings of 330 fathoms, and in 1773, in the Norwegian
Sea, Captain Phipps had all the sounding lines on board spliced together to obtain a
sounding of 683 fathoms. Matthew Fontaine Maury made his deep sea soundings by
securing a cannon shot to a ball of strong twine. The heavy weight caused the twine
to run out rapidly, and when bottom was reached, the twine was cut and the depth
deduced from the amount remaining on the ball.

The sounding machine. The biggest disadvantage of the deep sea lead is that the
vessel must be stopped if depths are to be measured accurately. This led to the develop-
ment of the sounding machine (art. 618).

Early in the 19th century a sounding machine similar to one of the earlier patent
logs was invented. A wheel was secured just above the lead and the cast made in
such a way that all the line required ran out freely and the lead sank directly to the
bottom. The motion through the water during the descent set the wheel revolving,
and this in turn caused the depth to be indicated on a dial. Ships sailing at: perhaps
12 knots required 20 or 30 men to heave aboard the heavy line with its weight of 50 or
more pounds after each cast. A somewhat similar device was the buoy sounder. The
lead was passed through a buoy in which a spring catch was fitted and both were cast
over the side. The lead ran freely until bottom was reached, when the catch locked,
preventing further running out of the line. The whole assembly was then brought on
board, the depth from the buoy to the lead being read.

The first use of the pressure principle to determine the depth of water occurred
early in the 19th century when the “Self-acting Sounder” was introduced. A hollow
glass tube open at its lower end contained an index which moved up in the tube as
greater water pressure compressed the air inside. The index retained its highest

28 HISTORY OF NAVIGATION

position when hauled aboard the vessel, and its height was proportional to the depth
of the water.

The British scientist, William Thomson (Lord Kelvin) in 1878 perfected the
sounding machine after repeated tests at sea. Prior to his invention, fibre line was
used exclusively in soundings. His introduction of piano wire solved the problem of
rapid descent of the lead and also that of hauling it back aboard quickly. The chem-
ically coated glass tube which he used to determine depth was an improvement of
earlier methods, and the worth of the entire machine is evidenced by the fact that it
is still used in essentially the same form.

Echo sounding. Based upon the principle that sound travels through sea water
at a nearly uniform rate, automatic depth-registering devices (art. 619) have been
invented to indicate the depth of water under a vessel, regardless of its speed. In
1911 an account was published of an experiment performed by Alexander Behm of
Kiel, who timed the echo of an underwater explosion, testing this theory. High
frequency sounds in water were produced by Pierre Langevin, and in 1918 he used the
principle for echo depth finding. The first practical echo sounder was developed by
the United States Navy in 1922.

The actual time between emission of a sonic or ultrasonic signal and return of its
echo from the bottom, the angle at which the signal is beamed downward in order
that its echo will be received at another part of the vessel, and the phase difference
between signal and echo have all been used in the development of the modern echo
sounder.

115. Aids to navigation.—The Cushites and Libyans constructed towers along the
Mediterranean coast of Egypt, and priests maintained beacon fires in them. These
were the earliest known lighthouses. At Sigeum in the Troad (part of Troy) a light-
house was built before 660 BC. One of the seven wonders of the ancient world was the
lighthouse called the Pharos of Alexandria, which may have been more than 200 feet
tall. It was built by Sostratus of Cnidus (Asia Minor) in the third century BC, during
the reign of Ptolemy Philadelphus. The word “pharos” has since been a general
term for lighthouses. Some time between 1584 and 1611 the light of Cordouan, the
earliest wave-swept lighthouse, was erected at the entrance to the Gironde river in
western France. An oak log fire illuminated this structure until the 18th century.

Wood or coal fires were used in the many lighthouses built along the European
and British coasts in the 17th and 18th centuries. One of these, the oak pile structure
erected by Henry Whiteside in 1776 to warn shipmasters of Small’s Rocks, subse-
quently played a major role in navigational history, as it was this light which figured
in the discovery of the celestial line of position by Captain Thomas Sumner some 60
years later (art. 131).

In England such structures were privately maintained by interested organizations.
One of the most famous of these groups, popularly known as “Trinity House,” was
organized in the 16th century, perhaps earlier, when a “beaconage and buoyage” fee
was levied on English vessels. This prompted the establishment of Trinity House “to
make, erect, and set up beacons, marks, and signs for the sea” and to provide vessels
with pilots. The organization is now in its fifth century of operation, and its chief
duties are to serve as a general lighthouse and pilotage authority, and to supply pilots.

The first lightship was a small vessel with lanterns hung from its yardarms. It
was stationed at the Nore, an estuary in the Thames River, England, in 1732.

The pilot’s profession is not much younger than that of the mariner. The Bible
relates (1 Kings 9:27) that Hiram of Tyre provided pilots for King Solomon. The
duties of these pilots are not specified. In the first century AD, fishermen of the

HISTORY OF NAVIGATION 29

Gulf of Cambay, India, met seagoing vessels and guided them into port. It is probable
that pilots were established in Delaware Bay earlier than 1756.

Seafaring people of the United States had erected lighthouses and buoys before
the Revolutionary War, and in 1789 Congress passed legislation providing for federal
expansion of the work. About 1767 the first buoys were placed in the Delaware
River. These were logs or barrels, but about 1820 they were replaced with spar
buoys. In that same year, the first lightship was established in Chesapeake Bay.

As the maritime interests of various countries grew, more and better aids to
navigation were made available. In 1850 Congress prescribed the present system of
coloring and numbering United States buoys (app. J). Conformity as to shape resulted
from the recommendations of the International Marine Conference of 1889. The second
half of the 19th century saw the development of bell, whistle, and lighted buoys, and
in 1910 the first lighted buoy in the United States utilizing high pressure acetylene
apparatus was placed in service. Stationed at the entrance to Ambrose Channel in
New York, it provided the basis for the high degree of perfection which has been
achieved in the lighted buoy since that time. The complete buoyage system main-
tained by the U. S. Coast Guard today is chiefly a product of the 20th century. In
1900 there were approximately 5,000 buoys of all types in use in the United States,
while today there are more than 20,000.

116. The sailings.—The various methods of mathematically determining course,
distance, and position arrived at have a history almost as old as mathematics itself.
Thales, Hipparchus, Napier, Wright, and others contributed the formulas that led to
the tables permitting computation of course and distance by plane, traverse, parallel,
middle-latitude, Mercator, and great-circle sailings.

Plane sailing (art. 813). Based upon the assumption that the surface of the earth
is plane, or flat; this method was used by navigators for many centuries. The navi-
gator solved problems by laying down his course relative to his meridian, and stepping
off the distance run to the new position. This system is used with accuracy today
in measuring short runs on a Mercator chart, which compensates for the convergence
of the meridians, but on the plane chart, serious errors resulted. Early navigators
might have obtained mathematical solutions to this problem, with no greater accuracy,
but the graphical method was commonly used.

Traverse sailing (art. 814). Because sailing vessels were subject to the winds,
navigators of old were seldom able to sail one course for great distances, and conse-
quently a series of small triangles had to be solved. Equipment was designed to help
seamen in maintaining their dead reckoning positions. The modern rough log evolved
from the log board, hinged wooden boards that folded like a book and on which courses
and distances were marked in chalk. Each day the position was determined from this
data and entered in the ship's journal, today's smooth log.

The log board was succeeded by the travas, a board with lines radiating from the
center in 32 compass directions. Regularly spaced along the lines were small holes
into which pegs were fitted to indicate time run on the particular course. In 1627
John Smith described the travas as a “little round board full of holes upon lines like
the compasse, upon which by the removing of a little sticke they (seamen) keepe an
account, how many glasses (which are but halfe houres) they steare upon every point
of the compasse.”

These devices were of great value to the navigator in keeping a record of the
courses and distances sailed, but still left him the long mathematical solutions necessary
to determine the new position. In 1436 what appears to have been the first traverse
table was prepared by Andrea Biancho. Using this table of solutions of right-angled

30 HISTORY OF NAVIGATION

plane triangles, the navigator was able to determine his course and distance made good
after sailing a number of distances in different directions. Før

Parallel sailing (art. 815) was an outgrowth of the navigator's inability to deter-
mine his longitude. Not a mathematical solution in the sense that the other sailings
are, it involved converting the distance sailed along a parallel (departure), as deter-
mined by dead reckoning, into longitude. =

Middle-latitude sailing (art. 816). The inaccuracies involved in plane sailing led
to the improved method of middle-latitude sailing early in the 17th century. A
mathematician named Ralph Handsen is believed to have been its inventor.

Middle-latitude sailing is based upon the assumption that the use of a parallel
midway between those of departure and arrival will eliminate the errors inherent in
plane sailing due to the convergence of the meridians. The assumption is reasonably
accurate and although the use of Mercator sailing usually results in greater accuracy,
middle-latitude sailing still serves a useful purpose.

Mercator sailing (art. 817). Included in Edward Wright’s Certaine Errors in
Navigation Detected and Corrected, of 1599, was the first published table of meridional
parts, which provided the basis for the most accurate of rhumb line sailings—Mercator
sailing.

Great-circle sailing (art. 819). For many hundreds of years mathematicians have
known that a great circle is the shortest distance between two points on the surface
of a sphere, but it was not until the 19th century that navigators began to regularly
make use of this information.

The first printed description of great-circle sailing appeared in Pedro Nunes’
1537 Tratado da Sphera. The method had previously been proposed by Sebastian
Cabot in 1498, and in 1524 Verrazano sailed a great-circle course to America. But the
sailing ships could not regularly expect the steady winds necessary to sail such a course,
and their lack of knowledge concerning longitude, plus the necessity of stopping at islands
along their routes to take supplies, made it impractical for most voyages at that time.

The gradual accumulation of knowledge concerning seasonal and prevailing winds,
weather conditions, and ocean currents eventually made it possible for the navigator
to plan his voyage with more assurance. Nineteenth century writers of navigational
texts recommended the use of great-circle sailing, and toward the close of that century
such sailing became increasingly popular, particularly in the Pacific.

The mathematics involved in great-circle sailing may be tedious, but the use of
the gnomonic projection in locating points along the great-circle track has simplified
the method.

117. Hydrographic offices.— The practice of recording hydrographic data was
centuries old before the establishment of the first official hydrographic office, in 1720.
In that year the Depot des Cartes, Plans, Journaux et Memoirs Relatifs a la Navi-
gation was formed in France with the Chevalier de Luynes in charge. The Hydro-
graphic Department of the British Admiralty, though not established until 1795, has
played a major part in European hydrographic work.

The U. S. Coast and Geodetic Survey was originally founded when Congress, in
1807, passed a resolution authorizing a survey of the coast, harbors, outlying islands,
and fishing banks of the United States. On the recommendation of the American
Philosophical Society, President Jefferson appointed Ferdinand Hassler, a Swiss immi-
grant who had founded the Geodetic Survey of his native land, the first Director of
the “Coast Survey.”

The approaches to New York were the first sections of the coast charted, and from
there the work spread northward and southward along the eastern seaboard. In 1844

HISTORY OF NAVIGATION 31

the work was expanded and arrangements made to chart simultaneously the Gulf and
East Coasts. ` Investigation of tidal conditions began, and in 1855 the first. tables of
tide predictions were published. The California gold rush gave impetus to the survey
of the West Coast, which began in 1850, the year California became a State. The
survey ship Washington undertook investigations of the Gulf Stream. Coast pilots,
or sailing directions, for the Atlantic coast of the United States were privately published
in the first half of the 19th century, but about 1850 the Survey began accumulating
data that led to federally produced coast pilots. The 1889 Pacific Coast Pilot was
an outstanding contribution to the safety of West. Coast shipping.

Today the U. S. Coast and Geodetic Survey, as it has been called since 1878,
provides the mariner with the charts and coast pilots of all waters of the United States
and its possessions, and tide and tidal current tables for much of the world.

U. S. Navy Hydrographic Office. In 1830 the U. S. Navy established a “Depot of
Charts and Instruments” in Washington, D. C. Primarily, it was to serve as a store-
house where such charts and sailing directions as were available, together with naviga-
tional instruments, could be assembled for issue to Navy ships which required them.
Lieutenant L. M. Goldsborough and one assistant, Passed Midshipman R. B. Hitch-
cock, constituted the entire staff.

The first chart published by the Depot was produced from data obtained in a
survey made by Lieutenant Charles Wilkes, who had succeeded Goldsborough in 1834,
and who later earned fame as the leader of a United States exploring expedition to
Antarctica.

From 1842 until 1861 Lieutenant Matthew Fontaine Maury served as Officer-
in-Charge. Under his command the office rose to international prominence. Maury
decided upon an ambitious plan to increase the mariner’s knowledge of existing winds,
weather, and currents. He began by making a detailed record of pertinent matter
included in old log books stored at the Depot. He then inaugurated a hydrographic
reporting program among shipmasters, and the thousands of answers received, along
with the log book data, were first utilized to publish the Wind and Current Chart
of the North Atlantic of 1847. The United States instigated an international con-
ference in 1853 to interest other nations in a system of exchanging nautical information.
The plan, which was Maury’s, was enthusiastically adopted by other maritime nations,
and is the basis upon which hydrographic offices operate today.

In 1854 the Depot was redesignated the “U. S. Naval Observatory and Hydro-
graphical Office," and in 1866 Congress separated the two, broadly increasing the
functions of the latter. The Office was authorized to carry out surveys, collect informa-
tion, and print every kind of nautical chart and publication, all “for the benefit and
use of navigators generally.”

One of the first acts of the new Office was to purchase the copyright of The New
American Practical Navigator. Several volumes of sailing directions had already been
published. The first Notice to Mariners appeared in 1869. Daily broadcast of naviga-
tional warnings was inaugurated in 1907, and in 1912, following the sinking of the
SS Titanic, Hydrographic Office action led to the establishment of the International
Ice Patrol.

The development by the U. S. Navy of an improved depth finder in 1922 made
possible the acquisition of additional information concerning bottom topography.
During the same year aerial photography was first employed as an aid in chart making.
The Hydrographic Office published the first chart for lighter-than-air craft in 1923.
Aerial geomagnetic surveys were instituted in 1953 to provide magnetic information
for ocean areas. Since World War II various electronic means have been employed
to improve and extend surveys.

32 HISTORY OF NAVIGATION

Meanwhile, numerous books have been published to assist the mariner and aviator
in the solution of celestial observations. The initials “H.O.” preceding a publication
number are familiar to most navigators. h

The International Hydrographic Bureau is an organization whose purpose is to
encourage world-wide uniformity in hydrographic procedures. From the time of the
International Marine Conference, held at Washington, D. C. in 1889, a need for such
an organization was felt, and in 1919, at the Conference held in London, a French
proposal for the establishment of such a body was adopted by delegates from the 24
nations represented. The International Hydrographic Bureau, located at Monaco, has
since served as a coordinating agency for hydrographic work throughout the world.

118. Navigation manuals.—Although navigation is as old as man himself, naviga-
tion textbooks, as they are thought of today, are a product of the last several centuries.
Until the end of the Dark Ages such books, or manuscripts, as were available were
written by astronomers for other astronomers. The navigator was forced to make use
of these, gleaning what little was directly applicable to his profession. After 1500,
however, the need for books on navigation resulted in the publication of a series of
manuals of increasing value to the mariner.

Sixteenth century manuals. Frequently a command of Latin was required to study
navigatiou during the 16th century. Regimento do estrolabio e do quadrante (fig. 130a),
which was published at Lisbon in 1509, or earlier, explained the method of finding
latitude by meridian observations of the sun and the pole star, contained a traverse table
for finding the longitude by dead reckoning, and listed the longitudes of a number of
places. Unfortunately, the author made several errors in transcribing the declination
tables published by Abraham Zacuto in 1474, and this resulted in errors being made for
many years in determining latitude. Nevertheless, the nameless writer of the Regimento
performed a great service for all mariners. His “Handbook for the Astrolabe and
Quadrant’’—to translate the title—had many editions and many emulators.

In 1519 Fernandez de Encisco published his Suma de Geographia, the first Spanish
manual. The book was largely a translation of the Regimento, but new information
was included, and revisions were printed in 1530 and 1546.

The Flemish mathematician and astronomer R. Gemma Frisius published a book
on navigation in 1530. This manual, entitled De Principiis Astronomiae, gave an
excellent description of the sphere, although the astronomy was that of Ptolemy, and
discussed at length the use of the globe in navigation. Gemma gave courses in terms
of the principal winds, proposed that longitude be reckoned from the Fortunate Islands
(Canary Islands), and gave rules for finding the dead reckoning position by courses
and distances sailed.

Tratado da Sphera, Pedro Nunes' great work, appeared in 1537. In addition to
the first printed description of great-circle sailing, Nunes' book included a section on
determining the latitude by two altitudes of the sun (taken when the azimuths differed
by not less than 40°) and solving the problem on a globe. The method was first
proposed by Gemma. Tratado da Sphera contained the conclusion of a study of
the “plane chart” which Nunes had made. He exposed its errors, but was unable
to develop a satisfactory substitute.

„During the years that followed, an extensive navigational literature became
available. The Spaniards Pedro de Medina and Martin Cortes published successful
manuals in 1545 and 1551, respectively. Medina's Arte de Navegar passed through 13
editions in several languages and Breve de la Spera y de la Arte de Navegar, Cortes” book,
was eventually translated into English and became the favorite of the British navigator.
Cortes discussed the principle which Mercator used 18 years later in constructing his

HISTORY OF NAVIGATION

THE NEW AMERICAN

PRACTICAL NAVIGATOR;

BEING AM

EPITOME or NAVIGATION ;

CONTAINING ALL THE TABLES NECESSARY TO BE USED WITH THÉ

NAUTICAL ALMANAC,

IN DETERMINING THE

Aw MI Teor pr rs:

AND THE

LONGITUDE BY LUNAR OBSERVATIONS ;

AND

KEEPING A COMPLETE RECKONING AT SEA:

ILLUSTRATED BY

PROPER RULES AND EXAMPLES:

THE WHOLE EXIMPLIFED D A

JOURNAL,

KEPT FROM
BOSTON TO MADE/RA,
IN WHICH ALL THE RULES OF NAVIGATION ARE INTRODUCED:

ALSO
fae Demonftratian of the met ufeful Rules of Taroomomerar : With meny afeful Problem in Massuvsavten, Svavsvese,
and Gavermé: And a Di&iosniy of za-Tansts ; with the Manger of performing the mof common Evesursems at dos.
TO WHICH ARE ABDED,
me CapznAt Iustavetions and Īnronmarrom p Manenasu, Magens of Vsnesnts, end ethers coacoreed izpēlavesa»
Tion, relative to Madīrims Lawsend Maacautias Customs.

Ee Dee n
FROM THE BEST AUTHORITIES.

ENRICHED WITH A NUMBER OF

NEW TABLES,

WITH ORIGINAL IMPROVEMENTS AND ADDITIONS, AND A LARGE
VARIETY OF NEW AND IMPORTANT MATTER:
Ardo,

MANY THOUSAND ERRORS ARE CORRECTED,

WHICH HAVE APPRARLD IN THE BEST SYSTEMS OF NAVIGATION YET FUMAS.

By NATHANIEI. BOWDITCH,

PRLLOW OP THE AMERICAN ACADEMY OF ARTS AND SCIENCE

mn
ILLUSTRATED WITH COPPERPLATES.

Sst Edition.

J * PRINTED AT NEWBURYPORT, (Mass.) 1808,
BY
EDMUND M. BLUNT, . (Proprietor)
For CUSHING & APPLETON, Sacam.

“AID BY FVT?Y BOOKSYTLIR, SMIP.CHANDUFR, ANU MATHEMATICASENGTRUMEMTOLARER,
IN THR UNITLD STATES AND WIST.INDIRS

Figure 118.—Original title page of The New American
Practical Navigator, written by Nathaniel Bowditch and
published in 1802.

34 HISTORY OF NAVIGATION

famous chart, and he also listed accurately the distance between meridians at all
latitudes.

The first western hemisphere navigation manual was published by Diego Garcia de
Palacio at Mexico City in 1587. His Instrucion Nauthica included a partial glossary of
nautical terms and certain data on ship construction.

John Davis’ The Seaman’s Secrets of 1594 was the first of the “practical” books.
Davis was a celebrated navigator who asserted that it was the purpose of his book to
give “all that is necessary for sailors, not for scholars on shore.” Davis’ book discussed
at length the navigator’s instruments, and went into detail on the “sailings.” He
explained the method of dividing a great circle into a number of rhumb lines, and the
work he had done with Edward Wright qualified him to report on the method and
advantages of Mercator sailing. He endorsed the system of determining latitude by
two observations of the sun and the intermediate bearing.

Although best known for the presentation of the theory of Mercator sailing,
Edward Wright’s Certaine Errors in Navigation Detected and Corrected (1599) was a
sound navigation manual in its own right. Particularly, he advocated correcting
sights for dip, refraction, and parallax (ch. XVI).

Later manuals. The next 200 years saw a succession of navigation manuals
made available to the navigator; so many that only a few can be mentioned. Among
those which enjoyed the greatest success were Blundeville’s Exercises, John Napier’s
Mirifici Logarithmorum Canonis Constructio (which introduced the use of logarithms
at sea), the tables and rules of Edmund Gunter, Arithmetical Navigation by Thomas
Addison, and Richard Norwood’s The Sea-mans Practice (which gave the length of the
nautical mile as 6,120 feet). Robert Dudley filled four volumes in writing the Arcano
del Mare (1646-47) as did John Robertson with Elements of Navigation. Jonas and
John Moore, William Jones, and several Samuel Dunns were others who contributed
navigation books before Nathaniel Bowditch in America and J. W. Norie in England
wrote the manuals which navigators found best suited to their needs.

Bowditch's The New American Practical Navigator was first published in 1802 (fig.
118), and Norie's Epitome of Navigation appeared the following year. Both were out-
standing books which enabled the mariner of little formal education to grasp the
essentials of his profession. The Englishman's book passed through 22 editions in
that country before losing its popularity to Captain Lecky's famous “Wrinkles” in
Practical Navigation of 1881. The American Practical Navigator is still read widely,
more than a century-and-a-half after its original printing.

A number of worthy navigation manuals have appeared in recent years.

Celestial Navigation

119. Astronomy is sometimes called the oldest of sciences. The movements of
the sun, moon, stars, and planets were used by the earliest men as guides in hunting,
fishing, and farming. The first maps were probably of the heavens.

Babylonian priests studied celestial mechanics at a very early date, possibly as
early as 3800 BC, more probably about 1500 years later. These ancient astronomers
predicted lunar and solar eclipses, constructed tables of the moon’s hour angle, and
are believed to have invented the zodiac. The week and month as known today
originated with their calendar. They grouped the stars by constellations. It is
probable that they were arranged in essentially their present order as early as 2000
BC. The five planets easily identified by the unaided eye were known to the Babylo-
nians, who were apparently the first to divide the sun’s apparent motion about the earth
into 24 equal parts. They published this and other astronomical data in ephemerides.
There is evidence that the prophet Abraham had an excellent knowledge of astronomy.

HISTORY OF NAVIGATION 35

The Chinese, too, made outstanding ‘contributions to the science of the heavens.
They may have fixed the solstices and equinoxes before 2000 BC. They had quad-
rants and armillary spheres, used water clocks, and observed meridian transits.
These ancient Chinese determined that the sun made its annual apparent revolution
about the earth in 365% days, and divided circles into that many parts, rather than
360. About 1100 BC the astronomer Chou Kung determined the sun’s maximum
declination within about 15’.

Astronomy was used by the Egyptians in fixing the dates of their religious festivals
almost as early as the Babylonian studies. By 2000 BC or earlier the new year
began with the heliacal rising of Sirius; that is, the first reappearance of this star in the
eastern sky during morning twilight after having last been seen just after sunset in the
western sky. The heliacal rising of Sirius coincided approximately with the annual
Nile flood. The famous Pyramid of Cheops, which was probably built in the 17th
century BC, was so constructed that the light of Sirius shone down a southerly shaft
when at upper transit, and the light of the pole star shone down a northerly shaft at
lower transit, the axes of the two shafts intersecting in the royal burial chamber.
When the pyramid was constructed, a Draconis, not Polaris, was the pole star.

The Greeks learned of navigational astronomy from the Phoenicians. The
earliest Greek astronomer, Thales, was of Phoenician ancestry. He is given credit for
dividing the year of the western world into 365 days, and he discovered that the sun
does not move uniformly between solstices. Thales is most popularly known, however,
for predicting the solar eclipse of 585 BC, which ended a battle between the Medes
and the Lydians. He was the first of the great men whose work during the next 700
years was the controlling force in navigation, astronomy, and cartography until the
Renaissance.

120. Shape of the earth.—Advanced as the Babylonians were, they apparently
considered the earth to be flat. Land surveys of about 2300 BC show a “salt water
river” encircling the country (fig. 120).

But seafarers knew that the last to be seen of a ship as it disappeared over the
horizon was the masthead. They recognized the longer summer days in England
when they sailed to the tin mines of Cornwall, as early as 900 BC. In that “north-

Courtesy of the Map Division of the Library of Congress.

— iginal and reconstruction of a Babylonian map of about 500 BC. The Babylonians
tu Kee the earth to be a flat disk encircled by a salt water river.

36 HISTORY OF NAVIGATION

land” the Mediterranean sailors noticed that the pole star was higher in the sky and
the lower southern constellations were no longer visible. When Thales invented the
gnomonic projection, about 600 BC, he must have believed the earth to be a sphere.
Two centuries later Aristotle wrote that the earth’s shadow on the moon during an
eclipse was always circular. Archimedes (287-212 BC) used a glass celestial globe
with a smaller terrestrial globe inside it. Although the average man has understood
the spherical nature of the earth for only a comparatively short period, learned astrono-
mers have accepted the fact for more than 25 centuries.

121. Celestial mechanics.—Among astronomers the principal question for 2,000
years was not the shape of the earth, but whether it or the sun was the center of the
universe. A stationary earth seemed logical to the early Greeks, who calculated that
daily rotation would produce a wind of several hundred miles per hour at the equator.
Failing to realize that the earth’s atmosphere turns with it, they considered the absence
of such a wind proof that the earth was stationary. |

The belief among the ancients was that all celestial bodies moved in circles about
the earth. However, the planets—the “wanderers,” as they were called—contradicted
this theory by their irregular motion. In the fourth century BC Eudoxus of Cnidus
attempted to account for this by suggesting that planets were attached to concentric
spheres which rotated about the earth at varying speeds. The plan of epicycles, the
theory of the universe which was commonly accepted for 2,000 years, was first proposed
by Apollonius of Perga in the third century BC. Ptolemy accepted and amplified
the plan, explaining it in his famous books, the Almagest and Cosmographia. - Accord-
ing to Ptolemy, the planets moved at uniform speeds in small circles, the centers of
which moved at uniform speeds in circles about the earth (fig. 121).

At first the Ptolemaic theory was accepted without question, but as the years
passed, forecasts based upon it proved to be inaccurate. By the time the Alfonsine
Tables were published in the 13th century AD, a growing number of astronomers
considered the Ptolemaic doctrine unacceptable. However, Purbach, Regiomontanus,
Bernhard Walther of Nuremberg, and even Tycho Brahe in the latter part of the 16th
century, were among those who tried to reconcile the earth-centered epicyclic plan to
the observed phenomena of the heavens.

As early as the sixth century BC, a brotherhood founded by Pythagoras, a Greek
philosopher, proposed that the earth was round and self-supported in space, and that
it, the other planets, the sun, and the moon revolved about a central fire which they
called Hestia, the hearth of the universe. The sun and the moon, they said, shone
by reflected light from Hestia.

The central fire was never located, however, and a few hundred years later Aris-
tarchus of Samos advanced a genuine heliocentric theory. He denied the existence of
Hestia and placed the sun at the center of the universe, correctly considering it to be
a star which shone by itself. The Hebrews apparently understood the correct relation-
ship at least as early as Abraham (about 2000 BC), and the early inhabitants of the
Western Hemisphere probably knew of it before the Europeans did.

k The Ptolemaic theory was generally accepted until its inability to predict future
positions of the planets could no longer be reconciled. Its replacement by the helio-
centric theory is credited principally to Nicolaus Copernicus (or Koppernigk). After
studying mathematics at the University of Cracow, Copernicus went to Bologna,
where he attended the astronomical lectures of Domenicao Maria Novara, an advocate
of the Pythagorean theory. Further study in Martianus Copella's Satyricon, which

includes a discussion of the heliocentric doctrine, convinced him that the sun was truly
the center of the universe. h

HISTORY OF NAVIGATION on

[>

APO RR.

A EAI

A m er e Le = = Y
>

FIGURE 121.—The plan of epicycles, by which the ancients explained the
retrograde motion of the planets. The planets were believed to rotate in
small circles whose centers moved about the earth in a large circle.

Until the year of his death Copernicus tested his belief by continual observations,
and in that year, 1543, he published De Revolutionibus Orbium Coelestium. In it he
said that the earth rotated on its axis daily and revolved in a circle about the sun once
each year. He placed the other planets in circular orbits about the sun also, recog-
nizing that Mercury and Venus were closer than the earth, and the others farther out.
He concluded that the stars were motionless in space and that the moon moved circu-
larly about the earth. His conclusions did not become widely known until nearly a
century later, when Galileo publicized them. Today, “heliocentric” and “Copernican”
are synonymous terms used in describing the character of the solar system.

122. Other early discoveries.—A knowledge of the principal motions of the planets
permitted reasonably accurate predictions of future positions. Other, less spectacular
data, however, were being established to help round out the knowledge astronomers
needed before they could produce the highly accurate almanacs known today.

More than a century before the birth of Christ, Hipparchus discovered the pre-
cession of the equinoxes (art. 1419) by comparing his own observations of the stars
with those recorded by Timocharis and Aristyllus about 300 BC. Hipparchus cata-
loged more than a thousand stars, and compiled an additional list of time-keeping stars
which differed in sidereal hour angle by 15° (one hour), accurate to 15’. A spherical
star map, or planisphere, and a celestial globe were among the equipment he designed.
However, his instruments did not permit measurements of such precision that stellar
parallax could be detected, and, consequently, he advocated the geocentric theory of

the universe.

38 HISTORY OF NAVIGATION

Three centuries later Ptolemy examined and confirmed Hipparchus' discovery of
precession. He published a catalog in which he arranged the stars by constellations
and gave the magnitude, declination, and right ascension (art. 1426) of each. Follow-
ing Hipparchus, Ptolemy determined longitudes by eclipses. In the Almagest he
included the plane and spherical trigonometry tables which Hipparchus had developed, i
mathematical tables, and an explanation of the circumstances upon which the equation
of time (art. 1912) depends.

The next thousand years saw little progress in the science of astronomy. Alex-
andria continued as a center of learning for several hundred years after Ptolemy, but
succeeding astronomers at the observatory confined their work to comments on his
great books. The long twilight of the Dark Ages had begun.

Alexandria was captured and destroyed by the Arabs in AD 640, and for the
next 500 years Moslems exerted the primary influence in astronomy. Observatories
were erected at Baghdad and Damascus during the ninth century. Ibn Yunis’ observa-
tory near Cairo gathered the data for the Hakimite tables in the 11th century. Earlier,
the Spanish, under Moorish tutelage, set up schools of astronomy at Cordova and
Toledo.

123. Modern astronomy may be said to date from Copernicus, although it was
not until the invention of the telescope, about 1608, that precise measurement of the
positions and motions of celestial bodies was possible.

Galileo Galilei, an Italian, made outstanding contributions to the cause of as-
tronomy, and these served as a basis for the work of later men, particularly Isaac New-
ton. He discovered Jupiter’s satellites, providing additional opportunities for de-
termining longitude on land. He maintained that it is natural for motion to be uniform
and in a straight line and that a force is required only when direction or speed is chang-
ing. Galileo’s support of the heliocentric theory, his use and improvement of the
telescope, and particulerly the clarity and completeness of his records provided firm
footing for succeeding astronomers.

Early in the 17th century, before the invention of the telescope, Tycho Brahe
found the planet Mars to be in a position differing by as much as 8’ from that required
by the geocentric theory. When the telescope became available, astronomers learned
that the apparent diameter of the sun varied during the year, indicating that the earth’s
distance from the sun varies, and that its orbit is not circular.

Johannes Kepler, a German who had succeeded Brahe and who was attempting
to account for his 8’ discrepancy, published in 1609 two of astronomy’s most important
doctrines, the law of equal areas, and the law of elliptical orbits. Nine years later he
announced his third law, relating the periods of revolution of any two planets to their
respective distances from the sun (art. 1407).

Kepler’s discoveries provided a mathematical basis by which more accurate
tables of astronomical data were computed for the maritime explorers of the age. His
realization that the sun is the controlling power of the system and that the orbital
planes of the planets pass through its center almost led him to the discovery of the law
of gravitation.

Sir Isaac Newton reduced Kepler's conclusions to the universal law of gravitation
(art. 1407) when he published his three laws of motions in 1687. Because the planets
exert forces one upon the other, their orbits do not agree exactly with Kepler's laws.
Newton's work compensated for this and, as a result, the astronomer was able to fore-
cast with greater accuracy the positions of the celestial bodies. The navigator benefited
through more exact tables of astronomical data.

Between the years 1764 and 1784, the Frenchmen Lagrange and Laplace con-
clusively proved the solar system's mechanical stability. Early in the 19th century,

HISTORY OF NAVIGATION 39

Nathaniel Bowditch translated and commented upon Laplace's Mécanique Céleste,
bringing it up-to-date. Prior to their work this stability had been questioned due to
apparent inconsistencies in the motions of some of the planets. After their demon-
strations, men were convinced and could turn to other important work necessary to
refine and improve the navigator's almanac.

But there were real, as well as apparent, irregularities of motion which could not
be explained by the law of gravitation alone. By this law the planets describe ellipses
about the sun, and these orbits are repeated indefinitely, except as the other planets
influence the orbits of each by their own gravitational pull. Urbain Leverrier, one-

time Director of the Paris Observatory, found that the line of apsides of Mercury was
advancing 43" per century faster than it should, according to the law of gravitation
and the positions of other known planets. In an attempt to compensate for the
resulting errors in the predicted positions of the planet, he suggested that there must be
a mass of circulating matter between the sun and Mercury. No such circulating matter
has been found, however, and Leverrier's discovery is attributed to a shortcoming of
Newton's law, as explained by Albert Einstein.

In Einstein's hands, Leverrier's 43" became a fact as powerful as Brahe's 8’ had
been in the hands of Kepler. Early in the 20th century, Einstein announced the
theory of relativity (art. 1407). He stated that for the planets to revolve about the
sun is natural, and gravitational force is unnecessary for this, and he asserted that there
need be no circulating matter to account for the motion of the perihelion of Mercury as
this, too, is in the natural order of things. Calculated from his theory, the correction
to the previously computed motion of the perihelion in 100 years is 4279.

Prior to Einstein's work, other discoveries had helped round out man's knowledge
of the universe.

Aberration (art. 1417), discovered by James Bradley about 1726, accounted for
the apparent shifting of the stars throughout the year, due to the combined orbital
speed of the earth and the speed of light. "Twenty years later Bradley described the
periodic wobbling of the earth's axis, called nutation (art. 1417), and its effect upon
precession of the equinoxes.

Meanwhile, in 1718 Edmond Halley, England's second Astronomer Royal, de-
tected a motion of the stars, other than that caused by precession, that led him to
conclude that they, too, were moving. By studying the works of the Alexandrian
astronomers, he found that some of the most prominent stars had changed their posi-
tions by as much as 32/. Jacques Cassini gave Halley's discovery further support when
he found, a few years later, that the declination of Arcturus had changed 5' in the 100
years since Brahe made his observations. This proper motion (art. 1414) is motion in
addition to that caused by precession, nutation, and aberration.

Sir William Herschel, the great astronomer who discovered the planet Uranus in
1781, proved that the solar system is moving toward the constellation Hercules. As
early as 1828 Herschel advocated the establishment of a standard time system. Nep-
tune was discovered in 1846 after its position had been predicted by the Frenchman
Urbain Leverrier. Based upon the work of Percival Lowell, an American, Pluto was
identified in 1930. Uranus, Neptune, and Pluto are of little concern to the navigator.

A more recent discovery may well have greater navigational significance. This
‘is the existence of sources of electromagnetic energy in the sky in the form of radio
stars (art. 1414). The sun has been found to transmit energy of radio frequency, and
instruments have been built which are capable of tracking it across the sky regardless
of weather conditions. | ,

124. Sextant.—Prior to the development of the magnetic compass, the navigator
used the heavenly bodies chiefly as guides by which to steer. The compass, however,

40 HISTORY OF NAVIGATION

Courtesy of the John Carter Brown Library, Brown University.

FIGURE 124a.—An ancient astrolabe, one of the earliest kinds of altitude-
measuring instruments.

led to more frequent long voyages on the open sea, and the need for a vertical-angle
measuring device which could be used for determining altitude, so that latitude could
be found.

Probably the first such device used at sea was the common quadrant, the simplest
form of all such instruments. Made of wood, it was a fourth part of a circle, held ver-
tical by means of a plumb bob. An observation made with this instrument at sea was
a two- or three-man job. This device was probably used ashore for centuries before
it went to sea, although its earliest use by the mariner is unknown.

Invented perhaps by Apollonius of Perga in the third century BC, the astrolabe
(fig. 124a)—from the Greek for star and to take—had been made portable by the Arabs
possibly as early as AD 700. It was in the hands of Christian pilots by the end of
the 13th century, often as an elaborate and beautiful creation wrought of precious
metals. Some astrolabes could be used as star finders (art. 2210) by fitting an engraved
plate to one side Large astrolabes were among the chief instruments of 15th and 16th
century observatories, but the value of this instrument at sea was limited.

The principle of the astrolabe was similar to that of the common quadrant, but
the astrolabe consisted of a metal disk, graduated in degrees, to which a movable sight

HISTORY OF NAVIGATION 41

Courtesy of Peabody Museum of Salem.

FIGURE 124b.— The cross-staff, the first instrument to utilize the visible horizon in making celestial
observations.

vane was attached. In using the astrolabe, which may be likened to a pelorus held on
its side, the navigator adjusted the sight vane until it was in line with the star, and
then read the zenith distance from the scale. As with the common quadrant, the
vertical was established by plumb bob.

Three men were needed to make an observation with the astrolabe (one held the
instrument by a ring at its top, another aligned the sight vane with the body, a third
made the reading) and even then the least rolling or pitching of a vessel caused large
acceleration errors in observa-
tions. Therefore, navigators
were forced to abandon the
plumb bob and make the ho-
rizon their reference.

The cross-staff (fig. 124b)
was the first instrument which
utilized the visible horizon in
making celestial observations.
The instrument consisted of a
long, wooden shaft upon which
one of several cross-pieces was l

. Courtesy of Peabody Museum of Salem.
mounted perpendicularly, The FIGURE 124c.—The backstaff, or sea quadrant, a favorite in-
cross-pieces were of various strument of American colonial navigators.
lengths, the one being used
depending upon the angle to be measured. The navigator fitted the appropriate
cross-piece on the shaft and, holding one end of the shaft beside his eye, adjusted
the cross until its lower end was in line with the horizon and its upper end with the
body. The shaft was calibrated to indicate the altitude of the body observed.

In using the cross-staff, the navigator was forced to look at the horizon and the
celestial body at the same time. In 1590 John Davis, author of The Seaman’s Secrets,
invented the backstaff (fig. 124c) or sea quadrant. He was one of the few practical

42 HISTORY OF NAVIGATION

seamen (Davis Strait is named for him, in honor of his attempt to find the Northwest
Passage) to invent a navigational device. The backstaff marked a long advance and
was particularly popular among American colonial navigators. | | ;

In using this instrument, the navigator turned his back to the sun and aligned its
shadow with the horizon. The backstaff had two arcs, and the sum of the values shown
on each was the zenith distance of the sun. Later, this instrument was fitted with
a mirror to permit observations of bodies other than the sun.

Another instrument developed about the same time was the nocturnal (fig. 124d).
Its purpose was to provide the mariner with the appropriate correction to be made to
the altitude of Polaris to determine latitude. By sighting on Polaris through the hole
in the center of the instrument and adjusting the movable arm so that it pointed at
Kochab, the navigator could
read the correction from the
instrument. Most nocturnals
had an additional outer disk
graduated for the months and
days of the year and by ad-
justing this the navigator could
also determine solar time.

Tycho Brahe designed sev-
eral instruments with ares of
60°, having one fixed sight and
another movable one. He called
the instruments sextants and
the name is now commonly ap-
plied to all altitude-measuring
devices used by the navigator
(ch. XV). In 1700 Sir Isaac
Newton sent to Edmond
Halley, the Astronomer Royal,

A a description of a device
CERA having double-reflecting mir-
CUN rors, the principle of the
us modern marine sextant. How-
ever, this was not made public
until after somewhat similar
instruments had been made in
FicunE 124d.— The nocturnal, an instrument used to deter- MEUM ccu ie Podio ues
mine latitude by an observation of Polaris. Hadley, and the American
Thomas Godfrey.

The original instrument constructed by Hadley was, in fact, an octant, but due to
the double-reflection principle it measured angles up to one-fourth of a circle, or 90°.
Godfrey's instrument is reported to have been a quadrant, and so could measure angles
through 180°. The two men received equal awards from England's Roval Society, as their
work was considered to be a case of simultaneous independent invention, although Hadley
probably preceded Godfrey by a few months in the actual construction of his sextant.

In the next few years both instruments were successfully tested at sea, but 20 years
or more passed before the navigator gave up his backstaff or sea quadrant for the
new device. In 1733 Hadley attached a spirit level to a quadrant, and with it was
able to measure altitudes without reference to the horizon. Some years later the
first bubble sextant (art. 1513) was developed.

British Crown copyright. Science Museum, London, England.

HISTORY OF NAVIGATION 43

Pierre Vernier, in 1631, had attached to the limb of a quadrant a second, smaller
graduated are, thereby permitting angles to be measured more accurately, and this
device was incorporated in all later angle-measuring instruments.

The sextant has remained practically unchanged since its invention more than two
centuries ago. The only notable improvements have been the addition of an endless
tangent screw and a micrometer drum, both having been added during the 20th century.

125. Determining latitude.—The ability to determine longitude at sea is com-
paratively modern, but latitude has been available for thousands of years.

Meridian transit of the sun. Long before the Christian era, astronomers had
determined the sun’s declination for each day of the year, and prepared tables listing
the data. This was a comparatively simple matter, for the zenith distance obtained
by use of a shadow cast by the sun on the day of the winter solstice could be sub-
tracted from that obtained on the day of the summer solstice to determine the range
of the sun’s declination, about 47°. Half of this is the sun’s maximum declination,
which could then be applied to the zenith distance recorded on either day to determine
the latitude of the place. Daily observations thereafter enabled the ancient astronomers
to construct reasonably accurate declination tables.

Such tables were available long before the average navigator was ready to use
them, but certainly by the 15th century experienced seamen were determining their
latitude at sea to within one or two degrees. In his 1594 The Seaman’s Secrets, Davis
made use of his experience in high latitudes to explain the method of determining
latitude by lower transit observations of the sun.

Ex-meridian observation of the sun. The possibility of overcast skies at the one
time each day when the navigator could get a reliable observation for latitude led to
the development of the “ex-meridian” sight. Another method, involving two sights
taken with a considerable time interval between, had previously been known, but
the mathematics were so involved that it is doubtful that many seamen made use
of it.

There are two methods by which ex-meridian observations can be solved.
The direct process was the more accurate, although it required a trigonometrical
solution. By the latter part of the 19th century, tables were introduced which made
the method of reduction to the meridian more practical and, when occasion demands
such an observation, this is the method generally used today. However, with the
development of line of position methods and the modern inspection table, ex-meridian
observations have lost much of their popularity.

Latitude by Polaris. First use of the pole star to determine latitude is not known,
but many centuries ago seamen who used it as a guide by which to steer were known
to comment upon its change of altitude as they sailed north or south.

By Columbus’ time some navigators were using Polaris to determine latitude,
and with the invention of the nocturnal late in the 16th century, providing corrections
to the observed altitude, the method came into more general use. The development
of the chronometer in the 18th century permitted exact corrections, and this made
determination of latitude by Polaris a common practice. Even today, more than a
century after discovery of the celestial line of position, the method is still in use. The
modern inspection table has eliminated the need for meridian observations as a special
method for determining latitude. Perhaps when the almanacs and sight reduction
tables make the same provision for solution of Polaris sights as they do for any other
navigational star, this last of the special methods will cease to be used for general
navigation. But customs die slowly, and one as well established as that of position
finding in terms of separate latitude and longitude observations—instead of lines of
position—is not likely to disappear completely for many years to come.

44 HISTORY OF NAVIGATION

126. The search for a method of “discovering” longitude at sea.—A statement
once quite common was, “The navigator always knows his latitude.” A more accurate
statement would have been, “The navigator never knows his longitude.” In 1594
Davis wrote: “Now there be some that are very inquisitive to have a way to get the
longitude, but that is too tedious for seamen, since it requireth the deep knowledge of
astronomy, wherefore I would not have any man think that the longitude is to be found
at sea by any instrument, so let no seamen trouble themselves with any such rule, but
let them keep a perfect account and reckoning of the way of their ship.” In speaking
of conditions of his day, he was correct, for it was not until the 19th century that the
average navigator was able to determine his longitude with accuracy.

Parallel sailing. Without knowledge of his longitude, the navigator of old found
it necessary on an ocean crossing to sail northward or southward to the latitude of his
destination, and then to follow that parallel of latitude until the destination was
reached, even though this might take him far out of his way. Because of this practice,
parallel sailing was an important part of the navigator's store of knowledge. The
method was a crude one, however, and the time of landfall was often in error by a
matter of days, and, in extreme cases, even weeks.

‘Eclipses. Almost as early as the rotation of the earth was established, astronomers
recognized that longitude could be determined by comparing local time with that at
the reference meridian. The problem was the determination of time at the reference
meridian.

One of the first methods proposed was that of observing the disappearance of
Jupiter's satellites as they were eclipsed by their planet. This method, originally
proposed by Galileo for use on land, required the ability to observe and identify the
satellites by using a powerful telescope, knowledge of the times at which the eclipses
would take place, and the skill to keep the instrument directed at the bodies while
aboard a small vessel on the high seas. Although used in isolated cases for many
years, the method was not satisfactory at sea, due largely to the difficulty of observa-
tion (some authorities recommended use of a telescope as long as 18 or 19 feet) and the
lack of sufficiently accurate predictions.

Variation of the compass was seriously considered as a method of determining
longitude for 200 years or more. Faleiro, Magellan’s advisor, believed it could be so
utilized, and, until the development of the chronometer, work was carried on to perfect
the theory. Although there is no simple relationship between variation and longitude,
those who advocated the method felt certain that research and investigation would
eventually provide the answer. Many others were convinced that such a solution
did not exist. In 1676, Henry Bond published The Longitude Found, in which he stated
that the latitude of a place and its variation could be referred to the prime meridian to
determine longitude. Two years later Peter Blackborrow rebutted with The Longitude
Not Found.

Variation was put to good use in determining the nearness to land by shipmasters
familiar with the waters they plied, but as the solution to the longitude problem it was
a failure, and with the improvement of lunar distance methods and the invention of
the chronometer, interest in the method waned. If it had been possible to provide the
mariner with an accurate chart of variation, and to keep it up-to-date, a means of
establishing an approximate line of position in areas where the gradient is large would
have resulted; in many cases this would have established longitude if latitude were
known.

| Lunar distances. "The first method widely used at sea to determine longitude
with some aceuracy was that of lunar distances (art. 131), by which the navigator

HISTORY OF NAVIGATION 45

determined GMT by noting the position of the relatively fast-moving moon among
the stars. ` Both Regiomontanus, in 1472, and John Werner, in 1514, have been credited
with being the first to propose the use of the lunar distance method. At least one source
states that Amerigo Vespucci, in 1497, determined longitude using the moon's position
relative to that of another body. One of the principal reasons for establishing the Royal
Observatory at Greenwich was to conduct the observations necessary to provide more
accurate predictions of the future positions of the moon. Astronomers, including the
Astronomers Royal, favored this method, and half a century after the invention of the
chronometer it was still being perfected. In 1802 Nathaniel Bowditch simplified the
method and its explanation, thus eliminating much of the mystery surrounding it and
making it understandable to the average mariner. By using Bowditch’s method, the
navigator was able to head more or less directly toward his destination, rather than
travel the many additional miles often required in “running down the latitude” and then
using parallel sailing. An explanation of the lunar distance method, and tables for
its use, were carried in the American Practical Navigator until 1914.

The Board of Longitude. The lunar distance method, using the data and equip-
ment available early in the 18th century, was far from satisfactory. Ships, cargoes,
and lives were lost because of inaccurately-determined longitudes. During the Age of
Discovery, Spain and Holland posted rewards for solution to the problem, but in vain.
When 2,000 men were lost as a squadron of British men-of-war ran aground on a foggy
night in 1707, officers of the Royal Navy and Merchant Navy petitioned Parliament
for action. As a result, the Board of Longitude was established in 1714, empowered
to reward the person who could solve the problem of “discovering” longitude at sea.
A voyage to the West Indies and back was to be the test of proposed methods which
were deemed worthy. The discoverer of a system which could determine the longitude
within 1° by the end of the voyage was to receive £10,000; within 40’, £15,000;
and within 30’, £20,000. These would be handsome sums today. In the 18th cen-
tury they were fortunes.

127. Evolution of the chronometer.—Many and varied were the solutions proposed
for finding longitude, and as the different methods were found unsatisfactory, it became
increasingly apparent that the problem was one of keeping the time of the prime merid-
ian. But the development of a device that would keep accurate time during a long
voyage seemed to most men to be beyond the realm of possibility. Astronomers were
flatly opposed to the idea and felt that the problem was properly theirs. There is
even some evidence to indicate that the astronomers of the Board of Longitude made
unfair tests of chronometers submitted to them.

Christian Huygens (1629-95), a Dutch scientist and mathematician, made a
number of contributions of great value in the field of astronomy, but his most memorable
work, to the navigator, was his attempt at constructing a perfect timepiece. It was
probably Galileo who first suggested using a pendulum in keeping time. Huygens
realized that an error would result from the use of a simple pendulum, however, and he
devised one in which the bob hung from a double cord that passed between two plates
in such a way that it traced a cycloidal path. " |

In 1660 Huygens built his first chronometer. The instrument utilized his cycloidal
pendulum, actuated by a spring. To compensate for rolling and pitching, Huygens
mounted the clock in gimbals. Two years later the instrument was tested at sea, with
promising results. The loss of tension in the spring as 16 ran down was the major
weakness in this clock. Huygens compensated for this by attaching oppositely tapered
cones and a chain to the spring. A 1665 sea test of the new timepiece showed greater
accuracy, but still not enough for determination of longitude. In 1674 he constructed

46 HISTORY OF NAVIGATION

a chronometer with a special balance and long balance-spring. Although it was the
best marine timepiece then known, Huygens’ last clock was also unsuited for use at sea
due to the error caused by temperature changes.

John Harrison was a carpenter’s son, born in Yorkshire in 1693. He followed his
father’s trade during his youth, but soon became interested in the repair and construc-
tion of clocks. At the age of 20 he completed his first timekeeper, a pendulum-type
clock with wooden wheels and pinions. Harrison's gridiron pendulum, one which
maintained its length despite temperature changes, was designed about 1720, and con-
tained alternate iron and brass rods to eliminate distortion. Until the time that metal

British Crown copyright. From the original in the National Maritime
Museum, London, England. Reproduced by permission of the Admiralty.

Figure 127.—Harrison's No. 1 chronometer. Th i
z e 2s ; e first of four time-
keepers constructed by Harrison, this clock weighs 65 pounds. ri

alloys having small coefficients of temperature expansion were developed, Harrison's
invention was the type pendulum used by almost all clockmakers. i

By 1728 Harrison felt ready to take his pendulum, an escapement he had invented
and plans for his own marine timepiece before the Board of Longitude. In onde
however, George Graham, a famous clockmaker, advised him to first construct the tities
keeper. Harrison did, and in 1735 he submitted his No. 1 chronometer (fi | 1270)
The Board authorized a sea trial aboard HMS Centurion. The following e that
vessel sailed for Lisbon with Harrison’s clock on board, and upon her AAA M error
was found to be three minutes of longitude, a performance which sto nuda imbibe of
the Board. But the chronometer was awkward and heavy, being TIME in glass

HISTORY OF NAVIGATION 47

and welghing some 65 pounds, and the Board voted to give Harrison only £500, to
be used in producing a more practical timepiece.

During the next few years he constructed two other chronometers, which were
stronger and less complicated, although there is no record of their being tested by the
Board of Longitude. Harrison continued to devote his life to the construction of an
accurate clock to be used in determining longitude, and finally, as he approached old
age, he developed his No. 4. Again he went before the Board, and again a test was
arranged. In November of 1761, HMS Deptford sailed for Jamaica with No. 4
aboard, in the eustody of Harrison's son, William. On arrival, after a passage lasting
two months, the watch was only nine seconds slow (2% minutes of longitude). In
January of 1762 it was placed aboard HMS Merlin for the return voyage to England.
When the Merlin anchored in English waters in April of that year, the total error shown
by the chronometer was 1 minute, 54.5 seconds. This is equal to less than a half
degree of longitude, or less than the minimum error prescribed by the Board for the
largest prize. Harrison applied for the full £20,000, but the Board, led by the Astron-
omer Royal, allowed him only a fourth of that, and insisted on another test.

William Harrison sailed again with No. 4 for Barbados in March of 1764, and
throughout the almost four-months-long voyage the chronometer showed an error of
only 54 seconds, or 13.5 minutes of longitude. The astronomers of the Board reluc-
tantly joined in a unanimous declaration that Harrison's timepiece had exceeded all
expectations, but they still would not pay him the full reward. An additional £5,000
were paid on the condition that plans be submitted for the construction of similar
chronometers. Even when this was done, the Board delayed payment further by
having one of its members construct a timepiece from the plans. Not until 1773,
Harrison's 80th year, was the rest of the reward paid, and only then because of inter-
vention by the king himself.

Pierre LeRoy, a great French clockmaker, constructed a chronometer in 1766
which has since been the basis for all such instruments. LeRoy's several inventions
made his chronometer a timepiece which has been described as a “masterpiece of
simplicity, combined with efficiency." Others to contribute to the art of watchmaking
included Ferdinand Berthoud of France and Thomas Mudge of England, each of
whom developed new escapements. "The balance wheel was improved by John Arnold,
who invented the escapement acting in one direction only, substantially that used
today. Acting independently, Thomas Earnshaw invented a similar escapement. He
built the first reliable chronometer at a relatively low price. The chronometer the
Board of Longitude had made from Harrison's plans cost £450; Earnshaw's cost £45.

Timepieces designed to provide the navigator with information other than time
were popular a century or more ago. One showed the times of high and low water,
the state of the tide at any time, and the phases of the moon; another gave the equation
of time and the apparent motions of the stars and planets; a third offered the position
of the sun and both mean and sidereal times. But the chronometers produced by
LeRoy and Earnshaw were the ones of greatest value to the navigator; they gave him
a simple and reliable method of determining his longitude. P

Time signals, which permit the mariner at sea to check the error in his chronom-
eter, are essentially a 20th century development. Telegraphic time signals were inau-
gurated in the United States at the end of the Civil War, and enabled ships to check
their chronometers in port by time ball signals. Previously, the Navy's “standard”
chronometer had been carried from port to port to allow such comparison. In their
most advanced form, time balls were dropped by telegraphic action. In 1904 the first
official “wireless”? transmission of time signals began from a naval station at Navesink,

48 HISTORY OF NAVIGATION

N. J. These were low-power signals which could be heard for a distance of about 50
miles. Five years later the range had been doubled, and, as other nations began
sending time signals, the navigator was soon able to check his chronometer around
the world.

The search for longitude was ended.

128. Establishment of the prime meridian.—Until the beginning of the 19th cen-
tury, there was little uniformity among cartographers as to the meridian from which
longitude was measured... The navigator was not particularly concerned, as he could
not determine his longitude, anyway.

Ptolemy, in the second century AD, had measured longitude eastward from a reference
meridian two degrees west of the Canary Islands. In 1493 Pope Alexander VI drew
a line in the Atlantic west of the Azores to divide the territories of Spain and Portugal,
and for many years this meridian was used by chart makers of the two countries.
In 1570 the Dutch cartographer Ortelius used the easternmost of the Cape Verde
Islands. John Davis, in his 1594 The Seaman's Secrets, said the Isle of Fez in the
Canaries was used because there the variation was zero. Mariners paid little atten-
tion, however, and often reckoned their longitude from several different capes and
ports during a voyage, depending upon their last reliable fix.

The meridian of London was used as early as 1676, and over the years its popu-
larity grew as England's maritime interests increased. The system of measuring longi-
tude both east and west through 180° may have first appeared in the middle of the
18th century. Toward the end of that century, as the Greenwich Observatory in-
creased in prominence, English map makers began using the meridian of that observ-
atory as a reference. The publication by the Observatory of the first British Nautical
Almanac in 1767 further entrenched Greenwich as the prime meridian. A later and
unsuccessful attempt was made in 1810 to establish Washington as the prime meridian
for American navigators and cartographers. At an international conference held in
Washington in 1884 the meridian of Greenwich was officially established, by the 25
nations in attendance, as the prime meridian. Today all maritime nations have desig-
nated the Greenwich meridian the prime meridian, except in a few cases where local
references are used for certain harbor charts.

129. Astronomical observatories.—Thousands of years before the birth of Christ,
crude observatories existed, and astronomers constructed primitive tables which were
the forerunners of modern almanacs. The famous observatory at Alexandria, the
first “true” observatory, was constructed in the third century BC, but the Egyptians,
as well as the Babylonians and Chinese, had already studied the heavens for many
centuries. The armillary sphere (fig. 129a) was the principal instrument used by the
early astronomers. It consisted of a skeleton sphere with several movable rings which
could be adjusted to indicate the orbits of the various celestial bodies. One source
attributes the invention of the armillary sphere to Eratosthenes in the third century
BC; another says the Chinese knew it 2,000 years earlier, as well as the water clock
and a form of astrolabe. The Alexandrian observatory was the seat of astronomical
learning in the western world for several centuries, and there Hipparchus discovered
the precession of the equinoxes, and Ptolemy did the work which led to his Almagest.

Astronomical study did not cease entirely during the Dark Ages. The Arabians
erected observatories at Baghdad and Damascus in the ninth century AD, and observ-
atories in Cairo and northwestern Persia followed. The Moors brought the astronomical
knowledge of the Arabs into Spain, and the Toledan Tables of 1080 resulted from an
awakening of scientific interest that brought about the establishment of schools of
astronomy at Cordova and Toledo in the tenth century.

HISTORY OF NAVIGATION 49

Courtesy of the Map Division of the Library of Congress.

Ficurs 129a.—An armillary sphere, one of the most important instruments
of the ancient astronomers.

The great voyages of western discovery began early in the 15th century, and chief
among those who recognized the need for greater precision in navigation was Prince
Henry “The Navigator” of Portugal. About 1420 he had an observatory constructed
at Sagres, on the southern tip of Portugal, so that more accurate information might
be available to his captains. Henry's hydrographic expeditions added to the geo-
graphical knowledge of the mariner, and he was responsible for the simplification of
many navigational instruments.

The Sagres observatory was rudimentary, however, and not until 1472 was the
first complete observatory built in Europe. In that year Bernard Walther, a wealthy
astronomer, constructed the Nuremberg Observatory, and placed Regiomontanus in
charge. Regiomontanus, born Johann Miiller, contributed a wealth of astronomical

data of the greatest importance to the navigator.

50 HISTORY OF NAVIGATION

The observatory at Cassel, built in 1561, had a revolving dome and an instrument
capable of measuring altitude and azimuth at the same time. Tycho Brahe's Urani-
burgum Observatory, located on the Danish island Hysen, was opened in 1576, and
the results of his observations contributed greatly to the navigator's knowledge.
Prior to the discovery of the telescope, the astronomer could increase the accuracy of
his observations only by using larger instruments. Brahe used a quadrant with a
radius of 19 feet, with which he could measure altitudes to 0/6, an unprecedented degree
of precision at that time. He also had an instrument with which he could determine
altitude and azimuth simultane-
ously (fig. 129b). After Brahe,
Kepler made use of the observ-
atory and his predecessor’s rec-
ords in determining the laws
which bear his name.

The telescope, the modern
astronomer’s most important
tool, was invented by Hans
Lippershey about 1608. Galileo
heard of Lippershey’s inven-
tion, and soon improved upon
it. In 1610 he discovered the
four great moons of Jupiter,
which led to the “longitude by
eclipse" method successfully
used ashore for many years
and experimented with at sea.
With the 32-power telescope he
eventually built, Galileo was
able to observe clearly the
motions of sun spots, by which
he proved that the sun rotates
on its axis. In Paris, in 1671,
the French National Observa-
tory was established.

Greenwich Royal Observa-
tory. England had no early
privately supported observator-

Courtesy of the Map Division of the Library of Congress. les such as those on the conti-

Figure 129b.—A reproduction of Brahe's pelorus. This in- j i
strument was used to determine altitude and azimuth nent. The need for navigational

simultaneously. advancement was ignored by
. Henry VIII and Elizabeth I,but
in 1675 Charles II, at the urging of John Flamsteed, Jonas Moore, Le Sieur de Saint-
Pierre, and Christopher Wren, established the Greenwich Royal Observatory. Charles
limited construction costs to £500, and appointed Flamsteed the first Astronomer Royal,
at an annual salary of £100. The equipment available in the early years of the observa-
tory consisted of two clocks, a “sextant” of seven-foot radius, a quadrant of three-foot
radius, two telescopes, and the star catalog published almost a century before by Tycho
Brahe. Thirteen years passed before Flamsteed had an instrument with which he could
determine his latitude accurately. In 1690 a transit instrument equipped with a telescope
and vernier was invented by Romer, and he later added a vertical circle to the device.
This enabled the astronomer to determine declination and right ascension at the same

HISTORY OF NAVIGATION ol

time. ` One of these instruments was added to the equipment at Greenwich in 1721,
replacing the huge quadrant previously used. The development and perfection of the
chronometer in the next hundred years added further to the accuracy of observations.

Other national observatories were constructed in the years that followed; at
Berlin in 1705, St. Petersburg in 1725, Palermo in 1790, Cape of Good Hope in 1820,
, Parramatta in New South Wales in 1822, and Sydney in 1855.

U. S. Naval Observatory.—The first observatory in the United States is said to
have been built in 1831-1832 at Chapel Hill, N.C. The Depot of Charts and Instru-
ments, established in 1830, was the agency from which the U. S. N avy Hydrographic
Office and the Naval Observatory evolved 36 years later. Under Lieutenant Charles
Wilkes, the second Officer-in-Charge, the Depot about 1835 installed a small transit
instrument for rating chronometers. The Mallory Act of 1842 provided for the
establishment of a permanent observatory, and the director was authorized to purchase
all such supplies as were necessary to continue astronomical study. The observatory
was completed in 1844 and the results of its first observations were published two
years later. Congress established the Naval Observatory as a separate agency in
1866. In 1872 a refracting telescope with a 26-inch aperture, then the world's largest,
was installed. The observatory, located at Washington, D. C., has occupied its
present site since 1893.

The Mount Wilson Observatory of the Carnegie Institution of Washington was
built in 1904-05. The observatory’s 100-inch reflector telescope opened wider the
view of the heavens, and enabled astronomers to study the movements of celestial
bodies with greater accuracy than ever before. But a still finer tool was needed, and
in 1934 the 200-inch reflector for the Palomar Mountain Observatory was cast. The
six-million-dollar observatory was built by the Rockefeller General Education Board
for the California Institute of Technology, which also operates the Mount Wilson Ob-
servatory. The 200-inch telescope makes it possible to see individual stars 20,000,000
light-years away and galaxies at least 1,600,000,000 light-years away.

As with earlier instruments, the telescope has about reached the limit of practical
size. Present efforts are being directed toward application of the electron microscope
to the telescope, to increase the range of present instruments.

130. Almanacs.—From the beginning, astronomers have undoubtedly recorded
the results of their observations. Tables computed from such results have been known
for centuries. The work of Hipparchus, in the second century BC, and Ptolemy,
in his famous Almagest, are examples. Then the Toledan Tables appeared in AD
1080, and the Alfonsine Tables in 1252. Even with these later tables, however, few
copies were made, for printing had not yet been invented, and those that were available
were kept in the hands of astronomers. Not until the 15th century were the first
almanacs printed and made available to the navigator. In Vienna, in 1457, George
Purbach issued the first almanac. Fifteen years later the Nuremberg Observatory,
under Regiomontanus, issued the first of the ephemerides it published until 1506.
These tables gave the great maritime explorers of the age the most accurate information
available. In 1474 Abraham Zacuto introduced his Almanach Perpetuum (fig. 1302)
which contained tables of the sun’s declination in the most useful form yet available
to the mariner. Tabulae Prutenicae, the first tables to be calculated on Copernican
principles, were published by Erasmus Reinhold in 1551 and gave the mariner a clearer
picture of celestial movements than anything previously available. "The work of
Brahe and Kepler at the Uraniburgum Observatory provided the basis for the
publication of the Rudolphine Tables in 1627.

Still, the information contained in these books was intended primarily for the use
of the astronomer, and the navigator carried the various tables only that he might

52 HISTORY OF NAVIGATION

make use of the portions applicable to his work. The first official almanac, Con-

naissance des Temps, was issued by the French National Observatory in 1696.

The

French Observatory rose to its greatest prominence during the 20 years that Urbain

Leverrier held the position of director.

In 1767 the British Nautical Almanac was first published. Nevil Maskelyne
was then Astronomer Royal, and he provided the navigator with the best information ,

available.

n

Marco la«moias. gg d focdméci- tot

boeno.sy. D1: Lugar.

8 2naopapasmaityre
£ Sam focas mar tyre.
Hiao victouno marri

t Zbomedagno confdiot
> Appollonto martyre.

€ Qs qreta martyres.

f Aleranozez gan o marty?
e £uarcnta mi martyres

Sam g|rcgoro papa ^to

E Oam lede bupo bilpo
c #eeopapa 1 martyrr 200 ian
o longinus martyr. af

€ &crtruoie virgem 7 mart |-

f mao bilpo zconfdto
g Anfclino bitpo7ooucoi
H 3oicpb onoiia fenbo:a
b Burbberto confeiior

€ ¡Bento abaoc funoadot
o Paulobifpo 4 confefío:
€ 2pigmctc preftez martyr
f 2bcovor0 pbi Za gg |—
8 Buuciacd ocnofla fenbora| 2 4—
x SZamcaftorio martyre
b Joam yrmiram confeil0?
€ Marcello papa gronoan
D Quinno martyrenftalios
€ Sam fegundo martyre”

f Sícice pappa 7 babina vi

—

Courtesy of the John Carter Brown Library, Brown University.

FIGURE 130a.—An excerpt from the Portuguese
Regimento do estrolabio e do quadrante of about
1509, giving the sun's declination and other
data based upon Zacuto’s calculations for the
month of March. The first day of spring, the
llth by the Julian calendar then in use, is
marked by the symbol of Aries, the ram (Y).

major stars were given for the first of each month.

tances were omitted.

The book contained tables of the sun's declination, and corrections to the

observed altitude of Polaris. The moon's
position relative to other celestial bodies
was included at 12-hour intervals, and
lunar distance tables gave the angular
distance between the moon and certain
other bodies at three-hour intervals.

For almost a hundred years the
British Nautical Almanac was the one
used by American navigators, but in 1852
the Depot of Charts and Instruments
published the first American Ephemeris
and Nautical Almanac, for the year 1855.

Early American almanacs were dis-
tinguished by their excessive detail in some
cases and shortage of data of importance
to the navigator in others. Declination
was given to the nearest 071 and the equa-
tion of time to the nearest 0°01. Most
figures were given only for noon at
Greenwich, and a tedious interpolation
was involved in converting the informa-
tion to that at a given time at the
longitude of the observer. Lunar dis-
tances were given at three-hour intervals.
Few star data were listed (fig. 130b).

Since 1858 the American Nautical
Almanac has been printed without the
ephemeris section, that part of value
chiefly to astronomers. Until 1908 the
positions of the brighter stars were given
only for January Ist, and in relation to
the meridian of Washington. Beginning
in that year, the apparent places of 55
In 1913, the tables of lunar dis-

In 1919, sunrise and sunset tables were added.

One of the greatest inconveniences involved in using the old almanacs was the

astronomical day, which began at noon of the civil day of the same date. This system
was abolished in 1925, and the United States adopted the expression “civil time” to
designate time by the new system. Greenwich hour angle was first published for the
moon in the Lunar Ephemeris for Aviators for the last four months of 1929. This publi-
cation became a supplement to the Nautical Almanac in 1931, and for 1932 the two
were merged.

The Air Almanac, designed by Lieutenant Commander P. V. H. Weems, was
published for 1933, giving Greenwich hour angle for all bodies included. For 1934

HISTORY OF NAVIGATION 53

this information was given in the Nautical Almanac, and the Air Almanac was dis-
continued. The first British air almanac was published for the last quarter of 1937,
and modified for 1939 with features followed closely in the first American Air Almanac,
for 1941. In 1950 a revised Nautical Almanac appeared, patterned after the popular
American Air Almanac. Starting with the 1953 edition, the British and American air
almanacs were combined in a single publication. In that year the United States
reverted to the expression “mean time” in place of “civil time.” In 1958, the British
and American nautical almanacs

were combined, and in 1960, the FIXED STARS, 1856.
name was standardized. — Ti PE PS. CIL OS
131. The navigational tri- MEAN PLACES OF 100 PRINCIPAL FIXED STARS, FOR

. JANUARY 1, 1855.
angle.— It is customary for

^ Pare Name. Mag. | Right Ascension. | An. Variation. Declination. An. Variation.
modern navigators to reduce EECH

h m. s. [3 ol f. |t ar <
: : : a ANDROMEDA 2 | 0 0 5397 + 3.067] +28 17 23.3, +18.93
their celestial observations by y Pēcasi (Algenib) | 3.2] 0 5 46.37] 3085| +14 2238.11 20.05
solving the triangle whose points B Hydri . . | 3 | 018 362 3.292] —78 423.1, 20.23
a CASSIOPEE var. 0 32 18.36 3.356] +-55 44 29.2 19.83
are the elevated pole, the celes- | 8 Ceti | 2 | 0 36 18.45] 3.016] —18 47 0.11 1986
tial body, and the zenith of the || 2 Us. Mix. (Polaris) 2 | 1 6 29.82) +10.117| +88 32 11.3) 419.23
À : Ceti. . . | 8 | 1 16 4657 3.000] — 855586 1874
observer. The sides of this |% Eridani (dekernar)| 1 | 132 18.42) 2238] —57 58 28.2 1859
1 1 a ÁRIETIS. 3 Al Hi .44 .365 | +22 46 28.4] 17.29
triangle are the polar distance y Ceti. 3.4] 2 35 47.42) 3.102] 237194 1544
of the body (codeclination), its
: . g «Cer. 2.31 2 54 42.21/+ 3.129] + 331 4.7 +14.40
zenith distance (coaltitude),and || a Perse: 2 | 313 59.52) 4243] 49920268 1325
. : y Tauri : 3 | 3 38 5231 3.553] +23 39 110) 1154
the polar distance of the zenith y Eridani . . 3 | 3511591 2796] —13 55 26.7, 1059
(colatitude of the observer). a Tauri (Aldedaran)| 1 4 27 36.26 3.436] +16 12 49.4 7.72
Lunar distances. A spheri- a Aur1cz (Capella) | 1 | 5 5 59.03| + 4.423] +45 50 41.8| + 4.27
` B Orionis (Rigel) 1 5 7 31.23 2.884] — 8 22 22.5 4.54
cal triangle was first used at | aTaum . . | 2 | 517 772 3791] +28284838 355
> lvi 1 dist 3 Orionis 2 5 24 36.06 3.066] — 0 24 37.8 3.05
sea 1n solving L unar distance a Leporis 3 | 5 26 20.19] 2.648] —17 5546.0 2.94
problems. m De Ma on « Orionis 2 | 528 5143|-- 3.044] — 1 17 54.6| + 2.71
i | serva- a Columbæ . 2| 5312405 217 9133| 2.23
nearly simultaneous 9 5 a ORIONIS ` .| var. 5 47 19.35 3.249] + 7 22 32.6| + 1.11
tions were made of the altitudes M Geo " 3 | 6141130 | 3.636] +22 34 59.9 — 1.37
a Argus (Canopus) | 1 | 6 20 4413| 1.330| —52 37 47| — 181
of the moon and the sun or &
m 51 (Hev.) Cephei . | 5 | 631 6.10 +30.650| +87 15 7.9| — 2.80
star near the Rao &nd Ei a Cats Maz. (iris) A] 38 4560) ` 2.646] —16 81 12.8) _ 4.52
l J € Uanis ; ajons . P e. ei — H .
angular distance between the | feme Majoris. ` aal 7 11 2765 3597| +22 14417| 6.16
moon and the other body. The | «*Gemixox. (Castor) | 2.1] 7 25 2049] 3.841] 3212 62 7.37
zenith of the observer and the | acan.Min.(Procyon)| 1 | 7 31 4252) + 3.145] + 5 35 35.7| — 8.79
two celestial bodies formed the B Geminor.(Pollur) | 1.2] 7 36 26.23 pee SE z "d du
1 15 Argus . c | 3 8 1 22.22 2.557} — l H
1 i Hydre . ‘ 3.41 8 39 sau 3.189] + 6 56 52.2; 12.86
vertices of the pru AE ‘Une Majoris. | 3 | 8 49 1544) 4123| +48 36 267, 13.78
i oaltitudes |
sides were the two in (Argus. . | 2 | 9 13 12.52/ + 1.602] —58 40 3.3 —1491
and the angular distance be- | «Hvpmæ. . . 2 | 9202765 2951| — 8 1568 1536
5 6 Ursæ Majoris 3 | 923 7.85| 4.048] +5220 6.3| 16.13
tween the bodies. By means pl [glass ao ta 494 24 26 220 1634
of a mathematical calculation | a Leonis (Regulus) | 12| 10 03872 3.205] +12 40 26.
the navigator “cleared” this | » Argus i PL 9919205 pd $906 | ENAERE

distance of the effects of refrac-

1 ; Figure 130b.—Star data from the 1855 Nautical Almanac.
tion and parallax applicable to "The annual corrections in declination and right ascension
each altitude, and other errors. can be used to obtain reasonably correct values today.

The corrected value was then j i
used as an argument for entering the almanac, which gave the true lunar distance from

the sun and several stars at three-hour intervals. | |

Previously, the navigator had set his watch or checked its error and rate, which
could be relied upon for short periods, with the local mean time determined by celestial
observations. The local mean time of the watch, properly corrected, applied to the
Greenwich mean time obtained from the lunar distance observation, gave the longitude.

54 HISTORY OF NAVIGATION

The mathematics involved was tedious, and few mariners were capable of solving
the triangle until Nathaniel Bowditch published his simplified method in 1802 in The
New American Practical Navigator. Chronometers were reliable by that time, but their
high cost prevented their general use aboard the majority of naval and merchant ships.
Using Bowditch's method, however, most navigators, for the first time, could determine
their longitude, and so eliminate the need for parallel sailing and the lost time associ-
ated with it. The popularity of the lunar distance method is indicated by the fact
that tables for its solution were carried in the American Nautical Almanac until the
second decade of the 20th century.

The determination of latitude was considered a separate problem, usually solved
by means of a meridian altitude or an observation of Polaris.

The time sight. The theory of the time sight (art. 2106) had been known to
mathematicians since the dawn of spherical trigonometry, but not until the chronometer
was developed could it be used by mariners.

The time sight made use of the modern navigational triangle. The codeclination,
or polar distance, of the body could be determined from the almanac. The zenith
distance (coaltitude) was determined by observation. If the colatitude were known,
three sides of the triangle were available. From these the meridian angle was com-
puted. The comparison of this with the Greenwich hour angle from the almanac
yielded the longitude.

The time sight was mathematically sound, but the navigator was not always
aware that the longitude determined was only as accurate as the latitude, and together
they merely formed a point on what is known today as a line of position. H the ob-
served body was on the prime vertical, the line of position ran north and south and a
small error in latitude generally had little effect on the longitude. But when the body
was close to the meridian, a small error in latitude produced a large error in longitude.

The line of position by celestial observation (art. 1703) was unknown until dis-
covered in 1837 by 30-year-old Captain Thomas H. Sumner, a Harvard graduate and
son of a United States Congressman from Massachusetts. The discovery of the “Sum-
ner line," as it is sometimes called, was considered by Maury “the commencement of
a new era in practical navigation.” In Sumner’s own words, the discovery took
place in this manner:

“Having sailed from Charleston, S. C., 25th November, 1837, bound to Greenock,
a series of heavy gales from the Westward promised a quick passage; after passing the
Azores, the wind prevailed from the Southward, with thick weather; after passing
Longitude 21° W., no observation was had until near the land; but soundings were had
not far, as was supposed, from the edge of the Bank. The weather was now more
boisterous, and very thick; and the wind still Southerly; arriving about midnight,
17th December, within 40 miles, by dead reckoning, of Tusker light; the wind hauled
S. E., true, making the Irish coast a lee shore; the ship was then kept close to the.
wind, and several tacks made to preserve her position as nearly as possible until day-
light; when nothing being in sight, she was kept on E. N. E: under short sail, with heavy
gales; at about 10 A. M. an altitude of the sun was observed, and the Chronometer time
noted; but, having run so far without any observation, it was plain the Latitude by dead
reckoning was liable to error, and could not be entirely relied on.

"Using, however, this Latitude, in finding the Longitude by Chronometer, it was
found to put the ship 15' of Longitude, E. from her position by dead reckoning; which in
Latitude 52° N. is 9 nautical miles; this seemed to agree tolerably well with the dead
reckoning ; but feeling doubtful of the Latitude, the observation was tried with a
Latitude 10" further N., finding this placed the ship E. N. E. 27 nautical miles, of the
former position, it was tried again with a Latitude 20^ N. of the dead reckoning; this

HISTORY OF NAVIGATION 55

40’ 30’ 20' 10’ 50' o
40 ] ; ; 5
cd l V hil 30 20 10
i yi / Et er
Tusker light » ( ; d -—
j SH / Ņ o) Si
) ete? !
4 i / Ze DH ] 10'
/ / V (i 74
i T | T S / A
\ m he ? S / 4
Ltd Y /
i O
i s e /
e E e 5
) i ;
w > D f
i S$ 9 ] D
© ; 3 M Ai a
— — ae — — — mm m SS SS a a
) i
2 1 : of. dd cuf S Beo e a
z 1 / c
9 Y
===> e Së
4071 / i
= a \
o = At u
M f ( uet ! SS ER
/000 @& — — —— © 2 l Rer
es R (I
j Ía E 30"
S ssim de
j
£ 4
20’ Zk 20’
m i POSITIONS OBTAINED FROM
Ka i
— ú THE THREE ASSUMED LATITUDES
B
1074 7^ / 10’
40" 30’ 20! 10’ 6° 50’ 40’ 207 207 10’ 59

FIGURE 131.— The first celestial line of position, obtained by Captain Thomas Sumner in 1837.

also placed the ship still further E. N. E., and still 27 nautical miles further; these three
positions were then seen to lie in the direction of Small’s light. It then at once appeared,
that the observed altitude must have happened at all the three points, and at Small’s
light, and at the ship, at the same instant of time; and it followed, that Small's light must
bear E. N. E., if the Chronometer was right. Having been convinced of this truth, the
ship was kept on her course, E. N. E., the wind being still S. E., and in less than an hour,
Small’s light was made bearing E. N. E. X E., and close aboard."

In 1843 Sumner published his book, A New and Accurate Method of Finding a
Ship's Position at Sea by Projection on Mercator's Chart, which met with great acclaim.
In it he proposed that a single time sight be solved twice, as he had done (fig. 131),
using latitudes somewhat greater and somewhat less than that arrived at by dead reckon-
ing, and joining the two positions obtained to form the line of position. It is significant
that Sumner was able to introduce this revolutionary principle without seriously up-
setting the method by which mariners had been navigating for years. Perhaps he
realized that a better method could be derived, but almost certainly navigators would
not have accepted the line of position so readily had he recommended that they abandon

altogether the familiar time sight.

56 HISTORY OF NAVIGATION

The Sumner method required the solution of two time sights to obtain each line
of position. Many older navigators preferred not to draw the lines on their charts,
but to fix their position mathematically by a method which Sumner had also devised
and included in his book. This was a tedious procedure, but a popular one. Lecky
recommended the method, and it was still in use early in the 20th century. |

The alternative to working two time sights in the Sumner method was to determine
the azimuth of the body and to draw a line perpendicular to it through the point,
obtained by working a single time sight. Several decades after the appearance of
Sumner's book, this method was made available to navigators through the publication
of accurate azimuth tables, and the system was widely used until comparatively recent
times. The 1943 edition of the American Practical Navigator included examples of its
use. The two-minute azimuth tables still found on many ships were designed
principally for this purpose. The mathematical solution for azimuth was not at first
a part of the time sight.

132. Modern methods of celestial navigation.—Sumner gave the mariner the
line of position; St.-Hilaire the altitude difference or intercept method. Others who
followed these men applied their principles to provide the navigator with rapid means
for determining his position. The new navigational methods developed by these
men, although based upon work done earlier, are largely a product of the 20th century.

Four hundred years ago Pedro Nunes used a globe to obtain a fix by two altitudes
of the sun, and the azimuth angles. Fifty years later Robert Hues determined his
latitude on a globe by using two observations and the time interval between them.
G. W. Littlehales, of the U. S. Navy Hydrographic Office, advocated using a stere-
ographic projection to obtain computed altitude and azimuth in his Altitude, Azimuth,
and Geographical Position, published in 1906.

Various graphic and mechanical methods have also been proposed. Of these,
only one, the Star Altitude Curves of Captain P. V. H. Weems, USN (Ret.), has had
wide usage, almost entirely among aviators. During World War II, some aircraft
were fitted with a device called an “astrograph,” which projected star altitude curves
from film upon a special plotting sheet. The curves could be moved to allow for the
earth’s rotation. When they were properly oriented, part of the line of position could
be traced on the plotting sheet. More generally, however, the navigational triangle
has been solved mathematically or by the use of tables.

Spherical trigonometry is the basis for solving every navigational triangle, and
until about 80 years ago the navigator had no choice but to completely solve each
triangle himself. The cosine formula is a fundamental spherical trigonometry formula
by which the navigational triangle can be conveniently solved. This formula was
commonly used in lunar distance solutions when they were first introduced, but,
because ambiguous results are obtained when the azimuth is close to 90% or 270%,
mathematicians turned to the haversine, which has the advantage of increasing
numerically from 0° to 180%. The cosine-haversine formula (art. 2109) was used
by navigators until recent years.

Toward the end of the 19th century the “short” methods began to appear. About
1875, A. C. Johnson of the British Royal Navy published his book On Finding the
Latitude and Longitude in Cioudy Weather. No plotting was involved in Johnson's
method, but he made use of the principle that a single time sight be worked, rather

HISTORY OF NAVIGATION 57

than the two that Sumner proposed, and the line of position drawn through the point
thus determined.

In 1879 Percy L. H. Davis, of the British Nautical Almanac Office, and Captain
J. E. Davis collaborated on a Sun's True Bearing or Azimuth Table, which enabled the
navigator to lay down a line of position using a computed azimuth. Chronometer
Tables, published by Percy Davis 20 years later, covered latitudes up to 50? and gave
local hour angle values for selected altitudes to one minute of are. In 1905 his Requisite
Tables were issued, enabling the mariner to “solve spherical triangles with three variable
errors.”

These were the first of a large number of “short” solutions which followed the
work of Marcq St.-Hilaire. Generally, they consist of adaptations of the formulas
of spherical trigonometry, and tables of logarithms in a convenient arrangement. It
is customary for such methods to divide the navigational triangle into two right spher-
ical triangles by dropping a perpendicular from one vertex to the side opposite. In
some methods, partial solutions are made and the results tabulated. Aquino and
Braga of Brazil; Ball, Comrie, Davis, and Smart of England; Bertin, Hugon, and
Souillagouet of France; Fuss of Germany; Ogura and Yonemura of Japan; Blackburne
of New Zealand; Pinto of Portugal; Garcia of Spain; and Ageton, Driesonstok, Gingrich,
Rust, and Weems of the United States are but a few of those providing such solutions.
Although “inspection tables" have largely superseded them, many of these “short”
methods are still in use, kept alive largely by the compactness of their tables and the
universality of their application. They are an intermediate step between the tedious
earlier solutions and the fast tabulated ones, and they encouraged the navigator to
work to a practical precision. The earlier custom of working to a precision not justified
by the accuracy of the information used created a false sense of security in the mind
of some navigators, especially those of little experience.

A book of tabulated solutions, from which an answer can be extracted by inspec-
tion, is not a new idea. Lord Kelvin, generally considered the father of modern
navigational methods, expressed interest in such a method. However, solution of the
many thousands of triangles involved would have made the project too costly if done
by hand. Electronic computers have provided a practical means of preparing tables.
In 1936 the first published volume of H.O. Pub. No. 214 was made available, and later
H.O. Pub. No. 249 was provided for air navigators. British Admiralty editions of both
these sets of tables have been published. Editions of H.O. Pub. No. 214 have also been
published by the Instituto Hidrographico de la Marina, Cadiz, Spain, and by the
Istituto Idrografico della Marina, Genova, Italy.

Electronic Navigation

133. Electricity.—Twenty-five hundred years ago Thales of Miletus commented
on basic electrical phenomena, but more than two millenniums passed before men first
approached an understanding of electricity and the uses to which it could be put.

Until about 1682 the only known method of creating electricity was by rubbing
glass with silk or amber with wool. Then Otto von Guericke of Magdeburg invented
an “electric machine” and made possible the creation of electricity for experimental
work. The Leyden jar, the electrical condenser (or machine) commonly used today,
had its origin in 1745 when its principle was accidentally discovered independently by
P. van Musschenbroek, of the University of Leyden, and von Kleist.

Stephen Gray, about 1729, demonstrated the difference between conductors and
non-conductors, or insulators, and ten years later Hawkesbee and DuFay, working
independently, each discovered the positive and negative qualities of electricity.

58 HISTORY OF NAVIGATION

In the middle of the 18th century Sir William Watson of England, developer of
the Leyden jar in essentially its present form, sent electricity more than two miles by
wire. Whether Watson was aware of the tremendous possibilities his experiment
demonstrated is not known. Twenty-five years later, about 1774, Lesage devised
what is believed to have been the first method of electrical communication. He had
a separate wire for each letter of the alphabet and momentarily charged the appropriate
wire to send each letter.

A German scholar, Francis Aepinus (1728-1802), was the first to recognize the
reciprocal relationship of electricity and magnetism. In 1837 Karl Gauss and Wilhelm
Weber collaborated in inventing a reflecting galvanometer for use in telegraphic work,
which was the forerunner of the galvanometer at one time employed in submarine
signaling. Michael Faraday (1791-1867), in a lifetime of experimental work, con-
tributed most of what is known today in the field of electromagnetic induction. In
1864 James Clerk Maxwell of Edinburgh made public his electromagnetic theory of
light. Many consider it the greatest single advancement in. man’s knowledge of
electricity.

134. Electronics.—In 1887 Heinrich Hertz provided the proof of Maxwell’s theory
by producing electromagnetic waves and showing that they could be reflected. A
decade later Joseph J. Thomson discovered the electron and so provided the basis for
the development of the vacuum tube by Fleming and DeForest. In 1899 R. A. Fes-
senden pointed out that directional reception of radio signals was possible if a single
coil or frame aerial was used as the receiving antenna. In 1895 Guglielmo Marconi
transmitted a “wireless” message a distance of about one mile. By 1901 he was able
to communicate between stations more than 2,000 miles apart. The following year
Arthur Edwin Kennelly and Oliver Heaviside introduced the theory of an ionized
layer in the atmosphere and its ability to reflect radio waves. Pulse ranging had its
origin in 1925 when Gregory Breit and Merle A. Tuve used this principle to measure
the height of the ionosphere.

135. Application of electronics to navigation.—Perhaps the first application of
electronics to navigation was the transmission of radio time signals (art. 1909) in 1904,
thus permitting the mariner to check his chronometer at sea. Telegraphic time signals
had been sent since 1865, providing a means of checking the chronometer in various
ports.

Next, radio broadcasts providing navigational warnings, begun in 1907 by the
U. 8. Navy Hydrographic Office, helped increase the safety of navigation at sea.

By the latter part of World War I the directional properties of a loop antenna
were successfully utilized in the radio direction finder (art. 1202). The first radiobeacon
was installed in 1921.

Karly 20th century experiments by Behm and Langevin led to the development,
by the U. S. Navy, of the first practical echo sounder (art. 619) in 1922.

As early as 1904, Christian Hulsmeyer, a German engineer, obtained patents in
several countries on a proposed method of utilizing the reflection of radio waves as an
obstacle detector and a navigational aid to ships. Apparently, the device was never
constructed. In 1922 Marconi said, “It seems to me that it should be possible to
design apparatus by means of which a ship could radiate or project a divergent beam
of these rays (electromagnetic waves) in any desired direction, which rays if coming
across a metallic object, such as another ship, would be reflected back to a receiver
screened from the local transmitter on the sending ship, and thereby immediately
reveal the presence and bearing of the other ship in fog or thick weather.”

In that same year of 1922 two scientists, Dr. A. Hoyt Taylor and Leo C. Young,
testing a communication system at the Naval Aircraft Radio Laboratory at

HISTORY OF NAVIGATION 59

Anacostia, D. C., noted fluctuations in the signals when ships passed between stations
on opposite sides of the Potomac River. Although the potential value of the discovery
was recognized, work on its exploitation did not begin until March 1934, when Young
suggested to Dr. Robert M. Page, an assistant, that this might bear further investi-
gation. By December, Page had constructed a pulse-signal device that determined
the positions of aircraft. This was the first radar (art. 1208). In the spring of 1935
the British, unaware of American efforts, began work in this field, and developed
radar independently. In 1937 the USS Leary tested the first seagoing radar. In 1940
United States and British scientists combined their efforts, resulting in more rapid
progress. Probably no scientific or industrial development in history expanded so
rapidly in all phases—research, development, design, production, trials, and training—
and on such a scale. In 1945, at the close of hostilities of World War II, radar was
made available for commercial use.

Meanwhile, the pulse technique upon which radar is based was utilized for other
navigational aids. "Work on loran (art. 1302) began at the Radiation Laboratory at
the Massachusetts Institute of Technology in 1941. By the end of 1942 the first
stations had been established, in the North Atlantic. Installations in the Aleutians
and the South Pacific soon followed. With the termination of hostilities, loran, like
radar, was made available for public use. A somewhat similar system, gee (art. 1308),
was developed simultaneously in Great Britain. Another pulse system, shoran (art.
1213), was developed by the United States for bombing through undercast. Following
World War II this aid was further perfected and used for measurement of distances
in surveying. A lower frequency, longer range system called electronic position indi-
cator (EPI) (art. 1213) was developed by the U. S. Coast and Geodetic Survey for use
in locating survey ships a considerable distance offshore. Another American develop-
ment, Raydist (arts. 1214, 1311), 1s used in accurate measurement of distance for
surveying and for ship speed trials. Raydist; Decca (art. 1309), a British hyperbolic
system of high accuracy used for navigation and surveying; and lorac (art. 1310), a
somewhat similar American system, use continuous waves, rather than pulses. Not
only are such devices improving the accuracy of charted features, but they may well
apply directly to geodesy, permitting a more accurate determination of the size and
shape of the earth, for they make possible measurement of distances across previously
inaccessible terrain. h

A rotating electronic beam was utilized during World War II in the German navi-
gation system called sonne (art. 1206), later further perfected by the British under the
name consol (art. 1206). Å

In air navigation electronics was used to develop an automatic direction finder.
Four-course radio ranges (art. 1207) and the more recent vortac (art. 1207) have
been used to mark the federal airways. Electronics has various applications to traffic
control in congested areas, and in low-visibility approach systems permitting landings
under conditions of reduced horizontal and vertical visibility. | ;

Electronics permits measurement of weather conditions at various heights and
distances from observing stations, and the transmission of observations from isolated
stations to weather centrals. Radar is permitting study of the structure and movement
of thunderstorms. | |

High-speed electronic computers make practicable the modern inspection table, and
rapidly perform lengthy computations which make it possible for loran tables and charts
to become available to the navigator almost as soon as new stations are operational.

The application of electronics to navigation is almost limitless. Many systems
not mentioned have been suggested, and undoubtedly new ones will be operational in

the future.

60 HISTORY OF NAVIGATION
Conclusion

136. Navigation has come a long way, but there is no evidence that it is nearing
the end of its development. Progress will continue as long as man remains unsatisfied
with the means at his disposal.

Perhaps the best guides to the future are the desires of the present, for a want
usually precedes an acquisition. Pytheas and his contemporaries undoubtedly dreamed
of devices to indicate direction and distance. The 16th century navigator had these,
and wanted a method of determining longitude at sea. The 18th century navigator
could determine longitude, but found the task a tedious one, and perhaps longed to be
freed from the drudgery of navigation. The modern navigator is still seeking further
release from the work of navigation, and now wants to be freed from the limitations of
weather.

There is little probability of further major development in the simplification of
tables for celestial navigation. Further release from the work of navigation is more
likely to come through another approach—automation.

This process might be said to have started with the application of electronics to
computation. The direct use of electronics in navigation is more spectacular, but in
this it is vulnerable to jamming by an unfriendly power, intentional or accidental
mechanical damage, natural failure, propagation limitations in certain areas and at
certain times, and accuracy limitations at long ranges.

In the future, it is likely that electronics will be applied increasingly as an additional
source of energy to extend the range of usefulness of other methods, rather than to re-
place them. To date electronics has been related primarily to piloting, extending its
range far to sea, and permitting its use in periods of foul weather. In the future it can
be expected to play an increasingly important role in the field of dead reckoning and
celestial navigation. Inertial and Doppler systems (art. 809) are under development
for use in guided missiles and aircraft, and a geomagnetic electrokinetograph (GEK)
(art. 611) has been developed to measure the cross component of a current by means
of two electrodes towed astern a vessel, utilizing the earth's magnetic field. Radio
astronomy (art. 1102) may provide a practical means of determining position astro-
nomically through overcast. Star trackers and electronic recorders and computers may
further extend the application of electronics to celestial navigation.

It is not inconceivable that a fix may someday be automatically and continuously
available, perhaps on latitude and longitude dials. However, when this is accomplished,
by one or a combination of systems, it will be but a short additional step to feed this
information electronically to a pen which will automatically trace the path of the vessel
across a chart. Another short step would be to feed the information electrically to a
device to control the movements of the vessel, so that it would automatically follow
& predetermined track.

When this has been accomplished, new problems will undoubtedly arise, for it is
not likely that the time will ever come when there will be no problems to be solved.

137. The navigator.—It might seem that when complete automation has been
pclae, = of the work of the navigator will have been eliminated. However, advance
ne EE Kia gi will undoubtedly reguire human intelligence. So will
BERT tikās de à SPON and the alteration of schedule when cireumstances
TAA e à nless the automatic system can be made 100 percent reliable—

` prospect for the foreseeable future—it will need checking from time to time,

Fs provision will have to be made for other, perhaps cruder, methods in the event of
ailure.

HISTORY OF NAVIGATION 61

Until such time as mechanization may become complete and perfect, the prudent
navigator will not permit himself to become wholly dependent upon “black boxes"
which may fail at crucial moments, or ready-made solutions that may not be'available
when most needed. "Today and in the future, as in the past, a knowledge of fundamental
principles is essential to adequate navigation. If the navigator contents himself with
the ability to read dials or look up answers in a book, he will be of questionable value.
His future, if he has one, will be in jeopardy.

Human beings who entrust their lives to the skill and knowledge of a navigator are
entitled to expect him to be capable of handling any reasonable emergency. When
his customary tools or methods are denied him, they have a right to expect him to have
the necessary ability to take them safely to their destination, however elementary the
knowledge and means available to him.

The wise navigator uses all reliable aids available to him, and seeks to understand
their uses and limitations. He learns to evaluate his various aids when he has means
for checking their accuracy and reliability, so that he can adequately interpret their
indieations when his resources are limited. He stores in his mind the fundamental
knowledge that may be needed in an emergency. Machines may reflect much of the
science of navigation, but only a competent human can practice the art of navigation,

References

Collinder, Per. A History of Marine Navigation. Tr. Maurice Michael. New York,
St. Martin's, 1955.

Hewson, J. B. A History of the Practice of Navigation. Glasgow, Brown, 1951.

Petze, C. L., Jr. The Evolution of Celestial Navigation. Vol. 26, Ideal Series. New
York, Motor Boating, 1948.

Stewart, J. Q., and Pierce, N. L. “The History of Navigation.” Marine and Air
Navigation (Boston, Ginn, 1944). Chap. 29.

Taylor, E.G. R. The Mathematical Practitioners of Tudor and Stuart England. Lon-
don, Cambridge University Press, 1955.

Waters, D. W. The Art of Navigation in England in Elizabethan and Early Stuart
Times. New Haven, Yale University Press, 1958.

Wroth, L. C. Some American Contributions to the Art of Navigation, 1519-1802.
Providence, John Carter Brown Library, 1947.
In addition, articles pertaining to the history of navigation are frequently carried

in certain periodicals, including:
“The American Neptune.” (Salem)
“The Journal of the Institute of Navigation." (London)
“The Nautical Magazine.” (Glasgow)
“Navigation, Journal of the Institute of Navigation.” (Los Angeles)
“Navigation, Revue Technique de Navigation Maritime et Aérienne.” (Paris)
“United States Naval Institute Proceedings.” (Annapolis)

CHAPTER Il

BASIC DEFINITIONS

201. Navigation is the process of directing the movements of a craft from one.
point to another. The word navigate is from the Latin navigatus, the past participle
of “he verb navigere, which is derived from the words navis, meaning “ship,” and
agere, meaning “to move” or “to direct.” Navigation of water craft is called marine
navigation to distinguish it from navigation of aircraft, called air navigation. Naviga-
tion of a vessel on the surface is sometimes called surface navigation to distinguish it
from underwater navigation of a submerged vessel. The expression submarine naviga-
tion is applicable to a submarine, whether submerged or on the surface. Navigation of
vehicles across land or ice is called land navigation. The expression lifeboat navigation
is used to refer to navigation of lifeboats or life rafts, generally involving rather crude
methods. The expression polar navigation refers to navigation in the regions near the
geographical poles of the earth, where special techniques are employed.

The principal divisions of navigation are as follows:

Dead reckoning is the determination of position by advancing a known position
for courses and distances. A position so determined is called a dead reckoning position.
It is generally accepted that the course steered and the speed through the water should
be used, but the expression is also used to refer to the determination of position by
use of the course and speed expected to be made good over the ground, thus making an
estimated allowance for disturbing elements such as current and wind. A position
so determined is better called an estimated position. The expression “dead reckoning”
probably originated from use of the Dutchman’s log, a buoyant object thrown over-
board, to determine the speed of the vessel relative to the object, which was assumed
to be dead in the water. Apparently, the expression deduced reckoning was used
when allowance was made for current and wind. It was often shortened to ded
reckoning and the similarity of this expression to dead reckoning was undoubtedly the
source of the confusion that is still associated with these expressions.

Piloting (or pilotage) is navigation involving frequent or continuous determina-
tion of position or a line of position relative to geographic points, to a high order of
accuracy. It is practiced in the vicinity of land, dangers, aids to navigation, etc., and
requires good judgment and almost constant attention and alertness on the part of the
navigator.

Electronic navigation involves the use of electronic equipment in any way. It
may be called radio navigation if any form of radio is used. Sonic navigation, involving
the use of sound waves, becomes part of electronic navigation when electronic equip-
ment is used in the control, production, transmission, reception, or amplification of
sound signals. Electronic navigation overlaps piloting, and as electronic equipment is
developed to make celestial obs»rvations (art. 1102), it becomes intimately associated
with celestial navigation.

Celestial navigation is navigation using information obtained from celestial bodies.

202. The earth is approximately an oblate spheroid (a sphere flattened at the
poles). Its dimensions and the amount of flattening are not known exactly, but the

values determined by the English geodesist A. R. Clarke in 1866, as defined by the
62

BASIC DEFINITIONS

U.S. Coast and Geodetic Survey in 1880,
are used for charts of North America. Ac-
cording to these dimensions the longer or
equatorial radius, a, is 3,443.96 nautical, or
3,963.23 statute, miles and the shorter or po-
lar radius, b, is 3,432.28 nautical, or 3,949.80
er?)
3
is3,440.07nautical,or3,958.76statute,miles.
The “oblateness” or amount of flattening is
pra? HAS el denga if a and b
a 3443.96 295 294.98
are computed to additional decimal places.
For many navigational purposes the earth
is assumed to be a sphere, without intoler-
able error.

The axis of rotation or polar axis of
the earth is the line connecting the north
pole and the south pole.

203. Circles of the earth.—A great
circle is the line of intersection of a sphere
and a plane through the center of the
sphere. This is the largest circle that can
be drawn on a sphere. The shortest line
on the surface of a sphere between two
points on that surface is part of a great
circle. On the spheroidal earth the short-
est line is called a geodesic.
desic for most problems of navigation.

statute, miles. The mean radius (

63

FIGURE 203a.—The planes of the meridians meet
at the polar axis.

A great circle is a near enough approximation of a geo-

A small circle is the line of intersection of a sphere and a plane which does not

Ficure 203b.—Circles and coordinates of the
earth. All parallels except the equator are
small circles; the equator and meridians are
great circles.

pass through the center of the sphere.

A meridian is a great circle through the
geographical poles of the earth. Hence, all
meridians meet at the poles, and their planes
intersect each other in a line, the polar axis
(fig. 203a). The term meridian is usually
applied to the upper branch only, that half
from pole to pole which passes through a
given point. The other half is called the
lower branch.

The prime meridian is that meridian
used as the origin for measurement of longi-
tude (fig. 203b). The prime meridian used
almost universally is that through the
original position of the British Royal Ob-
servatory at Greenwich, near London.

The equator is the terrestrial great
circle whose plane is perpendicular to
the polar axis (fig. 203c). It is midway
between the poles.

64 BASIC DEFINITIONS

A parallel or parallel of latitude is a circle on the surface of the earth, parallel to
the plane of the equator (fig. 203d). It connects all points of equal latitude. The -
equator, a great circle, is
a limiting case connecting
points of 0° latitude. The
poles, single points at lati-
tude 90%, are the other
limiting case. All other
parallels are small circles.

204. Position on the
earth.—A position on the
surface of the earth (except
at either of the poles) may
be defined by two magni-
tudes called coordinates.
Those customarily used are
latitude and longitude. A
position may also be ex-
pressed in relation to
Figure 203c.—The equator is a great circle midway between the poles. known geographical posi-

tions.

Latitude (L, lat.) is angular distance from the equator, measured northward or
southward along a meridian from 0? at the equator to 90° at the poles (fig. 203b). It
is designated north (N) or south (S) to indicate the direction of measurement.

The difference of latitude (1) between two places is the angular length of are of
any meridian between their parallels (fig. 203b). It is the numerical difference of the
latitudes if the places are
on the same side of the
equator, and the sum if
they are on opposite sides.
It may be designated north
(N) or south (S) when ap-
propriate.

The middle or mid
latitude (Lm) between two
places on the same side of
the equator is half the sum
of their latitudes. Mid
latitude is labeled N or S
to indicate whether it is
north or south of the equa-
tor. The expression is
occasionally used with ref-
erence to two places on

opposite sides of the equator, when it is equal to half the difference between the two
latitudes, and takes the name of the place farthest from the equator. However, this
usage is misleading, as it lacks the significance usually, associated with the expression.

When the places are on opposite sides of the equator, two mid latitudes are generally
used, the average of each latitude and 0°.

LZ
Í

F

Figure 203d.—A parallel of latitude is parallel to the equator.

BASIC DEFINITIONS 65

Longitude (A, long.) is the arc of a parallel or the angle at the pole between the
prime meridian and the meridian of a point on the earth, measured eastward or west-
ward from the prime meridian through 180° (fig. 203b). It is designated east (E) or
west (W) to indicate the direction of measurement.

The difference of longitude (DLo) between two places is the shorter arc of the
parallel or the smaller angle at the pole between the meridians of the two places (fig.
203b). If both places are on the same side (east or west) of Greenwich, DLo is the
numerical difference of the longitudes of the two places; if on opposite sides, DLo is
the numerical sum unless this exceeds 180°, when it is 360° minus the sum. The dis-
tance between two meridians at any parallel of latitude, expressed in distance units,
usually nautical miles, is called departure (p). It represents the distance made good
to the east or west as a craft proceeds from one point to another. Its numerical value
between any two meridians decreases with increased latitude, while DLo is numerically
the same at any latitude. Either DLo or p may be designated east (E) or west (W)
when appropriate.

205. Distance on the earth.—Distance (D, dist.) is the spatial separation of two
points, and is expressed as the length of a line joining them. On the surface of the
earth it is usually stated in miles.
Navigators customarily use the
nautical mile (mi., M) of 1852
meters exactly. This is the
value suggested by the Interna-
tional Hydrographic Bureau in
1929, and since adopted by most
maritime nations. It is often
called the international nautical
mile to distinguish it from
slightly different values used
by some countries. On July 1,
1959, the United States adopted
the exact relationship of 1 yard=
0.9144 meter. The length of the
international nautical mile is con-
sequently equal to 6,076.11549
U.S. feet (approximately).

For most navigational pur-
poses the nautical mile is con-
sidered the length of one minute =
of latitude, or of any great circle FIGURE 205.—A rhumb line or loxodrome.
of the earth, regardless of loca-
tion. On the Clarke spheroid of 1866, used for mapping North America, the length
of one minute of latitude varies from about 6,046 feet at the equator to approximately
6,108 feet at the poles. The length of one minute of a great circle of a sphere having
an area equal to that of the earth, as represented by this spheroid, is 6,080.2 United
States feet. This was the standard value of the nautical mile in the United States
prior to adoption of the international value. A geographical mile is the length of
one minute of the equator, or about 6,087 feet.

The land or statute mile (mi., m) of 5,280 feet is commonly used for navigation
on rivers and lakes, notably the Great Lakes of North America.

The nautical mile is about 38/33 or approximately 1.15 statute miles. A conver-
sion table for nautical and statute miles is given in table 20.

66 BASIC DEFINITIONS

Distance, as customarily used by the navigator, refers to the length of the rhumb
line connecting two places. This is a line making the same oblique angle with all
meridians. Meridians and parallels (including the equator) which also maintain con-
stant true directions, may be considered special cases of the rhumb line. Any other
rhumb line spirals toward the pole, forming a loxodromic curve or loxodrome (fig. 205).
Distance along the great circle connecting two points is customarily designated great-
circle distance.

206. Speed (S) is rate of motion, or distance per unit of time.

A knot (kn.), the unit of speed commonly used in navigation, is a rate of one nautical
mile per hour. The expression “knots per hour” refers to acceleration, not speed.

Sometimes the expression speed of advance (SOA) is used to indicate the speed
expected to be made good over the ground, and speed over ground (SOG) the actual
speed made good over the ground.

207. Direction on the earth.—Direction is the position of one point relative to
another, without reference to the distance between them. In navigation, direction is
customarily expressed as the angular difference in degrees from a reference direction,
usually north or the ship's head. Compass directions (east, south by west, etc.) or points
(of 1142 or % of a circle) are seldom used by modern navigators for precise directions.

Course (C, Cn) is the intended horizontal direction of travel, expressed as angular
distance from north, usually from 000° at north, clockwise through 360°. Strictly,
the term applies to direction through the water, not the direction intended to be made
good over the ground, but in common American usage it is applied to either. Course
made good is the single course from the point of departure to point of arrival at any
given time. Sometimes the expression course of advance (COA) is used to indicate
the direction expected to be made good over the ground, and course over ground
(COG) the actual direction made good over the ground. Course line is a line extending
in the direction of a course.

In making computations it is sometimes convenient to express a course as an
angle from either north or south, through 90° or 180°. In this case it is designated
course angle (C) and should be properly labeled to indicate the origin (prefix) and
direction of measurement (suffix). Thus, C N35? E = Cn 035? (000°+35°), C N 155° W
= Cn 205° (360°—155°), C S47? E — Cn 133? (180°—47°). But Cn 260? may be
either C N100°W or C S80°W, depending upon the conditions of the problem.

The symbol C is always used for course angle, and is usually used for course where
there is little or no possibility of confusion.

Track (TR) is the path actually followed by a vessel, or the path of proposed
travel. It differs from course and course made good by including the element of distance
as well as direction, although the term is occasionally used to refer to direction only.
However, the path actually followed is usually a somewhat irregular line. The path
of proposed travel consists of one or a series of course lines from the point of departure
to the destination, along which it is intended the vessel will proceed. A great circle
which a vessel intends to follow approximately is called a great-circle track.

Heading (Hdg., SH) is the direction in which a vessel is pointed, expressed as
angular distance from north, usually from 000% at north, clockwise through 360°.
Heading should not be confused with course. Heading is a constantly changing value
as a vessel oscillates or yaws back and forth across the course or as the direction of
motion is temporarily changed, as in avoiding an obstacle. Course is a predetermined
value and usually remains constant for a considerable time (fig. 207a).

Bearing (B, Bn) is the direction of one terrestrial point from another, expressed
^ angular diss from a reference direction, usually from 000? at the reference

ection, clockwise through 3609. When measured through 90? or 180? from either

BASIC DEFINITIONS 67

Wind or Current

? Destination

Point of Departure 9

Point of
Arrival

FIGURE 207a.—Course (line), course (line) made good, track, and heading.

north or south, it is called bearing angle (B), which bears the same relationship to
bearing as course angle does to course. Bearing and azimuth are sometimes used inter-
changeably, but the latter is better reserved exclusively for reference to horizontal
direction of a point on the celestial sphere from a point on the earth.

A relative bearing (RB) is one relative to the heading, or to the vessel itself. It is
usually measured from 000° at the heading, clockwise through 360°. However, it is
sometimes conveniently measured right or left from 0° at the ship’s head through 180°.
This is particularly true when using table 7. Older methods, such as indicating the
number of degrees or points from some part of the vessel (10° forward of the starboard
beam, two points on the port quarter, etc.) are seldom used by modern navigators to
indicate precise directions, except for bearings dead ahead or astern, or broad on the
bow, beam, or quarter.

To convert a relative bearing to a bearing from north (fig. 207b), express the rela-
tive bearing in terms of the 0°-360° system and add the heading:

Bn=RB+SH

+

NORTH
nazeuzx

5⁄4 |]
K. |

i e
ze

e

Figure 207b.—Relative bearing.

68 Å BASIC DEFINITIONS

Thus, if another vessel bears 127° relative from a ship whose heading is 150°, the bearing
from north is 127°-+150°=277°. If the total exceeds 360°, subtract this amount.
To convert a bearing from north to a relative bearing, subtract the heading:
RB=Bn—SH
Thus, a lightship which bears 241° from north bears 241°—137 ?— 104? relative from
a ship whose heading is 137°. If SH is larger than Bn, add 360° to Bn before sub-
tracting.
Problems

204. Given. —Point A: L 37%21/4N, ^ 1439188 W; Point B: L 43%04/1N, A
11°47/3E; Point C: L 63%24/4S, A 132?06:9 E; Point D: L 2%36/68, A 168?01:2W.

Required.—(1) The difference of latitude between A and B, between A and C,
and between C and D. Å

(2) The difference of longitude between A and B, A and C, and B and C.

Answers.—(1) lan 5°42'7N, Le 100%45'8S, lop 60°47!8 N; (2) Dos 155°06/1E,
DLo,c 84%34'3W, DLosc 120919/6 E.

205a. The distance between points E and F is 258.4 nautical miles.

Required.—The distance in statute miles between points E and F (1) by proportion,
using the ratio given in article 205; (2) by conversion factor, using the value given in
article 205; (3) by table 20.

Answers.—(1) D 297.6 m, (2) D 297.2 m, (3) D 297.4 m.

205b. The distance between points G and H is 83.3 statute miles.

Reguired.—The distance in nautical miles between points G and A (1) by propor-
tion, using the ratio given in article 205; (2) by conversion factor, using the value given
in article 205; (3) by table 20.

Answers.—(1) D 72.3 M, (2) D 72.4 M, (3) D 72.4 M.

206a. A ship is steaming at 18.5 knots.

Required.—The speed in statute miles per hour.

Answer.—S 21.3 mph.

206b. A motorboat is traveling at 30 statute miles per hour.

Required.—The speed in knots.

Answer.—S 26 kn.

207a. Reguired.—Convert the following course angles to courses: (1) N127°W,
(2) 539 W, (3) N99° E, (4) S171? E.

Answers.—(1) Cn 233°, (2) Cn 188°, (3) Cn 099°, (4) Cn 009°.

207b. Reguired.—Convert the following courses to course angles, giving the two
possible answers of each: (1) 153°, (2) 257°.

Answers.—(1) C N 153? E or S27? E, (2) C N103°W or S77? W.

207c. À ship is on course 151?. "The following relative bearings are observed:
(1) 006°, (2) 109°, (3) 255°, (4) broad on the port bow.

Required.—The bearings from north.

Answers.—(1) Bn 157°, (2) Bn 260°, (3) Bn 046°, (4) Bn 106°.

207d. A ship is on course 244°. The following bearings from north are observed:
(1) 041°, (2) 188°, (3) 332°.

Required.—The relative bearings.

Answers.—(1) RB 157°, (2) RB 304°, (3) RB 088°.
= 20Te. The captain of a ship on course 055? wishes to change course when a certain
lighthouse is broad on the starboard beam.

Required.—The bearing from north when the course is to be changed.
Answer.—Bn 145°.

CHAPTER III

CHART PROJECTIONS

General

301. The navigator's chart.—A map is a conventional representation, usually on
a plane surface, of all or part of the physical features of the earth’s surface or any part
of it. A chart is such a representation intended primarily for navigation. A nautical
or marine chart is one intended primarily for marine navigation. It generally shows
depths of water (by soundings and sometimes also by depth curves), aids to navigation,
dangers, and the outline of adjacent land and such land features as are useful to the
navigator.

Chart making presents the problem of representing the surface of a spheroid upon
a plane surface. The surface of a sphere or spheroid is said to be undevelopable because
no part of it can be flattened without distortion. A map projection or chart projection
is a method of representing all or part of the surface of a sphere or spheroid upon a
plane surface. The process is one of transferring points on the surface of the sphere
or spheroid onto a plane, or onto a developable surface (one that can be flattened to
form a plane) such as a cylinder or cone. If points on the surface of the sphere or
spheroid are projected from a single point (including infinity), the projection is said to
be perspective or geometric. Most map projections are not perspective.

302. Selecting a projection.—Each projection has distinctive features which make
it preferable for certain uses, no one projection being best for all conditions. These
distinctive features are most apparent on charts of large areas. As the area becomes
smaller, the differences between various projections become less noticeable until on the
largest scale chart, such as of a harbor, all projections become practically identical.
Some of the desirable properties are:

1. True shape of physical features.

2. Correct angular relationship. A projection with this characteristic is said to
be conformal or orthomorphic.

3. Equal area, or the representation of areas in their correct relative proportions.

4. Constant scale values for measuring distances.

5. Great circles represented as straight lines.

6. Rhumb lines represented as straight lines.

It is possible to preserve any one and sometimes more than one property in any
one projection, but it is impossible to preserve all of them. For instance, a projection
cannot be both conformal and equal area, nor can both great circles and rhumb lines
be represented as straight lines.

303. Types of projection.—Projections are usually classified primarily as to the
type of developable surface to which the spherical or spheroidal surface is transferred.
They are sometimes further classified as to whether the projection (but not neces-
sarily the charts made by it) is centered on the equator (equatorial), a pole (polar),
or some point or line between (oblique). The name of a projection often indicates its
type and sometimes, in addition, its principal feature.

The projection used most frequently by mariners is commonly called Mercator,
after its inventor (art. 109). Classified according to type this is an equatorial cy-

69

70 CHART PROJECTIONS

lindrical orthomorphic projection, the cylinder conceived as being tangent along the
equator. A similar projection based upon a cylinder tangent along a meridian is
called transverse Mercator or transverse cylindrical orthomorphic. It is sometimes
called inverse Mercator or inverse cylindrical orthomorphic. If the cylinder is tangent
along a great circle other than the equator or a meridian, the projection is called
oblique Mercator or oblique cylindrical orthomorphic.

In a simple conic projection points on the surface of the earth are conceived as
transferred to a tangent cone. In a Lambert conformal projection the cone inter-
sects the earth (a secant cone) at two small circles. In a polyconic projection, a series
of tangent cones is used.

An azimuthal or zenithal projection is one in which points on the earth are trans-
ferred directly to a plane. If the origin of the projecting rays is the center of the earth,
a gnomonic projection results; if it is the point opposite the plane’s point of tangency, a
stereographic projection; and if at infinity (the projecting lines being parallel to each
other), an orthographic projection (fig. 303). The gnomonic, stereographic, and
orthographic are perspective projections.
In an azimuthal equidistant projection,
which is not perspective, the scale of dis-
tances is constant along any radial line
from the point of tangency.

Cylindrical and plane projections can
be considered special cases of conical
projections with the heights infinity and
zero, respectively.

A graticule is the network of latitude
and longitude lines laid out in accordance
with the principles of any projection.

Cylindrical Projections

Figure 303.—Azimuthal projections: A, gno- wi ;
uad rL qc n mm 304. Features.—If a cylinder is placed
orthographic. around the earth, tangent along the equa-

tor, and the planes of the meridians are
extended, they intersect the cylinder in a number of vertical lines (fig. 304). These
lines, all being vertical, are parallel, or everywhere equidistant from each other, un-
like the terrestrial meridians, which become closer together as the latitude increases.
On the earth the parallels of latitude are perpendicular to the meridians, forming circles
of progressively smaller diameter as the latitude increases. On the cylinder they are
shown perpendicular to the projected meridians, but because a cylinder is everywhere
of the same diameter, the projected parallels are all the same size.

2 the cylinder is cut along a vertical line (a meridian) and spread out flat, the
meridians appear as equally spaced, vertical lines, and the parallels as horizontal
lines. The spacing of the parallels relative to each other differs in the various types
of cylindrical projections.

The cylinder may be tangent along some great circle other than the equator
EE "a ast i transverse cylindrical projection, on which the pattern of Jati-

ude and longitude lines a d ite differ ] j |
iens Y AUD eR usos quite different, since the line of tangency and the
| 305. Mercator projection.—The only cylindrical projection widely used for navi-
ME the Mercator or equatorial cylindrical orthomorphic, named for its inventor
erhard Kremer (Mercator), a Flemish geographer. It is not perspective and the

CHART PROJECTIONS 71

parallels cannot be located by geometrical projection, the spacing being derived mathe-
matically. The use of a tangent cylinder to explain the development of the projection
has been used, but the relationship of the terrestrial latitude and longitude lines to
those on the cylinder is often carried beyond justification, resulting in misleading
statements and illustrations.

„The distinguishing feature of the Mercator projection (fig. 305) among cylindrical
projections is that both the meridians and parallels are expanded at the same ratio
with increased latitude. The expansion is equal to the secant of the latitude, with a
small correction for the ellipticity of the earth. Since the secant of 90° is infinity, the
projection cannot include the poles. Ex-
pansion is the same in all directions and
angles are correctly shown, the projection
being conformal. Rhumb lines appear as
straight lines, the directions of which can
"be measured directly on the chart. Dis-
tances can also be measured directly, to
practical accuracy, but not by a single
distance scale over the entire chart, unless
the spread of latitude is small. The lati-
tude scale is customarily used for measur-
ing distances, the expansion of the scale
being the same as that of distances at the
same latitude. Great circles, except me-
ridians and the equator, appear as curved
lines concave to the equator (fig. 310a).
Small areas appear in their correct shape
but of increased size unless they are near
the equator. Plotting of positions by
latitude and longitude is done by means
of rectangular coordinates, as on any
cylindrical projection.

306. Meridional parts.—At the equa-
tor a degree of longitude is approximately
equal in length to a degree of latitude.
As the distance from the equator increases,
degrees of latitude remain approximately
the same (not exactly because the earth is
not quite a sphere), while degrees of longi-
tude become progressively shorter. Since FravunE 304.—A cylindrical projection.
degrees of longitude appear everywhere
the same length in the Mercator projection, it is necessary to increase the length of
the meridians if the expansion is to be equal in all directions. Thus, to maintain the
correct proportions between degrees of latitude and degrees of longitude, the former
are shown progressively longer as the distance from the equator increases (fig. 305).

The length of the meridian, as thus increased between the equator and any given
latitude, expressed in minutes of the equator as a unit, constitutes the number of
meridional parts (M) corresponding to that latitude. Meridional parts, given in table
5 for every minute of latitude from the equator to the pole, afford facilities for con-
structing a Mercator chart and for solving problems in Mercator sailing (art. 817).
These values are for the Clarke spheroid of 1866. By means of table 4 they can be
converted to the values for certain other spheroids and the sphere.

12 CHART PROJECTIONS

FIGURE 305.—A Mercator map of the world.

The formula for meridional parts, given in the explanation to table 5, is derived from
an integral representing the exact relationship.

307. Mercator chart construction.—To construct a Mercator chart, first select
the scale and then proceed as follows:

Draw a series of vertical lines to represent the meridians, spacing them in accord-
ance with the scale selected. If the chart is to include the equator, the distances of
the various parallels from the equator are given directly in table 5, although it may be
desirable to convert the tabulated values to more convenient units. Thus, if 1°(60’)

$ e £7 k 1
of longitude is to be shown as one inch, each meridional part will be 60 9r 0.01667

inch in length. The distance, in inches, of any parallel from the equator is then
determined by dividing its meridional parts by 60 or multiplying them by 0.01667.

If the equator is not to be included, the meridional difference (m) is used. This
is the difference between the meridional parts of the various latitudes and that of the
lowest parallel (the one nearest the equator) to be shown. Distances so determined
are measured from the lowest parallel.

It is often desired to show a minimum area on a chart of limited size, to the largest
possible scale. The scale is then dictated by the limitations.

When the graticule has been completed, the features to be shown are located by
means of the latitude and longitude scales.

Example.—A Mercator chart is to be constructed at the maximum scale on a sheet
of paper 35 X 46 inches, with a minimum two-inch margin outside the neat line limiting

CHART PROJECTIONS 73

the charted area. The minimum area to be covered is lat. 449-50? north and long.
56?—68? west.

Solution.—Step one: Determine which dimension to place horizontal. From table
5 the meridional difference is:

Ms 3456.6

Ma 2929.6
m 5270

The chart is to cover at least 12° (68°—56°) of longitude. The longitude is therefore
to cover a distance of 12 X 60=720 meridional parts. Since there are a greater number
of meridional parts of longitude to be shown than of latitude, the long dimension is
placed horizontal.

Step two: Determine whether the latitude or longitude is the limiting scale factor.
The number of inches available for latitude coverage is 31 (35 inches minus a two-inch
margin top and bottom). If 527 meridional parts are to be shown in 31 inches, each
31
527

meridional part will be — 0.05882 inch. There are 46—4=42 inches available for

' 42
longitude, and therefore the length of each meridional part will be 790 = 0.05833

inch. Thus, the longitude is the limiting scale factor, for all of the desired area
could not be shown in the available space if the larger scale were to be used. Using
the smaller scale, it is found that 30.74 inches (0.05833 X527) will be needed to
show the desired latitude coverage. The top and bottom margins can be increased
slightly, or additional latitude coverage can be shown. If it is desired to include
the additional coverage, the amount can be determined by dividing the available
space, 31 inches, by the scale, 0.05833. This is 531.5 meridional parts, or 4.5 more than
the minimum. By inspection of table 5, it is seen that the latitude can be extended
either 3/3 below 44° or 2/9 above 50°. Suppose it is decided that the margin will be
increased slightly and only the desired minimum coverage shown.

Step three: Determine the spacing of the meridians and parallels. Meridians 1° or
60’ apart will be placed 60 X 0.05833 —3.50 inches apart. Next, determine each degree
of latitude separately. First, compute the meridional difference between the lowest
parallel and the various parallels to be shown:

Mase 3013.5 Mase 3098.8 Maze 3185.7 Mage 3274.2 Mage 3364.5 Ms 3456.6
My 2929.6 Mase 2929.6 Mage 2929.6 Mayo 2929.6 Mase 2929.6 Maso 2929.6
m 83.9 m 16972) im 200. IELU 344.6 m 4349 m 527.0

Next, determine the distance of each parallel from that of L 44°N by multiplying its
meridional difference by the scale, 0.05833:

1, 44° to Lb 45°=0.05833 X%, 83.9= 4.89 in.

11:449 to. L,:46%=0.05833169.2=1 0.8 kan.

11:449 tod 4790.05833,< 250-1 — 14.04.

L 44° to L 48°=0.05833 X344.6=20.10 in.

L 44° to L 49°=0.05833 X434.9=25.37 in.

L 44° to L 50°=0.05833 X 527.0= 30.74 in.

; : 35— 30.74

Step four: Draw the graticule. Draw a horizontal line 2.13 inches (7)
from the bottom. Thisisthelower neatline. Labelit “449 N." Draw the right-hand
neat line two inches from the edge. Label it “56% W.” Along the lower parallel
measure off distances in units of 3.50 inches from A 56? W at the right to A 68 W at
the left. Through the points thus located draw vertical lines to represent the meridians.

74 CHART PROJECTIONS

Gaw GPW GEW G5W GAW GFW GZW GIW GOW 59w 58W 57W 56W
== = Ce K = en Ee A sE ECH

50°N

49^N

48 N

247 N

46N

45N

4 ÆN
G8W GTW GGW GW GÆW 63W G2W QVW GOW 59)W 58W 57W 56 W

Figure 307.—The graticule of a Mercator chart m L 449 N to L 50°N and from A 56 W to
A 68? W.

Along any meridian measure upward from the horizontal line a series of distances as
determined by the calculations above. "Through these points draw horizontal lines
to represent the parallels. Label the meridians and parallels as shown in figure 307.

Step five: Mark off the latitude and longitude scales around the neat line. The
scales can be graduated in units as small as desired. Determine the longitude scale
by dividing the degrees into equal parts. Establish the latitude scale by computing
each subdivision of a degree in the same manner as described above for whole degrees.
In low latitudes degrees of latitude can be divided into equal parts without serious loss
of accuracy.

Step siz: Fill in the desired detail.

In south latitude the distance between consecutive parallels increases toward
the south. The top parallel is drawn first and distances measured downward from it.
Latitude labels increase toward the south (down).

In east longitude the longitude labels increase toward the east (right).

308. Transverse and oblique Mercator projections.—If Mercator principles are
used to construct a chart, but with the cylinder tangent along a meridian, a transverse
Mercator or transverse cylindrical orthomorphic projection results. The word “in-
verse” is sometimes used in place of "transverse" with the same meaning. If the cylinder
is tangent at some great circle other than the equator or a meridian (fig. 308a), the
projection is called oblique Mercator or oblique cylindrical orthomorphic. "These
projections utilize a fictitious graticule similar to but offset from the familiar network
of meridians and parallels (fig. 308b). The tangent great circle is the fictitious
equator. Ninety degrees from it are two fictitious poles. A group of great circles
through these poles and perpendicular to the tangent great circle are the fictitious

CHART PROJECTIONS

Figure 308b.—The fictitious graticule of an oblique Mercator
projection. `

75

76 CHART PROJECTIONS

meridians, while a series
of circles parallel to the |
plane of the tangent great
circle form the fictitious
parallels.

The actual meridians
and parallels appear as
curved lines (figs. 309,
310b, and 322).

A straight line on the
transverse or oblique Mer-
cator projection makes the
same angle with all ficti-
tious meridians, but not
with the terrestrial merid-
ians. It is therefore a fic-
titious rhumb line. Near
the tangent great circle a
straight line closely ap-
proximates a great circle.
It is in this area that the
chart is most useful.

The Universal Trans-
verse Mercator (UTM)
grid is a military grid su-
perimposed upon a trans-
verse Mercator graticule,
or the representation of
these grid lines upon any
graticule.

This grid system and
these projections are often
used for large-scale (har-
bor) nautical charts and
military charts.

309. Transverse Mer-

"cator projection.—A spe-
cial case of the Mercator
projection in which the
cylinder is tangent along

FIGURE 309.—A transverse Mercator map of the western hemisphere. a meridian is called a

transverse (inverse) Mer-
cator or transverse (inverse) cylindrical orthomorphic projection. Since the area of

minimum distortion is near a meridian, this projection is useful for charts covering a

large band of latitude and extending a relatively short distance on each side of the
tangent meridian (fig. 309) or for charts of the polar regions (fig. 322). It is sometimes

Rod star charts showing the evening sky at various seasons of the year (figs. 2205—

2208).

310. Obliqne Mercator projection.— The Mercat
is tangent along

or projection in which the cylinder
à great circle other than the equator or a meridian is called an oblique

CHART PROJECTIONS 17

FIGURE 310a.— The great circle between Washington and Moscow as it appears on a Mercator map.
See figures 308b and 310b.

Mercator or oblique cylindrical orthomorphic projection. This projection is used prin-
cipally where it is desired to depict an area in the near vicinity of an oblique great
circle, as, for instance, along the great-circle route between two important, widely
separated centers. Figure 310a is a Mercator map showing Washington and Moscow
and the great circle joining them. Figure 310b is an oblique Mercator map with the
great circle between these two centers as the tangent great circle or fictitious equator
(as in fig. 308b). The limits of the chart of figure 310b are indicated in figure 310a.
Note the large variation in scale as the latitude changes.

FīcuRe 310b.—An oblique Mercator map based upon a cylinder tangent along the great circle through
Washington and Moscow. The map includes an area 500 miles on each side of the great circle.
The limits of this map are indicated on the Mercator map of figure 310a.

311. Rectangular projection.—A cylindrical projection similar to the Mercator but
with uniform spacing of the parallels is called a rectangular projection (fig. 311).
It is convenient for graphically depicting information where distortion is not important.
The principal navigational use of this projection is for the star chart of the Air Almanac
(art. 2204), where positions of stars are plotted by rectangular coordinates representing
declination (ordinate) and sidereal hour angle (abscissa). Since the meridians are
parallel, the parallels of latitude (including the equator and the poles) are all repre-

sented by lines of equal length.

78 CHART PROJECTIONS

Figure 311.—A rectangular graticule. Compare with figure 305.

Conic Projections

312. Features. —A conic projection is produced by transferring points from the
surface of the earth to a cone or series of cones which are then cut along an element
and spread out flat to form the chart. If the axis of the cone coincides with the axis
of the earth, the usual situation, the parallels appear as arcs of circles and the meridians
as either straight or curved lines converging toward the nearer pole. Excessive dis-
tortion is usually avoided by limiting the area covered to that part of the cone near
the surface of the earth. A parallel along which there is no distortion is called a
standard parallel. Neither the transverse conic projection, in which the axis of the
cone is in the equatorial plane, nor the oblique conic projection, in which the axis of
the cone is oblique to the plane of the equator, are ordinarily used for navigation,
their chief use being for illustrative maps.

The appearance and features of conic projections are varied by using cones tangent
at various parallels, using a secant (intersecting) cone, or by using a series of cones.

313. Simple conic projection.—A conic projection using a single tangent cone is
called a simple conic projection (fig. 313a). The height of the cone increases as
the latitude of the tangent parallel decreases. At the equator the height reaches
infinity and the cone becomes a cylinder. At the pole its height is zero and it becomes
a plane. As in the Mercator projection, the simple conic projection is not perspective,
as only the meridians are projected geometrically, each becoming an element of the
cone. When this is spread out flat to form a map, the meridians appear as straight
lines converging at the apex of the cone. The standard parallel, or that at which the
cone 1s tangent to the earth, appears as the arc of a circle with its center at the apex
of the cone, or the common point of intersection of all the meridians. The other
parallels are concentric circles, the distance along any meridian between consecutive
parallels being in correct relation to the distance on the earth, and hence derived

CHART PROJECTIONS

mathematically. The pole is
represented by a circle (fig.
313b). The scale is correct
along any meridian and along
the standard parallel. All other
parallels are too great in length,
the error increasing with in-
creased distance from the
standard parallel. Since the
scale is not the same in all direc-
tions about every point, the
projection is not conformal,
its principal disadvantage for
navigation. Neither is it an
equal-area projection.

Since the scale is correct
along the standard parallel and Figure 313a.—A simple conic projection.
varies uniformly on each side,

79

with comparatively little distortion near the standard parallel, this projection is
useful for mapping an area covering a large spread of longitude and a comparatively
narrow band of latitude. It was developed by Claudius Ptolemy in the second

century after Christ to map Just such an area, the Mediterranean.

314. Lambert conformal projection.—The useful latitude range of the simple
conic projection can be increased by using a secant cone intersecting the earth at two

F

Figure 313b.—A simple conic map of the northern hemisphere.

80 CHART PROJECTIONS

FIGURE 314.—A secant cone for a conic projection with two stand-
ard parallels.

standard parallels (fig. 314). The area between the two
standard parallels is compressed, and that beyond is ex-
panded. Such a projection is called a secant conic or
conic projection with two standard parallels.

If, in such a projection, the spacing of the parallels
is altered so that the distortion is the same along them
as along the meridians, the projection becomes conformal.
This is known as the Lambert conformal projection, after
its eighteenth century Alsatian inventor, Johann Heinrich
Lambert. Itis the most widely used conic projection for
navigation, though its use is more common among aviators
than mariners. Its appearance is very much the same as
that of the simple conic projection. If the chart is not
carried far beyond the standard parallels, and if these are
not a great distance apart, the distortion over the entire
chart is small. A straight line on this projection so nearly Fibunn ASA ole eee
approximates a great circle that the two can be considered projection.
identical for many purposes of navigation. Radio bear-
ings, from signals which are considered to travel great circles, can be plotted on this
projection without the correction needed when they are plotted on a Mercator chart.
This feature, gained without sacrificing conformality, has made this projection popular
for aeronautical charts, since aircraft make wide use of radio aids to navigation.
It has made little progress in replacing the Mercator projection for marine navigation,

except in high latitudes. In a slightly modified form this projection has been used
for polar charts (art. 321).

CHART PROJECTIONS 81

315. Polyconic projection.—The latitude limitations of the secant conic projection
can be essentially eliminated by the use of a series of cones, resulting in a polyconic
projection. In this projection each parallel is the base of a tangent cone (fig. 315a).
At the edges of the chart the area between parallels is expanded to eliminate gaps.
The scale is correct along any parallel and along the central meridian of the projection.
Along other meridians the scale increases with increased difference of longitude from
the central meridian. Parallels appear as nonconcentric circles and meridians as
curved lines converging toward the pole and concave to the central meridian.

The polyconic projection
is widely used in atlases, par- i wae
ticularly for areas of large |
range in latitude and reason-
ably large range in longitude, _.
as for a continent such as
North America (fig. 315b).
However, since it is not con-
formal, this projection is not
customarily used in naviga-
tion, except for boat sheets
used in hydrographic survey- l
ing (art. 4118). 45%N 45 N

Azimuthal Projections

316. Features.—If points
on the earth are projected
directly to a plane surface, à ,
map is formed at once, with- 30N
out cutting and flattening, or
"developing." This can be
considered a special case of a
conic projection in which the S
` cone has zero height. I5°N N * Mis N

The simplest case of the
azimuthal projection is one
in which the plane is tangent
at one of the poles. The
meridians are straight lines ` o
intersecting at the pole, and ` !20W
the parallels are concentric FiauRE 315b.—A polyconie map of North America.
circles with their common
center at the pole. Their spacing depends upon the method of transferring points
from the earth to the plane.

If the plane is tangent at some point other than a pole, straight lines through the
point of tangency are great circles, and concentric circles with their common center at
the point of tangency connect points of equal distance from that point. Distortion,
which is zero at the point of tangency, increases along any great circle through this
point. Along any circle whose center is the point of tangency, the distortion is con-
stant. The bearing of any point from the point of tangency 18 correctly represented.
It is for this reason that these projections are called azimuthal. They are also called
zenithal. Several of the common azimuthal projections are perspective.

o

0
60°W

105 W 90°W 75 W

82 CHART PROJECTIONS

317. Gnomonic pro-
jection.—If a plane is
tangent to the earth, and
points are projected geo-
metrically from the center
of the earth, the result is a
gnomonic projection (fig.
317a). This is probably
the oldest of the projec-
tions, believed to have
been developed by Thales
about 600 BC. Since
the projection is perspec-
tive, it can be demonstrat-
ed by placing a light at.
the center of a transparent
terrestrial globe and hold-
ing a flat surface tangent
to the sphere.

For the oblique case

Figure 317a.—An oblique gnomonie projection. the meridians appear as

straight lines converging

toward the nearer pole. The parallels, except the equator, appear as curves (fig.

317b). As in all azimuthal projections, bearings from the point of tangency are cor-

rectly represented. The distance scale, however, changes rapidly. The projection

is neither conformal nor equal area. Distortion is so great that shapes, as well as
distances and areas, are very poorly represented, except near the point of tangency.

The usefulness of tne projection rests upon the one feature that any great circle
appears on the map as a straight line. This is apparent when it is realized that a great
circle is the line of intersection of a sphere and a plane through the center of the sphere,
this center being the origin of the projecting rays for the map. This plane intersects
any other nonparallel plane, including the
tangent plane, in a straight line. It is
this one useful feature that gives charts
made on this projection the common name
great-circle charts.

Gnomonic charts published by the
U. S. Navy Hydrographic Office bear in-
structions for determining direction and
distance on the charts. The principal
navigational use of such charts is for
plotting the great-circle track between
points, for planning purposes. Points
along the track are then transferred, by
latitude and longitude, to the navigational
chart, usually one on the Mercator pro-
jection. The great circle is then followed
approximately by following the rhumb
line from one point to the next (art. 820).

318. Stereographic projection.—If

1 FIGURE 3176 A i ;
points on the surface of the earth are pro- tangency at latitude. San doe W E

CHART PROJECTIONS 83

jected geometrically onto a tangent plane,
from a point on the surface of the earth
opposite the point of tangency, a stereo-
graphic projection results (fig. 318a). It
is also called an azimuthal orthomorphic
projection.

The scale of the stereographic projec-
tion increases with distance from the point
of tangency, but more slowly than in the
gnomonic projection. An entire hemi-
sphere can be shown on the stereographic
projection without excessive distortion (fig.
318b). As in other azimuthal projections,
great circles through the point of tangency
appear as straight lines. All other circles,
including meridians and parallels, appear
as circles or arcs of circles.

The principal navigational use of the
stereographic projection is for charts of FIGURE 318a.—An equatorial stereographic pro-
the polar regions and devices for me- aie
chanical or graphical solution of the navigational triangle (art. 2122).

319. Orthographic projection.—If terrestrial points are projected geometrically
from infinity (projecting lines parallel) to a tangent plane, an orthographic projection
results (fig. 319a). This projection is neither conformal nor equal area and has no
advantages as a map projection. Its principal navigational use is in the field of naviga-
tional astronomy, where it is useful for illustrating or graphically solving the naviga-
tional triangle and for illustrating celestial coordinates. If the plane is tangent at a
point on the equator, the usual case, the parallels (including the equator) appear as
straight lines and the meridians as ellipses, except that the meridian through the point
of tangency appears as a Straight
line and the one 90? away as a
circle (fig. 319b).

320. Azimuthal equidistant
projection.—An azimuthal pro-
jection in which the distance
scale along any great circle
through the point of tangency
is constant is called an azimuthal
equidistant projection. If a
pole is the point of tangency,
the meridians appear as straight
radial lines and the parallels
ds concentric circles, equally
spaced. If the plane is tangent
at some point other than a pole,
the concentric circles represent
distance from the point of tan-
gency. In this case meridians
and parallels appear as curves.
The projection can be used to
portray the entire earth, the

GH

FiGURE 318b.—A stereographic map of the western hemisphere.

Bx

84 CHART PROJECTIONS 3

Figure 319a.—An equatorial orthographic projection.

point 180° from the point of tangency appearing as the largest of the concentric circles.
The projection is neither conformal nor equal area, nor is it perspective. Near the
point of tangency the distortion is small, but it increases with distance until shapes
near the opposite side of the earth are unrecognizable (fig. 320).
The projection is useful be-
Ð ee cause it combines the three fea-
Boe ff SSSSS tures of being azimuthal, having
a constant distance scale from
the point of tangency, and per-
mitting the entire earth to be
shown on one map. ‘Thus, if an
important harbor or airport is `
selected as the point of tangency,
the great-circle course, distance,
and track from that point to
any other point on the earth
are quickly and accurately de-
termined. For communication
work at a fixed point, the point
of tangency, the path of an in-
coming signal is at once appar-
ent if the direction of arrival
has been determined. The di-
rection to train a directional
FIGURE 319b.—An orthographic map of thewesternhemisphere. antenna for desired results can

CHART PROJECTIONS 85

FIGURE 320.—An azimuthal equidistant map of the world with the point of tangency at latitude
40° N, longitude 100° W.

be determined easily. The projection is also used for polar charts and for the familiar
star finder and identifier, H. O. 2102—D (art. 2210).

Polar Charts

321. Polar projections.—Special consideration is given to the selection of pro-
jections for polar charts, principally because the familiar projections become special
cases with unique features.

In the case of cylindrical projections in which the axis of the cylinder is parallel
to the polar axis of the earth, distortion becomes excessive and the scale changes rapidly.
Such projections cannot be carried to the poles. However, both the transverse and
oblique Mercator projections are used.

Conic projections with their axes parallel to the earth’s polar axis are limited in
their usefulness for polar charts because parallels of latitude extending through a full
360° of longitude appear as arcs of circles rather than full circles. This is because a

86 CHART PROJECTIONS

cone, when cut along an element and flattened, does not extend through a full 360°
without stretching or resuming its former conical shape. The usefulness of such pro-
jections is also limited by the fact that the pole appears as an arc of a circle instead
of a point. However, by using a parallel very near the pole as the higher standard
parallel, a conic projection with two standard parallels can be made which requires
little stretching to complete the circles of the parallels and eliminate that of the pole.
Such a projection, called the modified Lambert conformal or Ney’s projection, is useful
for polar charts. It is particularly acceptable to those accustomed to using the ordinary
Lambert conformal charts in lower latitudes.

Azimuthal projections are in their simplest form when tangent at a pole, since the
meridians are straight lines intersecting at the pole, and parallels are concentric circles
with their common center at the pole. Within a few degrees of latitude of the pole
they all look essentially alike, but as the distance becomes greater, the spacing of the
parallels becomes distinctive in each projection. In the polar azimuthal equidistant
it is uniform; in the polar stereographic it increases with distance from the pole until:
the equator is shown at a distance from the pole equal to twice the length of the radius
of the earth, or about 27% too much; in the polar gnomonic the increase is considerably
greater, becoming infinity at the equator; in the polar orthographic it decreases with
distance from the pole (fig. 321). All of these but the last are used for polar charts.

322. Selection of a polar projection.—The principal considerations in the choice
of a suitable projection for polar navigation are:

1. Conformality. It is desirable that angles be correctly represented so that
plotting can be done directly on the chart, without annoying corrections.

2. Great-circle representation. Since great circles are more useful than rhumb
lines in high latitudes, it is desirable that great circles be represented by straight lines.

3. Scale variation. Constant scale over an entire chart is desirable.

Gnomonic

Figure 321.—Expansion of polar azimuthal projections.

CHART PROJECTIONS 87

o
165 W 180 lese

135'W S
135? E
120°W k K S
; ; NYC 120%
0 O
5W
8 105%
o
90W e
75W Ë
75%
60°
P 60°E
el 45 E
30W 30

Figure 322.—A polar transverse Mercator map with the cylinder tangent
at the 90° E-90° W meridian.

4. Meridian representation. Straight meridians are desirable for convenience
and accuracy of plotting, and for grid navigation (art. 2510).

5. Limits of utility. Wide limits are desirable to reduce to a minimum the number
of projections needed. The ideal would be a single projection for world coverage.

The projections commonly used for polar charts are the transverse Mercator,
modified Lambert conformal, gnomonic, stereographic, and azimuthal equidistant.
Near the pole there is little to choose between them. Within the limits of practical
navigation all are essentially conformal and on all a great circle is nearly a straight line.

As the distance from the pole increases, however, the distinctive features of each
projection become a consideration. The transverse Mercator is conformal and its type
of distortion is familiar to one accustomed to using a Mercator chart. Distances can
be measured in the same manner as on any Mercator chart. T he tangent meridian
and all straight lines perpendicular to it are great circles. All other great circles,
including the meridians, are curves. The departure of a great circle from a straight
line becomes a maximum at the outer edges parallel to the tangent meridian, where
the straight lines are nearer the pole than the ares of great circles between the same
points. A slight inconvenience in measurement of angles may result from the curva-
ture of the meridians (fig. 322). The projection is excellent for a narrow band along
the tangent meridian and for use with automatic navigation equipment generating

transverse latitude and transverse longitude.

88 CHART PROJECTIONS

The modified Lambert conformal projection is virtually conformal over its entire
extent, and the amount of its scale distortion is comparatively little if itis carried only to
about 25° or 30° from the pole. Beyond this, the distortion increases rapidly. A
great circle is very nearly a straight line anywhere on the chart. Distances and direc-
tions can be measured directly on the chart in the same manner as on a Lambert
conformal chart. However, for highly accurate work this projection is not suitable, `
for it is not strictly conformal, and great circles are not exactly straight lines. |

The polar gnomonic projection is the one polar projection on which great circles |
are exactly straight lines. "The excessive distortion and lack of conformality of this
projection make it unsuitable for ordinary navigation.

The polar stereographic projection is conformal over its entire extent, and a great
circle differs but little from a straight line. The scale distortion is not excessive for a
considerable distance from the pole, but is greater than that of the modified Lambert
conformal projection.

The polar azimuthal equidistant projection is useful for showing a large area such
as a hemisphere, because there is no expansion along the meridians. However, the
projection is not conformal, and distances cannot be measured accurately in any but
a north-south direction. Great circles other than the meridians differ somewhat from
straight lines. The equator is a circle centered at the pole.

The three projections most commonly used for charts for ordinary navigation near
the poles are the transverse Mercator, modified Lambert conformal, and the polar
stereographic. The transverse Mercator permits use of automatic dead reckoning
equipment designed for use on a Mercator projection, transverse coordinates being
substituted for geographical coordinates. However, for accuracy, it requires input
of a constant transverse rhumb direction, which no present instrument provides. When
a directional gyro is used as a directional reference, as in many aircraft, the track of
the craft is approximately a great circle. A desirable chart is one on which a great
circle is represented as a straight line with a constant scale and with angles correctly
represented. These requirements are not met entirely by any single projection, but
they are approximated by both the modified Lambert conformal and the polar stereo-
graphic. The scale is more nearly constant on the former, but the projection is not
strictly conformal. The polar stereographic is conformal, and its maximum scale
variation can be reduced by using a plane which intersects the earth at some parallel inter-
mediate between the pole and the lowest parallel, so that that portion within this
standard parallel is compressed, and that portion outside is expanded.

The selection of a suitable projection for use in polar regions, as in other areas,
depends upon the requirements, which establish relative importance of the various
features. For a relatively small area, any of several projections is suitable. For a
large area, however, the choice is more critical. If grid directions (art. 2510) are to be
used, it is important that all units in related operations use charts on the same projec-
tion, with the same standard parallels, so that a single grid direction exists between any
two points. Nuclear powered submarine operations under the polar icecap have
increased the need for grid directions in marine navigation. Increasing installations

of gyro compasses with directional gyro modes in surface ships should increase the
need for grid directions further.

Plotting Sheets

323. Definition and use.—A plotting sheet is a blank or incomplete chart. It has
the latitude and longitude lines, and it may have one or more compass roses (art. 516)

for measuring direction, but little or no additional information. The meridians are

CHART PROJECTIONS 89

usually unlabeled by the publisher so the plotting sheet can be used for any longitude.
If it is suitable for use in any latitude, the parallels, also, may be unlabeled.

Plotting sheets are less expensive to produce than charts and are equally suitable
or superior for some purposes. They are used primarily for plotting lines of position
from celestial observations and for dead reckoning, particularly when land, aids to
navigation, and depth of water are not important.

Any projection can be used for constructing a plotting sheet, but that used for
the navigator’s charts is customarily employed also for his plotting sheets.
| 324. Small area plotting sheets.—A Mercator plotting sheet can be constructed
by the method explained in article 307. For a relatively small area a good approxima-
tion can be more quickly constructed by the navigator by either of two alternative
methods based upon a graphical solution of the secant of the latitude, which approxi-
mates the expansion.

First method (fig. 324a). Step one. Draw a series of equally spaced, vertical

lines at any spacing desired. These are the meridians; label them at any desired

interval, as 1’, 2’, 5’, 10’, 30’, 1°, etc.

Step two. Through the center of the sheet draw a horizontal line to represent the
parallel of the mid latitude of the area to be covered, and label it.

Step three. Through any convenient point, such as the intersection of the central
meridian and the parallel of the mid latitude, draw a line making an angle with the
horizontal equal to the mid latitude. In figure 324a this angle is 35°.

Step four. Draw in and label additional parallels. The length of the oblique
line between consecutive meridians is the perpendicular distance between consecutive
parallels, as shown by the dashed arc. The number of minutes of arc between con-
secutive parallels thus drawn is the same as that between the meridians shown.

(Step +)

(Step 2)

(Step 4)

Figure 324a.— Small area plotting sheet with selected longitude scale.

90 i CHART PROJECTIONS

Figure 324b.—Small area plotting sheet with selected latitude scale.

Step five. Graduate the oblique line into convenient units. If 1’ is selected, this
scale serves as both a latitude and mile scale. It can also be used as a longitude scale
by measuring horizontally from a meridian instead of obliquely along the line.

Second method (fig. 324b). Step one. At the center of the sheet draw a circle
with a radius equal to 1° (or any other convenient unit) of latitude at the desired scale.
If a sheet with a compass rose is available, as in figure 324b, the compass rose can be
used as the circle and will prove useful for measuring directions. It need not limit the
scale of the chart, as an additional concentric circle can be drawn and desired gradua-
tions extended to it.

Step two. Draw horizontal lines through the center of the circle and tangent at
the top and bottom. These are parallels of latitude; label them accordingly, at the
selected interval (as every 1°, 30’, ete.).

Step three. Through the center of the circle draw a line making an angle with
the horizontal equal to the mid latitude. In figure 324b this angle is 40°.

Step four. Draw in and label the meridians. The first is a vertical line through
the center of the circle. The second is a vertical line through the intersection of the
oblique line and the circle. Additional meridians are drawn the same distance apart
as the first two.

Step five. Graduate the oblique line into convenient units. If 1’ is selected, this
scale serves as a latitude and mile scale. It can also be used as a longitude scale by
measuring horizontally from a meridian instead of obliquely along the line.

. The same end result is produced by either method. The first method, starting
with the selection of the longitude scale, is particularly useful when the longitude
limits of the plotting sheet determine the scale. When the latitude coverage is more
important, the second method may be preferable. If a standard size is desired, part

CHART PROJECTIONS : 91

of the sheet can be printed in advance, forming what is called a universal plotting sheet.
This is done by the U. S. Navy Hydrographic Office (art. 431). In either method a
central compass rose might be printed. In the first method the meridians may be
shown at the desired interval and the mid parallel may be printed and graduated in
units of longitude. In using the sheet it is necessary only to label the meridians and
draw the oblique line and from it determine the interval and draw in and label addi-
tional parallels. If the central meridian is graduated, the oblique line need not be. In
the second method the parallels may be shown at the desired interval, and the central
meridian may be printed and graduated in units of latitude. In using the sheet it is
necessary only to label the parallels, draw the oblique line and from it determine the
interval and draw in and label additional meridians. If the central meridian js grad-
uated, as shown in figure 324b, the obligue line need not be.

Both methods use a constant relationship of latitude to longitude over the entire
sheet and both fail to allow for the ellipticity of the earth. For practical navigation
these are not important considerations for a small area. Ifa larger area is to be shown
or if more precise results are desired, the method of article 307 should be used.

Grids

325. Purpose and definition of grid.—No system has been devised for showing
the surface of the earth on a flat surface, without distortion. Moreover, the appearance
of any portion of the surface varies with the projection and, in many cases, with the
location of the portion with respect to the point or line of tangency. For some pur-
poses (particularly military) it is desirable to be able to identify a location or area by
rectangular coordinates, using numbers or letters, or a combination of numbers and
letters, without the necessity of indicating the units used or assigning a name (north,
south, east, or west), thus reducing the possibility of a mistake. This is accomplished
by means of a grid. In its usual form this consists of two series of lines which are
mutually perpendicular on the chart, with suitable designators. The grid used in grid
navigation (art. 2510) is a similar network, or a single series of parallel lines, used to
provide a uniform directional reference, particularly in polar regions. In any system
the difference in direction between true north at any point and grid north at that
same point is called grid declination.

326. Types of grids.—A grid may use the rectangular graticule of the Mercator
projection, or a set of arbitrary lines on a particular projection. The most widely used
system of the first is called the World Geographic Referencing System (Georef). It
is merely a method of designating latitude and longitude by a system of letters and
numbers instead of by angular measure, and therefore is not strictly a grid, except on a
Mercator projection. It is particularly useful for operations extending over a wide area.
Examples of the second type of grid are the Universal Transverse Mercator (UTM) grid,
the Universal Polar Stereographic (UPS) grid, and the Temporary Geographic Grid
(TGG). Since these systems are used primarily by military forces, they are sometimes
called military grids.

References

Chamberlin, Wellman. The Round Earth on Flat Paper. Washington, National

Geographic Society, 1947. Weg
Deetz, C. H., and Adams, O. S. Elements of Map Projection. 5th ed. U.S. Coast and
Geodetic Survey Special Publication No. 68. Washington, U.S. Govt. Print.

Off., 1945.

92 CHART PROJECTIONS

Greenhood, David. Down to Earth: Mapping for Everybody. New York, Holiday
House, 1944.

Hinks, A. R. Map Projections. 2nd ed. London, Cambridge University Press, 1921.

Jameson, A. H., and Ormsby, M. T. M. Mathematical Geography. Vol. I, Ele-
mentary Surveying and Map Projection. London, Pitman, [1942 ?].

Jervis, W. W. The World in Maps. New York, Oxford, 1937.

Mainwaring, James. An Introduction to the Study of Map Projection. London,
Macmillan, 1942.

Raisz, Erwin. General Cartography. New York, McGraw-Hill, 1938.

Steers, J. A. An Introduction to the Study of Map Projections. Rev. ed. London,
U. of London Press, 1929.

|
|
|

CHAPTER IV

CHARTS AND PUBLICATIONS

Sources

401. Introduction.—Charts and publications are important navigational aids.
It is desirable that the navigator have a knowledge of what is available in this field,
how he can obtain the various items, how he can be sure they are accurate and up-to-
date, and what information he can expect to get from each. Instructions for the use
of a number of these items are given elsewhere in this book.

402. Sources of charts and publications.—There is no central government office

| from which the navigator can satisfy all of his chart and publication requirements.
The principal sources are the U. S. Navy Hydrographic Office, U. S. Coast and Geo-

detic Survey, U. S. Coast Guard, and U. S. Naval Observatory. Other sources include
the U. S. Geological Survey, Mississippi River Commission, U. S. Engineer Office of

| the Department of the Army, U. S. Weather Bureau, USAF Aeronautical Chart and
. Information Center, Federal Aviation Agency, and various commercial sources.

403. The U. S. Navy Hydrographic Office maintains liaison with foreign hydro-
graphic departments; makes hydrographic, topographic, oceanographic, and geomag-
netic surveys in international waters and along foreign coasts; conducts research in
oceanography and in navigational methods (both marine and air); systematically col-
lects data in these fields from public and private institutions and persons in all parts
of the world; prepares, prints, and distributes nautical and aeronautical charts; and
prepares and issues publications and timely advice, including radio broadcasts, for the
safe navigation of surface and subsurface vessels and of aircraft.

The products of the U. S. Navy Hydrographic Office include nautical and aero-
nautical charts of the high seas and foreign waters, sailing directions for foreign
shores, light lists, various navigational manuals and tables, weather summaries, various
oceanographic charts and publications, pilot charts, loran and radar charts, plotting
sheets, a number of special charts, and several periodical publications to notify navigators
of changes to their charts and publications.

404. The U. S. Coast and Geodetic Survey, of the Department of Commerce,
conducts research in hydrography, cartography, tides, currents, geodesy, geomagnet-
ism, and seismology. It publishes coast and harbor charts of the United States and
its possessions and aeronautical charts of the United States, tide and tidal current
tables for both United States and foreign waters, coast pilots (sailing directions) for
coasts of the United States and its possessions (including the intracoastal waterway)
and a number of special publications covering results of its research.

405. The U. S. Coast Guard has charge of the inspection of merchant marine
vessels, licensing of merchant marine officers, and the installation and maintenance of
aids to marine navigation (lighthouses, beacons, buoys, etc.). It publishes light lists
for the waters of the United States and its possessions, and international and inland
rules of the road and pilot rules.

406. The U. S. Naval Observatory conducts research in various branches of

astronomy, including measurement and dissemination of time. It furnishes time sig-
93

94 CHARTS AND PUBLICATIONS

nals, publishes nautical and air almanacs and an ephemeris, as well as tables of sunrise,
twilight.
Ee sources. —The U. S. Geological Survey, Department of the
Interior, publishes topographic maps of the United States. ` The Mississippi River
Commission publishes charts of the Mississippi River from Cairo, Illinois, to the delta.
District offices of the U. S. Corps of Engineers, Department of the Army, publish
charts of the Ohio River and other United States rivers, Illinois Waterway system, the
Great Lakes (but not Canadian harbor charts nor charts of Georgian Bay), Lake
Champlain, Oneida Lake, New York canals, and the St. Lawrence River above St.
Regis and Cornwall. The U.S. Weather Bureau, Department of Commerce, publishes
a chart and booklet showing principal types of clouds, instructions for marine mete-
orological observers, a glossary of weather terms, and other meteorological publications.
The USAF Aeronautical Chart and Information Center produces aeronautical charts
and publications. The Federal Aviation Agency produces a number of publications of
interest chiefly to aviators. Various other publications and their sources are listed in
appendix N. i

408. Obtaining charts and publications.—In most instances charts and publica-
tions are distributed directly by the publishing agency. A notable exception is the
U. S. Navy Hydrographic Office, which, except for official distribution, distributes
its charts and publications through authorized sales agents throughout the world.
These agents are listed in (H.O.) Pub. No. 1-N, Part I. Publications of the U.S. Coast
Guard, U.S. Naval Observatory, and the U.S. Weather Bureau are sold by the Super-
intendent of Documents, U.S. Government Printing Office. Some of the publications
of other agencies are sold both by this office and the publisher (or its agents).

The U. S. Navy Hydrographic Office, U. S. Coast and Geodetic Survey, and the
Superintendent of Documents have sales agents in various United States and foreign
ports. In addition, the U.S. Navy Hydrographic Office maintains a number of branch
offices at major ports to collect, compile, and distribute timely information to afford
the maximum safety and facility of operation to vessels of the N avy and the merchant
marine. These branch offices issue pilot charts, the Daily Memorandum, and Notice to
Mariners. The U. S. Coast and Geodetic Survey maintains district offices at which
their charts and publications can be purchased.

Appendix N lists sources of charts and publications of interest to the navigator.

409. Numbering of charts.—Each chart is given a number by its publishing agency.
Vessels of the U. S. Navy use charts of various publishers, with some duplication of
numbers. To avoid confusion, charts issued to these vessels are given a consecutive
number and arranged in convenient groups in chart portfolios. This system is not
available to commercial or private users.

410. Terminology.—The following terminology applies generally to charts and
publications of government agencies:

A new chart or publication is the first edition.

A new edition is a revision that supersedes previous issues, containing changes of

such importance that earlier issues are obsolete.

A corrected (new) print is a revision that does not supersede previous issues,

containing minor changes and corrections, principally those published in the Notice
to Mariners since the preceding edition.

À reprint is a reproduction without change.

A supplement contains corrections and additions to an existing publication.

A change consists of corrections and additions to a loose-leaf publication.

A summary is a collection in one publication of related items of a specified class.

CHARTS AND PUBLICATIONS 95

Oceanographic and Meteorological Charts and Publications

411. Tide tables are published annually by the U. S. Coast and Geodetic Survey.
In them are tabulated the predicted times and heights of high and low waters for
every day in the year for a number of reference stations, and differences for obtaining
similar predictions for numerous other places. They also give other useful information
such as a method for obtaining the height of the tide at any time, local mean time of
sunrise and sunset for various latitudes, reduction of local mean time to standard time,
zone time of moonrise and moonset for certain ports, and other astronomical data.
The use of these tables is explained in chapter IX.

Tide tables are available in separate volumes for (1) east coast of North and South
America, including Greenland, (2) west coast of North and South America, including the
Hawaiian Islands, (3) Europe and west coast of Africa, including the Mediterranean
Sea, and (4) central and western Pacific Ocean and Indian Ocean.

412. Tidal current tables, published annually by the U. S. Coast and Geodetic
Survey, tabulate daily predictions of the times of slack water and the times and speeds of
maximum flood and ebb currents for a number of waterways, together with differences
for obtaining predictions at numerous other places. They also include other useful
information on tidal currents, such as a method for obtaining the speed of current at any
time and one for determining the duration of slack water, coastal tidal currents, the
combination of currents, and current diagrams. Information on the Gulf Stream is
included in the tidal current tables for the Atlantic coast of North America. The use
of these tables is explained in chapter IX.

Tidal current tables are available in separate volumes for (1) Atlantic coast of
North America, and (2) Pacific coast of North America and Asia. For places not
covered by these tables the navigator must rely upon notes, tables, and arrows on charts,
special current charts, sailing directions, and any other available sources.

413. Tidal current charts for various United States harbors are published by
the U.S. Coast and Geodetic Survey. Each of the nine sets consists of about 12 charts
which depict the direction and speed of the tidal current for each hour of the tidal cycle,
thus presenting a comprehensive view of the tidal current movement in the respective
waterways as a whole, and supplying a means for readily determining for any time the
direction and speed of the current at various localities throughout the areas covered.
The charts are intended for use in connection with the tidal current tables for the same
areas, except for New York Harbor, where the tide tables are to be used.

414. Pilot charts are published by the U.S. Navy Hydrographic Office for each
month for (1) the North Atlantic Ocean, and (2) the North Pacific Ocean. Pilot
charts are published in atlas form for (1) the Northern North Atlantic Ocean, (2) the
South Atlantic Ocean and Central American Waters, and (3) the South Pacific and
Indian Oceans.

These charts present in graphical form the available facts or conclusions obtained
from many years of research in navigation, oceanography, and meteorology, to assist
the mariner in selecting the safest and quickest routes and avoiding dangers. Their
principal features are monthly averages for: prevailing winds and currents; percentage
of gales, calms, and fog; lines of equal air and water temperature, and atmospheric
pressure; and limits of the drift of both field ice and icebergs. Also presented are
lines of equal magnetic variation, location of ocean station vessels, and recommended
routes or steamer tracks. Timely articles are printed on the backs of many pilot charts.

Pilot charts of the North Atlantic and North Pacific are furnished without charge

to cooperating observers.

96 CHARTS AND PUBLICATIONS

415. Miscellaneous oceanographic publications.—The U. S. Navy Hydrographic
Office promotes basic oceanographic research and collects and codifies data which it
makes available in the form of charts, manuals, and special reports. Charts in this
category include those showing bottom sediment, surface temperature, currents, sea
and swell, bathymetric charts (showing bottom gradient tints), as well as the pilot
charts (art. 414). Representative books are Breakers and Surf, Principles in Fore-
casting (H.O. Pub. No. 234); Oceanographic Atlas of the Polar Seas (Pub. No. 705),
Part I, Antarctica and Part II, Arctic; Wind, Sea, and. Swell: Theory of Relations Jor
Forecasting (H.O. Pub. No. 601). This Office also publishes several instruction
manuals of use to the navigator. These include Manual of Ice Seamanship (Pub. No.
551), Sonic Soundings (H.O. Pub. No. 606-b), Bathythermograph Observations (H.O.
Pub. No. 606-c), Ice Observations (H.O. Pub. No. 606-d), and Sea and Swell Observa-
tions (H.O. Pub. No. 606-e). The U.S. Navy Hydrographic Office Catalog of Nautical |
Charts and Publications (Pub. No. 1-N series) lists the various oceanographie charts
and publications available.

The U.S. Coast and Geodetic Survey conducts research in tides and currents and
makes available several publications relating to them.

Electronic Navigation Charts and Publications

416. Loran.— Tables for plotting loran lines of position are published by the U.S.
Navy Hydrographic Office as H.O. Pub. No. 221, in a number of volumes. Loran lines
of position are printed on certain nautical and aeronautical charts by the U.S. Navy
Hydrographic Office and the Coast and Geodetic Survey. Information on loran charts
and publications is contained in H.O. Pub. 1-N, Catalog of Nautical Charts and Publi-
cations, the Catalog of U.S. Navy Aeronautical Charts and Related Publications, the Coast
and Geodetic Survey catalog of Aeronautical Charts and Related Publications, and the DOD
Catalog of Aeronautical Charts and Flight Information Publications which is available
only to military users. H.O. Pub. No. 1—V, Catalog of Aeronautical Charts and Publi-
cations, has been canceled.

417. Radar.—The U.S. Coast and Geodetic Survey has published several experi-
mental nautical charts showing a great number of land contours and gradient tints,
for use with radar.

418. Miscellaneous.—The U.S. Navy Hydrographic Office publications entitled
Radio Navigational Aids (H.O. Pubs. Nos. 117-A, Atlantic and Mediterranean Area
and 117-B, Pacific and Indian Oceans Area) contain detailed information on radio-
beacons and other aids to navigation. The light lists includes some details of radio-
beacons. Volume II of International Code of Signals (H.O. Pub. No. 104) deals with
radio communication. Various other publications relating to radio navigation are
listed in appendix N.

419. Information by radio.—H.O. Pubs. Nos. 117-A and 117-B, Radio Naviga-
tional Aids, contain complete lists of the radio stations that perform services of value
to the mariner, and give general and detailed information concerning these services,
and present the regulations of various nations on this subject.

In addition to its information on radiobeacons and radio direction finder stations,
H.O. Pub. No. 117 gives full information on time signals, navigational warnings,
distress signals, medical advice, quarantine report stations, long-range navigational
aids, wartime emergency procedures for U. S. merchant vessels, and plain language
weather reports and storm and hurricane warnings. For information concerning radio
traffic stations, the mariner should consult the lists published by the Bureau of the
International Telecommunication Union, Berne, Switzerland.

CHARTS AND PUBLICATIONS 97

. H.O. Pubs. Nos. 118-A and 118-B, Radio Weather Aids, contain general informa-
tion, marine broadcasts, synoptic broadcasts, facsimile broadcasts, weather codes and
code forms, and miscellaneous conversion tables.
' H.O. Pub. No. 119, Weather Station Index, contains a complete list of international
index numbers with locations of stations, key groups, and call signs, and includes a
supplemental listing of U.S. meteorological reporting stations.

Corrections to these volumes are published in Notice to Mariners. The publica-
tions themselves are corrected by “Changes” which are issued quarterly for H.O. Pubs.
Nos. 117-A, 117-B, 118-A, and 118-B.

Navigational Publications

420. Sailing Directions or pilots are books containing descriptions of coast lines,
harbors, dangers, aids to navigation, winds, currents, and tides; instructions for navi-
gating narrow waterways and for approaching and entering harbors; information on
port facilities, signal systems, and pilotage services; and other data that cannot be
conveniently shown on charts. Those covering the coasts of the United States and
its possessions, including the Intracoastal Waterway, are called coast pilots, and are
published by the U. S. Coast and Geodetic Survey. "Those covering foreign coasts,
called sailing directions, are published in looseleaf form by the U. S. Navy Hydrographic
Office.

Supplements to coast pilots are published annually, and change pages to sailing
directions are published periodically. The more important changes are published in
Notice to Mariners.

421. Light lists for the United States and its possessions, including the Intracoastal
Waterway, the Great Lakes (both United States and Canadian shores), and the Mis-
sissippi River and its navigable tributaries, are published annually by the U. S. Coast
Guard. Similar publications covering foreign coasts are published in looseleaf form
by the U.S. Navy Hydrographic Office in seven volumes (H.O. Pubs. Nos. 111-A,
111-B and 112 through 116). “Changes” are published at appropriate intervals.
Light lists give detailed information regarding navigational lights, light structures,
radiobeacons, and fog signals. Corrections to both sets of light lists are published
weekly in the Notice to Mariners. Coast Guard light lists also give unlighted buoys.

422. Navigational tables.—Many types of navigational tables are published.
While many of these appear as parts of other books, such as those at the back of this
volume, a number of separate books of tables are available. Nearly all of these are
published by the U. S. Navy Hydrographic Office. The ones of principal interest to
the navigator are:

H.O. Pub. No. 260, Azimuth Tables, lists the azimuth angle of the sun at intervals
of 10% between sunrise and sunset for each degree of latitude between the equator and
70° (north or south). It is also applicable to other bodies having declinations of 0° to
23°. Azimuth angles are tabulated to a precision of 1”. These are popularly known
as the “Red Azimuth Tables” to distinguish them from H.O. Pub. No. 261. The use
of these tables is explained in article 2126.

H.O. Pub. No. 151, Table of Distances between Ports, tabulates about 40,000

distances between various ports throughout the world.

98 CHARTS AND PUBLICATIONS

Distances between United States Ports, published by the U. S. Coast and Geodetic
Survey, tabulates approximately 10,000 distances along the shortest routes marked by
aids to navigation between various United States ports. It also includes conversion
tables similar to table 20 and parts of table 21 of this volume.

H.O. Pub. No. 261, Azimuths of Celestial Bodies, is similar to H.O. Pub. No. 260,
but for declinations of 24° to 70%. These are popularly known as the “Blue Azimuth
Tables.” Their use is explained in article 2126.

H.O. Pub. No. 208, Navigation Tables for Mariners and Aviators, is a set of trigo-
nometric tables arranged in convenient form for solving the navigational triangle by the
formulas of Dreisonstok (art. 2110).

H.O. Pub. No. 211, Dead Reckoning Altitude and Azimuth Table, is a trigo-
nometric table arranged in convenient form for solving the navigational triangle by the
formulas of Ageton (art. 2111).

H.O. Pub. No. 214, Tables of Computed Altitude and Azimuth, tabulates the solution
of the navigational triangle for each 1° of latitude from the equator to 89° (north or
south), each 1° of meridian angle where the altitude is 5% or more, and each 0°5 of
declination from 0° to 29° with selected values above 29°. Altitude is given to the
nearest 0/1 and azimuth angle to the nearest 0°1. There are nine volumes, each cover-
ing 10° of latitude, with separate tabulations for same and contrary names of declina-
tion and latitude. These are the basic tables for marine celestial navigation, and are
explained fully in chapter XX.

H.O. Pub. No. 218, Astronomical Navigation Tables, is somewhat similar to
H.O. Pub. No. 214, but designed primarily for aviators. Altitudes are tabulated to the
nearest 1’ and azimuth angles to the nearest 1°. Altitudes are corrected for refraction
at a height of eye of 5,000 feet. In addition to the tabulation for same and contrary
names of declination and latitude there is a section giving altitude and azimuth of 22
selected stars, the name of the star being given as one of the entering arguments to
eliminate interpolation for declination. There are 14 volumes, each covering 5° of
latitude, the total coverage extending from the equator to latitude 69° (north or south).
These tables have been largely superseded by H.O. Pub. No. 249.

H.O. Pub. No. 221, Loran Tables, is discussed in article 416.

H.O. Pub. No. 249, Sight Reduction Tables, is intended primarily for air navigation.
Volume I tabulates the altitude to the nearest 1’, and azimuth (not azimuth angle) to
the nearest 1°, for seven selected stars. Entries are given for each 1° (2° beyond latitude
69°) of local hour angle of the vernal equinox for each 1° of latitude from 89° N to
89? S, in a single volume.

Volumes II and III tabulate the altitude to the nearest 1” and azimuth angle to
the nearest 1°, for each 1? of meridian angle (2° beyond 69°) and 1° of declination, from
0° to 29° (with separate tabulations for same and contrary name), for each 1? of latitude
from 89° N to 8925. Volume II covers latitudes 0? to 39%, and volume III covers
latitudes 40° to 89?. Altitudes extend to negative values to provide for observation
of bodies near the horizon from aircraft in flight.

423. Almanacs.—The positions of celestial bodies on the celestial sphere ; times
of Sunrise, sunset, moonrise, moonset, and beginning and ending of twilight; sextant
altitude corrections; and other astronomical information of particular interest to
navigators are published by the U. S. Naval Observatory in books called “almanacs.”
E ME NU CRI Lika 7 tabulates the basic information to the,
lates Sól, the Eod dert Puit w M Se ki sen ae Sgt AS
E Gant End A Y : ) e e 1e nearest I' at time intervals of ten minutes.

a can Ephemeris and Nautical Almanac and The Astronomical
Ephemeris have also been unified. Published annually, they tabulate a great amount

CHARTS AND PUBLICATIONS 99

of astronomical information of interest primarily to astronomers. The information is
generally tabulated to a precision much greater than needed by either marine or air
navigators. All of these publications are published jointly by the United States and
Great Britain.

424. Manuals.—Reference or instruction books are published by many sources,
both governmental and commercial. Some of these are general, such as the present
volume, and others are limited to particular aspects of the subject, such as H.O. Pub.
No. 257, Radar Plotting Manual, H.O. Pub. No. 217, Maneuvering Board Manual, and
H.O. Pub. No. 226, Handbook of Magnetic Compass Adjustment and Compensation.
There are a great number and variety of such books. In general, they can be obtained
from stores handling nautical publications, government agencies having cognizance
over the subjects of the manuals, or instrument makers (in the case of manuals describ-
ing specific instruments). The U.S. Government Printimg Office publishes lists of
publications on a number of subjects and most other government agencies and commer-
cial publishing companies have similar lists for distribution.

Periodical Publications and Broadcasts

425. Notice to Mariners, published weekly by the U.S. Navy Hydrographic Office,
lists changes in aids to navigation throughout the world, newly reported dangers such
as wrecks, important new soundings, and official regulations affecting navigation. It
is the official publication for the correction of charts, sailing directions, light lists, ete.
It also carries announcements of new charts, new editions of charts, and new publica-
tions. Two editions are published, one for the Atlantic and Mediterranean, and one
for the Pacific and Indian Oceans. Notice to Mariners is distributed without charge to
qualified users. It can be consulted at offices of sales agents for products of the U. S.
Navy Hydrographic Office, U. S. Coast and Geodetic Survey, and U.S. Coast Guard;
Branch Hydrographic Offices; District Offices of the Coast Guard; United States
consulates abroad; and Centralization Offices in various ports of the world.

426. Daily Memorandum, published each working day by the U.S. Navy Hydro-
graphic Office, gives a synopsis of late information relating to aids to navigation and
dangers to vessels, including reports of ice, derelicts, etc. The urgent items are also
broadcast by radio (art. 427). It also contains advance information of the more
important material that will appear in the Notice to Mariners. This publication is
distributed locally by the Branch Hydrographic Offices. An East Coast edition is
published at Washington, a West Coast edition by the Branch Hydrographic Office in
San Francisco, a Pacific edition by the Branch Hydrographic Office in Honolulu, a
Far East edition by the Branch Hydrographic Office in Yokosuka, and a Canal Zone
edition by the Branch Hydrographic Office in Cristobal, C. Z.

427. Radio broadcasts.—Nearly all maritime nations broadcast radio navigational
warnings. In general, such broadcasts contain information of importance to the
safety of vessels at sea, such as the position of ice and derelicts, inadequacy and changes
in aids to navigation, mine fields, etc. Most of the information is furnished by cooperat-
ing observers at sea. à;

As a general rule, each nation broadcasts only those navigational warnings affecting
its own coasts. In the United States the broadcasts are made by Navy and Coast
Guard radio stations. The information is compiled by the U. S. Navy Hydrographic
Office and the U. S. Coast Guard. Frequently, broadcasts include warnings from
both agencies. The major items affecting the Atlantic and Gulf coasts and, occasion-
ally, important Pacific and foreign notices are broadcast daily by station NSS, Wash-
ington. The major Pacific items are broadcast daily by station NPG, San Francisco.
Usually the information contained in these general broadcasts is adequate for offshore

100 CHARTS AND PUBLICATIONS

navigation, but before nearing the coast, vessels should obtain the information available
in local broadcasts from the area to be entered. In general, the information contained
in a local broadcast affects only the area in which the broadcasting station is located
and, occasionally, adjacent areas. &

Urgent messages, such as those concerning tsunamis (art. 3310), hurricanes, etc.,
are broadcast immediately upon receipt and at frequent intervals thereafter as long as
they are applicable. In some countries provision is made whereby navigational
warnings can be obtained upon request. In the majority of cases this information is a
repetition of scheduled broadcasts.

Urgent messages pertaining to the Atlantic area are called hydrolants and those
pertaining to the Pacific hydropacs. These terms refer to messages broadcast by the
United States. Urgent messages pertaining to the Eastern Atlantic and Mediterranean
and broadcast by the British Admiralty are called naveams.

In addition to navigational warnings, radio services include time signals, weather
and ice reports and predictions, distress information, and medical advice. Full in-
formation on navigational radio broadcasts, including the times, stations, frequencies,
and instructions for utilizing this service, is given in H.O. Pubs. Nos. 117-A and
117-B, Radio Navigational Aids, and H.O. Pubs. Nos. 118-A and 118-B, Radio
Weather Aids.

Miscellaneous Charts and Publications

428. Isomagnetic charts.— The U. S. Navy Hydrographic Office publishes a series
of charts of magnetic information. There are five groups, each consisting of one chart
for each polar region and one for the remainder of the world, plus grid variation charts
for each polar region. There is one group each showing lines of equal dip (inclination),
horizontal intensity, vertical intensity, total intensity, and variation of the compass
(magnetic declination). In addition to these charts, the Hydrographic Office publishes
a 12-sheet series of charts showing world coverage of magnetic variation of the compass.
The U. S. Coast and Geodetic Survey publishes charts showing lines of equal variation
for the United States and Alaska, and other isomagnetic charts.

Variation is also shown on the navigator's regular nautical charts.

429. Great-circle charts. —The U. S. Navy Hydrographic Office publishes a num-
ber of charts on the gnomonic projection with the points of tangency selected so as to
make the charts suitable for planning ocean voyages. These charts are customarily
used in connection with regular nautical charts, the desired great circle being plotted as a
straight line on the gnomonic chart and various points along the line being transferred
by means of its geographical coordinates (latitude and longitude) to the nautical chart
to mark the ends of a series of rhumb lines. Points along any desired great circle
can also be established by computation (art. 822).

430. Aeronautical charts, although designed primarily for air navigation, are
sometimes useful to the marine navigator as well. They often show more details of
adjacent land than do nautical charts, and they show aeronautical beacons (lighted
and radio) which can be of value to the marine navigator who understands their use.
Such charts are published principally by the Aeronautical Chart and Information
Center of the U. S. Air Force, the U. S. Coast and Geodetic Survey, and the U. S.

Navy Hydrographic Office. "These agencies publish catalogs listing their aeronautical
charts and publications.

CHARTS AND PUBLICATIONS 101

Tie eee charts and plotting sheets are published by the U. S. Navy Hydro-

Plotting charts show the land area in outline. Soundings, aids to navigation
and other information customarily shown on nautical charts are not given The
charts are used principally for planning. |

Plotting sheets are blank charts showing only the graticule of latitude and longi-
tude lines, at a specified range of latitude, and compass roses. The meridians are not
labeled, permitting the plotting sheet to be used at any longitude. A universal plotting
sheet (art. 324) shows only the parallels of latitude, a central compass rose, and a
single mid meridian. The user draws in the meridians at the correct interval dap
upon the latitude. In addition to the universal plotting sheet, there are four series of
ordinary plotting sheets, each series of a different size. Details are given in Pub. No.
1-N, Introduction Part I (Catalog of Nautical Charts and Publications). Plotting sheets
are used primarily for plotting celestial fixes and dead reckoning at sea. The navigator
customarily uses a chart when near land.

432. Miscellaneous charts.—Both the U. S. Navy Hydrographic Office and the
U. S. Coast and Geodetic Survey publish a number of special charts listed in their
catalogs. Some of the H.O. charts are listed in Pub. No. 1-N. Among these are
track charts, an air route chart of the world, an airline distance map of the United

"States, a time zone chart of the world, outline charts and maps, azimuthal equidistant

charts centered on certain strategic cities, star charts, special charts for the fishing
industry, and others.

433. Miscellaneous publications.—There are numerous other publications of
greater or less interest to navigators. Among these are:

Chart No. 1, Nautical Chart Symbols and Abbreviations. A pamphlet showing
the standard symbols in color and the various abbreviations which have been approved
for use on nautical charts published by the United States of America. Much of this
information is reproduced in appendix K.

H.O. Pub. No. 103, International Code of Signals, Vol. I (visual).

H.O. Pub. No. 110, DAPAC (Danger Areas in the Pacific).

Nemedri. A publication giving routing instructions for areas in northern European,
Mediterranean, and Black Sea waters declared dangerous because of mines. This
publication is distributed by the British Admiralty for the International Routing and
Reporting Authority. A United States reprint is distributed without cost by the UES.
Navy Hydrographic Office.

H.O. Pub. No. 150, World Port Indez.

H.O. Pub. No. 216, Air Navigation.

H.O. Pub. No. 220, Navigation Dictionary.

Weather maps and reports, available from the U. S. Weather Bureau.

H.O. Pub. No. 606-a, Navigational Observations. An instruction manual for the
various observations on which the U. S. Navy Hydrographic Office desires reports.

H.O. Pub. No. 609, A Functional Glossary of Ice Terminology.

H.O. 2102-D, Star Finder and Identifier.

H.O. Misc. 10578, Eskimo Place Names and Aids to Conversation, compiled by
Commander Donald B. MacMillan, USNR.

102 CHARTS AND PUBLICATIONS

Rules of the Road—International— Inland. A pamphlet giving the international
and inland rules of the road in parallel columns, followed by pilot rules for certain inland
waters, published by the U.S. Coast Guard. Additional pamphlets or individual
sheets published by the same agency give the specific rules applying to U.S. waterways.
An example is the booklet entitled Rules of the Road—Western Rivers.

Aids to Marine Navigation of the United States, published by the U.S. Coast Guard.

CHAPTER V

THE NAUTICAL CHART

General Information

501. Introduction.—A nautical chart is a conventional graphic representation, on
a plane surface, of a navigable portion of the surface of the earth. It shows the depth
of water by numerous soundings, and sometimes by depth curves, the shore line of
adjacent land, topographic features that may serve as landmarks, aids to navigation,
dangers, and other information of interest to navigators. It is designed as a work
sheet on which courses may be plotted, and positions ascertained. It assists the
navigator in avoiding dangers and arriving safely at his destination. The nautical
chart is one of the most essential and reliable aids available to the navigator.

502. Projections.—Nearly all nautical charts used for ordinary purposes of navi-
gation are constructed on the Mercator projection (art. 305). Large-scale harbor charts
on standard scales (1:12,500, 1:25,000, 1:50,000) are often constructed on the trans-
verse Mercator projection. Charts for special purposes, such as great-circle sailing or
polar navigation, often are on some other projection. Many aeronautical charts are
constructed on the Lambert conformal projection (art. 314). The principal projections,
with their navigational uses, are discussed in chapter ITI.

503. Scale.—The scale of a chart is the ratio of a given distance on the chart to
the actual distance which it represents on the earth. It may be expressed in various
ways. The most common are:

Natural scale, expressed as a simple ratio or fraction. For example, 1:80,000 or
E means that one unit (such as an inch) on the chart represents 80,000 of the
same unit on the surface of the earth.

Numerical scale, or a statement of that distance on the earth shown in one unit
(usually an inch) on the chart, or vice versa. For example, “30 miles to the inch"
means that one inch on the chart represents 30 miles of the earth'ssurface. Similarly,
*9 inches to à mile" indicates that 2 inches on the chart represent 1 mile on the earth.

Graphic scale. A line or bar may be drawn at a convenient place on the chart
and subdivided into nautical miles, yards, etc. All charts vary somewhat in scale
from point to point, and in some projections the scale is not the same in all directions
about a single point. A single subdivided line or bar for use over an entire chart is
shown only when the chart is of such scale and projection that the scale varies a neg-
ligible amount over the chart, usually one of about 1:50,000 or larger. Since one
minute of latitude is very nearly equal to one nautical mile, the latitude scale serves as
an approximate graphical scale. On most nautical charts the east and west borders
are subdivided to indicate the latitude scale.

On a Mercator chart the scale varies with the latitude. This is noticeable on a
chart covering a relatively large distance in a north-south direction. On such a chart
the scale at the latitude in question should be used for measuring distances.

Of the various methods of indicating scale, the graphical method is normally
available in some form on the chart. In addition, the natural scale is customarily

stated on charts on which the scale does not change appreciably over the chart.
103

104 THE NAUTICAL CHART

The natural and numerical scales of a chart are readily interchangeable. For in-
stance, in a nautical mile there are about 6,076.11549 feet or 6,076.11549 X 12=72,913.39
inches. If the natural scale of a chart is 1:80,000, one inch of the chart represents
80,000 inches of the earth, or a little more than a mile. To find the exact amount,
divide the scale by the number of inches in a mile, or 7913.39 1 097- Thus, a
natural scale of 1:80,000 is the same as a numerical scale of 1.097 (or approximately
72,913.39

80,000
0.9) inch to a mile. Similarly, if the numerical scale is 60 nautical miles to an inch,
the natural scale is 1:(60 72,913.39) —1:4,374,803.

It should be clearly understood that scale, as discussed above, refers to distances,
not areas. If the area scale is desired, it is found by squaring the natural scale. Thus,
if the natural scale of a chart is 1:50,000, the corresponding area scale is 1:(50,000 X
50,000)=1 :2,500,000,000 or one square inch on the chart represents 2,500,000,000 square
inches on the earth, or a square 50,000 inches on a side.

A chart covering a relatively large area is called a small-scale chart and one covering
a relatively small area is called a large-scale chart. Since the terms are relative, there
is no sharp division between the two. Thus, a chart of scale 1:100,000 is large scale
when compared with a chart of 1:1,000,000 but small scale when compared with one
of 1:25,000.

504. Chart classification by scale.—Charts are constructed on many different
scales, ranging from about 1:2,500 to 1:14,000,000 (and even smaller for some world
charts). Small-scale charts covering large areas are used for planning and for offshore
navigation. Charts of larger scale, covering smaller areas, should be used as the vessel
approaches pilot waters. Several methods of classifying charts according to scale
are in use in various nations. The following classifications of nautical charts are
those used by the U. S. Navy Hydrographic Office and the U. S. Coast and Geodetic
Survey:

Sailing charts are the smallest scale charts used for planning, fixing position at
sea, and for plotting the dead reckoning while proceeding on a long voyage. The scale
is generally 1:600,000 or smaller. The shore line and topography are generalized and
only offshore soundings, the principal navigational lights, outer buoys, and landmarks
visible at considerable distances are shown.

General charts are intended for coastwise navigation outside of outlying reefs and
shoals. The scales range from about 1:100,000 to 1:600,000.

Coast charts are intended for inshore coastwise navigation where the course may
lie inside outlying reefs and shoals, for entering or leaving bays and harbors of consid-
erable width, and for navigating large inland waterways. The scales range from about
1:50,000 to 1:100,000.

Harbor charts are intended for navigation and anchorage in harbors and small
waterways. The scale is generally larger than 1:50,000.

In addition, there are special series of charts, such as the 1:40,000 U. S. Coast
and Geodetic Survey charts of the Intracoastal Waterway (inside route) and various
series of river and canal charts.

505. Accuracy.—The accuracy of a chart depends upon:

ws Thoroughness and up-to-dateness of the survey and other navigational informa-
tion. Some estimate of the accuracy of the survey can be formed by an examination
of the source notes given in the title of the chart. If the chart is based upon very old
surveys, 1t should be used with caution. Many of the earlier surveys were made under

1.1) miles to an inch. Stated another way, there are — 0.911 (approximately

THE NAUTICAL CHART

105

conditions that were not conducive to great accuracy. It is safest to question every
"chart based upon surveys of doubtful accuracy.

The number of soundings and their spacing is some indication of the completeness
of the survey. Only a small fraction of the soundings taken in a thorough survey are

shown on the chart, but sparse or un-
evenly distributed soundings indicate that
the survey was probably not made in
detail. Large or irregular blank areas, or
absence of depth curves, generally indicate
lack of soundings in the area. If the water
surrounding such a blank area is deep,
there is generally considerable depth in the
blank; conversely, shallow water surround-
ing such an area indicates the strong pos-
sibility of shoal water. If neighboring
areas abound in rocks or are particularly
uneven, the blank area should be regarded
with additional suspicion. However, it
should be kept in mind that relatively
few soundings are shown when there is a
large number of depth curves or where the

14 14
TEN
Weis dë

l 14 Mig
4 146 EK te

ll
Nu de 1414

IIA
14 35 gy! 13 y Oy

14,14 Bs

3
We ja eu

3 e 133
3: 02^ ptr 23 4 SON ]
Se ARE, y een e

ASTE
PAZ S

FIGURE 505a.—Part of a boat sheet, showing the
soundings obtained in a survey.

bottom is flat or gently and evenly sloping. Additional soundings are shown
when they are helpful in indicating the uneven character of a rough bottom (figs. 505a

and 505b).

Even a detailed survey may fail to locate every rock or pinnacle, and in waters
where their existence is suspected, the best methods for determining their presence are

a «4 i

A
ER ol Æ 5, Eh
14 27% PA Lët, ste =p
a Vae 3 afp ^ PROS
14 í H CA
/

FıcurE 505b.—Part of a nautical chart made

from the boat sheet of figure 505a. Compare
the number of soundings in the two figures.

wire drag surveys or use of electronic un-
derwater obstacle detection gear. Areas
that have been dragged may be indicated
on the chart and a note added to show
the effective depth at which the drag was
operated.

Changes in the contour of the bottom
are relatively rapid in areas where there
are strong currents or heavy surf, partic-
ularly when the bottom is composed prin-
cipally of soft mud orsand. The entrances
to bar harbors are especially to be regarded
with suspicion. Similarly, there is some-
times a strong tendency for dredged chan-
nels to shoal, especially if they are sur-
rounded by sand or mud, and cross cur-
rents exist. Notes are sometimes shown
on the chart when the bottom contours

are known to change rapidly. However, the absence of such a note should not be
regarded as evidence that rapid change does not occur. |
Changes in aids to navigation, structures, etc., are more easily determined, and
charts are generally corrected in this regard to the date of distribution. However,
there is always the possibility of a change having occurred since the chart was mailed
or received. The date to which the chart was corrected is stamped on it

106 THE NAUTICAL CHART

before distribution. All issues of Notice to Mariners printed after that date should be
checked to ensure accuracy in this respect.

2. Suitability of the scale for the design and intended navigational use. The same
detail cannot be shown on a small-scale chart as on one of a larger scale. For this
reason it is good practice to use the largest scale chart available when in the vicinity of
shoals or other dangers.

3. Presentation and adequacy of data. The amount and kind of detail to be shown,
and the method of presentation, are continually under study by charting agencies.
Development of a new navigational aid may render many previous charts inadequate.
An example is radar. Many of the charts produced before radar became available lack
the detail needed for confident identification of targets.

Part of the responsibility for the continuing accuracy of charts lies with the user.
If charts are to remain reliable, they must be corrected as indicated by the Notice to
Mariners. In addition, the user's reports of errors and changes and his suggestions
often are useful to the publishing agencies in correcting and improving their charts.
Navigators and maritime activities have contributed much to the reliability and use-
fulness of the modern nautical chart. If a chart becomes wet, the expansion and
subsequent shrinkage when the chart dries are likely to cause distortion.

506. Dates on charts.—The system of dates now used on charts published by the
U.S. Coast and Geodetic Survey and the U. S. Navy Hydrographic Office is as follows:

First edition. The original date of issue of a new chart is shown at the lower left-
hand corner and at the top center margin, thus:

1st Ed., Sept. 1901

New edition. A new edition is made when, at the time of printing, the corrections
are too numerous or too extensive to be reported in Notice to Mariners, making previous
printings obsolete. The date of the first edition is retained at the top margin. At the
lower left-hand corner it is replaced by the number and date of the new edition, thus:

5th Ed., July 11, 1955

Corrected (New) print. A corrected print contains corrections which have been
published in the Notice to Mariners, and other information which is not of sufficient
importance to justify a new edition. The date of a corrected print is the date on which
the last check is made to see that all important corrections have been applied.
Normally, this date is the Monday following the date of the last Notice to Mariners
used. It is added at the lower left-hand corner of the chart, thus:

5th Ed., July 11, 1955; Revised 2/4/57
For any subsequent corrected prints the date is replaced by the later one, thus:

5th Ed., July 11, 1955; Revised 2/17/58

Hydrographic Office chart terminology is discussed in article 4406.
Hand-correction date. Stocks of charts kept on hand by the publishing agencies or

their distribution centers are hand corrected for changes shown in Notice to Mariners
published prior to the date of distribution. The date of the latest issue for which hand
corrections have been made is stamped in the margin. This is the most important date
shown on the chart. Important changes after the date of the latest hand-corrected
change are published in the weekly Notice to Mariners and should be applied immedi-
ately by the user. |

Chart Reading

507. Chart symbols.—Much of the information contained on charts is shown by
conventional symbols which make no attempt at accuracy in scale or detail, but are
)

d

D

KILOMETERS

41 /

Hý
bs | = 43 QUARANTINE ANCHORAGE » 3s
43

0000

5 an = SE
43
iO at 74

Æ BEL, | 044 by
S Ý i
ES N“ all P PP,

es
o
a
=
<
Ka
=]
o
Ë

01!
z >
=
o
a
a
<x
>

9!
|
I
14
1
A
Ju, ES
Ý ë
ÚT

ļ
DH

hig
Á
/
ti
In
d,

+

73 PE

0270
N
nant
270
"T

D
u
x
o 2 7
Harbor Limit
est
Au D
o
WS
`

o
74 n i

LM

ANNA
73 ow apro Ý N o

|

|

|

|

| osS 83 180
| T >
|

Í

83 8 o
7s Lights in line 087

Y
: : is 6s 6, /6 4
Ne 1s 3 74 Occ R 6sec 46ft 12M
| eg 1 SI

o
=

Uncov 5 fer

YARDS (IN THOUSANDS) —

go NUES la it
"5 SG 34 ies Së
621 4, 94 ts
\ 55
t AR
75 64. 5” 6; Sa S
(6%: 4 sec [2M di 7s EI
55” 59' 15” 30” 45” 155”

lst Ed.,June 18,1956

Published a
STANDARD NAUTICAL CHART
OOOO price 00 CENTS (Area Fictitious) nee eee

under the authority of t

30” 45" 02’

0000

NORTH PACIFIC
SUITLAND ISLAND

PORT COCHRAN

From a survey in 1953

SOUNDINGS IN FATHOMS
(Under Eleven in Fathoms and Feet)
reduced to Lowest Low Water 45"

HEIGHTS IN FEET

o
— YARDS (IN THOUSANDS)

For Symbols and Abbreviations, see H. O. Chart No. 1

MERCATOR PROJECTION
SCALE 1:20,000
NOTE 30"

The area tinted green was wire-dragged
in 1948 to a depth in feet indicated thus: 40

x
\

o

p how Ay, ly
| z Á
Tf
Ge

j Marable
Lake

: | ft
Ser El E Tas"
ri SES qe. IE T DE S Å 7 55” ||
| VERE : g 4] Be
A OAN at ee 22 NE h |
Y my y eU 2 32 42 3 A | 2 Ua
) AUS 0 e 2 me SCo 32 PA D
EN S mati uo "ie dio wrumpá 8
N o ly 594. : Da o E nimis E 5, 33 fas 8823) z
> > 2 í í Á o
i I MEI In 3s HE e 2
0 Ma 15. s 4s C | 9
2 Qro Uncov 1 ft t n : N T
EX An P" 2s S
, Ze," Da í d 33 3 2 Š Lë SE z
E neee 65 X » | o
i a R TZ a
h 25 42 64) 24 : A : 24 =
a SC? "la ¿33 Obstr pace > A
d 4. x d E dU d oom NETTE
EN Kas 5 oa S :
we (e, Dr E og quc use
Ze Tā Abe z se” 63 ES E le |
| De p Va 4 i ME gor OA og deus SE
| Ron 9s |65 64 55 34 3 25 22
I

7.58" N-S, 11.38" E-W

B D. C:, Port Cochran H.O. OOOO

NN Navy SOUNDINGS IN FATHOMS — SCALE 1:20,000 (1st Ed.) PRICE 00 CENTS
FIGURE 507.— A fictitious sample

nautical chart.

THE NAUTICAL CHART 107

shown at the correct location and make possible the showing of a large amount of
information without congestion or confusion. The standard symbols and abbrevia-
tions which have been approved for use on regular nautical charts published by the
United States of America are shown in appendix K. A knowledge of the meanings of
these symbols is essential to a full understanding of charts. A fictitious sample chart
showing a number of these symbols is given in figure 507.

Most of the symbols and abbreviations shown in appendix K are in agreement with
those recommended by the International Hydrographic Bureau. Where there is dis-
agreement, the number of the symbol or abbreviation is in leaning figures. Vertical
figures enclosed in parentheses indicate that the symbol or abbreviation is an addition
to those recommended by the International Hydrographic Bureau.

The symbols and abbreviations on any given chart may differ somewhat from
those shown in appendix K because of a change in the standards since printing of the
chart or because the chart was published by an agency having a different set of standards.

508. Lettering.—Certain standards regarding lettering have been adopted, except
on charts made from reproducibles furnished by foreign nations.

Vertical type is used for features which are dry at high water and not affected by
movement of the water, except for heights above water.

Leaning type is used for water, underwater, and floating features, except soundings.

The type of lettering used may be the only means of determining whether a feature
may be visible at high tide. For instance, a rock might bear the title 2. Rock”
whether or not it extends above the surface. If the name is given in vertical letters,
the rock constitutes a small islet; if in leaning type, the rock constitutes a reef.

509. The shore line shown on nautical charts is the boundary between water and
land at high tide (usually mean high water). A broken line indicates that the charted
position is approximate only. The nature of the shore may be indicated, as shown
by the symbols in part A of appendix K.

Where the low-water line differs considerably from the high-water line, the low-
water line may be indicated by dots in the case of mud, sand, gravel, or stones, with the
kind of material indicated, and by a characteristic symbol in the case of rock or coral.
The area alternately covered and uncovered may be shown by a tint which is a com-
bination of the land tint and a blue water tint.

In marsh or mangrove areas, the outer edge of vegetation is used as the shore line.
The inner edge is marked by a broken line when no other symbol (such as a cliff, levee,
ete.) furnishes such a limit. The area between inner and outer limits may be given the
combined land-water tint or the land tint.

510. Water areas.—Soundings or depths of water are shown in several ways.
Individual soundings are shown by numbers. These do not follow the general rule for
lettering. They may be either vertical or leaning, or both may be used on the same
chart to distinguish between the data based upon different surveys, different datums,
or furnished by different authorities. h

On all charts.produced from surveys by United States vessels, soundings are shown
in English units (feet or fathoms). The unit used ls shown in the chart legend.
Foreign charts may show depths in meters, and occasionally in other units. The units
used on charts of various nations are shown in appendix L.

“No bottom” soundings are indicated by a number with a line over the top and a
dot over the line, thus: 35. This indicates that the spot was sounded to the depth

indicated without reaching the bottom. Areas which have been wire dragged are
shown by a limiting line, and the clear effective depth is indicated, with a characteristic

symbol under the numbers, thus: 24,

108 THE NAUTICAL CHART

The soundings are supplemented by a series of bottom contours or depth curves
connecting points of equal depth. These lines present a graphic indication of the
configuration of the bottom. The types of lines used for various depths are shown in
part R of appendix K. On some of the recent charts of the U. S. Coast and Geodetic
Survey an increased number of depth curves have been shown in solid blue or black
lines, the depth represented by each being shown by numbers placed in breaks in the
lines, as with land contours. This type chart, presenting a more detailed indication of
the bottom configuration with fewer numerical soundings, is particularly useful to the
vessel equipped with an echo sounder permitting continuous determination of a profile
of the bottom. Such a chart, to be reliable, can be made only for areas which have
been surveyed in great detail.

Areas which uncover at low tide are tinted as indicated in article 509. Those
areas out to a given depth, usually one, two, or three fathoms, often are given a blue
tint, and occasionally a lighter blue is carried to some greater depth, usually five fathoms.
On older charts the one-, two-, and three-fathom curves have stippled edges. Charts
designed to give maximum emphasis to the configuration of the bottom show depths
over the entire chart by a series of blue gradient tints similar to the tints sometimes
shown on land areas to indicate graduations in height. These are called bathymetric
charts.

The side limits of dredged channels are indicated by broken lines. The controlling
depth and the date it was determined, if known, are shown by a statement in or along
the channel. The controlling depth is not necessarily an indication of the least depth
in the channel on the date of determination. For channels less than 100 feet in width,
at least 80 percent at the center is clear to the charted (controlling) depth. For
channels more than 100 feet in width, at least the 50 percent at the center is clear to
the charted depth. The possibility of shoaling since the controlling depth was deter-
mined should be considered.

The chart scale is generally too small to permit all soundings to be shown. In the
selection of soundings to be shown, least depths are generally chosen first and a sounding
pattern worked out to provide safety, a practical presentation of the bottom configura-
tion, and a neat appearance. Depths greater than those indicated may be found close
to charted depths, but steep changes in depth are given every consideration in sounding
selection. Also, the state of the tide affects the depth at any given moment. An
isolated shoal sounding should be approached with caution, or avoided, unless it is
known that the area has been wire dragged, for there is always the possibility that a
depth less than the least shown may have escaped detection. Also, the shoal area near
a coast little frequented by vessels is sometimes not surveyed with the same thorough-
ness as other areas. Such areas and those where rocks, coral, etc., are known to exist
should be entered with caution, or avoided.

The substance forming the bottom is shown by abbreviations, as listed in part
S of appendix K. The meaning of some of the less-well-known terms is given below:

Ooze is a soft, slimy, organic sediment composed principally of shells or other hard
parts of minute organisms.

. Marl is a crumbling, earthy deposit, particularly one of clay mixed with sand,
lime, decomposed shells, etc. A layer of marl may become quite compact.

Shingle consists of small, rounded, waterworn stones. It is similar to gravel
but with the average size of stone generally larger.

Schist is crystalline rock of a finely laminated nature.

e R de ge which often forms an important building material for reefs.

11 state, or such material after it has solidified. It is formed
at very high temperature and issues from the earth through volcanoes.

THE NAUTICAL CHART 109

Pumice is cooled volcanic glass with a great number of minute cavities caused by
the expulsion of water vapor at high temperature, resulting in a very light material.

Tufa is a porous rocky deposit sometimes formed in streams and in the ocean near
the mouths of rivers.

Scoria (plural scoriae) is rough, cinderlike lava.

Seatangle is any of several species of seaweed, especially those of large size.

Spicules are the small skeletons of various marine animals such as sponges.

Foraminifera (plural) are small marine animals with hard shells of from one to
many chambers.

Globigerina is a very small marine animal of the foraminifera order, with a cham-
bered shell, or the shell of such an animal. In large areas of the ocean the calcareous
shells of these animals are very numerous, being the principal constituent of a soft
mud or globigerina ooze, forming part of the ocean bed.

Diatom is a microscopic animal with external skeletons of silica, often found in
both fresh and salt water. Part of the ocean bed is composed of a sedimentary ooze
consisting principally of large collections of the skeletal remains of diatoms.

Radiolaria (plural) are minute sea animals with a siliceous outer shell. The
skeletons of these animals are very numerous, especially in the tropics.

Pteropod is a small marine animal with or without a shell and having two thin,
winglike feet. These animals are often so numerous they cover the surface of the sea
for miles. In some areas their shells cover the bottom.

Polyzoa (plural) are very small marine animals which reproduce by budding,
many generations often being permanently connected by branchlike structures.

Cirripeda (plural) are barnacles and certain other parasitic marine animals.

Fucus is a coarse seaweed growing attached to rocks.

Matte is a dense, twisted growth of a sea plant such as grass.

“Calcareous” is an adjective meaning “containing or composed of calcium or one
of its compounds.”

511. Chart datum.—Depths. All depths indicated on charts are reckoned from
some selected level of the water, called the chart datum. The various chart datums
are explained in chapter XXXI. On charts made from surveys conducted by the
United States the chart datum is selected with regard to the tides of the region, so
that depths might be shown in their least favorable aspect. On charts based upon
those of other nations the datum is that of the original authority. When it is known,
the datum used is stated on the chart. In some cases where the chart is based upon
old surveys, particularly in areas where the range of tide is not great, the actual chart
datum may not be known.

For U. S. Coast and Geodetic Survey charts of the Atlantic and Gulf coasts of the
United States and Puerto Rico the chart datum is mean low water. For charts of the
Pacific coast of the United States, including Alaska, it is mean lower low water. Most
U. S. Navy Hydrographic Office charts are based upon mean low water, mean lower low
water, or mean low water springs. The chart datum for British Admiralty charts based
upon British surveys is mean low water springs in areas where the daily inequality is
small, and Indian spring low water where the daily inequality is large. The chart
datum for charts published by other countries varies greatly, but is usually lower than
mean low water. On charts of the Baltic Sea, Black Sea, the Great Lakes, and other
areas where tidal effects are small or without significance, the datum adopted is an
arbitrary height approximating the mean water level. Chart datums used in various
areas are shown in appendix M.

The chart datum of the largest-scale charts of an area is generally the same as the
reference level from which height of tide is tabulated in the tide tables.

110 THE NAUTICAL CHART

The height of a chart datum is usually only an approximation of the actual mean
value specified, for determination of the actual mean height usually requires a longer
series of tidal observations than is available to the cartographer, and the height changes
somewhat over a period of time.

Since the chart datum is generally a computed mean or average height at some state
of the tide, the depth of water at any particular moment may be less than shown on
the chart. For example, if the chart datum is mean lower low water, the depth of water
at lower low water will be less than the charted depth about as often as it is greater.
A lower depth is indicated in the tide tables by a minus sign (—).

Heights. The shore line shown on charts is the high-water line, generally the
level of mean high water. The heights of lights, rocks, islets, etc., are generally reckoned
from this level. However, heights of islands, especially those at some distance from
the coast, are often taken from sources other than hydrographic surveys, and may be
reckoned from some other level, often mean sea level. The plane of reference for
topographic detail is frequently not stated on the chart.

Since heights are usually reckoned from high water and depths from some form of
low water, the reference levels are seldom the same. This is generally of little practical
significance, but it might be of interest under some conditions, particularly where the
range of tide is large.

512. Dangers are shown by appropriatesymbols, as indicated in part O of appendix K.

A rock which is uncovered at mean high water is shown as an islet enclosed by a
dotted line to make it more prominent. If an isolated, offlying rock is known to un-
cover at the chart datum but to be covered at high water, the appropriate symbol is
shown and the height above the chart datum, if known, is usually given, either by
statement such as “Uncov 2 ft" or by the figure indicating the number of feet above
the chart datum underlined and usually enclosed in parentheses, thus: (2). This is illus-
trated in figure 512a. A rock which does not uncover is shown by the appropriate symbol.
If it is considered a danger to surface vessels, the symbol is enclosed by a dotted curve.

A distinctive symbol is used to show a detached coral reef which uncovers at the
chart datum. For a coral or rocky reef which is submerged at chart datum, the
sunken rock symbol or an appropriate statement is used, enclosed by a dotted or dashed
line if the limits have been determined.

Several different symbols are used for wrecks, depending upon the nature
of the wreck or scale of the chart. The usual symbol for a visible wreck is
shown in figure 512b. A sunken
wreck with less than ten fathoms
of water over it is considered
dangerous and its symbol is sur-
rounded by a dotted curve. The
safe clearance depth found over a
wreck is indicated by a standard
sounding number placed at the
wreck. If this depth is determined
by a wire drag, the sounding is
underscored by the wire drag sym-
bol (art. 510).

Tide rips, eddies, and kelp are
shown by symbol or lettering.

Piles, dolphins (clusters of
piles), snags, stumps, etc., are
Figure 512a.—A rock awash. shown by small circles and a label

A high)
zi Josh gh)

THE NAUTICAL CHART 111

identifying the type of obstruction.
If such dangers are submerged,
the letters “Subm” precede the
label.

513. Aids to navigation are
shown by symbol, as given in ap-
pendix K, usually supplemented
by abbreviations and sometimes
by additional descriptive text.
In order to render the symbols
conspicuous it is necessary to
show them in greatly exaggerated
size relative to the scale of the
chart. It is therefore important
that the navigator know which — ES
part of the symbol represents Figure 512b.—A visible wreck.
the actual position of the aid. For floating aids (lightships and buoys), the
position part of the symbol marks the location of the anchor or sinker, the aid
swinging in an orbit around this position.

The principal charted aids to navigation are lighthouses, beacons, lightships, radio-
beacons, and buoys. The number of aids shown and the amount of information con-
cerning them varies with the scale of the chart. Wherever distance of visibility is
given, it is computed for a height of eye of the observer of 15 feet. Unless otherwise
indicated, lights which do not alternate in color are white, and alternating lights are
red and white. Light lists give complete navigational information concerning them.

Lighthouses and lighted beacons are shown as black dots surrounded by magenta
disks. The disks for primary lighthouses are a little larger than those for beacons.
In either case, the center of the black dot within the magenta disk is the position of
the light. On older charts a six-pointed star symbol was used for primary lighthouses
and a five-pointed star symbol for beacons. The center of the star symbol marks the
position of the light.

On large-scale charts the characteristics of lights are shown in the following order:

Characteristic Example Meaning
1. Character Gp. Fl. group flashing
2. Color R red
3. Period (2) 10 sec. two flashes every 10 seconds
4. Height 160 ft. 160 feet
5. Visibility 19M visible 19 nautical miles (15 ft. height of eye)
6. Number SE light number 6

The legend for this light would appear on the chart:
Gp. Fl. R (2) 10 sec. 160 ft. 19 IR

On older charts this form is varied slightly. As the chart scale becomes smaller the six
items listed above are omitted in the followiag order: first, height; second, period
(seconds); third, number (of flashes, etc.) in group; fourth, light number; fifth, visi-
bility. Names of unnumbered lights are shown when space permits.

Daybeacons (unlighted beacons) are shown by small triangles, the center of the
triangle marking the position of the aid. Except on Intracoastal Waterway charts the
abbreviation Bn is shown beside the symbol, with the appropriate abbreviation for color.
For black beacons the triangle is solid black and there is no color abbreviation. All

112 THE NAUTICAL CHART

beacon abbreviations are in vertical lettering, as appropriate for fixed aids (fig. 513a).

Lightships are shown by ship symbol, the center of the small circle at the base of
the symbol indicating the position of the lightship’s anchor. On recent charts the
circle is overprinted by a small
magenta disk as shown in figure
513b. As a floating aid, the light
characteristics and the name of the
lightship are given in leaning letters.

Radiobeacons are indicated on
the chart by a small magenta circle,
as shown in figure 513b, accom-
panied by the appropriate abbre-
viation to indicate whether an
ordinary radiobeacon (R Bn) or a
radar beacon (Racon). The same
symbol is used for a radio direction
finder station with the abbreviation
“RDF” and a coast radar station
with the abbreviation Ra. Other
radio stations are indicated by a

Figure 513a.—A daybeacon. small black circle with a dot in the

center, or a smaller circle without a

dot, and the appropriate abbreviation. In every case the center of the circle marks
the position of the aid.

Buoys, except mooring buoys, are shown by a diamond-shaped symbol and a small
dot outside the diamond and near one of its points (at one of its acute angles). The dot
indicates the position of the buoy’s sinker. A mooring buoy is shown by a distinctive
symbol as indicated at number
22 of part L, appendix K. The
small circle interrupting the
symbol’s base line indicates the
position of the sinker.

A black buoy is shown by
a solid black diamond symbol,
without abbreviation. For all
other buoys, color is indicated
by an abbreviation, or in full by
a note on the chart. In addi-
tion, the diamond shape of
symbols of red buoys are colored
magenta. A buoy symbol with
a line connecting the side points
(shorter axis), half of the sym- FravnE 513b.—A lightship with a radiobeacon.
bol being magenta or open and
the other half black, indicates horizontal bands. A line connecting the upper and
lower points (longer axis) represents vertical stripes. Two lines connecting the oppo-
site sides of the symbol indicate a checkered buoy.

There is no significance to the angle at which the diamond-shape appears on the
chart. The symbol is placed so as to avoid interference with other features of the chart.

Lighted bouys are indicated by a small magenta disk centered on the dot or small

a a D

TAE NAUTICAL CHART 113

circle indicating the position of the buoy’s sinker, as shown in figure 513c. On older
charts a series of radiating lines representing light rays was drawn about the dot or
circle, and no magenta disk was given.

Abbreviations for light characteristics, type and color of buoy, number of the buoy,
and any other pertinent information given near the symbol are in leaning letters. The
letter C, N, or S, indicates a can, nun, or spar, respectively (art. 917). The words
“bell,” “gong,” and “whistle,” are shown as BELL, GONG, and WHIS, respec-
tively. The number or letter designation of the buoy is given in quotation marks on
small-scale charts. On large-scale charts they are given without quotation marks or
punctuation, thus: No 1, No 2, etc.

Station buoys are not shown on small-scale charts, but are given on some large-
scale charts.

Aeronautical lights included in the light lists are shown by the lighthouse symbol,
accompanied by the abbreviation “AERO”. The completeness to which the character-
istics are shown depends principally upon the effective range of other navigational
lights in the vicinity, and the
usefulness of the light for marine |
navigation.

Ranges are indicated by a
dashed or solid line. If the di- 9%
rection is given, it is expressed
in degrees clockwise from true
north.

Fog signal apparatus isindi-
cated by the appropriate wordin 42
capital letters (HORN, BELL, |
GONG, etc.) or an abbreviation do
indicating the type of sound. d uen
The letters *'D.F.S.” indicate a ge E
distance finding station having FIGURE 513c.—A lighted buoy.
synchronized sound and radio
signals. The location of a fog signal which does not accompany a visual aid, either
lighted or unlighted, is shown by a small circle and the appropriate word in vertical
block letters.

Private aids are not indicated on the chart except in special cases. When they are
shown, they are marked “Privately maintained" or “Priv. maintd.” Any privately
maintained unlighted aid is indicated by a small circle accompanied by the word
“Marker,” or a larger circle with a dot in the center and the word “MARKER,”
the symbols for any landmark or conspicuous object not having a distinctive symbol.
The center of the circle indicates the position of the aid. A privately maintained
lighted aid has the light symbol and is accompanied by the characteristics and the
usual indication of its private nature.

Floats are indicated by the open buoy symbol accompanied by the word “FLOAT.”
Either the lighted or unlighted symbol is used, as appropriate, to indicate whether or
not the float displays a light. l

A light sector is the sector or area bounded by two radii and the arc of a circle in
which a light is visible or in which it has a distinctive color different from that of
adjoining sectors. The limiting radii are indicated on the chart by dotted lines.

Colors of the sectors are indicated by words spelled out if space permits, or by

abbreviation (W, R, etc.) if it does not.

182

109

8l

73

114 THE NAUTICAL CHART

Limits of light sectors and ares of visibility as observed from a vessel are given in
the light lists, in clockwise order.

514. Land areas.—The amount of detail shown on the land areas of nautical
charts depends upon the scale, the intended purpose of the chart, and available informa-
tion. Since the advent of radar, topographical details have increased and have been
extended farther inland, where this information has been available.

Relief is shown by contours, form lines, hachures, or tint shading. Tint shading
is used principally to stress those terrain features affecting surface radar returns. It
may be shown with or without contours and spot elevations.

Contours are lines connecting points of equal elevation. The heights represented
by the contours are indicated in leaning figures at suitable places along the lines. Heights
are usually expressed in feét (or in meters with means for conversion to feet on certain
special charts). The interval between contours is uniform over any one chart, except
that certain intermediate contours are sometimes shown by dashed line. When contours
are broken, their locations are approximate.

Form lines are approximations of contours used for the purpose of indicating
relative elevations. They are used in areas where accurate information is not available
in sufficient detail to permit exact location of contours. Elevations of individual
form lines are not indicated on the chart.

Hachures are short lines, or groups of lines, indicating the direction and extent of
steep slopes. The lines generally follow the direction of the slope, the length of the lines
indicating the height of the slope. Distinctive symbols somewhat resembling hachures
are used for cliffs or other steep slopes on or near the coast line, where contours or form
lines, being virtually over each other, would be difficult to interpret or would fail to
give a true indication of the nature of the terrain.

Spot elevations are generally given only for summits or for tops of conspicuous
landmarks. The heights of spot elevations and contours are given with reference to
mean high water when this information is available.

When there is insufficient space to show the heights of islets or rocks, they are
indicated by leaning figures enclosed in parentheses in the water area nearby.

Cities and roads. Except on the smaller scale charts, cities are usually represented
by their street systems or a conventional system of intersecting lines. The symbol for
large cities approximates their extent and shape. Street names are generally not
charted except those along the waterfront on the largest scale charts. Only the more
important streets are shown on smaller scale charts. In general, only the important
through highways and roads leading from them to the waterfront are shown. Oc-
casionally, highway numbers are given. When shown, trails are indicated by a light
broken line. Buildings along the waterfront or individual ones back from the water-
front but of special interest to the mariner are shown on large-scale charts. Special
symbols are used for certain kinds of buildings, as indicated in part I of appendix K.
Both single and double track railroads are indicated by a single line with cross marks.
In general, city electric railways are not charted. A fence or sewer extending into
the water is shown by a broken line, usually labeled. Airports are shown on small-
scale charts by symbol and on large-scale charts by shape and extent of runways.
Breakwaters and jetties are shown by single or double lines depending upon the scale
of the chart. A submerged portion and the limits of the submerged base are shown
by broken lines.

515. Landmarks are shown by symbols, as given in appendix K. Some of the
accompanying labels encountered on a chart are interpreted as follows:

Building or house. One of these terms, as appropriate, is used when the entire
structure is the landmark, rather than an individual feature of it.

THE NAUTICAL CHART 115

A spire is a slender pointed structure extending above a building. It is seldom
less than two-thirds of the entire height of the structure, and its lines are rarely broken
by stages or other features. The term is not applied to a short pyramid-shaped structure
rising from a tower or belfry.

A cupola (kü'pó-là) is a small dome-shaped tower or turret rising from a building
(fig. 515).

A dome is a large, rounded, hemispherical structure rising above a building, or a
roof of the same shape. A prominent example is that of the Capitol of the United States,
in Washington.

A chimney is a relatively small, upright structure projecting above a building for
the conveyance of smoke.

A stack is a tall smokestack or
chimney. The term is used when Á N J^ stica
the stack is more prominent as SJ : Opes iJ m
& landmark than accompanying ` d ALT dE
buildings.

A flagpole is a single staff from
which flags are displayed. The
term is used when the pole is not
attached to a building.

The term flagstaff. is used for
a flagpole rising from a building.

A flag tower is a scaffold-like
tower from which flags are dis-
played.

A radio tower is a tall pole or
structure for elevating radio an-
tennas. Figure 515.—A cupola.

A radio mast is a relatively
short pole or slender structure for elevating radio antennas, usually found in groups.

A tower is any structure with its base on the ground and high in proportion to its
base, or that part of a structure higher than the rest, but having essentially vertical
sides for the greater part of its height.

A lookout station or watch tower is a tower surmounted by a small house from
which a watch is kept regularly.

A water tower is a structure enclosing a tank or standpipe so that the presence of
the tank or standpipe may not be apparent.

A standpipe is a tall cylindrical structure, in a waterworks system, the height
of which is several times the diameter.

The term tank is used for a water tank elevated high above the ground by a tall
skeleton framework. |

The expression gas tank or oil tank is used for the distinctive structures described
by these words.

516. Miscellaneous.—Measured mile. A measured nautical mile indicated on a
chart is accurate to within six feet of the correct length. Most measurements in the
United States were made before 1959, when the United States adopted the international
nautical mile. The new value is within six feet of the previous standard length ol
6,080.20 feet, adjustments not having been made. If the measured distance differs
from the standard value by more than six feet, the actual measured distance is stated
and the words “measured mile” are omitted.

116 THE NAUTICAL CHART

Periods after abbreviations in water areas are omitted, as these might be mistaken
for rocks. However, a lower case ¿ or j is dotted.

Courses shown on charts are given in true directions, to the nearest minute of arc.

Bearings shown are in true directions toward (not from) the objects.

Commercial radio broadcasting stations are shown on charts when they are of
value to the mariner either for obtaining radio bearings or as landmarks.

Rules of the road. Lines of demarcation between the areas in which international
and inland rules apply are shown only when they cannot be adequately described in
notes on the chart.

Compass roses are placed at convenient locations on Mercator charts to facilitate
the plotting of bearings and courses. The outer circle is graduated in degrees with
zero at true north. The inner circle is graduated in points and degrees with the arrow
indicating magnetic north.

Magnetic information. On many charts magnetic variation is given to the nearest
15’ by notes in the centers of compass roses. When this is done, the annual change is
given to the nearest 1’ to permit correction of the given value at a later date. However,
since the annual change is a variable quantity, and since the values given are rounded
off, as well as for other reasons, it is wise to use a chart of recent date. On other charts
the variation is given by a series of isogonic lines connecting points of equal variation,
usually a separate line being given for each degree of variation. The line of zero varia-
tion is called the agonic line. Many plans and insets show neither compass roses nor
isogonic lines, but indicate magnetic information by note. A local magnetic disturbance
of sufficient force to cause noticeable deflection of the magnetic compass, called
local attraction, is indicated by a note on the chart.

Currents are sometimes shown on charts by means of arrows giving the directions,
and figures giving the speeds. The information thus given refers to the usual or average
conditions, sometimes based upon very few observations. It is not safe to assume that
conditions at any given time will not differ considerably from those shown.

Longitudes are reckoned eastward and westward from the meridian of Greenwich,
England, unless otherwise stated. Nearly all modern charts use Greenwich. |

Notes on charts should be read with care, as they may give important information
not graphically presented. Several types of notes are used. First, those in the margin
give such information as the chart number and (sometimes) price, publication and
edition notes, identification of adjoining charts, etc. Second, notes in connection with
the chart title include such information as scale, sources of charted data, tidal informa-
tion, the unit in which soundings are given, cautions, etc. A third class of notes is that
given in proximity to the detail to which it refers. Examples of this type of note are
those referring to local magnetic disturbance, controlling depths of channels, measured
miles, dangers, dumping grounds, anchorages, etc. i

Title. The chart title may be at any convenient location, usually in some area
not important to navigation. It is composed of several distinctive parts as shown in
figure 516.

Use of Charts

517. Advance preparation.—Before a chart is to be used, it should be studied
carefully. All notes should be read and understood. There should be no question of
the meanings of symbols or the unit in which depths are given, for there may not be
time to determine such things when the ship is underway, particularly if an emergency
should arise. Since the graduations of the latitude and longitude scales differ con-
siderably on various charts, those of the chart to be used should be noted carefully.
Dangers and abnormal conditions of any kind should be noted.

THE NAUTICAL CHART 117

ASIA
PERSIAN GULF—SAUDI ARABIA

APPROACHES TO
are oan >RA'S AT TANNURAH

SOURCE AND DATE(S) > From U.S. Navy surveys between 1940 and 1952

GENERAL GEOGRAPHIC AREA ——>

OF SURVEY with additions from British surveys in 1949 and 1950
| SOUNDINGS IN FATHOMS
(Under Eleven in Fathoms and Feet)
CHART DATUM ———> reduced to the approximate level of Indian Spring Low Water

HEIGHTS IN METERS ABOVE MEAN SEA LEVEL
Value of heights in feet shown thus: (102 fe)

LEGEND ——— — — — —39 For Symbols and Abbreviations, see Chart No. 1

PROJECTION —————————> MERCATOR PROJECTION

HORIZONTAL DATUM ——————————3 NAHRWAN DATUM

SCALE ———————————3 SCALE 1:150,000 AT LAT. 27°
Figure 516.—A chart title.

Particular attention should be given to soundings. It is good practice to select
a realistic danger sounding (art. 911) and mark this prominently with a colored pencil.

It may be desirable to place additional information on the chart. Arcs of circles
might be drawn around navigational lights to indicate the limit of visibility at the
height of eye of an observer on the bridge. Notes regarding the appearance of light
structures, tidal information, prominent ranges, or other information from the light
lists, tide tables, tidal current tables, and sailing directions might prove helpful.

The particular preparation to be made depends upon the requirements and the
personal preferences and experience of the individual navigator. The specific infor-
mation selected is not important. But it ts important that the navigator familiarize
himself with his chart so that in an emergency the information needed will be available
and there will be no question of its meaning.

518. Maintaining charts.—When a chart is received, the date to which it has been
hand corrected will be found stamped in the margin. Responsibility for maintaining it
after this date lies with the user. An uncorrected chart is a menace. The various issues
of Notice to Mariners subsequent to the stamped hand correction date contain all
the information needed for maintaining charts. The more urgent items are also given
in advance in the Daily Memorandum or by radio broadcast. A convenient way of
keeping a record of the Notice to Mariners corrections made to each chart on hand is
by means of 58-inch chart correction record cards (PRNC-NHO-5610/2, formerly
form N.H.O. 1278), which can be purchased for a nominal sum.

When a new edition of a chart is published, it should be obtained and the old one
retired from use. The very fact that a new edition has been prepared generally indi-
cates that there have been changes that cannot adequately be shown by hand correction.

519. Use and stowage of charts.—Charts are among the most important aids of
the navigator, and should be treated as such. When in use they should be spread
out flat on a suitable chart table or desk, and properly secured to prevent loss or

118 THE NAUTICAL CHART

damage. Every effort should be made to keep charts dry, for a wet chart stretches
and may not return to the original dimensions after drying. The distortion thus
introduced may cause inaccurate results when measurements are made on the chart.
If a chart does become wet, the distortion may be minimized by ironing the chart
with a warm iron until it is dry.

Permanent corrections to charts should be made in ink so that they will not be
inadvertently erased. All other lines should be drawn lightly in pencil so that they
can be easily erased without removing permanent information or otherwise damag-
ing the chart. To avoid possible confusion, lines should be drawn no longer than
necessary, and adequately labeled. When a voyage is completed, the charts should
be carefully and thoroughly erased unless there has been an unusual incident such
as a grounding or collision, when they should be preserved without change, as they
will undoubtedly be requested by the investigating authority. After a chart has been
erased, it should be inspected carefully for possible damage and for incompletely
erased or overlooked marks that might prove confusing when the chart is next used.

When not in use charts should be stowed flat in their proper drawers or portfolios,
with a minimum of folding. The stowed charts should be properly indexed so that
any desired one can be found when needed. In removing or replacing a chart, care
should be exercised to avoid damage to it or other charts.

A chart that is given proper care in use and stowage can have a long and useful life.

520. Chart lighting.—In the use of charts it is important that adequate lighting
be provided. However, the light on the bridge of a ship underway at night should
be such as to cause the least interference with the darkness-adaptation of the eyes of
bridge personnel who watch for navigational lights, running lights, dangers, etc.
Experiments by the Department of the Navy have indicated that red light is least
disturbing to eyes which have been adapted to maximum vision during darkness. In
some instances red lights, filters, or goggles have been provided on the bridges or in
chartrooms of vessels. However, the use of such light seriously affects the appearance
of a chart. Red, orange, and buff disappear. Other colors may appear changed.
This has led to the substitution of magenta cr purple for red and orange, and gray for
buff on some charts. However, before a chart is used in any light except white, a
preliminary test should be made and the effect noted carefully. If a glass or plastic
top is provided for the chart table or desk, a dim white light below the chart may provide
sufficient illumination to permit chart reading, without objectionable disturbance of
night vision.

PART TWO

PILOTING AND DEAD RECKONING

CHAPTER VI. Instruments for Piloting and Dead Reckoning
CHAPTER VII. Compass Error
CHaPTER VIII. Dead Reckoning

CHAPTER IX. Piloting -

PART TWO

PILOTING AND DEAD RECKONING

121
158
213
240

[= CHAPTER VI

INSTRUMENTS FOR PILOTING AND DEAD RECKONING

Introduction

601. Kinds of instruments.—The word “instrument” has several meanings, at
least two of which apply to navigation: (1) an implement or tool, and (2) a device by
which the present value of a quantity is measured. Thus, a straightedge and a mechan-
ical log are both instruments, the first serving as a tool, and the second as a measuring
device. This chapter is concerned with the navigational instruments used for plotting,
and those for measuring distance or speed, depth, and direction. Instruments for
measuring time are discussed in chapter XV. These quantities are the basic data in
dead reckoning (ch. VIII) and piloting (ch. IX). Other instruments are discussed in
chapters XI, XV, XX XVII, and XL.

In addition to the instruments discussed, several others are important to the
navigator. Binoculars are helpful in observing landmarks. A flashlight has many
uses, the principal one being to illuminate the scales of instruments when they are to
be read at night. Erasers should be soft, and pencils should not be so hard that they
damage the surface of the chart. The navigator's chart is discussed in chapter V.

Plotting Instruments

)

602. Dividers and compasses.— Dividers, or “pair of dividers,” is an instrument
originally used for dividing a line into equal segments. The instrument consists essen-
tially of two hinged legs with pointed ends which can be separated to any distance

from zero to the maximum imposed by physical limitations. The setting is retained
either by friction at the hinge, as in the usual navigational dividers, or by means of a
screw acting against a spring.

If one of the legs carries a pencil or ruling pen, the instrument is called compasses.
The two legs may be attached to a bar of metal or wood instead of being hinged, thus
permitting greater separation of the points. Such an instrument is called beam
compasses or beam dividers (fig. 4011b).

The principal use of dividers in navigation is to measure or transfer distances on
a chart, as described in article 804. Compasses are used for drawing distance circles
(art. 905), circles of visibility (art. 916), or any plotting requiring an arc of a circle.

The friction at the hinge of most dividers and compasses can be varied, and should
be adjusted so that the instrument can be manipulated easily with one hand, but will
retain the separation of the points in normal handling. A drop of oil on the hinge
may be required occasionally. The points should be sharp, and should have equal
length, permitting them to be brought close together for the measurement of very short
distances.

For navigation, it is desirable to have dividers and compasses with comparatively
long legs, to provide adequate range for most requirements. It is desirable to learn
to manipulate dividers or compasses with one hand.

603. Parallel rulers are an instrument for transferring a line parallel to itself. In
its most common form it consists of two parallel bars or rulers, connected in such &
manner that when one is held in place on a flat surface, the other can be moved, remain-

121

122 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

ing parallel to its original direction. Firm pressure is required on one ruler while the
other is being moved, to prevent slippage. The principal use of parallel rulers in
navigation is to transfer the direction of a charted line to a compass rose, and vice versa.

The edges of the rulers should be truly straight; and in the case of double-edged
rulers, should be parallel to each other in order that either edge can be used. Paral-
lelism can be tested by comparison of all edges with the same straight line, as a meridian
or parallel of a Mercator chart. The linkage can be tested for looseness and lack of
parallelism by “walking” the rulers between parallel lines on opposite sides of the chart
and back again.

Some metal parallel rulers have a protractor engraved on the upper surface to
permit orientation of the ruler at any convenient meridian.

In one type of instrument, parallelism during transfer is obtained by supporting
a single ruler on two knurled rollers. Both rollers have the same diameter, and the
motion of one is transmitted to the other by an axle having a cover which provides a
convenient handle. This type of ruler is convenient and accurate, and is less likely
to slip than the linked double-ruler type. However, care is necessary to prevent its
rolling off the chart table when the vessel is rolling or pitching.

Directions can also be transferred by means of two triangles such as are used in
drafting, or by one triangle and a straightedge. One edge of a triangle is aligned in
the desired direction and the triangle is then moved along a straightedge held firmly
against one of its other edges until the first edge is at the desired place on the chart.
Some triangles have protractors (art. 604) engraved on them to assist in transferring
lines. Such a triangle becomes
a form of plotter (art. 605).

604. Protractor.—A pre-
tractor is a device for measuring
angles on a chart or other surface.
It consists essentially of a gradu-
ated arc, usually of 180°, on suit-
able material such as metal or
plastic.

A three-arm protractor con-
sists essentially of a circular pro-
tractor with three radial arms
attached. This instrument,
discussed in greater detail in
article 4011, is used primarily
in hydrographic surveying.

605. Plotters.—The in-
creased popularity of graphical
methods in practical navigation
during recent decades has re-
sulted in the development of a
wide variety of devices to facili-
tate plotting. In its most
common form, such a device con-
sists essentially of a protractor
combined with a straightedge.
There are two gcneral types, one
Figure 605.—Two plotters having no movable parts. having no movable parts, and

|
READ DIRECTION 60°—240° HERE

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 123

the other having a pivot at the center of the arc of the protractor, to permit rotation
of the straightedge around the protractor. Examples of the fixed type are illustrated
in figure 605. Those shown were designed for air navigation, but are applicable to
many processes of marine navigation. The direction of the straightedge is controlled
by placing the center of the protractor arc and the desired scale graduation on the
same reference line. If the reference line is a meridian, the directions shown by the
straightedge are true geographic directions. If, as in some processes of celestial navi-
gation, it is desired to plot a line perpendicular to another line, the direction may be
measured from a parallel of latitude or its equivalent, instead of adding or subtract-

FIGURE 606.—Drafting machine.

ing 90° from the value and measuring from a meridian. Some fixed-type plotters have
auxiliary scales labeled to indicate true direction if a parallel is used as the reference.

Most plotters also provide linear distance scales, as shown in figure 605. In the
movable-arm type of plotter, a protractor is aligned with a meridian, and the movable
arm is rotated until it is in the desired direction.

606. Drafting machine.—If a chart table of sufficient size is available, a drafting
machine (fig. 606) is probably the most desirable plotting instrument. The straight-
edge of this instrument can be clamped so as to retain its direction during movement
over the entire plotting area. Straightedges of various lengths and linear scales are
interchangeable. Some models make provision for mounting two straightedges per-
pendicular to each other. However, for most purposes of navigation, the perpendicular
is more conveniently obtained by the use of a triangle with a single straightedge. The
movable protractor also retains its orientation, and can be adjusted to conform to the

124 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

compass rose of a chart secured in any position on the chart table. Directions of the
straightedge can then be read or set on the protractor without reference to charted
compass roses. Use of the clamped protractor requires that charted meridians be
straight and parallel, as on a Mercator chart (art. 305). Its use is restricted with
projections such as the Lambert conformal (art. 314), on which meridians converge.

When a drafting machine is used, the chart or plotting sheet is first secured
to the chart table. The straightedge is aligned with a meridian (or parallel) and
clamped in position. The protractor is then adjusted so that 000° and 180° (090° and
270° if a parallel is used) are at the ruler indices, and clamped. With this setting, any
subsequent position of the ruler is indicated as a true direction. If the protractor is
offset by the amount of the compass error (ch. VII), true directions can be plotted by
setting the straightedge at the compass direction on the protractor, without need for
applying compass error arithmetically. However, it is generally preferable to keep it
set to true directions, and apply compass error mentally.

If accurate results are to be obtained, the anchor base must be rigidly fastened to
the chart table. This should be checked from time to time, as the base may be loosened
by vibration or normal use. The pivots in the anchor base should be firm without
binding. The endless belts of the parallel motion mechanism should be taut if rigidity
of the ruler is to be preserved. Provision is usually made for adjusting each of the
various rulers to uniformity of alignment so that any other ruler can be substituted
without changing the setting. As with parallel rulers, the device can be checked for
parallelism by means of meridians or parallels on opposite sides of a Mercator chart.

Distance and Speed Measurement

607. Units of measurement.—Mariners generally measure horizontal distances in
nautical miles (art. 205), but occasionally in yards or feet. Either feet or fathoms are
used for measuring depth of water, and feet for measuring height above water. The
British yard is now equal to that of the United States (art. 205). However, the differ-
ence was never significant in the ordinary practice of navigation. Nations which
have adopted the metric system use meters in place of yards, feet, and fathoms, and
for some purposes they use kilometers in place of nautical miles. Conversion factors
for these and other units are given in appendix D. Nautical miles of 6,076.11549 feet
(approximately) and land or statute miles of 5,280 feet can be interconverted by means
of table 20. Meters, feet, and fathoms can be interconverted by means of table 21.

Speed is customarily expressed in knots (art. 206), or for some purposes, in kilo-
meters per hour, or yards or feet per minute. For short distances, a nautical mile can be
considered equal to 2,000 yards or 6,000 feet. This is a useful relationship because
6,000 feet
60 minutes
hundreds of feet per minute or, hundreds of yards per 3-minute interval.

608. Distance, speed, and time are related by the formula

—100 feet per minute. Thus, speed in knots is equal approximately to

distance — speed X time.

Therefore, if any two of the three quantities are known, the third can be found. The
units, of course, must be consistent. Thus, if speed is measured in knots, and time
in hours, the answer is in nautical miles. Similarly, if distance is measured in yards,
and time in minutes, the answer is in yards per minute.

Table 19 is a speed, time, and distance table which supplies one of the three values
if the other two are known. It is intended primarily for use in finding the distance
steamed in a given time at a known speed. Table 18 is for use in determining speed
by measuring the time needed to steam exactly one mile.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 125

The solution of problems involving distance, speed, and time can easily be accom-
plished by means of a slide rule (art. O15). If the index of scale C is set opposite speed
in knots on scale D, the distance in nautical miles appears on scale D opposite time in
hours on scale C. If 60 of scale C is set opposite speed in knots on scale D, the distance
covered in any number of minutes is shown on scale D opposite the minutes on scale C.
Several circular slide rules particularly adapted for solution of distance, speed, and

DISTANCE

RED NAUT MILES
BLACK--YARDS

NAUTICAL SLIDE RULE
U. S. NAVY BUREAU OF SHIPS
MFR'S. PART NO. FNS-3
CONTRACT NO. NXss-60767
G. FELSENTHAL & SONS, CHICAGO

Figure 608.—The nautical slide rule.

time problems have been devised. One of these, called the “Nautical Slide Rule” is

shown in figure 608.
609. A Aii rement of distance to an object can be made in a variety of ways, as

by radar (art. 1208), sonar (art. 1103), RAR beacon (art. 1205), US x Mte
tion (art. 1205), sextant angle (art. 905), range finder, or by several in e me : i
Another method used principally for measuring distance between ships in forma o
but useful in measuring other distances, is by means of a small, hand-held instrumen

called a stadimeter.

126 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

RAR Areta A VOILE A

Ficure 609a.—Stadimeters. Brandon (sextant) type at left; Fisk type at right.

Two types of stadimeters are illustrated in figure 609a. Both the Brandon
or sextant type and the Fisk type operate on the principle used in table 9:

In a plane right triangle, ABO, having opposite sides a, b, and c,

tan A=} and b=a cot A.

This is applied to the stadimeter as shown in figure 609b. The height of the object
is set on the height scale of the instrument, and the measured subtended angle is ex-
pressed in yards on the distance (range) scale. To measure the angle, one directs the
line of sight through the instrument to the water line of the object observed, and ad-
justs the range index until the reflection of the top of the object is seen in coincidence
with the water line. If the readings are not within the scale of the instrument, some
fraction or multiple of the height can be used and a corresponding adjustment made
to the answer. Thus, if half the height is set on the instrument, the distance indicated
is half the correct value.

Since the observer’s eye is not at the water level, a right angle is not necessarily
formed between the line of sight and the top of the observed object. However, the

Figure 609b.—Geometry of a stadimeter measurement.

The distance b=a cot A.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 127

resulting error is so small that it can be neglected under ordinary circumstances.
í The aspect of a ship observed should be considered in stadimeter ranges. Thus,
little error is introduced if the observer is broad on the beam of the other vessel, as in
figure 609b, but less accuracy is obtained if the other vessel presents an end-on view,
unless the water line directly below the masthead is correctly estimated.

A stadimeter can be used to indicate that a change in distance has occurred, even
when the height of the object is not known. Similar indication of a change in distance
can be obtained by a sextant (art. 905), or the actual distance can be determined by
the measured angle and table 9 if the height is known.

610. Measurement of distance traveled may be made directly, or the distance
can be determined indirectly by means of the speed and time, using the relationship
given in article 608.

One of the simplest mechanical distance-measuring devices is the taffrail log, con-
sisting of (1) a rotator which turns like a screw propeller when it is towed through the
water; (2) a braided log line, up to 100 fathoms in length, which tows the rotator and
transmits its rotation to an indicator on the vessel; and (3) a dial and pointer mech-
anism which registers the distance traveled through the water. In some installations,
the readings of the register are transferred electrically to a dial on or near the bridge.

The taffrail log is usually streamed from the ship’s quarter, although it may be
carried at the end of a short boom extending outboard from the vessel. The log line
should be sufficiently long, and attached in such position, that the rotator is clear of
the disturbed water of the wake of the vessel; otherwise an error is introduced. Errors
may also be introduced by a head or following sea; by mechanical wear or damage, such
as a bent fin; or by fouling of the rotator, as by seaweed or refuse.

An accurately calibrated taffrail log in good working order provides information
of sufficient reliability for most purposes of navigation. Its readings should be checked
at various speeds by towing it over a known distance in an area free from currents.
Usually, the average of several runs, preferably in opposite directions, is more accu-
rate than a single one. If an error is found, it is expressed as a percentage and applied
to later readings. The calibration should be checked from time to time.

Although a taffrail log is included in the equipment carried by many oceangoing
vessels, the convenience and reliability of other methods of determining distance or
speed have reduced the dependence formerly placed upon this instrument.

611. Measurement of speed.—Speed can be determined indirectly by means of
distance and time, or it can be measured directly. All instruments now in common
use for measuring speed determine rate of motion through the water. This is done
(1) electromagnetically, (2) by measuring the water pressure due solely to the for-
ward motion of the vessel, (3) by means of a small screw propeller having a speed of
rotation proportional to speed of the vessel, and (4) by determining the relationship
between ship speed and speed of rotation of its screw or screws. Instruments for
measuring speed, like those for measuring distance, are called logs.

Before the development of modern logs, speed was determined in a number of
ways. Perhaps the most common primitive device is the chip log (art. 112), although a
ground log (a weight, with line attached, which was thrown overboard and rested on
the bottom in shallow water) and a Dutchman’s log (art. 112) have also been used.
These devices are rarely used by modern navigators.

Speed over the bottom can be determined (1) by direct measurement; (2) by
measuring on the chart or plotting sheet the distance made good between fixes, and
dividing this by the time; or (3) by finding the vector sum of velocity through the
water and velocity of the current. A suitable instrument for measuring speed over
the bottom is not generally available, although some developmental work along this

128 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

line has been done. Measurement of the distance between two fixes requires a method
of obtaining accurate fixes. The third method requires knowledge of velocity through
the water, and current. An estimate of the current can be used to determine the approxi-
mate course and speed over the bottom. However, estimates are not always accurate,
and an instrument to measure current would provide better results. Such an instru-
ment, called the geomagnetic electrokinetograph (GEK), has been developed. By
means of two electrodes towed astern, beyond the magnetic influence of the vessel,
the component of current perpendicular to the course is measured. By measurement
of two such components, preferably on perpendicular courses, one can determine the
total current. This device has given satisfactory results in experimental work, having
been used primarily by oceanographers in their study of ocean currents, but has not
been adapted for use in ordinary navigation.

612. The electromagnetic type underwater log consists essentially of a rodmeter, `
an oscillator-amplifier, and an indicator-transmitter. The rodmeter, which protrudes
below the hull of the vessel, contains an electromagnetic sensing element which pro-
duces a voltage directly proportional to speed through the water. This voltage is
amplified in the oscillator-amplifier, and is converted to pointer and synchro indica-
tions of speed in the indicator-transmitter. The speed signals are also converted to
distance, by means of a roller-and-disk mechanism in the indicator-transmitter. This
system has no orifice or moving parts external to the vessel, and has high precision
and accuracy from zero speed to full scale.

613. Speed measurement by dynamic water pressure.—When an object is moving
through a fluid such as water or air, its forward side is exposed to a dynamic pressure
which is proportional to the speed at which the object is moving, in addition to the
static pressure due to depth and density of the fluid above the object. When the fluid
is water, and ship speeds are involved, dynamic pressure is equal to

S2

P 8324

where P is dynamic pressure, S is speed through the water, and g is the acceleration
due to gravity (32.2 feet per second per second, approximately). If this formula is
solved for S, it becomes
S=1.353 /gP.
If 32.2 is substituted for g:
ST DSTI

Therefore, if dynamic pressure can be measured, this principle can be used for deter-
mining speed.

One of the most widely used means of measuring dynamic pressure is by a Pitot
tube. This device consists of a tube having an opening on its forward side or end.
If the tube is stationary in the water, this opening is subject to static pressure only.
But when the tube is in motion, the pressure at the opening is the sum of static and
dynamic pressures. This is called Pitot pressure or total pressure. The Pitot tube is
surrounded by an outer tube which has openings along its athwartship sides. Whether
the tube is stationary or in motion, these openings are subject to static pressure only.

| In the Pitot-static log (fig. 613) the Pitot tube is in the form of a vertical “rodmeter”
which extends through and is supported by a sea valve in the vessel’s bottom. The
tube extends 24 to 30 inches below the bottom of the vessel, into water relatively
undisturbed by motion of the hull. The two pressures, Pitot and static, are led to
separate bellows attached to opposite ends of a centrally pivoted lever. This lever is

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 129

LOW PRESSURE
!
IM
sec, CONTROL UNIT ss H
——— Vinss MA MS ui $ Á i
e

ROTARY DISTANCE TRANSMITTER HIGH PRESSURE

MASTER SPEED INDICATOR

ROD METER ——- |

SPEED A DISTANCE
INDICATOR

Courtesy of Pitometer Log Corporation.
FrcuRE 613.—A Pitot-static log.

130 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

electrically connected to a mechanism which controls the speed of a pump. When the
vessel is dead in the water, the pressures are equal, and the pump is stopped. When
the ship is moving, the pump speed is regulated so that the pressures in the two bellows
are egualized. Thus, the pump speed is proportional to the ship speed.

Through suitable gearing, the pump provides a mechanical output at the rate
of 60 revolutions per nautical mile. This rotation is transmitted electrically to the
master indicator, where the distance traveled appears on the distance counter in units
of 0.01 nautical mile. In addition, the master indicator has a timing device which
transforms distance and time into speed, the latter appearing on the speed dial

Both speed and distance indications may be transmitted to various repeaters
throughout the ship. Logs of this type have been replaced in ships of the US. N avy
by those of the electromagnetic type to provide both greater accuracy at each calibration
speed and over a given range of speeds. d l : E

In an early model of this type log, the two pressures from the Pitot tube are led
to opposite sides of a manometer. The difference in pressure is indicated by a pressure
gage graduated to read directly in knots. Distance is determined by a mechanical
integrator and cam attached to the speed dial.

Various less accurate instruments have been devised for determining speed by
measuring water pressure due to forward motion of the vessel. These are relatively
simple, inexpensive instruments intended primarily for use by small craft. One instru-
ment has a finger which the water pressure forces aft against a calibrated spring. A
flexible hydraulic cable transmits the motion to a speed indicator. Another instrument
uses a small scoop attached to the hull of the vessel. The pressure of the water scooped
up is transmitted by tubing to the speed indicator, which is essentially a pressure gage
graduated in knots. A third type measures the drag of a small towed object. The
accuracy of such devices depends to a large extent upon the refinements of design,
manufacture, installation, maintenance, and calibration.

614. Impeller-type log.—An impeller-type log has a small propeller-driven alter-
nating-current generator located near the outer end of a rodmeter which extends through
a sea valve on the hull plating, and projects approximately two feet into the water.
The propeller rotates as it moves through the water. The number ofits revolutions is
proportional to the distance traveled through the water, and its speed of rotation is
proportional to the ship's speed. The output of the generator is amplified, and passed
to the master indicator-transmitter, where the number of cycles, reduced by gearing, is
recorded on mileage counter dials in units of 0.01 nautical mile. "The frequency of the
alternating current, being proportional to ship speed, is transmitted to a tachometer
mechanism geared to the pointer of the speed indicator. Calibration is accomplished
by adjusting the position of driving rollers along the radius of a driven disk.

The speed and distance indications of the master indicator can be transmitted to
remote indicators. Speed indications of this equipment are accurate to approximately
0.15 knot at speeds between 0.25 knot and 25 knots.

615. Speed by engine revolution counter.—The number of turns of a propeller
shaft is proportional to the distance traveled. If the element of time is added, speed
can be determined. If the screw were advancing through a solid substance, the dis-
tance it would advance in one revolution would be the pitch of the screw. Thus, if a
propeller having a pitch of ten feet turns at 200 revolutions per minute, it advances
2,000 feet in one minute, equivalent to a speed of 19.75 knots. It does not do so in
water because of slip, the difference between the distance it would advance in a solid
substance and actual distance traveled, expressed as a percentage of the former. For
example, if slip is 18 percent, both the ship's speed and distance covered are reduced

by this percentage. "Thus, instead of 19.75 knots, the speed is only 19.75 X0.82=16.2
knots.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 131

Slip depends upon the type and speed of rotation of the propeller, the type of
ship, the condition of loading and ship's bottom, the state of the sea and the ship’s
course relative to it, and the apparent wind. Despite the many variables, slip can be
determined with sufficient accuracy for practical navigation. This is usually accom-
plished by steaming a known distance and noting the time of passage. The speed
corresponding to the number of revolutions being used can then be determined by
means of the formula of article 608, in the form

distance

Erde time

or by reference to table 18 (if the distance is exactly one mile). Thus, speed can be
determined directly, without computing slip, and a table or curve of ship speed for
various engine revolution speeds can be made. In determining speed in this manner,
the average speed of two runs (one in each direction) should be used. The vessel
should be on course and speed long enough to stabilize slip before starting each run.
Any suitable distance can be used, but a distance of one nautical mile has been measured
at various convenient locations. Each such measured mile is suitably marked on the
beach, and shown on the chart, with the course to steer.

This method of determining speed is widely used in the merchant marine. By means
of an engine revolution counter the number of revolutions during any suitable time
interval can be measured. If a tachometer is available, the rate of shaft revolution is
determined, usually in revolutions per minute. For best results, allowance should
be made for condition of the bottom, draft and trim of the vessel, and the state of the sea.

Depth Measurement

616. Importance.—Accurate knowledge of the depth of water under a vessel is
of such navigational importance that there is a legal requirement that American
merchant vessels of 500 gross tons or more engaged in ocean and coastwise service
“shall be fitted with an efficient mechanical deep-sea sounding apparatus in addition
to the deep-sea hand leads."

617. The lead (léd) is a device consisting of a suitably marked line having a
weight attached to one of its ends. It is used for measuring depth of water. Although
the lead is probably the oldest of all navigational aids, it is still a highly useful device,
particularly in periods of reduced visibility. Although its greatest service is generally
in the shoal water near the shore, it sometimes can provide valuable information when
the vessel is out of sight of land.

Two types of lead are in common use, the hand lead, weighing from 7 to 14 pounds
and having a line marked to about 25 fathoms; and the deep-sea (dipsey) lead, weighing
from 30 to 100 pounds and having a line marked to 100 fathoms or more in length.
The markings commonly used on lead lines are as follows:

Distance Distance
from lead from lead
in fathoms Marking in fathoms Marking
2 two strips of leather 20 short line with two knots
3 three strips of leather 25 short line with one knot
5 white rag (usually cotton) 30 short line with three knots
7 red rag (usually wool) 35 short line with one knot
10 leather with hole 40 short line with four knots
13 same as three fathoms 45 short line with one knot
15 same as five fathoms 50 short line with five knots
Ki same as seven fathoms etc.

132 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

Fathoms marked on the lead line are called marks. The intermediate whole
fathoms are called deeps. In reporting depths it is customary to use these terms, as
“by the mark five,” “deep six,” etc. The only fractions of a fathom usually reported
are halves and quarters, the customary expressions being “and a half, eight,” “less a
quarter, four,” etc. A practice sometimes followed is to place distinctive markings on
the hand lead line at each foot near the critical depths of the vessel with which it is to
be used. The markings should be placed on the lead line when it is wet, and the ac-
curacy of the marking should be checked from time to time to detect any changes in the
length of the line. The distance from the hand of the leadsman to the surface of the
water under various conditions of loading should be determined so that correct allow-
ance can be made when the marking nearest the surface cannot be observed.

The lead itself has a recess in its bottom. If this recess is filled with tallow or other
suitable substance, a sample of the bottom can sometimes be obtained. This informa-
tion can prove helpful in establishing the position of the vessel. If tallow is not avail-
able, some other substance can be used. Soap is suitable if it is replaced from time to
time. When the recess is filled for obtaining a sample, the lead is said to be armed
with the substance used.

618. The sounding machine, developed by William Thomson (Lord Kelvin) as a
substitute for the deep-sea lead, provides means for obtaining approximate soundings
to a depth of about 100 fathoms without slowing or stopping the vessel. This is ac-
complished by attaching a depth-registering device to the lead so that a vertical cast is
unnecessary.

Several types of depth-registering device have been developed, all depending upon
the increase of pressure with depth (art. 3008). The most common form is a slender glass
tube coated on the inside with a chemical which changes color when contacted by sea
water, or having a ground surface on the inside so that it appears white when dry and
clear when wet. The chemical tube requires recoating after each sounding, but the
ground glass tube can be used over and over again, if it is cleaned thoroughly and
allowed to dry after each using. The top of the tube is closed. As the lead sinks,
water is forced into the tube, compressing the entrapped air. The height to which
the water rises is an indication of depth. The upper end of a ground glass tube is
sealed with a cap which can be removed to facilitate cleaning and drying.

Errors are introduced if the inside diameter of the glass tube is not uniform through-
out its length, if the chemical has deteriorated, or if salt is not washed out of the ground
glass tube after use. Errors from these sources may be as much as 20 percent. If the
indicated depth is too great, a dangerous situation exists. A slight error may be
introduced by atmospheric pressure, but since the scale is calibrated for a lower-than-
normal pressure, the usual error is on the side of safety. For usual pressures, readings
are about three percent too little. If the temperature of the air is different from that
of the sea, the entrapped air will expand or contract as it is immersed in the water,
causing an error of about one percent for each 3° change of temperature. If the air
is cooled, the indicated depth is too great. Error will also be introduced if the cap
permits leakage of air.

| A mechanical depth recorder is sometimes used. This consists essentially of a
pointer which is attached to a piston forced against the tension of a spring as the water
pressure increases. The pointer remains at the greatest depth reached, requiring re-
setting before the next sounding is made.

In critical areas, it is wise to check the readings of a sounding machine, or to use
another method of sounding. If an echo sounder (art. 619) is not available, a check
can be made by stopping the vessel, running out a measured length of sounding wire

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 133

(at least 50 fathoms if depth permits), and comparing this measured length with the
indication of the depth-registering device.

Å 619. Echo sounder.—Most soundings are now made by means of an echo sounder.
This instrument produces an underwater sound-wave signal, and measures the elapsed
time until return of an echo from the bottom. Itis a form of sonar (art. 1108), although
this term is usually applied only to similar equipment which directs the sound-wave
signal horizontally to measure range. An echo sounder operating within the range of
audible sound (about 20 to 20,000 cycles per second) may be called a sonic depth
finder. One using sound
waves of a higher frequency
may be called an ultrasonic
depth finder. The trend has
been toward higher frequen-
cy, to reduce interference
from ship noise. caca

There are many forms of | INDICATOR
echo sounder. In a typical
installation (fig. 619) a light
tube is mounted vertically
behind an opaque shield which
rotates at a predetermined
speed. A narrow slot in the
shield permits the light to
be seen at one place only.
This slot is under or adjacent
to a circular scale graduated
in depth. The sound-wave
signal is transmitted when
the slot is at the top or zero
of the scale. At this instant,
the light flashes. When an
echo is received, the light
again flashes. The gradua-
tion adjacent to the second

flash indicates the depth.
Several different scales may FIGURE 619.—The indicator of an echo sounder.

be available for use in various

depths. The scale is controlled by adjusting the speed of rotation of the opaque shield.
If the depth is greater than the maximum graduation of the scale in use, an erroneous
reading may be obtained unless the operator is alert. Thus, if the maximum reading
is 400 fathoms, and the depth of the water is 600 fathoms, the shield will make a com-
plete rotation and half of another before the echo returns. The scale would indicate
a reading of 200 fathoms. If allowance is made for the number of complete rota-
tions, accurate soundings can be obtained at a relatively large scale. However, there is
less possibility of error if the correct scale is used. Doubt as to the correct scale can be
removed by switching to a smaller scale (greater depth), if one is available. In some
models the light itself rotates. Some of the newer echo sounders are equipped with a
recording device that produces a written trace of the bottom, called a bottom profile
(fig. 4206a). This is accomplished by means of an arm which moves across a graduated
tape, making one transit for each sounding. When the echo is received, a short line is
produced on a moving tape graduated in time and depth units.

134 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

Echo sounders of American manufacture are calibrated for a speed of sound of
4,800 feet per second. The actual speed varies primarily with the temperature, pres-
sure, and salinity, as discussed in article 3503, but in the ocean is nearly always faster
than the speed of calibration. The error thus introduced is on the side of safety unless
the water is fresh or very cold. Soundings shown on charts of the U. S. Navy Hydro- -
eraphic Office are those obtained by an echo sounder without correction, and can
therefore be compared directly with the readings obtained aboard ship since the varia-
tion in speed from mean conditions is not great. Only in precise scientific work should
it be necessary to correct the readings for actual sound speed under prevailing conditions.
Accurate adjustment can be made only if information is available on conditions at
various depths. *

Errors are sometimes introduced by false bottoms. If soft mud covers the ocean
floor, some of the sound-waye energy may penetrate to a harder layer beneath, resulting
in indication of two bottoms. It is not unusual in deep water to receive a strong return
at a depth of about 200 fathoms during the day, and somewhat nearer the surface at
night. This is called the phantom bottom or deep scattering layer. It is believed to be
due to large numbers of tiny marine animals. Schools of fish return an echo sufficiently
strong to make the echo sounder a valuable aid to commercial fishermen.

In modern equipment the sound waves, whether sonic or ultrasonic, are produced
electrically by means of a transducer, a device for converting electrical energy to sound
waves, or vice versa. The transducer utilizes either the piezo-electric properties of
quartz or the magnetostriction properties of nickel and its alloys.

Early models produced sound signals by striking the ship’s hull with a mechanical
hammer in the forward part of the vessel. The echo was received by a microphone in
the after part of the vessel, depth being determined by the angle at which the signal
returned.

Direction Measurement

620. Reference directions.—A horizontal direction is generally expressed as an
angle between a line extending in some reference direction and a line extending in the
given direction. The angle is numerically equal to the difference between the two
directions, called the angular distance from the reference direction. Unless the refer-
ence direction is stated or otherwise understood, the intended direction is in doubt.
Thus, to a navigator, direction 135° is southeast. To an astronomer or surveyor, it
may be northwest.

A number of reference directions are used in navigation. If a direction is stated in
three figures, without designation of reference direction, it is generally understood that
the direction is related to true (geographical) north. When grid navigation (art. 2510)
is being used, particularly in high latitudes, grid north is generally used as the reference
direction. The reference direction for magnetic directions is magnetic north, and that
for compass directions is compass north. For relative bearings it is the heading of the
ship. For amplitudes, the reference direction is east or west, usually 090° or 270° true,
but magnetic, compass, or even grid east or west may be used. In maneuvering situa-
tions, the heading of another vessel might be used as the reference direction.

The primary function of an instrument used for measuring direction is to determine
the reference direction. This having been done, other directions can be indicated by a
compass rose oriented in the reference direction. North is established by some form of
compass. A compass rose is attached to the north-seeking element so that other direc-
tions can be determined directly. However, if one always keeps in mind that the primary
function of the instrument is to indicate a reference direction, he should be able to avoid
some of the mistakes commonly made in the application of compass errors.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 135

621. Desirable characteristics of a navigational compass.—To adequately serve
its purpose, a navigational compass needs to have certain characteristics to permit it
to meet requirements of accuracy, reliability, and convenience.

The most important characteristic is accuracy. No other quality, however im-
portant or to whatever extent it may be possessed, compensates for the lack of accuracy.
This does not mean that the compass need be without error, but that such errors as it
may possess can be readily determined. Provision should be made for removing
deviation or reducing it to a minimum (ch. VII). If accurate horizontal directions
are to be determined, the compass needs to be provided with some type of compass
rose maintained in a horizontal position (art. 2903). Adequate sighting equipment is
needed if bearings are to be observed, and an index is needed to mark the forward
direction parallel to the keel if heading is to be measured. Accurate readings cannot
be expected from a compass that hunts (oscillates) excessively. A characteristic closely
related to accuracy is precision (art. 03). The amount of precision required varies
somewhat with the use and depends as much upon the steadiness of the compass and
its design as upon its inherent qualities.

A compass is reliable when its operation is not often interrupted; when its indica-
tions are relatively free from unknown or unsuspected disturbances; when it is little
affected by extremes of temperature, moisture, vibration, or the shock of gunfire; and
when it is not so sensitive that large errors are introduced by ordinary changes in condi-
tions or equipment near the compass.

The value of a compass is dependent somewhat upon the convenience with which
it can be used. Accuracy, too, may be involved. Thus, a compass should not be
installed in such a position that one must be in an unnatural or uncomfortable position
to use it. A compass intended for use in obtaining bearings is of reduced value if it
is installed at a location that does not permit an unobstructed view in most directions.
The compass graduations and index should be clean, adequately lighted if the instru-
ment is to be used at night, and clearly marked.

622. Kinds of compasses.—The compasses commonly used by the mariner are
(1) magnetic and (2) gyroscopic. The magnetic compass tends to align itself with the
magnetic lines of force of the earth, while the gyro compass seeks the true (geographic)
meridian. The word “compass”” is also applied to instruments which do not contin-
uously indicate some form of north. Thus, an aircraft directional gyro (art. 2803)
tends to remain approximately aligned with any great circle to which it is set. An
astro compass, sun compass, or sky compass (art. 2515) is used to determine the head-
ing or other reference directly at any given moment, by means of celestial bodies.

A compass may be designated to indicate its principal use, as a standard, steering,
or boat compass. The compass designated as standard is usually a magnetic compass
installed in an exposed position having an unobstructed view in most directions, per-
mitting accurate determination of error. Preferably, it is located at a magnetically
favorable position near the bridge. Before the development of a reliable gyro com-
pass, the standard compass was used for navigation of the vessel and for determining
the error of the steering compass.

Although the modern, reliable gyro compass has largely superseded the magnetic
compass for most purposes, directional information is so important to a vessel that the
availability of a second method is considered justified. It is wise to understand both
types, keep a record of errors and the performance of all compasses, and to compare
the indications of magnetic and gyro compasses at frequent intervals, as every half
hour when underway. gata |

623. Magnetic compasses.—1f a small magnet 1s pivoted at its center of gravity
in such manner that it is free to turn and dip, it will tend to align itself with the magnetic

136 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

field of the earth (art. 706). It thus provides a directional reference and becomes a
simple compass. However, such a compass would not be adequate for use aboard
ship. For this purpose a compass should have a stronger directive element than that
provided by a single, pivoted magnet, should have provision for measuring various
directions, should have some means of damping the oscillations of the directive element,
should be approximately horizontal, and should have some means of neutralizing local
magnetic influences.

In a mariner's compass, several magnets are mounted parallel to each other. To
them is attached a compass card having a compass rose to indicate various directions
(art. 624). Both magnets and compass card are enclosed in a bowl having a glass top
through which the card can be seen. The bowl is weighted at the bottom and 1s sus-
pended in gimbals in such manner that it remains nearly horizontal as the vessel rolls
and pitches. In nearly all modern compasses the bowl is filled with a liquid that
supplies a buoyant force almost equal to the force of gravity acting upon the directive `
element and card. This reduces the friction on the pivot (a metal point in a jeweled
bearing), and provides a means of damping the oscillations of the compass card. The
card is mounted in such manner as to remain in an essentially horizontal position.
A mark called a lubber's line is placed on the inner surface of the bowl, adjacent to
the compass card, to indicate the forward direction parallel to the keel when the bowl
is correctly installed. The gimbals used for mounting the compass bowl are attached
to a stand called a binnacle, which in most installations is permanently and rigidly
attached to the deck of the vessel, usually on its longitudinal center line. Most bin-
nacles provide means for neutralization of local magnetic influences due to magnetism
within the vessel. A cover or “hood” is provided to protect the compass from the
elements, dust, ete.

Directional information is of such importance that selection and installation of a
suitable compass should be made carefully, seeking such guidance as may be needed.
In the U. S. Navy this is covered by Bureau of Ships’ directives. For merchant
vessels and yachts, one would do well to consult a dependable compass adjustor before
selecting and installing a compass or making any alteration in the vicinity of the
compass. Common errors are the use of a compass designed for a different type craft
(as an aircraft compass in a boat), permitting chrome plating of a binnacle by someone
who does not know how to do this without creating a magnetic field, authorizing elec-
tric welding of steel near the compass, improper installation of magnetic equipment
or electric appliances near the compass, allowing short circuits to occur in the vicinity
of the compass, etc.

After the compass has been selected and installed, proper adjustment and com-

pensation (ch. VII) are important, and future care of the instrument should not be
neglected. It should be checked and overhauled at regular intervals, and any indica-
tion of malfunctioning or deterioration, however slight, should not be overlooked.
Discoloration of the liquid or the presence of a bubble, for instance, indicates a condition
that should be investigated and corrected at once. If it becomes necessary to add
liquid, one should be certain that he has the correct substance, and should attempt to
determine the source of the leak. Except as a temporary expedient, this is best done
by a professional. Some compasses should be protected from prolonged exposure to
sunlight, to prevent discoloration of the card and liquid.
M If a vessel is to be inactive for a long period of time—at least several months—
it is good practice to remove the magnetic compass from its binnacle and store it in a
place relatively free from magnetic influences, and of approximately even temperature.
Unless Instructions indicate otherwise, the compass should be stored upside down, to
remove the weight from the pivot, and prevent the card from swinging.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 137

624. The compass card is composed of light, nonmagnetic material. In nearly
all modern compasses the card is graduated in 360°, increasing clockwise from north
through east, south, and west. An older system still used somewhat is to graduate
the card through 90° in each quadrant, increasing from both north and south. Some
compass cards are graduated in “points,” usually in addition to the degree gradua-
tions. There are 32 points of the compass, 11%” apart. The four cardinal points
are north, east, south, and west. Midway between these are four intercardinal points
at northeast, southeast, southwest, and northwest. These eight points are the only
ones appearing on the cards of compasses used by the U. S. Navy. The eight points
between cardinal and intercardinal points are named for the two directions between
which they lie, the cardinal name being given first, as north northeast, east northeast,
east southeast, etc. The remaining 16 points are named for the nearest cardinal or
intercardinal point “by” the next cardinal point in the direction of measurement, as
north by east, northeast by north, etc. Smaller graduations are provided by dividing
each point into four "quarter points," thus producing 128 graduations altogether.
There are several systems of naming the quarter points. "That used in the U. S. Navy
when quarter points were used is given in table 2.

The naming of the various graduations of the compass card in order is called
boxing the compass, an important attainment by the student mariner of earlier gener-
ations. The point system of indicating relative bearings (art. 904) survived long
after degrees became almost universally used for compass and true directions. Except
for the cardinal and intercardinal points, and occasionally the two-point graduations,
all of which are used to indicate directions generally (as “northwest winds," meaning
winds from a general northwesterly direction), the point system has become largely
historical.

625. The U.S. Navy 712-inch compass has a liquid-filled bowl in which a 7%-inch
aluminum card is pivoted. "There is provision for either one or two pairs of magnets,
symmetrically placed. The card and magnet assembly is provided with a central
float or air chamber to reduce the weight on the pivot to between 60 and 90 grains
(0.14 and 0.21 oz.) at 60? F when the correct compass fluid is used. Older compasses
use a fluid consisting of 45 percent ethyl alcohol and 55 percent distilled water. Newer
compasses use a highly refined petroleum distillate similar to varsol. Use of this oil
increases the stability and efficiency of the compass. A hollow cone extends into the
underside of the float. The bottom of this cone is open. The pointed top has a jewel
bearing of synthetic sapphire. The card-float-magnet assembly rests on an osmium-
iridium tipped pivot at the jewel center. This pivot extends upward from the bottom
of the bowl. This compass is illustrated in figure 625.

The compass bowl is made of cast bronze, and has a tightly gasketed glass top
cover to prevent leakage of the liquid. A bellows-type expansion chamber is pro-
vided to allow for changes in volume of the liquid as the temperature changes. The
top rim or bezel of the bowl is accurately machined so that an azimuth or bearing
circle can be placed over it. The compass is equipped with a gimbal ring for keeping
the compass level when mounted in a binnacle. In addition to providing support for
the compass, the binnacle has provision for housing the correctors used to neutralize
local magnetic effects within the vessel.

626. The U. S. Navy six-inch compass is a newly developed instrument which
differs in a number of respects from older magnetic compasses. It is lighter in weight,
requires less space, and is expected to prove more reliable with less maintenance than
the 7%-inch compass. The six-inch diameter card is of magnesium foil, strengthened
by concentric and radial ribs. This card and the small, powerful Alnico V magnets
are sufficiently light in weight that a float is unnecessary. An osmium-tipped pivot

138 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

attached to the underside of the card, at its center, rests on a concave synthetic sap-
phire jewel in the top of a spindle attached to the bottom of the compass bowl. Expan-
sion of the liquid, an oil similar to varsol, is taken care ofbya bubble-trap type expansion
chamber. This chamber is in the form of a cylinder surrounding the card area and con-
nected to it by a single, small opening at the bottom. The top half, approximately, of the
expansion chamber is filled with air which is compressed as the liquid expands. As
the liquid contracts, the trapped air pushes more of it into the card area. This ar-
rangement eliminates the need for the troublesome bellows of older compasses. The
light for illuminating the compass card and lubber’s line is housed at the bottom of the
compass. Its intensity can be adjusted by a rheostat at the base of the binnacle.
Both the binnacle and pedestal upon which it stands are of cast aluminum. The
binnacle has provision for neutralizing the effects of the magnetism within the vessel,

Figure 625.—U. S. Navy 7%-inch compass.

and the pedestal houses electrical coils and resistor panels for reducing or eliminating
the magnetic effects introduced by degaussing (ch. VID). The soft iron correctors (ch.
VII), both quadrantal and Flinders bar, are thin-walled tubes supported in aluminum
spacers with heavier aluminum housings bracketed to the outer wall of the binnacle.
The quadrantal correctors can be slewed to reduce E error (ch. VII). Provision is
made for mounting the Flinders bar on either the forward or after side of the compass.

627. Other magnetic compasses.—In addition to the 7%-inch and 6-inch com-
passes, the U. S. Navy has a five-inch alcohol-and-water filled compass, and two three-
inch varsol-filled compasses. One of the three-inch compasses is top-reading like the
larger compasses, and the other has the graduations on the side of the beveled outer
edge of the card, so that the reading can be made through a window on the after side
of the compass bowl, in a manner similar to the reading of an aircraft compass mounted
on an instrument panel.

A wide variety of magnetic compasses are used in merchant ships and yachts.
The basic principles of operation of all magnetic compasses are the same, the various

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 139

types differing only in details of
construction. A feature which
is widely used in commercial
compasses is a hemispherical top F
(fig. 627) which provides magni- ear "lr M sec

Py, Mey

fication of the graduations.

An older type which is now
rarely encountered is the dry
compass, so called because it
does not have a liquid-filled
bowl. A typical dry compass
has a card of strong paper, with
the central part cut away and
the outer edge stiffened by
a thin aluminum ring. The
welght of the paper card is sus-
tained by 32 radial silk threads.
Eight small, magnetized steel
needles are suspended by silk
threads from the aluminum ring.

628. Magnetic compass
limitations.—Because of its es-
sential simplicity, a magnetic
compass does not easily become
totally inoperative. Being in-
dependent of any power supply or other service, a magnetic compass may survive
major damage to its ship without losing its utility. Small boat compasses often
remain serviceable under the most rigorous conditions.

Despite its great reliability, however, a magnetic compass is subject to some
limitations. Since it responds to any magnetic field, it is affected by any change in
the local magnetic situation. Hence, the undetected presence or change of position
of magnetic material near the compass may introduce an unknown error. Thus, an
error might be introduced by a steel wrench or paint can left near the compass, or by
a change in position of a steel boom or gun in the vicinity of the compass. Even such
small amounts of magnetic material as might be included in a pocketknife or steel keys
are sufficient to affect the compass if brought as close as they are when on the person
of an individual standing by a compass. Nylon clothing may also introduce error in
a magnetic compass. As distance from the compass increases, the strength of the
magnetic field needed to introduce an error increases. A cargo of large amounts of iron
or steel may be sufficient to affect the compass. The compass may also be affected by
changes of the magnetic characteristics of the vessel itself. Such changes may occur
during a protracted docking period, during a long sea voyage on substantially the
same course, when repairs or changes of equipment are made, if the ship sustains
heavy shock as by gunfire or riding out a heavy sea, if the vessel is struck by lightning,
or if a short circuit occurs near the compass.

The directive force acting upon a magnetic compass is the horizontal component
of the earth’s magnetic field. This component is strongest at or near the magnetic
equator, decreasing to zero at the magnetic poles (ch. VII). Near the magnetic poles,
therefore, the magnetic compass is useless (art. 2513), and in a wider area its indications
are of questionable reliability. The magnetic field of the earth has a number of local
anomalies due to the presence of magnetic material within the earth. During magnetic

Courtesy of Wilfrid O. White and Sons, Inc.

FIGURE 627.—A compass with a hemispherical top.

140 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

storms (art. 2526) it may be altered considerably. Changes in the magnetic. field
surrounding a vessel, due either to changes of the field itself or to change of position of
the vessel within the field, affect the magnetism of the vessel and the correctors used
to neutralize this effect, with a possible disturbance of the balance set up between them.

For these and other reasons, frequent determination of compass error 1s necessary
for safe navigation. Methods of determining and correcting compass error are discussed
in chapter VII. ad

629. Magnetic compass accessories.—Compass heading is indicated by the
lubber's line. Compass bearings may be measured by sighting across the compass,
bringing the object and the vertical axis of the compass in line. Accuracy in making
this alignment is increased by the use of a device to direct the line of sight across the
center of the compass. Perhaps the simplest device of this kind is a bearing bar, con-
sisting of two vertical sighting vanes mounted at opposite ends of a horizontal bar
having a small pivot which fits into a hole drilled part way through the glass cover of
the compass, at its center. The “near” vane (nearer the eye of the observer) has a
very thin, open, vertical slot through which the line of sight is directed; the “far”
vane has a thin, vertical wire or thread mounted on a suitable frame. The bar is rotated
until the object is in line with the two vanes. The bearing is the reading of the compass
in line with the vanes, on the far side from the observer. If a reflecting surface is pivoted
to the far vane to permit observation of the azimuth (art. 1428) of a celestial body,
the device is called an azimuth instrument. Bearing bars and azimuth instruments
are usually used only with smaller compasses, and never with an after-reading com-
pass (art. 627).

Larger compasses or repeaters (art. 641) are usually provided with a bearing circle
or azimuth circle (fig. 629). These devices take a variety of forms, but consist essen-
tially of two parts: (1) & pair of sighting vanes attached to a ring which fits snugly
over the compass, and (2) a mirror to reflect the compass graduation into the line of
sight. 'The use of these devices is similar to that of the bearing bar and azimuth
instrument. The azimuth circle has a pivoted reflecting surface attached to the far
vane, to permit observation of celestial bodies. In most cases it also has a reflecting
mirror and prism mounted on opposite sides of the ring, midway between the vanes.
The prism is covered with opaque material except for a thin, vertical slot at its center.
The surface of the mirror is curved so that reflection of sunlight falling upon it is in
the form of a slender vertical line (at the distance of the prism) of about the same
width as the slot. When the azimuth circle is adjusted so that this line of light falls
upon the slot, a thin, bright line appears on the compass card graduations at the bearing
of the sun. Most bearing and azimuth circles are provided with reverse compass ros?
graduations to permit reading of relative bearings or azimuths (by the vanes) at a
mark on top of the compass bowl, in line with the lubber's line; bubbles for indicating
the level position during observation; means for adjusting the snugness of the fit over
the compass bowl; and handles for turning the device.

If a bearing or azimuth circle does not fit snugly over the compass bowl, an error
might be introduced. Inaccuracy may also result from tilting cf the reflecting surface
of an azimuth circle with respect to the vertical plane through the line of sight. This
can be checked by comparing an azimuth of the sun observed by means of the prism
with one observed with the sighting vanes (with suitable protection being provided for
the eyes). Ifthe prism attachment is not available, a check can be made by comparing
observed (compass) azimuths at different altitudes with computed (true) values at the
time of observation. If both observed and computed azimuths are correct, the difference

between them will be constant (if the compass error remains constant throughout the
observation).

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 141

€, MARK ` `
e SE EE

AN oe:
e e S

Figure 629.— An azimuth circle.

None of the bearing or azimuth instruments described above can be used with a
compass not designed for it, as one having a hemispherical top, or an after-reading
compass.

Some modern magnetic compasses are provided with electrical pick-offs of sufficient
sensitivity that the instrument can be used to control such devices as remote indicators,
automatic steering equipment, course recorders, and dead reckoning equipment without
disturbing the reliability of the compass. However, these devices are more commonly
controlled by a gyro compass and hence are considered later in the chapter, after a
discussion of this type compass.

630. The gyroscope.— Leon Foucault, a French physicist, first demonstrated the
rotation of the earth by means of a pendulum. However, the pendulum was not
entirely acceptable as proof of rotation because it required the earth’s gravity for
operation. In 1852, he gave the name gyroscope to a toy top which had been known
for a quarter of a century as a “rotascope.” By means of the gyroscope, Foucault
illustrated the earth’s rotation without the use of gravity.

A conventional gyroscope consists of a comparatively massive, wheel-like rotor
balanced in gimbals which permit rotation in any direction about three mutually
perpendicular axes through the center of gravity. The three axes are called the spin
axis, the torque axis, and the precession axis, as shown in figure 630.

Since the rapidly spinning rotor is balanced at its center of gravity, it is in a state

142 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

of neutral rotational equilibrium. If the gimbal bearings were completely frictionless,
the spin axis would retain its direction in space despite any motion applied to the
system as a whole, as by the rotation of the earth. This property is called gyroscopic
inertia. Thus, if the spin axis were directed toward a star, the axis would continue to
point toward the star during its apparent motion across the sky. To an observer on
the earth, the spin axis would appear to change direction as the earth rotated eastward.
If the spin axis were placed parallel to the earth’s axis, the earth’s rotation would have
no effect and the device would become a kind of compass, since the spin axis would be
in the plane of a meridian. However, such a device would require frictionless bearings
and perfect balance. Even if these obstacles could be overcome, the device would not
be suitable as a compass because it would not be north-seeking.

The method by which a gyroscope is made to seek north involves the surprising
behavior exhibited by any rotating mass, when a force is applied which tends to change
the direction in space of the spin
axis. The motion resulting from
such a force is not in line with
the force, as might be expected,
but perpendicular to it. This
property is called gyroscopic
precession.

Refer to figure 630 and sup-
pose that the torque and spin
axes are horizontal, that the spin
axis is directed north and south,
and that the rotation about the
spin axis is clockwise, looking
north. If a force is applied to
the rotor at A tending to raise
the south end of the spin axis,
the south end, if free to move,
wil turn or “precess’’ to the
east, as shown. The direction
of precession is such that it ap-
pears as though a force applied
Figure 630.—Axes of a gyroscope, and the direction of ee un REN md “Ps

precession. plied at a point 90° away in

the direction of spin from point A.

Precession tends to move the plane and direction of rotation of the gyroscope into align-

ment with the force applied to the rotor. If precession is prevented, as by restrain-

ing motion of the spin axis, this axis will rotate in the direction of the applied force,

as if the rotor were not spinning. Thus, in figure 630, a force applied to the rotor at

A causes the south end of the spin axis to rise. The reason for this is that if precession

is blocked, the force thus introduced causes precession in the direction of the original

force. This effect is used to stabilize some types of gyro compasses and avoid cumula-
tive errors due to rolling while the vessel is on intercardinal headings.

A recently developed gyroscope called a Gyrotron vibratory gyro uses a vibrating
mass instead of a rotating one. It is based upon the same principle used in the halteres
of certain two-winged insects, such as the common housefly, to give them the sensing
needed to achieve stability in flight. Instead of a single vibrating reed, the vibratory
gyro uses a two-pronged device similar to a tuning fork. The vibratory gyro has no
bearings, and so is free from the errors introduced by bearing friction.

It is a rugged

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 143

CASA having long 2 and requiring little attention. Its most promisiug application is
easurement of rate of turn, which it performs more accurately than a rotating
gyro, and over a wide range from a rate of as little as one or two degrees per hour to 100
revolutions or more per minute. The Gyrotron vibratory gyro has a number of
possible applications to navigation.
631. The gyro compass.—A gyro compass is essentially one or more north-seeking
gyroscopes with a suitable compass rose, housing, etc.
à One method of utilizing precession to cause a gyroscope to seek north is illustrated
in figure 631a. Two reservoirs connected by a tube are attached to the bottom of the
case enclosing the gyro rotor, with one reservoir north of the rotor and the other south
ofit. The reservoirs are filled with mercury to such a level that the weight below the
spin axis is equal to the weight above it, so that the gyroscope is nonpendulus. The
system of reservoirs and connecting tubes is called a mercury ballistic. In practice,
there are usually four symmetrically placed reservoirs.

SOUTH
RESERVOIR . NORTH
RESERVOIR

Figure 631a.— The mercury ballistic (left) and the elliptical path (right) of the axis of spin without
damping.

Suppose that the spin axis is horizontal but is directed to the eastward of north.
As the earth rotates eastward on its axis, the spin axis tends to maintain its direction in
space; that is, it appears to follow a point, such as a star rising in the northeastern sky.
With respect to the earth, the north reservoir rises and some of the mercury flows under
the force of gravity into the south reservoir. The south side becomes heavier than the
north side, and a force is applied to the bottom of the rotor case at point A. If the gyro
rotor is spinning in the direction shown, the north end of the spin axis precesses slowly
to the westward, following an elliptical path. When it reaches the meridian, upward
tilt reaches a maximum. Precession continues, so that the axis is carried past the
meridian and commences to sink as the earth continues to rotate. When the sinking
has continued to the point where the axis is horizontal again, the excess mercury has
returned to the north reservoir and precession stops. As sinking continues, due to
continued rotation of the earth, an excess of mercury accumulates in the north reservoir,
thus reversing the direction of precession and causing the spin axis to return slowly to
its original position with respect to the earth, following the path shown at the right of
figure 631a. One circuit of the ellipse requires about 84 minutes.

144 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

FIGURE 631b.—Spiral path of the axis of spin with damping.

The elliptical path is sym-
metrical with respect to the
meridian, and, neglecting fric-
tion, would be retraced indefi-
nitely, unless some method of
damping the oscillation were
found. One method is by off-
setting the point of application
of the force from the mercury
ballistic. Thus, if the force is
applied not in the vertical plane,
but at a point to the eastward
of it, as at B in figure 631a, the
resulting precession causes the
spin axis to trace a spiral path
as shown in figure 631b, and

eventually to settle near the meridian. The gyroscope is now north-seeking and can
be used as a compass. Some compasses are provided with means for automatically
moving the point of application to the center line during a large change of course or

speed, to avoid introduction of a temporary error.

Courtesy of the Sperry Gyroscope Co.

Figure 631c.— The Mark 14 Mod 2 gyro compass.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 145

Another method of damping the oscillations caused by the rotation of the earth is
to reduce the precessing force of a pendulous gyro as the spin axis approaches the
meridian. One way of accomplishing this is to cause oil to flow from one damping tank
to another in such a manner as to counteract some of the tendency of an offset pendulous
weight to cause precession. Oscillations are completely damped out in approximately
one and one-half swings.

Details of construction differ considerably in the various compasses. Each in-
strument is provided with a manual giving such information and operating instructions.
Figure 631c illustrates the Mark 14, Mod 2 gyro compass, a type that is widely used
in the U. S. Navy and the merchant marine. The Mark 23 Mod 0 gyro compass,
illustrated in figure 631d, is a much smaller compass recently developed in accordance
with U. S. Navy specifications
to provide an instrument that
can be used in vessels of many
types.

632. Desirable character-
istics of the gyro compass.—
Since a gyro compass is not
aftected by a magnetic field,
it is not subject to magnetic
compass errors (ch. VII), nor
is it useless near the earth’s
magnetic poles. If an error is
present, it is the same on all
headings, and no table of cor-
rections is needed. The direc-
tive force is sufficiently strong to
permit directional pick-off for
use in remote-indicating repeat-
ers, automatic steering, dead
reckoning and fire-control equip-
ment, course recorders, etc.

633. Undesirable charac-
teristics of the gyro compass.—
A gyro compass is dependent
upon a source of suitable electric Courtesy of the Sperry Gyroscope Co.
power. Figure 631d.— The Mark 23 Mod 0 gyro compass.

If operation of the compass
is interrupted long enough to permit uncertainty in its indications, a considerable
period (as much as four hours for some gyro compasses) may be needed for it to settle
on the meridian after it reaches operating speed. This period can be reduced by
orienting the compass in the proper direction before it is started. If this is not
practicable, the settling period can be hastened by leveling the compass when it
reaches the meridian (one-fourth of a cycle or 21 minutes after starting at maximum
deflection) or by leveling and precessing the gyro to the approximate meridian after
its direction and rate of precession are observed for several minutes. Either process
may need to be repeated several times and followed by a settling period.

The gyro compass is subject to certain errors requiring applications of corrections,
either manually or automatically (art. 634).

The compass is an intricate mechanism of many parts. Thus, it requires some
maintenance. In heavy seas a gyro compass may become unreliable unless certain

146 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

features are included in the design—features which are generally omitted from the
smaller, simpler compasses. |

The directive force of a gyro compass decreases with latitude, being maximum
at the equator and zero at the geographical poles. The compass remains usable at all
latitudes thus far attained by surface vessels, except those which have become beset
and drifted with the ice across the Arctic Ocean. The use of the gyro compass in high
latitudes is discussed in articles 640 and 2514.

A gyro compass has generally been considered unsuitable for use in aircraft because
of its weight and the question of whether it will operate at the high speeds (approaching
or exceeding that of rotation of the earth) and accelerations to which it would be sub-
jected in aircraft. A gyro compasss weighing only nine pounds has been developed
for use in small craft. A light compass designed for use in aircraft is being developed
and evaluated.

634. Gyro compass errors.—Gyro compasses are subject to several systematic
errors (art. 2903). Some of these can be eliminated or offset in the design of the compass,
while others require manual adjustment for their correction.

The total combined error (the resultant error) at any time is called gyro error (GE),
which is expressed in degrees east or west to indicate the direction in which the axis
of the compass is offset from true north. If the gyro error is east, the readings are too
low; and if it is west, they are too high. Thus, if GE is 1° W, 1° is subtracted from all
readings of the compass, either headings or bearings, to determine the equivalent true
directions. One degree is added to all true directions to determine the equivalent gyro
directions. The gyro error of modern compasses is generally so small that it can be
ignored for practical navigation. However, significant errors can be introduced in
several ways, and it is good practice to compare the gyro heading with the magnetic
heading at frequent intervals (as every half hour and after each change of course)
and to check the accuracy of the gyro compass by celestial observation or landmarks
from time to time (as every morning and afternoon when means are available).

The errors generally associated with the gyro compass are speed error, damping
error, ballistic deflection error, quadrantal error, and gimballing error. In addition,
gyro compasses are subject to the errors common to directional instruments, such as
those introduced by inaccurate graduation of the compass rose or incorrectly located
lubber’s line. Error may also be introduced, of course, by malfunctioning of the
compass.

635. Speed error is introduced by motion of the vessel along its track. Refer to
figure 635a. If a vessel is at anchor at any point A, it is being carried eastward by
rotation of the earth at the rate of 902.46 minutes of longitude per hour (with respect
to the stars). In terms of knots, this is equal to 902.46 times the cosine of the latitude,
approximately. Because of the ellipticity of the earth, the actual value is a little more
than this in low latitudes, and a little less in high latitudes. The actual value at any
latitude can be found by multiplying the length of a degree of longitude at that latitude
(from table 6) by 20550 15.041.

This eastward motion due to rotation of the earth is shown in figure 635a by the
vector AB. The north-south axis of the gyro compass settles in a direction 90° from
the direction of motion. Therefore, if the vessel is stationary with respect to the earth,
0° on the compass card coincides with a true meridian, and no error is introduced. This
is also true if the vessel is moving due east or due west. In this case the speed of the ship
over the surface of the earth is added to or subtracted from the motion due to rotation of
the earth, but the direction of motion is unchanged (unless the speed of the vessel is

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 147

greater than the rotational
speed of the earth, and in the
opposite direction). The only
effect, therefore, is to strengthen
or weaken the directive force,
usually by a small amount.

If the vessel is on course
north or south, as shown by
the vector AC in figure 635a,
the motion in space is tilted
toward the north or south of
due east. In this case, it is the
vector sum (art. O18) of the mo- W
tion due to rotation of the earth
and the velocity of the vessel
over the surface of the earth, or
AD in figure 635a. Since AD
is not due east, the perpendicu-
lar to it does not lie in the true
meridian, but at some angle 6 to
it, along AM,. Since the axis
of the gyro lies along AM,, the
“virtual meridian,” the angle
is the error introduced by the FIGURE 635a.—Speed error.
motion of the vessel along its
track. Since AD is perpendicular to AM,, and AB is perpendicular to AC, angle BAD
is equal to angle 6. Therefore, the angle 6 can be found by the formula

AC
tan R
Since AC is the speed of the vessel and AB is 902.46 cos L, approximately, the formula
can be written S
tan 902.46 cos L

where S is the speed and L the latitude of the vessel.

If the course of the vessel is not a cardinal direction, the resultant is still the
vector sum of the two speed vectors, and can be found graphically or by computation.
One method is to resolve the vessel's speed vector into two components, as shown in
figure 635b, obtaining the N-S component along the true meridian, and the E-W
component in the direction of rotation of the earth.
The N-S component is equal to S cos C, and the
E-W component to S sin C, where C is the true
course angle. The total N-S motion is then S cos C.
The total easterly motion is that due to rota-
tion of the earth plus or minus the E-W com-
ponent of the ship's speed across the surface
of the earth, or 902.46 cos L+S sin C, approx-
E-W COMPONENT imately. The term S sin C is positive (+) for
easterly courses and negative (—) for westerly
The formula for finding 6 now becomes

N-S COMPONENT

Figure 635b.—Components of
vessel's motion. courses.

148 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

S cos C
902.46 cos L+S sin C

tan 6= (approximately).

At ship speeds in latitudes less than 70°, the term S sin C is much smaller than
902.46 cos L and has so little effect upon the answer that it can be ignored. The
angle ¿ is small enough that its tangent can be considered the angle itself (expressed
in radians). Thatis, a tangent to a circle can be considered of the same length as an
arc of the circle over a short distance from the point of tangency. Therefore, the
formula for 6 can be written

5—73 S cos C
~ 902.46 cos L

or
5=0.0635 S cos C sec L.

As shown in this formula, the speed error 6 is affected by the three variables,
speed, course, and latitude. If the course has a northerly component, the error is
westerly; and if it has a southerly component, the error is easterly.

Example —A ship at latitude 30°N is steaming on true course 045°, at a speed
of 20 knots.

Required.—Speed error.

Solution.—
0.0635 log 8.80277
S 20 kn. log 1.30103
C N45°E Leos 9. 84949
L 302 N l sec 10. 06247
6 1204 W log 10. 01576

Answer.— 6 1204 W.

In most gyro compasses this error is corrected mechanically. Speed and latitude
are set in by hand, and the cosine of the course is introduced automatically by means
of a “cosine cam" running in an eccentric groove on the underside of the azimuth gear.
In some compasses these corrections combine to offset the lubber’s line by the correct
amount. Small changes in speed or latitude have relatively little effect upon the
result. Therefore, in normal operations, infrequent changes are sufficient for satis-
factory results. If no provision is made for mechanically applying this correction, a
table or curves can be used to indicate the correction to be applied mathematically
to readings of the compass. These are made up from the formula given above, and.
are entered with the speed, course, and latitude (art. 640).

636. Damping error applies only to those gyro compasses in which damping is
accomplished by offsetting the point of application of the force from a mercury bal-

listic (art. 631). For this reason it is sometimes called ballistic damping error. It
can be found from the equation

a=r tan L

in which a is the damping error, r is the angle between the vertical through the spin
axis of the gyro rotor and a line through this axis and the point of application of the
force from the mercury ballistic (1°7 for Sperry compasses), and L is the latitude.
The error is easterly in north latitude and westerly in south latitude.

Example.—A gyro compass having a value of r of 197 is at latitude 50% N.
Required —The damping error.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 149

Solution.—
«=r tan L

=1°7X1.1918

=2°03 E
Answer.—a=2°03 E.

As in the case of speed error, provision is made in most compasses (to which it
applies) for correcting this error. An auxiliary latitude-correction scale is provided
for this purpose. In some compasses this offsets the lubber’s line. In others, it
alters the position of a small weight attached to the casing near one end of the axle.
The first method is preferable because it is unaffected by changes of gyro speed of
rotation.

If this error is not corrected mechanically, it can be combined algebraically with
speed error and a single set of tables or graphs made up. This is a method sometimes
used in polar regions, beyond the scale of the latitude corrections (arts. 640, 2514).

637. Ballistic deflection error.—When the north-south component of the
speed changes, an accelerating force acts upon the compass, causing a surge of
mercury from one part of the system to another, or a deflection (along the meridian)
of the mass of a pendulous compass. In either case, this is called ballistic deflection.
It results in a precessing force which introduces a temporary ballistic deflection
error in the readings of the compass unless it is corrected.

A change of course or speed also results in a change in the speed error, and unless
the correcting mechanism responds promptly to this change, a temporary error from
this source is also introduced. The sign of this error is opposite that of the ballistic
deflection, and so the two tend to cancel each other. If they are of equal magnitude
and equal duration, the cancellation is complete and the compass responds immedi-
ately and automatically to changes of speed error. This can be accomplished by de-
signing the compass so that

= 0.0211 sec L

in which B is the pendulous moment of a pendulous compass and the couple per unit
angle applied by a mercury ballistic, H is the angular momentum of the gyro rotor,
and L is the latitude.

SED
It is customary to design a gyro compass so that the ratio H B correct for some

particular latitude (as 41? or 45?) and accept the small residual error that is tem-
porarily present at other latitudes. This is satisfactory for vessels which remain within
relatively narrow limits of latitude, or which are seldom subjected to large accelerating
forces. However, where these conditions are not met, provision is made for varying
the ratio with latitude. In a compass having a mercury ballistic, this is customarily
accomplished by moving the mercury reservoirs radially toward or away from the center
of the compass, thus altering the value of B. In a pendulous gyro, the value of H
is changed by altering the rotational speed of the gyro.

When the ratio E is as given in the equation above, the period of oscillation about

the vertical axis is given by the equation

SE
SET g

150 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

in which T is the period in minutes, R is the radius of the earth in feet (approximately
20,900,000) and g is the acceleration due to gravity (approximately 32.2 feet per second
per second). Substituting in the formula,

20,900,000
T=0.1047,/ ood

—84 minutes (approximately).

This is sometimes stated as the period of a pendulum having a radius equal to
the radius of the earth, since the equation for a short pendulum is the same as that
given above with / (length) being substituted for R. More accurately, it is the period
of a pendulum of infinite length with its bottom at the surface of the earth, or the
largest period that a simple pendulum can have when acting under the gravitational
force of the earth. When a device is adjusted so as to have this period it is said to be
“Schuler tuned,” after Ivan Schuler, a German scientist who discovered the relation-
ship. It is because of this tuning of the gyro compass that one oscillation occurs in
about 84 minutes, and that the maximum effect of certain disturbing forces occurs
about 21 minutes (one-fourth cycle) after application of the force.

638. Quadrantal error.—If a body mounted in gimbals is not suitably balanced, a
disturbing force causes it to swing from side to side. A swinging body tends to rotate
so that its long axis of weight is in the plane of the swing. The rolling of a vessel intro-
duces the force needed to start a gyro compass swinging. The effect reaches a maximum
on intercardinal headings, midway between the two horizontal axes of the compass,
and changes direction of error in consecutive quadrants. "This is called quadrantal
error, or sometimes intercardinal rolling error. It is corrected by the addition of weights
to balance the compass so that the weight 1s the same in all directions from the center.
Without a long axis of weight, there is no tendency to rotate during a swing.

A second cause of quadrantal error is more difficult to eliminate. As a vessel rolls,
the apparent vertical is displaced first to one side and then to the other, due to the
accelerations involved. The vertical axis of the gyro compass tends to align itself with
the apparent vertical. If the vessel is on a northerly or southerly course, the pivot of
the compass is displaced from the vertical, resulting in a precession first to one side,
then to the other. The effect is negligible and would be exactly balanced if suc-
cessive rolls on opposite sides were equal. On an easterly or westerly heading, the pivot
remains under the gyro axle, but the dynamic effect of the roll, acting upon the damping
mechanism, introduces a precessing force which causes an error. However, the period
is short and the error is in opposite directions on opposite rolls, so the effect is negligible.
On noncardinal headings, both effects are present, and the relationship is such that
the error is in the same direction regardless of the direction of roll. Thus, a persistent
error is introduced, which changes direction in successive quadrants. This error is
generally eliminated by the use of a second gyroscope. In some compasses, this is in
the form of a small gyroscope called a floating ballistic which stabilizes the point of
application of the mercury ballistic with respect to the true vertical as the vessel rolls.
In others, two gyroscopes are used for the directive element and these are so installed
that they tend to precess in opposite directions. Thus, they neutralize each other.
Another way of eliminating this error is to design the mercury ballistic system so that
the surge of liquid due to north-south component of the roll is diminished in amount
and delayed so ¿hat it is about a quarter of a cycle out of phase with the roll.

639. Gimballing error is that due to tilt of the compass rose. Directions are
measured in the horizontal plane. If the compass card is tilted, the projection of its

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 151

outer rim onto the horizontal is an ellipse, and the graduations are not equally spaced
with respect to a circle. This error, which applies to all instruments making use of a
compass rose that can be tilted, is discussed in article 2903. For normal angles of tilt,
this error is small and can be neglected. For accurate results, readings should be made
when the card is horizontal. This error applies to the reading of the compass or its
repeaters (art. 641), rather than to the compass itself. If the compass and its repeaters
are installed so that the outer gimbals are in the longitudinal axis of the vessel, this
error is minimized.

640. Use of the gyro compass in polar regions is discussed in article 2514. If
means are not available for determining an equivalent setting or correction, a correction
graph can be constructed. Ballistic deflection error, quadrantal error, and gimballing
error are temporary or corrected in the design of the compass, and so can be ignored.
Speed error and damping error (if it applies to the particular compass involved) can
be combined into a single table or curve of corrections, using the formulas of articles
635 and 636. In high latitudes the east-west component of the vessel’s speed is sig-
nificant, and the error may be too large to consider its tangent equal to the angle
itself expressed in radians. Therefore, the applicabie formulas are:

S cos C
EE (1)

a=r tan L. (2)

The only approximation remaining is the use of 902.46, which varies slightly with
latitude. The error thus introduced is not significant. The U. S. Navy Bureau of
Ships' curves for latitude 80% are shown in figure 640. From the intersection of the
appropriate speed curve and the radial line representing the true course (interpolating
if necessary) a horizontal line is drawn to the vertical line through the origin, where
the correction is indicated. To construct the curve for speed 35 knots, proceed as
follows:

(1) Compute the speed error, à, for true courses at intervals of perhaps 30%. As
an example, the error for course 210? (C S30% W) is:

à 35 <0.86603
tan 0—502.46 X0.17365—35 X0.50000
5021773.
051295. E.

The error is easterly because the course has a southerly component (art. 635).
(2) Compute the damping error. The curves of figure 640 are for a value of r
Otel. 7 :
a=1°7X5.6713=9°6E.

In northern latitudes damping error is easterly.

152 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

unt
ul
SE
FUIL Lis
EDT
Á
N

r
m
i
i

SERE
S
Aa las di

=

N

ET RH
ØK Š

Seit

XUI

c

Iu
EE

7

TK
e E Í
Na

Din’.

gi

za
Iu

E
S
X

DY
ER

li
UI
CITT?
FINI
H
E

ÉS
Bes

øl
|
T
H
Em
[||
I EZ

Md
SES
ESA

ee
j
AZ)
3
e
mr

ex
RI
ZAN A XL
RY

FIGURE 640.—Gyro compass error curves for latitude 80°.

(3) Combine 6 and a algebraically to obtain gyro error (GE):

TC 6 a GE

o o o o

000 12.6 W 9.6 E 3.0W
030 9.0W 9.6 E 0.3W
060 5.3W 9.6 E 4.3 E
090 0. 0 9.6 E 9.6 E
120 5.3 E 9.6 E 14.9 E
150 9.9 E 9.6 E 19.5 E
180 12.6 E 9.6 E 22.2 E
210 12.3 E 9.6 E 21.9 E
240 7.9 E 9.6 E 17.5 E
270 0. 0 9.6 E 9.6 E
300 7.9 W 9.6 E AN
330 12.3 W 9.6 E TS VV,

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 153

(4) To draw the curve, select a convenient origin and label this with the value of
a. Draw a vertical line through the origin and mark off a convenient scale such that
all values of ¿ can be shown both above and below the origin. The zero on this scale
is at point a units above the origin (below in the southern hemisphere). Label the
scale according to GE. Through the origin draw various radial lines at any convenient
interval to represent true courses. For each computed course draw a horizontal
construction line from the GE on the central scale to the appropriate radial line. The
intersection of each pair of lines is one point on the curve. Connect all such points
with a smooth curve, and erase the construction
lines. If a straightedge or graph paper is used,
the construction lines need not be drawn.

It is good practice to draw the curve for the
highest speed first, to be sure that succeeding curves
will fit on the paper. From such curves the gyro
courses corresponding to various true courses can
be determined and the radial lines labeled with
these values for converting gyro directions to true
directions.

The curves described in this article are for use
when all correctors are set on zero, or if no provision
is made for mechanically correcting for speed and
damping errors. If the compass does not have a
mercury ballistic, the damping error is omitted from
the calculations and curves.

641. Gyro compass repeaters.—A gyro compass
is customarily located at a favorable position below ;
decks, and its indications transmitted electrically E
to various positions throughout the vessel. Each
repeater consists of a compass rose on a suitable
card so mounted that the direction of the ship’s
head is indicated at a lubber's line. Although the
repeater may be mounted in any position, including

ea A.

vertically on a bulkhead, it is generally placed in |
gimbals in a bowl, similar to the mounting of a M
compass, which it resembles (fig. 641). This is true

particularly of repeaters used for obtaining bearings. d e

A gyro repeater used primarily to indicate the

adi is sometimes called a ship’s course
SIT? dus < P Courtesy of Ahrendt Instrument Co,

indicator. AE A y
1 = s 1 IGURE E gyro repeater use
Gyro compass indications are also used in PUR M
automatic steering devices, direction-stabilized radar 2 Mod 5).

scopes, wind indicators, fire control equipment, etc.

A compass used to control other equipment, particularly repeaters, is sometimes
called a master compass. In the case of a gyro compass, it is usually called a master
gyro compass. It is good practice to check all repeaters periodically with the master
compass to insure continued synchronization. ds

642. Alidade.—A gyro repeater with a telescopic sight mounted over it is called
an alidade. If the telescopic sight is mounted so that it remains pointed in the same
gyro direction regardless of motions of the vessel, the instrument is called a self-
synchronous alidade. This instrument will retain its setting until oriented to a new

gyro direction.

154 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

643. Pelorus.—Although it is desir-
able to have a compass, a compass repeat-
er, or an alidade for obtaining bearings,
satisfactory results can be obtained by
means of an inexpensive device known as
a pelorus (fig. 643). In appearance and
use this device resembles a compass or
compass repeater, with sighting vanes or a
sighting telescope attached, but it has no
directive properties. That is, it remains at
any relative direction to which it is set.
It is generally used by setting 000° at the
lubber’s line. Relative bearings are then
observed. They can be converted to bear-
ings true, magnetic, grid, etc., by adding
the appropriate heading. The direct use

Courtesy of Wilfrid O. White and Sons, Inc. of relative bearings is sometimes of value.

FIGURE 643.—A pelorus. A pelorus is useful, for instance, in deter-

mining the moment at which an aid to

navigation is broad on the beam. It is also useful in measuring pairs of relative

bearings for use with table 7 or for determining distance off and distance abeam without
a table (art. 910).

If the true heading is set at the lubber’s line, true bearings are observed directly.
Similarly, compass bearings can be observed if the compass heading is set at the lub-
ber’s line, etc. However, the vessel must be on the heading to which the pelorus is set
if accurate results are to be obtained, or else a correction must be applied to the ob-
served results. Perhaps the
easiest way of avoiding error is
to have the steersman indicate
when the vessel is on course.
This is usually done by calling
out “mark, mark, mark” as
long as the vessel is within a
specified fraction of a degree of
the desired heading. The ob-
server, who is watching a dis-
tant object across the pelorus,
selects an instant when the
vessel is steady and is on course.
An alternative method is to have
the observer call out “mark”
when the relative bearing is
steady, and the steersman note
the heading. If the compass is
swinging at the moment of
observation, the observation
should be rejected. "The num-
ber of degrees between the
desired and actual headings is
added if the vessel is to the right
of the course, and subtracted if

Courtesy of Sperry Gyroscope Co.
FIGURE 644.—A course recorder.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 155

to the left. Thus, if the course is 060° and the heading is 062° at the moment of
observation, a correction of 2° is added to the bearing.

l Each observer should determine for himself the technique that produces the most
reliable results.

644. Course recorder.—A continuous graphical record of the headings of a vessel
can be obtained by means of a course recorder (fig. 644). In its usual form, paper
with both heading and time graduations is slowly wound from one drum to another,
its speed being controlled by a spring-powered clockwork mechanism. A pen is in
contact with the paper, tracing a line to indicate the heading at each moment. The
pen is attached to an arm controlled by indications from a compass, usually the master
gyro compass.

645. Dead reckoning equipment.—The primary navigational functions of dead
reckoning equipment (DRE) are to (1) provide continuous indications of the vessel's
present latitude and longitude, and (2) provide a graphical record of the vessel's dead
reckoning track. In addition, most types of dead reckoning equipment provide means
for tracking one or more other craft, to obtain a graphical record of the other craft’s
course and speed. This equipment is generally installed only on warships.

Dead reckoning equipment consists in general of four components: (1) an analyzer;
(2) latitude and longitude indicator dials; (3) a desk-size unit called a dead reckoning
tracer (DRT), usually installed in the chart house; and (4) a glass plotting surface over
the dead reckoning tracer.

The analyzer receives directional signals from the vessel's gyro compass, and dis-
tance signals from the underwater log. The course and distance data are transformed
automatically to electrical signals proportional to the north-south and east-west com-
ponents of the vessel’s movement. These distance signals are transmitted to the
latitude and longitude indicators, changing their readings by the correct amount to
indicate the new latitude and the new longitude in degrees and minutes. Since the
number of miles in the north-south component of distance traveled is nearly equal to the
change in latitude expressed in minutes, the latitude indicator is fed directly. Depar-
ture (art. 204) is automatically transformed to difference of longitude before being
registered on the longitude indicator dials. If the indicator dials are correctly set to
latitude and longitude, they continuously show subsequent dead reckoning positions
of the vessel.

The north-south and east-west component signals from the analyzer are also
transmitted to the DRT (fig. 645), where they control the motion of a pencil which
moves across a chart or plotting sheet attached to the DRT base. The pencil draws
a line which conforms to the maneuvers of the vessel. The mechanism can be set to
plot the track at any scale from 1⁄4 mile per inch ( mile on some) to 16 miles per inch.
A clock-controlled contact lifts the pencil from the paper for 15 seconds of each minute
and for a longer period each 10 minutes, thus providing automatic time measurement.
The pencil carriage can be moved manually to any part of the chart for initial setting
and the direction of travel can be adjusted so that the chart can be placed with any
cardinal direction “up.”

The cover of the DRT is a sheet of glass to which a plotting sheet or blank paper
can be fastened. An electric lamp on the top of the pencil carriage throws a spot of
light through the paper directly over the carriage, thus providing a moving reference
scaled to the course and speed of the vessel. If the position of the spot of light is
marked periodically on the paper, a second record of the vessel’s track is obtained.
However, the principal use of this sheet is for plotting successive positions of another
craft, using the spot of light as the origin. A polar grid centered on the light may be
projected onto the paper to facilitate measurement. The course of the other vessel

156 INSTRUMENTS FOR PILOTING AND DEAD RECKONING

Courtesy of Ahrendt Instrument Co.

Figure 645.—A dead reckoning tracer.

can be measured directly from the plot, and its speed can be determined by means of
the time needed to travel any distance measured on the plot. This process is called
tracking. If the ranges and bearings are plotted from a fixed point, relative movement
is determined, a practice commonly followed in connection with radar (art. 1212)

While dead reckoning equipment is a great convenience, particularly when changes
of course or speed are numerous, its indications should be checked by graphical plot
on the chart or plotting sheet. Reliable dead reckoning is too important to be left
entirely to mechanical equipment without an independent check.

Problems
634. Gyro error is 19 E.
Fequired.—(1) True heading when the gyro heading is 155°.
(2) The course to steer by gyro compass if the desired true course is 211°.
(3) The true bearing of a lighthouse if the bearing by gyro compass is 043°.
Answers.—(1) TH 156°, (2) Cpge 210°, (3) TB 044°,

635. A ship at latitude 53°N is steaming on true course 205°, at a speed of 18
knots.

Required.—Speed error.
Answer.— 6 1°72 E.

INSTRUMENTS FOR PILOTING AND DEAD RECKONING 157

636. A gyro compass having a value of r of 1°0 is at latitude 2098.

Required.—The damping error.

Answer.— a 0°36 W.

643a. A pelorus is set with 000% at the lubber's line, and a bearing of 216° is
observed when the heading is 155° true.

Required.—The true bearing.

Answer.—TB 011°.

643b. A pelorus is set with 070° at the lubber’s line. A bearing of 030° is observed
when the compass heading is 068°.

Required.—The compass bearing.

Answer.—CB 028°.

CHAPTER VII

COMPASS ERROR
Magnetism

701. Theory of magnetism.—The fact that iron can be magnetized (given the
ability to attract other iron) has been known for thousands of years, but the explanation |
of this phenomenon has awaited the recently acquired knowledge of atomic structure. `
According to present theory, the magnetic field around a current-carrying wire and |
the magnetism of a permanent magnet are the same phenomenon—fields created by `
moving electrical charges. This occurs whether the charge is moving along a wire, —
flowing with the magma of the earth's core, encircling the earth at high altitude as a `
stream of charged particles, or rotating around the nucleus of an atom.

It has recently been shown that microscopically small regions, called domains, `
exist in iron and other ferromagnetic substances. In each domain the fields created
by electrons spinning around their atomic nuclei are parallel to each other, causing
the domain to be magnetized to saturation. In a piece of unmagnetized iron, the
directions of the various domains are arranged in a random manner with respect to
each other. If the substance is placed in a weak magnetic field, the domains rotate
somewhat toward the direction of that field. Those domains which are more nearly.
parallel to the field increase in size at the expense of the more non parallel ones. If the
field is made sufficiently strong, entire domains rotate suddenly by angles of as much as
90° or 180? so as to become parallel to that “crystal axis" which is most nearly parallel
to the direction of the field. If the strength of the field is increased to a certain value
depending upon individual conditions, all of the domains rotate into parallelism with
the field, and the iron itself is said to be magnetically saturated. If the field is re-
moved, the domains have a tendency to rotate more or less rapidly to a more natural
direction parallel to some crystal axis, and more slowly to random directions under the
influence of thermal agitation.

Magnetism which is present only when the material is under the influence of
an external field is called induced magnetism. That which remains after the magnetiz-
ing force is removed is called residual magnetism. That which is retained for long
periods without appreciable reduction, unless the material is subjected to a demagnetizing
force, is called permanent magnetism.

Certain substances respond readily to a magnetic field. These magnetic materials
are principally those composed largely of iron, although nickel and cobalt also exhibit
magnetic properties. The best magnets are made of an alloy composed mostly of iron,
nickel, and cobalt. Aluminum and some copper may he added. Platinum and silver,
eT ms wi NS exopllent magnets, but for ordinary purposes
magnets occur in ODE in de f E fl d ; E (1 D ais a
possessing magnetic SE 2 = GEN E Ene 2 magnente (an orid oa

ROOM Hard'and soft e GER hos 2 1S ur constitutes a natural magnet.
NONO io osa ima Ae a ome alloys of iron, the crystals can be so arranged
e ae EE SE er remain parallel to each other indefinitely, and
Nou, vs GE SC Sr? SE Such alloys are used for the magnets of
ROTE canoas RR reorient themselves rapidly to conform

xte 1d, and soon take random directions if the field

Is removed. A ferromagnetic substance which retains much of its magnetism in the
158

COMPASS ERROR 159

absence of an external field, is said to have high remanence or retentivity. The strength
ofa reverse field (one of opposite polarity) required to reduce the magnetism of a magnet
to zero is called the coercivity or coercive force of the magnet. Hence, a compass magnet
should have high remanence in order to be strong, and high coercivity so that stray fields
will not materially affect it. For convenience, iron is called “hard” if it has high rema-
nence, and “soft” if it has low remanence. Permeability (u) is the ratio of the strength
of the magnetic field inside the metal (B) to the strength of the external field

B
H P =Z.
(H), or u H

703. Lines of force.—The direction of a magnetic field is usually represented by
lines, called lines of force. Relative intensity in different parts of a magnetic field is
indicated by the spacing of the lines of force, a strong field having the lines close together.
If a piece of unmagnetized iron is placed in a magnetic field, the lines of force tend to
crowd into the iron, following its long axis, and the field is stronger in the vicinity of the
iron, somewhat as shown in figure 703a. If theiron becomes permanently magnetized

> — wgl

Pa A A

ALLS A ai

Eun ie ME
Debu 3

FIGURE 703a.— Lines of force crowd
into ferromagnetic material placed FIGURE 703b.—Field of a permanent
in a magnetic field. magnet.

and is removed from this field, the lines of force around the iron follow paths about as
shown in figure 703b.

704. Magnetic poles.— The region in which the lines of force enter the iron is
called the south pole, and the region in which they leave the iron is called the north
pole. Thus, the lines of force are directed from south to north within the magnet, and
and from north to south in the external field. Every magnet has a north pole and a
south pole. If a magnet is cut into two pieces, each becomes a magnet with a north
pole and south pole. A single pole cannot exist independently. If two magnets are
brought close together, unlike poles attract each other and like poles repel. Thus, a
north pole attracts a south pole but repels another north pole.

The earth itself has a magnetic field (art. 706), with its magnetic poles being some
distance from the geographical poles. If.a permanent bar magnet is supported so that
it can turn freely, both horizontally and vertically, it aligns itself with the magnetic field
of the earth, which at most places is in a general north-south direction and inclined to
the horizontal. Since the north pole of the magnet points in a northerly direction, the
earth’s magnetic pole in the northern hemisphere has south magnetism. Nevertheless,
it is called the north magnetic pole because of its geographical location. For a similar
reason, the pole in the southern hemisphere, although it has north magnetism, is called
the south magnetic pole. To avoid confusion, north magnetism is usually called
“red,” and south magnetism, “blue.” The red (north) pole of a magnet is usually
painted red, and in some cases the south (blue) pole is painted blue. The north magnetic
pole of the earth is a blue pole, and the south magnetic pole is a red pole.

160 COMPASS ERROR

2 «.—— —

mna 705. The magnetism of soft
iron, in which remanence is low,
depends upon the position of the
iron with respect to an external
field. It is strongest if the long
axis is parallel to the lines of
force, and decreases to a mini-
mum if the material is rotated
so that the long axis is perpen-
dicular to the lines of force.
Figure 705 shows three positions
of a bar magnet with respect to
a magnetic field. At position
FīcuRE 705.— The polarity of a soft iron bar in a X the pole at the upper end of
MS Rp the bar is red and relatively
strong. As the bar is rotated
toward position Y, the upper end remains red, but its strength decreases. At position
Y, no pole is apparent at either end, but a red pole extends along the entire left side of
the bar, and a blue pole along the right side. Poles are strongest when concentrated into
a small area. Hence, when spread over an entire side, as at position Y, they are
relatively weak. At position Z, the upper end is blue.

The change in polarity as a bar of soft iron is rotated in a magnetic field can easily
be demonstrated. If a bar of soft iron is placed vertical in northern magnetic latitudes
(as in any part of the United States), the north (red) end of a compass magnet brought
near it will be attracted by the upper end of the bar, and repelled by the lower end.
If the bar is inverted, so that its ends are interchanged, the upper end (which as the
lower end previously repelled the compass needle) will attract the north end of the
needle, and the lower end will repel it. Thus, the polarity of the rod is reversed,
either end having blue magnetism if it is at the top. This changing polarity of soft iron
in the earth's field is a major factor affecting the magnetic compasses of a steel vessel.

706. Terrestrial magnetism.— The earth itself can be considered to be a gigantic
magnet. Although man has known for many centuries that the earth has a magnetic
field, the origin of the magnetism is
not completely understood. Never- \ ve
theless, the horizontal component of
this field is a valuable reference in
navigation, for it provides the direc-
tive force for the magnetic compass,
which indicates the ship’s heading
tn relation to the horizontal component
of this field.

The world-wide pattern of the
earth’s magnetism is roughly like
that which would result from a, short,
powerful, bar magnet near the earth’s
center, as shown in figure 706. The
geographical poles are at the top and
bottom, and the magnetic poles are
offset somewhat from them. This
representation, however, is greatly
simplified. The actual field is more

FIGURE 706.—The magnetic field of the earth.

COMPASS ERROR 161

complex, and requires measurement of its strength and direction at many places (art.
707) before it can be defined accurately enough to be of practical use to the navigator.
Not only are the magnetic poles offset from the geographical poles, but the magnetic
poles themselves are not 180° apart and, in general, a magnetic compass aligned with
the lines of force does not point toward either magnetic pole. In 1960, the north
magnetic pole was located at latitude 74°9 N, longitude 101?0 W, approximately, to
the northward of Prince of Wales Island; and the south magnetic pole was at latitude
67:1 S, longitude 142°7 E, approximately, in the northeastern part of Wilkes Land.
However, the magnetic poles are not stationary. The entire magnetic field of the earth,
including the magnetic poles, undergoes a small daily or diurnal change, and a very
slow, progressive secular change. In addition, temporary sporadic changes occur
from time to time during magnetic storms (art. 2526). During a severe storm, varia-
tion may change as much as 5°, or more. However, such disturbances are never so
rapid as to cause noticeable deflection of the compass card, and in most navigable waters
the change is so little that it is not significant in practical navigation. Even when there
is no temporary disturbance, the earth’s field is considerably more intricate than indi-
cated by an isomagnetic chart (art. 708). Natural magnetic irregularities occurring
over relatively small areas are called magnetic anomalies by the magneticians, but the
navigator generally refers to these phenomena as local disturbances. Notes warning
of such disturbances are shown on charts. In addition, artificial disturbances may
be quite severe when a vessel is in close proximity to other vessels, piers, machinery,
electric currents, etc.

The elements of the earth’s field are as follows:

Total intensity (F) is the strength of the field at any point, measured in a direction
parallel to the field. Intensity is usually measured in oersteds, one oersted being equal
to a force of one dyne acting on a unit pole. The range of intensity of the earth’s field
is about 0.25 to 0.70 oersted. For convenience in geomagnetic surveying, a smaller unit
is used, called the gamma. One oersted equals 100,000 gammas, so that the range of
intensity of the earth’s field is about 25,000 to 70,000 gammas.

Horizontal intensity (H) is the horizontal component of the total intensity. At
the magnetic equator, which corresponds roughly with the geographic equator, the field
is parallel to the surface of the earth, and the horizontal intensity is the same as total
intensity. At the magnetic poles of the earth, the field is vertical and there is no
horizontal component. The direction of the horizontal component at any place defines
the magnetic meridian at that place. This component provides the desired directive
force of a magnetic compass.

North component (X) is the horizontal intensity's component along a geographic
(true) meridian.

East component (Y) is the horizontal intensity's component perpendicular to the
north component.

Vertical intensity (Z) is the vertical component of the total intensity. It is zero
at the magnetic equator. At the magnetic poles it is the same as the total intensity.
While the vertical intensity has no direct effect upon the direction indicated by a
magnetic compass, it does induce magnetic fields in vertical soft iron, and these may
affect the compass.

Variation (V, Var.), called declination (D) by magneticians, is the angle between the
geographic and magnetic meridians at any place. The expression magnetic variation
is used when it is necessary to distinguish this from other forms of variation. This
element is measured in angular units and named east or west to indicate the side of true
north on which the (magnetic) northerly part of the magnetic meridian lies. For
computational purposes, easterly variation is sometimes designated positive (+),

162 COMPASS ERROR

and westerly variation negative (—). Grid variation (GV) or grivation is the angle
between the grid and magnetic meridians at any place, measured and named in a manner
similar to variation. "T i 3

Magnetic dip (D, called inclination (D by magneticians, is the vertical angle,
expressed in angular units, between the horizontal at any point and a line of force
through that point. The magnetic latitude of a place is the angle having a tangent
equal to half that of the magnetic dip of the place.

At a distance of several hundred miles above the earth's surface, the magnetic field
surrounding the earth is believed to be uniform, as it appears in figure 706, and centered
around two geomagnetic poles. These do not coincide with either the magnetic poles
(art. 704) or the geographical poles. However, they are 180° apart, the north geo-
magnetic pole being at latitude 78°5 N, longitude 69° W (near Etah, Greenland) and
the south geomagnetic pole being at latitude 78?5 S, longitude 111° E. The great circles
through these poles are called geomagnetic meridians. That geomagnetic meridian
passing through the south geographical pole is the origin for measurement of geo-
magnetic longitude, which is measured eastward through 360°. The complement of the
arc of a geomagnetic meridian from the nearer geomagnetic pole to a place is called the
geomagnetic latitude. When the sun is over the upper branch of the geomagnetic
meridian of a place, it is geomagnetic noon there, and when it is over the lower branch
of the geomagnetic meridian, it is geomagnetic midnight. The angle between the lower
branch of the geomagnetic meridian of a place and the geomagnetic meridian over
which the sun is located is called geomagnetic time. The diurnal change is related to
geomagnetic time. The auroral zones (art. 2526) are centered on the geomagnetic poles.

707. Measurement of the earth’s magnetic field is made continuously at about 70
permanent magnetic observatories throughout the world. In addition, large numbers
of temporary stations are occupied for short periods to add to man’s knowledge of the
earth’s field. In the past, measurements at sea have been made by means of non-
magnetic ships constructed especially for this purpose. However, this is a slow and
expensive method, and quite inadequate to survey properly the 71 percent of the
earth’s surface covered with water. Since World War II, a satisfactory airborne
magnetometer has been developed by the U. S. Navy. By means of this instrument,
continuous readings can be recorded automatically during long overwater flights.

708. Isomagnetic charts showing lines of equality of some magnetic element are
published by the U. S. Navy Hydrographic Office in collaboration with the U. S.
Coast and Geodetic Survey. Formerly, three charts of each element were published,
in addition to a north polar grid variation chart, making a total of 22 in the series.
Beginning with the series for epoch 1955, charts for the north and east components
(X and Y) are not published, as this information is of limited use and can be deterriined
easily from the horizontal component and variation. The three charts of each element
consist of one on the Mercator projection (art. 305) covering most of the world, and
one on a polar projection (azimuthal equidistant (art. 320) or stereographic) for each
of the two polar areas. All charts now included in the series are published at intervals
of 10 years, showing the values for the beginning of each year ending in five. Charts
showing variation are also published for the years ending in zero (1950, 1960, etc.).

The isomagnetic chart of most concern to a navigator is H.O. Chart No. 1706,
The Variation of the Compass, a simplified version of which is shown in figure 708a. The
lines connecting points of equal magnetic variation are called isogonic lines. These are
not magnetic mer idians (lines of force). The line connecting points of zero variation is
called the agonic line. Variation is also shown on nautical charts. Those of relatively
small scale generally show isogonic lines. Those of scale larger than 1:100,000 generally
give the information in the form of statements inside compass roses placed at various

"9021 ON WYO OCH Jo uoneogrduus y “UOBLBA—B80Z TANDIN

163

2091

COMPASS ERROR

E | BBUeYD jenuue ajeoipuy seul] ang
mm S61 AVAA AHL AOA L a eegene
= LABANS tege pue 15€09) "S ` A A
Ge SSYdKOO AHL AO NOLLVINVA HH

SUONgAJasqo 2nauBeu a|gejieAe |je wos} paaijap aJam Sau orjeuBeuos|

—— ÁÁ— A "

164 COMPASS ERROR

places on the chart, and sometimes, also, by a magnetic compass rose within the true
compass rose and offset from it by the amount of the variation. By means of this
arrangement, true directions can be plotted without arithmetically applying variation
to magnetic directions, or magnetic directions can be read directly from the chart. The
magnetic compass rose is generally graduated in both degrees ape points. Variation is
given to the nearest 15’, and the annual change to the nearest 1'. However, since the
rate of change is not constant, a very old chart should not be used, even though it has
been corrected for all changes shown in Notices to Mariners.

Another isomagnetic chart of value to the mariners is H.O. Chart No. 1700, Mag-
netic Dip, figure 708b. Lines connecting points of equal magnetic dip are called
isoclinal lines. The line connecting points of zero dip is called the magnetic equator.

Other isomagnetic charts are H.O. Chart No. 1701, showing horizontal intensity;
H.O. Chart No. 1702, showing vertical intensity; and H.O. Chart No. 1703, showing
total intensity. Lines connecting points of equal intensity on any of these charts are
called isodynamic lines.

In all series of isomagnetic charts, the same number is used for polar charts, but
with N or S following the number (and N-G or S-G for the grid variation charts) to
indicate the north or south polar region, respectively. All of the isomagnetic charts
also show isopors, in a distinctive color, connecting points of equal annual change of
the element at the epoch of the chart.

The charts are as accurate as can be made with available information, except that
the lines are smoothed somewhat, rather than depicting every small irregularity.
The larger irregularities are reflected in the information shown on nautical charts,
but local disturbance is indicated by warning notes at appropriate places. In areas
where measurements of the magnetic field have not been made for a long period,
the previous information is altered in accordance with the best information available
on secular change, with some adjustment to provide continuous smooth curves. When
information is thus carried forward for many years, errors may be introduced, particu-
larly in areas where the rate of change is large and variable. Magneticians have not
detected a recognizable world-wide pattern in secular change, such as would occur if it
were due only to shifting of the positions of the magnetic poles. Rather, these shifts
are part of the general complex, little-understood secular change.

The Compass Error

709. Magnetic compass error.—Directions relative to the northerly direction
along a geographic meridian are true. In this case, true north is the reference direc-
tion. If a compass card is horizontal and oriented so that a straight line from its
center to 000° points to true north, any direction measured by the card is a true
direction and has no error (assuming there is no calibration or observational error).
If the card remains horizontal but is rotated so that it points in any other direction
the amount of the rotation is the compass error. Stated differently, compass ð
is the angular difference between true north and compass north (the direction north as
indicated by a magnetic compass). It is named east or west to indicate the side of
true north on which compass north lies.

If a magnetic compass is influenced by no other magnetic field than that of the
earth, and there is no instrumental error, its magnets are aligned with the magnetic
meridian at the compass, and 0002 of the compass card coincides with magnetic
north. All directions indicated by the card are magnetic. As stated in article 706
the angle between geographic and magnetic meridians is called variation (V or Varn!

‘dip orjousv w —'q80/, AYHADIA

ES '004T "ON HYYO “OH JO uorvogiduirs y
KE
= = y 370d
DILANOVW HLNOS
e
È
D
K
E
[^
E
A
=
e
o

yita S ni 8961 AVAA HHL 404 "soe1Bap uj dip Jo uoyeuyjoui oneuBmu ojouop Saul] 2uijoos pay
dId HO NOLLVNTIONI OLLANOVW AHL

Rss an A EE ` e D

MEN'S “N 94} ji uon toqejoo uj KeAins onepoas pue 15809) *S ‘N PY}
Aq pajanujsuo seu) pue pays|nuina2e aja Pep su] “6681 sais apen
suoneriesqo oneuBeu ejae[iske je WO.) paausp aen eu) anauBeuos

d

"ue jo S@INUIW ui dip JO uonevu: jo aBueuo jenuue eieaipur saui) ang

166 COMPASS ERROR

When a compass is mounted in a vessel, it is generally subjected to various mag-
netic influences other than that of the earth. These arise largely from induced mag-
netism in metal decks, bulkheads, masts, stacks, boat davits, guns, ete., and from
electromagnetic fields associated with direct current in electrical circuits. Some
metal in the vicinity of the compass may have acquired permanent magnetism. The
actual magnetic field at the compass is the vector sum, or resultant (art. 018), of all
individual fields at that point. Since the direction of this resultant field is generally
not the same as that of the earth’s field alone, the compass magnets do not lie in the
magnetic meridian, but in a direction that makes an angle with it. This angle is called
deviation (D or Dev.). Thus, deviation is the angular difference between magnetic
north and compass north. It is expressed in angular units and named east or west to
indicate the side of magnetic north on which compass north lies. Thus, deviation
is the error of the compass in pointing to magnetic north, and all directions measured
with compass north as the reference direction are compass directions. Since varia-
tion and deviation may each be either east or west, the effect of deviation may be to
either increase or decrease the error due to variation alone. The algebraic sum
(art. 06) of variation and deviation is the total compass error. x

For computational purposes (art. 727), deviation and compass error, like variation,
may be designated positive (+) if east and negative (—) if west.

Variation changes with location, as indicated in figure 708a. Deviation depends
upon the magnetic latitude and also upon the individual vessel, its trim and loading,
whether it is pitching or rolling, the heading (orientation of the vessel with respect
to the earth's magnetic field), and the location of the compass within the vessel.
Therefore, deviation is not published on charts.

710. Deviation table.—In practice aboard ship, the deviation is reduced to a
minimum, as explained later in this chapter. The remaining value, called residual
deviation, is determined on various headings and recorded in some form of deviation
table. Figure 710 shows both sides of the form used by the United States Navy. This
table is entered with the magnetic heading, and the deviation on that heading is deter-
mined from the tabulation, separate columns being given for degaussing (DG) off and
on (art. 740). If the deviation is not more than about 2? on any heading, satisfactory
results may be obtained by entering the values at intervals of 45? only.

If the deviation is small, no appreciable error is introduced by entering the table
with either magnetic or compass heading. If the deviation on some headings is large,
the desirable action is to reduce it, but if this is not practicable, a separate deviation
table for compass heading entry may be useful. This may be made by applying the
tabulated deviation to each entry value of magnetic heading, to find the correspond-
ing compass heading, and then interpolating between these to find the value of devia-
tion at each 15? compass heading. Another method is to plot the values on eross-
section paper and select the desired values eraphically.

A nomogram especially designed for interconversion of magnetic and compass
headings is called a Napier diagram, having been devised by James Robert Napier
(1821-79). It consists of a dotted, vertical center line graduated from 000° to 360°
(usually in two parallel parts of 180° each), with two series of cross lines making angles
of 60° with the dotted vertical line and with each other. If magnetic headings are used,
deviation is measured along a solid cross line; and if compass headings are used, devia-
tion is measured along a dotted cross line. A deviation curve is drawn through the
TOUS ES To convert a magnetic heading to a compass heading, one finds the
magnetic heading on the vertical center line, moves parallel to a solid cross line until
the curve is reached, and returns to the center line by moving parallel to a dotted line.

COMPASS ERROR

The compass heading is the value at the point of return.

167

The reverse process is used

for converting a compass heading to a magnetic heading. This nomogram is of par-

ticular value where the deviation is large and changing rapidly.

It is now possible,

however, to reduce deviation to such small values that the Napier diagram has lost

much of its appeal and is seldom used.

MAGNETIC COMPASS TABLE

NAVSHIPS 1104 (REV. 10-57)

REPORT-SHIPS-3530-2

ISS Blank NO.
SECONDARY
PILOT
HOUSE Ð SR OTHER
NAVY
De eile one

compass [71/2 uae C. Ga Conn `

===

(R5, CL, DD, etc.)

BINNACLE TYPE:

SERIAL no. _ 8560
TYPE CC COILS ER oare _ 10/11/65

READ INSTRUCTIONS ON BACK BEFORE STARTING ADJUSTMENT

SHIPS DEVIATIONS SHIPS DEVIATION
HEAD HEAD à

MAGNETIC] pc oer | oc ow || MAGNETIC DG ON
o | o.se [ose [109 — | o.sw | o.o
` 0.5
29

a 1.0W | 1.0W
45 2.0E 225 1.5W | 1.5%
60 2.0E 240 2.0W | 2.0W
Ge 2.5E = 2.0W | 2.5W
E 1.54 | 2.08
105 2.0E 2.5E 285 1.0W | 1.5W
120 T25E> |) 2.08 1.0W | 1.0W
135 SA Se F 0.5W | 0.5W
150 1.0E 1.0E 330 0.5W | 0.5W
165 0.0 0.5E 245 0.0 0.0
DETERMINED BY: O AZIMUTH [X] GYRO m SHORE BEARINGS
B. Ó MAGNETS RED : ks AT 12 coupass
C. ^ _wacnets RED E EL AT ER copas
et, c O
HeeLino DUMP 6 i aie TE FRE 12
MAGNET: Bd BLUE UP. CARD O AFT
& ur 18%00'N & om 120*-00'E
On 0.385 DRM Os LADA

SIGNED (Adjuster or Navigator)

APPROVED (Commanding)

VERTICAL INDUCTION DATA
(Fill out completely before adjusting)

RECORD DEVIATION ON AT LEAST TWO ADJACENT CARDINAL HEADINGS

BEFORE STARTING ADJUSTMENT: N 8 W, E 0 ;s4 E; w9 E.

RECORD BELOW INFORMATION FROM LAST NAVSHIPS 1104 DEVIATION TABLE:

vare 4/22/66 D ur 39-53n 0 "117-18W
Ou aen Hr Aan
T DEVIATIONS

i
12 FLINDERS BAR E FORWARD
AET N2.5W c ZE ; s6.5E; w5W_.

RECORD HERE DATA ON RECENT OVERHAULS, GUNFIRE, STRUCTURAL CHANGES, FLASHING,
DEPERMING, WITH DATES AND EFFECT ON MAGNETIC COMPASSES

APPROXIMATELY 30 DAYS ALONGSIDE DOCK
FOR OVERHAUL

PERFORMANCE DATA

[] UNSTEADY
m SLOW
[z] CHANGE

DEGAUSSED DEVIATIONS: [x] VARY

COMPASS AT SEA: STEADY

COMPASS ACTION: SATISFACTORY

NORMAL DEVIATIONS: REMAIN RELIABLE

[ls] x]

DO NOT VARY

REMARKS

INSTRUCTIONS

1. This form shall be filled out by the Navigator for each magnet-
ic compass as set forth in Chapter 24, Part 2, and Chapter 81,
Section III, of Bureau of Ships Manual.

. When a swing for deviations is made, the deviations should be
recorded both with degaussing coils off and with degaussing
coils energized at the proper currents for heading and magnetic
zone.

. Each time this form is filled out after a swing for deviations,
a copy shall be submitted to the Bureau of Ships. A letter of
transmittal is not required.

. When choice of box is given, check applicable box.

. Before adjusting, fill out section on "Vertical Induction
Data" above.

no

w

na

oa — -
NAVSHIPS-1104 (REV. 10-57) BACK D-26887

Figure 710.—Deviation table.

Another solution is to make a deviation table with one column for magnetic
heading, a second column for deviation, and a third for compass heading. Still an-
other solution, most popular among yachtsmen, is to center a compass rose inside a
larger one so that an open space is between them and a radial line would connect points

of the same graduation on both roses.

Each magnetic heading for which deviation

has been determined is located on the outer rose, and a straight line is drawn from
this point to the corresponding compass heading on the inner rose.

168 COMPASS ERROR

A variation of this method is to draw two parallel lines a short distance apart, and
graduate each from 0 to 360 so that a perpendicular between the two lines connects
points of the same graduation. Straight lines are drawn from magnetic directions on
one line to the corresponding compass directions on the other. If the lines are hori-
zontal and the upper one represents magnetic directions, the slope of the line indicates
the direction of the deviation. That is, for westerly deviation the upper part of the
connecting line is left (west) of the bottom part, and for easterly deviation it is right.

An important point to remember regarding deviation is that it varles with the
heading. "Therefore, a deviation table is never entered with a bearing (art. 904). If the
deviation table converts directly from one type heading to another, deviation 1s found
by taking the difference between the two values. On the compass rose or straight-line
type, the deviation can be written alongside the connecting line, and the intermediate
values determined by estimate. If one has trouble determining whether to add or
subtract deviation when bearings are involved, he has only to note which heading,
magnetic or compass, is larger. The same relationship holds between the two values
of bearing.

The deviation table should be protected from damage due to handling or weather,
and placed in a position where it will always be available when needed. A method
commonly used is to mount it on a board, cover it with shellac or varnish, and attach
it to the binnacle. Another method is to post it under glass near the compass. It is
good practice for the navigator to keep a second copy available at a convenient place
for his use.

711. Applying variation and deviation.—As indicated in article 709, a single
direction may have any of several numerical values depending upon the reference
direction used. One should keep clearly in mind the relationship between the various
expressions of a direction. Thus, true and magnetic directions differ by the variation,
magnetic and compass directions differ by the deviation, and true and compass direc-
tions differ by the compass error. Other relationships are also useful. "Thus, grid
(art. 2510) and magnetic directions differ by the grid variation or grivation, and true
and relative directions differ by the true heading. The use of variation and deviation `
is considered here. Other relationships are discussed elsewhere in this volume.

If variation or deviation is easterly, the compass card is rotated in a clockwise
direction. This brings smaller numbers opposite the lubber's line. Conversely, if
either error is westerly, the rotation is counterclockwise and larger numbers are brought
opposite the lubber’s line. Thus, if the heading is 090? true (fig. 711, A) and variation
is 69 E, the magnetic heading is 090°—6°=084° (fig. 711, B). If the deviation on this
heading is 2%W, the compass heading is 084?--29— 086? (fig. 711, C). Also, compass
error is 6° E.—2? W —4? E, and compass heading is 090—4%=086%. If compass error is
easterly, the compass reads too low (in comparison with true directions), and if it is
westerly, the reading is too high. Many rules-of-thumb have been devised as an aid
to the memory, and any which assist in applying compass errors in the right direction
are of value. However, one may forget the rule or its method of application, or may
wish to have an independent check. If he understands the explanation given above,
he can determine the correct sign without further information. The same rules apply
to the use of gyro error. Since variation and deviation are compass errors, the process
of removing either from an indication of a direction (converting compass to magnetic

or magnetic to true) is often called correcting. Conversion in the opposite direction
(inserting errors) is then called uncorrecting.

Example.—A vessel is on course 215° true in an area where the variation is 7° W.
The deviation is as shown in figure 710. Degaussing is off. The gyro error (GE) is 1° E
A lighthouse bears 306°5 by magnetic compass, i |

COMPASS ERROR 169

90

20 90
o © o =
8 & o o
0Zc Ocz OL2

80 = 100 80 90 80 90

FīIGURE 711.— Effect of variation and deviation on the compass card.

Required —(1) Magnetic heading (MH).

(2) Deviation.

(3) Compass heading (CH).

(4) Compass error.

(5) Gyro heading.

(6) Magnetic bearing of the lighthouse.

(7) True bearing of the lighthouse.

(8) Relative bearing (art. 904) of the lighthouse.

Solution.—
(1142158

Via «oW.
(1) MH 222°
(2) BS
(3) OH 223%

The deviation is taken from the deviation table (fig. 710), to the nearest half degree.
(4) Compass error is 7? W +1?5 W=8.5 W.
"'He2155
GE 1°E
(5) Hpge 214°
CB 306°5
D ESN
(6) MB 305°
TW
(7) TB 298°
(8) RB=TB—TH = 298°— 215? =083°.
Answers.—(1) MH 222°, (2) D 1°5W, (3) CH 22305, (4) CE 8°5 W, (5) Hpge 214°,
(6) MB 305°, (7) TB 298°, (8) RB 083°.

170 COMPASS ERROR

Deviation and Its Reduction

712. Magnetism of a steel vessel.—The materials of which a vessel is constructed
are not, in general, selected for their magnetic properties. As a result, many degrees
of permeability, remanence, and coercivity (art. 702) exist within its structure. De-
tailed analysis of the complex field existing at a magnetic compass is a specialized
study not ordinarily required of the navigator. However, a general knowledge of the
basic principles involved is of value to the navigator in helping him understand better
the behavior of his magnetic compasses.

For most purposes, a vessel can be considered to be composed of two types of
material: “hard iron” and “soft iron.”

“Hard iron” is all material having some degree of permanent magnetism. This
magnetism is acquired largely during construction of the vessel, when the rearrangement
of the domains (art. 701) is facilitated by the bending, riveting, welding, and other
violent mechanical processes. Since a vessel remains on a constant magnetic heading

(AN

Figure 712.—Permanent magnetism of a vessel built on heading magnetic north (left) and magnetic
east (right) at a place where the magnetic dip is 70°N.

SE

while it is on the building ways, a field of permanent magnetism becomes established.
the positions of the poles being dependent largely upon the orientation of the hull with
respect to the magnetic field of the earth. If a vessel is constructed on a heading of
magnetic north, at a place where the magnetic dip is 70° N (the approximate value at the
midpoint of the east coast of the United States), its field of permanent magnetism is
about as shown at the left of figure 712. The upper and stern portions are magnetically
blue, while the lower and forward portions are magnetically red. If the vessel is built
on a heading of magnetic east, the starboard and upper portions are blue, and the port
and lower portions are red, as shown by the stern view at the right of ās 712 n
«at 1s magnetic northeast, the upper, starboard, and stern portions are blie and
pd uo ME red. The red and blue portions for any BN
as tais zed by drawing a sketch similar to that of figure 712, with the
CR ee? e SE thus acquired during construction is less permanent
D P ow ‘Magnet such as one of those used in a compass, and is modified

) ching, particularly if the vessel remains on another heading for a

COMPASS ERROR 171

considerable time during fitting out. The change is especially rapid during the first
few days after launching, when the domains of the softer iron become reoriented. At
this stage, deviation due to permanent magnetism may change several degrees. Further
changes in the permanent magnetism may occur during long periods of being tied up
or moored on a constant heading, or during a run of several days on nearly the same
heading. This change is gradual and affects the strength, but usually not the polarity,
of the magnetic field. The permanent field may be changed quickly, in polarity as
well as in strength, if the vessel grounds, collides with another vessel, is struck by
lightning, undergoes magnetic treatment (art. 744), fires its guns, or is struck by shells
or bombs, ete.

The effect that the permanent magnetism of hard iron has upon a compass depends
upon the position and strength of the poles relative to the compass. When the poles
are in line with the north-south axis of the compass card, the only effect is to strengthen
or weaken the directive force of the compass. When the compass heading is approxi-
mately 90° away, so that the poles are east and west of the compass, the deviating
effect is maximum. The direction of the deviation is the same as that of the blue pole
with respect to the compass.

“Soft iron” is all that material in which induced magnetism (art. 701) is present.
With respect to its effect upon the magnetic compass, it is classed as either vertical or
horizontal. Unlike hard iron, its magnetic field changes quickly as its orientation with
respect to the earth’s field changes. It also changes as the strength of the earth’s
field changes. For some purposes induced magnetism can be treated as if it were
concentrated in two bars of soft iron, one vertical and the other horizontal. The
polarity depends upon the position of the vessel relative to the earth’s magnetic field,
and the strength depends upon the strength of the vertical and horizontal components
of the earth's field. This is illustrated in figure 712. In north magnetic latitude the
bottom of the vertical rod has red magnetism and the top has blue magnetism. In
south magnetic latitude these are reversed. In both north and south magnetic latitudes
the magnetic north end of the horizontal bar has red magnetism, and the magnetic
south end has blue magnetism. Thus, whatever the position of the rod, that part
in the direction of magnetic north has red magnetism, and that part in the direction of
magnetic south has blue magnetism. That is, each end has magnetism opposite to that
of the magnetic pole indicated by the direction in which it is pointed.

The effect upon a magnetic compass of the induced magnetism in soft iron depends
upon the strength and direction of the field relative to the compass. The cumulative
effect of the induced magnetism in vertical soft iron is generally on the center line of the
vessel (if of conventional construction), and for a compass located forward, as on
the bridge, is aft of the compass. In magnetic north latitude the effect is generally
that of a blue pole at the level of the compass card. In magnetic south latitude the
pole is red. On a heading of compass north or south the pole is in line with the magnets
of a center line compass and serves only to strengthen or weaken the directive force.
On a heading of compass east or west the pole is perpendicular to the north-south
axis of the compass card, and the deviating force is greatest.

For a compass located on the center line of a vessel of conventional construction,
the horizontal soft iron close enough to have appreciable effect upon the compass 1s
arranged in a more-or-less symmetrical manner with respect to the compass. Thus,
on any cardinal compass heading, the fore-and-aft and athwartship horizontal soft iron
is either in line with the compass magnets or equally and similarly arranged on both
sides. No error is introduced by such symmetrical horizontal soft iron because the
iron north and south of the compass magnets serves only to strengthen or weaken the
directive force, and that east and west of the compass sets up an equal and opposite

172 COMPASS ERROR

field on each side. On intercardinal headings, the poles of the induced magnetism are
offset and a maximum deviating force occurs. That part of horizontal soft iron which
is not symmetrically arranged with respect to the compass—the asymmetrical soft
iron—produces deviation which is maximum on the cardinal headings and zero on the
intercardinal headings (by compass). This type of deviation is particularly great in a
compass not mounted on the center line of the vessel. It may also produce deviation
which is constant on all headings.

In wooden-hulled vessels such as certain yachts and small fishing vessels, one or
more of these types of magnetism may be weak or entirely missing, but this does not
justify the omission of any part of the correction procedure.

As far as its effect upon the compass is concerned, the magnetic field at a center
line compass located forward on a vessel of conventional construction, and on an even
keel, is essentially the same as that which would result from four sources: (1) the earth’s
magnetism; (2) a single blue pole the location and strength of which depends upon the
magnetic history of the vessel; (3) a single pole which is blue in north magnetic latitude
and red in south magnetic latitude, is on the center line aft of the compass, and increases
in strength with higher magnetic latitude; and (4) a single blue pole on the starboard
side for easterly headings and on the port side for westerly headings, being of zero
strength on a heading of north or south and decreasing in strength with increased
magnetic latitudes. The single pole concept assumes that the effect of one pole pre-
dominates. The locations of the poles depend partly upon the position of the compass
to which they apply. The actual field surrounding any magnetic compass may be
considerably more complex than indicated.

713. Compass adjustment.—There are at least two possible solutions to the prob-
lem of compass error. The error can be permitted to remain, and the various directions
interconverted by means of variation and deviation, or compass error, as explained in
article 711; or the error cun be removed. In practice, a combination of both of these
methods is used.

Variation depends upon location of the vessel, and the navigator has no control
over it. Provision could be made for offsetting the lubber’s line, but this would not
be effective in correcting magnetic compass bearings, and this practice is not generally
followed. Variation does not affect the operation of the compass itself, and so is not
objectionable from this standpoint.

Deviation is undesirable because it is more troublesome to apply, and the magnetic
field which causes it partly neutralizes the directive force acting upon the compass,
causing it to be unsteady and sluggish. As the véssel rolls and pitches, or as it changes
magnetic latitude, the magnetic field changes, producing a corresponding change in the
deviation of an unadjusted compass.

Deviation is eliminated, as nearly as practicable, by introducing at the compass a
magnetic field that is equal in magnitude and opposite in polarity to that of the vessel.
This process is called compass adjustment, or sometimes compass compensation,
although the latter designation is now more generally applied to the process of neutral-
izing the effect due to degaussing of the vessel (art. 745).

In general, the introduced field is of the same kind of magnetism as well as of the
same intensity as those of the field causing deviation.
are used to neutralize permanent magnetism, and soft iron to neutralize induced mag-
netism, so that the adjustment remains effective with changes of heading and magnetic

latitude. A relatively small mass of iron near the compass introduces a field equal to
that of a much larger mass at a distance. i

When a compass is properl
and practically constant at var

That is, permanent magnets

y adjusted, its remaining or residual deviation is small
lous magnetic latitudes, the directive force is as strong

COMPASS ERROR 173

as is obtainable on all headings, and the compass returns quickly from deflections and is
comparatively steady as the vessel rolls and pitches.

714. Effect of latitude.—As indicated in article 706, the magnetic field of the earth
is horizontal at the magnetic equator, and vertical at the magnetic poles, the change
occurring gradually as a vessel proceeds away from the magnetic equator. At any
place the relative strength of the horizontal and vertical components depends upon the
magnetic dip. The directive force of a magnetic compass, provided by the horizontal
component of the earth's magnetic field, is maximum on or near the magnetic equator
and gradually decreases to zero at the magnetic poles. Within a certain area sur-
rounding each magnetic pole the directive force is so weak that the compass is unre-
liable (art. 2513).

Deviation changes with a change of the relative strength of either the deviating
force or the directive force. Thus, with either an increase in deviating force or a de-
crease in directive force, the deviation increases. However, if both the deviating and
directive forces change by the same proportion, and with the same sign, there is no
change in deviation. Also, if a deviating force is neutralized by an equal and opposite
force of the same kind, there is no change of deviation with a change of magnetic
latitude.

Permanent magnetism is the same at any latitude. If the permanent magnetism
of the vessel is neutralized by properly placed permanent magnets of the correct strength,
à change of magnetic latitude can be made without introduction of deviation. But if
residual deviation due to permanent magnetism is present, it increases with a change
to higher latitude. The deviating force remains unchanged while the directive force
decreases, resulting in an increase in the relative strength of the deviating force.

As magnetic latitude increases, the vertical component of the earth's magnetic field
becomes stronger, increasing the amount of induced magnetism in vertical soft iron.
At the same time the directive force of the compass decreases. Both effects result in
increased deviation unless the deviating force 1s neutralized by induced magnetism in
vertical soft iron.

As magnetic latitude increases, the induced magnetism in the horizontal soft iron
decreases in the same proportion as the decrease in the directive force of the compass,
since both are produced by the horizontal component of the earth's magnetic field.
Therefore, any deviation due to this cause is the same at any latitude.

715. Parameters.—Compass adjustment might be accomplished by locating the
pole of each magnetic field, and establishing another pole of opposite polarity and
equal intensity at the same place, or of less intensity and nearer to the compass; ora
pole of opposite polarity and suitable intensity might be established at the correct dis-
tance on the opposite side of the compass. Thus, a blue pole east of a compass attracts
the red northern ends of the compass magnets and repels the blue southern ends. Both
effects cause rotation of the compass magnets and the attached compass card in a clock-
wise direction, producing easterly deviation. Either a red pole east of a compass, ora
blue pole west of it, causes westerly deviation. If there are two fields of opposite polarity,
one will tend to neutralize the other. If the intensities of the two fields are equal at
the compass, one will cancel the other, and no deviation occurs.

Because of the complexities of the magnetic field of a vessel, and the fact that each
individual field making up the total is present continuously, the process of isolating
individual poles would be a difficult and time-consuming one. Fortunately, this is
unnecessary. The vessel’s field is resolved into certain specified components. Each of
these components, regardless of its origin or the number of individual fields contributing
to it, can be neutralized separately. Each component is called a parameter, and the
various parameters are designated by letter, as follows:

174 COMPASS ERROR

Permanent magnetism. Parameter P is the fore-and-aft component. It is positive
(+) if it is the equivalent of a blue pole forward of the compass, and negative ( 7) if red.

Parameter Q is the athwartship component. It is positive if it is the equivalent of
a blue pole to starboard. nic Å

Parameter R is the vertical component. It is positive if it is the equivalent of a
blue pole below the compass.

Induced magnetism has nine parameters, each the equivalent of that produced by
a slender rod of soft iron. Each end of a rod is positive if it is forward, to starboard, or
below the compass. Each rod is positive if both ends are positive or if both ends are
negative, and negative if the two ends are of opposite sign. The rods are as follows:

a, b, c—one end level with the compass and in its fore-and-aft axis, either forward or
aft. Itisanarod if it extends fore-and-aft, a b rod if athwartships, and a c rod if vertical.

d, e, f —one end level with the compass and in its athwartships axis, either to star-
board or to port. Itisa d rod if it extends fore-and-aft, an e rod if athwartships, and
an f rod if vertical.

g, h, k—one end in the vertical axis of the compass, either above it or below it.
It is a y rod if it extends fore-and-aft, an h rod if athwartships, and a k rod if vertical.

716. Coefficients.—Deviation which is easterly throughout approximately 180°
of heading and westerly throughout the remainder is called semicircular deviation,
indicating that its sign remains unchanged throughout a semicircle. Deviation caused
by permanent magnetism and that caused by induced magnetism in vertical soft iron
are semicircular. Deviation which changes sign in each quadrant, being easterly in two
opposite quadrants and westerly in the other two, is called quadrantal deviation. It
is caused by induced magnetism in horizontal soft iron. The types of deviation re-
sulting from the various parameters are called coefficients. There are six, as follows:

Coefficient A is constant on all headings. If its cause is magnetic, as from an
asymmetrical combination of parameters, it is a “true” constant. If its cause is
mechanical, as from an incorrectly placed lubber's line, or mathematical, as from an
error in computation of magnetic azimuth, it is an “apparent” constant.

Coefficient B is semicircular deviation which is proportional to the sine of the
compass heading. It is maximum on compass headings east or west, and zero on
compass headings north or south. Coefficient B is caused by permanent magnetism,
and also by induced magnetism in asymmetrical vertical soft iron.

Coefficient C is semicircular deviation which is proportional to the cosine of the
compass heading. It is maximum on compass headings north or south, and zero on
compass headings east or west. Coefficient C is caused by permanent magnetism or
by induced magnetism in asymmetrical vertical soft iron athwartship of the compass.

Coefficient D is quadrantal deviation which is proportional to the sine of twice
the compass heading. It is maximum on intercardinal compass headings, and zero on
cardinal compass headings. Coefficient D is caused by induced magnetism in horizontal
soft iron which is symmetrical with respect to the compass. |

Coefficient E is quadrantal deviation which is proportional to the cosine of twice
the compass heading. It is maximum on cardinal compass headings, and zero on inter-
cardinal compass headings. Coefficient E is caused by induced magnetism in hori-
zontal soft iron which is asymmetrical with respect to the compass.

Coefficient J is the change of deviation for a heel of 1?
heading 009°.

The determination and use of the approximate coefficients in the analysis of com-
pass deviation are discussed in article 727. The force components producing these
coefficients are called exact coefficients. They are designated by the corresponding
upper case German letters. The exact coefficients are now little used in practical

while the vessel is on compass

COMPASS ERROR 175

navigation. They are fully discussed in various books on compass adjustment.
717. Effect of compass location.— The location of a magnetic compass greatly
influences the amount and type of deviation, as well as the adjustment. Thus, if a
compass is on the center line, forward, the effective pole of vertical soft iron is aft of it;
but if the compass is in the after part of the vessel, the effective pole is forward. If the
compass is not on the center line, as the steering compass of an aircraft carrier, the
magnetic field of the vessel is not symmetrical with respect to the compass. If a compass
is located in a steel pilot house, the surrounding metal acts as a shield and reduces the
strength of the magnetic field of the earth. This is of particular significance in high
magnetic latitudes, where the directive force is weak.

Many factors influence the selection of a position for the compass. The most
important consideration is the use to be made of it. A steering compass is of little
use unless it is located so that it can be seen by the steersman. A compass to be used
for emergency steering should be at the emergency steering station. A compass to be
used for observing bearings or azimuths, or a standard compass to be used for checking
other compasses, should be located so as to have a clear view in most directions.

However, some choice is possible. A compass should not be placed off the center
line if it can be placed on the center line and still serve its purpose. It should not be
placed near iron or steel equipment that will frequently be moved, if this can be avoided.
Thus, a location near a gun, boat davit, or boat crane is not desirable. The immediate
vicinity should be kept free from sources of deviation—particularly those of a changing
nature—if this can be done. That is, no source of magnetism, other than the structure
of the vessel, should be permitted within a radius of several feet of the magnetic com-
pass. Some sources which might be overlooked are electric wires carrying direct current;
magnetic instruments, searchlights, windshield wipers, electronic equipment, or motors;
steel control rods, gears, or supports as-
sociated with the steering apparatus; fire
extinguishers, gas detectors, etc.; and
metal coat hangers, flashlights, keys,
pocketknives, metal cap devices, or nylon
clothing. The effect of some items such
as an ammeter or electric windshield wiper
varies considerably at different times. If
direct current is used to light the com-
pass, the wires should be twisted.

A magnetic compass cannot be ex-
pected to give reliable service unless it is
properly installed and protected from
disturbing magnetic influences.

718. The binnacle.— The compass is
housed in a binnacle. This may vary
from a simple wooden box to an elaborate
device of bronze or other nonmagnetic
material. Most binnacles provide means
for housing or supporting the various ob-
jects used for compass adjustment, as well
as the equipment for compensating for de-
viation caused by degaussing. The stand-
ard binnacle for the U. S. Navy 7%-inch
compass is shown in figure 718. The Figure 718.— The standard binnacle for a U. $.
trays for holding the fore-and-aft and Navy 7%-inch compass.

176 COMPASS ERROR

athwartship magnets (art. 719), and the tube for the heeling magnet (art. 724), can

through the open door. — |

A 719. GÉIE for deviation due to pnt map a
1 i d concentrated in a single pole, the pos

e GE i hich the vessel was constructed, and

nds upon the magnetic heading upon whic as S

R pea magnetic history of the vessel. Figure 719a indicates the condi

e. | SQ

FIGURE 719a.—Deviation due to permanent magnetism if the resultant field is that of a blue pole
on the starboard quarter of the vessel.

tion if the permanent magnetism can be considered con
pole which is directly south of the compass when the
east. The only effect on this heading is to weaken tl
is produced because the pole is in line with the com
netic southwest, the pole is also in line with the e
deviation, but the directive force is strengthened.

is not in line with the compass magnets, and deviatio
tion as that of the blue pole from the compass, sin

centrated in a single blue
vessel is headed magnetic north-
10 directive force. No deviation
pass magnets. On heading mag-
ompass magnets and there is no
On any other heading, the pole
n occurs, being in the same direc-
ce the blue pole attracts the red

eur at the compass. Although this

COMPASS ERROR 177

northerly ends of the compass magnets and repels the blue southerly ends. The maxi-
mum effect occurs when the compass heading is approximately 90% from that of zero
deviation. In figure 719a the headings shown on the compass card are the magnetic
headings of the vessel. Their offset from the lubber's line shows the direction and
relative magnitude of deviation.

If there were no other magnetism in the vessel, the poles might easily be located
and neutralized by placing a magnet in such a position that a field of permanent mag-
netism but opposite polarity would oc-

method of adjustment has been used,
it has not proven entirely satisfactory.
The usual method is to adjust for
the fore-and-aft (parameter P) and
athwartship (parameter Q) components
separately. These are shown in figure
719b. The vertical parameter R does
not produce deviation while the vessel
S Figure 719b.— The horizontal component of the
is on an even keel. Its effect when permanent field of figure 719a resolved into its
the vessel heels is discussed in article components, parameters P and Q.
724. Thus, the effect of a single blue
pole at the position shown in figure 719a is the same as that which would be pro-
duced by two weaker poles as shown in figure 719b. On heading east or west by the
compass, parameter () does not produce deviation directly. However, on easterly
headings it does weaken the directive force due to the earth's magnetic field and there-
fore the deviating force of parameter P (causing deviation coefficient B) is relatively
stronger and has a greater deviating effect. On a westerly heading the directive force
would be strengthened, with a corresponding decrease in the B coefficient of deviation.
By weakening the directive
force on easterly headings, pa-
WCS = rameter Q also makes the com-
(a) T pass sluggish on these headings.
In high latitudes, where the
horizontal component of the
earth’s magnetic field is weak,
the compass may lose its di-
rectivity at a greater distance
from the magnetic pole. Nearer
the pole, it might point in the
opposite direction.
FIGURE 719c.—The field of a permanent magnet below the Many binnacles provide a
compass and opposing parameter P of figure 719b. group of several small tubes or
“trays” extending in a fore-
and-aft direction below the compass. One or more permanent magnets can be
inserted in these trays, and the whole assembly moved up or down to vary the effect
upon the compass. Figure 719c shows the situation if a single magnet is placed with
its red end aft. The field at the compass is in the opposite direction of that of
parameter P, and if it is of equal strength, the effect of this parameter is eliminated.
If now the vessel is headed north or south by the compass, the only pole remain-
ing is that due to parameter Q (causing deviation coefficient C), as shown in figure 719d.
A set of trays in an athwartship direction below the compass permits insertion of one
or more permanent magnets to neutralize the remaining permanent magnetism. The

PARAMETER P

178 COMPASS ERROR

effect of inserting a single magnet with red end to starboard is shown in figure 719e.
With both components removed, the field at the compass 1s completely neutralized,

Both the fore-and-aft (B) and athwartship (C) trays are in pairs with an equal
number of trays on each side of the vertical axis of the compass. In each set of trays
it is generally desirable to use an even number of magnets equally distributed on each
side, to produce a symmetrical field at the compass. However, under some conditions,
maximum reduction of deviation occurs with an odd number of magnets, particularly
when two magnets at maximum distance from the compass overcorrect. If there is
a choice, a greater number of magnets at a distance is preferable to a lesser number
close to the compass. i

With each parameter, the trays to use are those which are approximately perpen-
dicular to the compass magnets. The magnets are placed so that the red ends will
be on that side of the compass corresponding to the deviation. Thus, if deviation is
easterly, the magnets should be placed so that the red ends will be east of the compass

PARAMETER Q

=
R
———————————
€———
— -y
PORT STARBOARD

FIGURE 719e.—The field of a permanent magnet
below the compass and opposing parameter Q
FIGURE 719d.—The per- of figure 719b.
manent field of figure
719a after neutraliza-
tion of parameter P.

(forward if the heading is east, and to starboard if the heading is north). However,
if the wrong end is inserted in the trays, the fact will be immediately apparent be-
cause the compass card will rotate in the wrong direction. If the binnacle is not
constructed to receive appropriate corrector magnets, these might be secured to some
supporting surface near the compass.

During adjustment, the unused magnets should be kept far enough from the com-
pass so that they will not affect it.

720. Adjustment for deviation due to induced magnetism in vertical soft iron.—
Figure 720 shows the effect upon the compass of a single blue pole on the center line
of the vessel, aft of the compass. This is a typical situation for induced magnetism in
vertical soft iron, for a centerline compass located in the forward part ot a vessel in
magnetic north latitude. On heading north by compass there is no deviating force,
but the directive force is weakened. In high northern latitudes, where this pole
becomes strong and the directive force becomes weak, magnetism of this type, if not
neutralized, can cause the compass to be unreliable in a much larger area than if the
force is neutralized. On a heading of south by compass there is no deviation, but the

PE =

COMPASS ERROR 179

FīGURE 720.—Deviation due to induced magnetism in vertical soft iron if the resultant field is that
of a blue pole on the center line aft of the compass.

directive force is strengthened. On headings with an easterly component the devia-
tion is westerly, and on headings with a westerly component the deviation is easterly.
In each case the maximum occurs when the vessel is on compass heading approximately
east or west. Thus, the deviation due to induced magnetism in vertical soft iron is
semicircular, coefficient B. In figure 720 the headings shown on the compass card are
the magnetic headings of the vessel. Their offset from the lubber’s line shows the
direction and relative magnitude of deviation.

The deviating force due to induced magnetism in vertical soft iron is neutralized
by placing a bar of soft iron in a vertical position on the opposite side of the compass
from the effective pole due to the field of the vessel. This piece of metal is called a
Flinders bar, after Captain Matthew Flinders, RN (1774-1814), an English navigator
and explorer who is generally given credit for discovering both the effect and method
of adjustment (art. 111). Today, most binnacles for large ships provide a tube for
insertion of a Flinders bar. The bar consists of various lengths of soft iron placed end
to end; with the remainder of the tube being filled with spacers of nonmagnetic mate-

180 COMPASS ERROR

rial, usually wood, brass, or aluminum. The standard Flinders bar E two e x
diameter and is divided into six sections, one each of i236: 3, and 1% inches, and tw

% inch. This permits use of any multiple of % inch to 24 inches. All the iron pieces
should be above the spacers in the tube, without a gap between pieces, the We piece
being on top. The upper end is then about two inches above the level of t S cn
card. For short lengths, one or more spacers should be omitted so that abou

Y, of the length of the bar is above the level of the compass card.

The various pieces should be inserted in the tube carefully. If they are dropped,
they may acquire some permanent magnetism. This reduces their effectiveness for
the purpose intended. Each piece should be tested from time to time to determine
whether or not it has acquired permanent magnetism. This can be done by holding
it vertical with one end east or west of the compass and very near the compass magnets,
noting the reading of the compass, and then inverting the piece so that the ends are
interchanged. If the reading differs, permanent magnetism has been acquired by the
iron rod. The temporary change of reading while the rod is being inverted should be
ignored. In making the test, one should be careful to place the rod in the same position
relative to the compass before and after inversion. On an easterly or westerly heading
the Flinders bar holder can be used. A small amount of permanent magnetism can be
removed by holding the rod approximately parallel to the lines of force of the earth’s
field, with the blue pole of the rod toward the north, and tapping one end of the rod
gently with a hammer. Several alternate tests and treatments may be needed to
make the rod magnetically neutral. If this process is not effective in removing the
permanent magnetism, the rod should be heated to a dull red and allowed to cool
slowly. l

An older type Flinders bar, rarely encountered with modern compasses, consists
of a number of slender rods of equal length, the number of rods being varied rather
than the length of a single rod. Another old system consists of using a single rod
of fixed length, and varying its distance from the compass.

721. Determination of Flinders bar length.—As indicated in articles 719 and 720,
coefficient B magnetism may be introduced both by permanent magnetism of the vessel
and by induced magnetism in asymmetrical vertical soft iron. A problem thus arises as
to what part of the deviation on headings magnetic east and west is due to each cause.
If the vessel remains on an even keel at about the same magnetic latitude, adjustment
can be made without this knowledge. However, satisfactory performance under all
conditions requires separate adjustment for each cause.

There are several possible solutions to this problem. The two sources can be
separated by use of the fact that a change of magnetic latitude affects them differently.
On the magnetic equator there is no vertical component of the earth’s magnetic field,
and consequently no induced magnetism in vertical soft iron. Therefore, if the compass
is adjusted on the magnetic equator, all coefficient B deviation is due to permanent
magnetism, and is removed by the fore-and-aft magnets. After a considerable change
of magnetic latitude, the deviation on a heading of magnetic east or west is again
measured. By means of the curves of figure 721, A, the required amount of standard
two-inch Flinders bar is determined. Accurate results will be obtained only if the
vessel is magnetically the same at both latitudes. That is, a structural change, an
alteration in the number or position of magnets or other devices used in the adjustment,
magnetic treatment, etc., invalidates the measurement. After the required amount
of Flinders bar has been inserted, some deviation may be present due to mutual induc-
tion.among the various devices used for adjustment. This should be removed by
means of the permanent magnets. Once the correct amount of Flinders bar has been

COMPASS ERROR 181

installed, no change should be needed unless there is a substantial change in the amount

or location of vertical soft iron, or unless the compass is relocated.

This method is not always practical. If the correct length and location of Flinders

bar for another vessel of similar construction and compass location have been determined
previously, the same length can be used for the compass being adjusted. If a large
change in magnetic latitude can be made without appreciable change of deviation on

headings east and west, the amount of Flinders bar is correct. If the deviation changes,

FLINDERS BAR CURVES
(2 in. Bar)
DEGREES CORRECTION

DIP IN DEGREES
CONSTANT "K"

6" 74 8" AG A K ARA 15 cp us 3US UR WE Cup RA O

LENGTH OF BAR IN INCHES

i ; i lati i ed magnetism in vertical soft iron is
FīcuRE 721.—Flinders bar curves: A, if deviation due to induc g
known; B, if coefficient K is known.

readjustment is needed. By studying the structure of the vessel, an experienced com-
pass adjuster may be able to make a reasonably accurate estimate of the length to use.

In the absence of enough reliable information to permit a reasonably accurate
determination of the correct length, the Flinders bar may be omitted entirely, and the
deviation on east and west headings removed by means of the fore-and-aft pommanent
magnets. This is common practice for yachts, fishing vessels, and s for some
coastal vessels which do not change magnetic latitude more than à foy degr ges) -—

The correct length of Flinders bar can be determined by figure 721, B, Ee la le
data are available on the deviation occurring on magnetic east or west headings at two

182 COMPASS ERROR

widely separated magnetic latitudes. The constant K is determined by computation, `
using the formula

H. tan d,— H; tan di
KEN FER
in which
K=a constant proportional to the required length of Flinders bar.

\=shielding factor, or the proportion of the earth’s field effective at the compass.
Generally, it varies from about 0.7 to 1.0, averaging about 0.9 for compasses
in exposed positions, and 0.8 for those surrounded by metal deck houses.

H,=horizontal intensity of earth's magnetic field at place of first deviation reading.
H,=horizontal intensity of earth's magnetic field at place of second deviation

reading.
d,=total deviation on heading magnetic east or west at place of first deviation
reading. KI
,—total deviation on heading magnetic east or west at place of second deviation
reading.

Z,=vertical intensity of earth's magnetic field at place of first deviation reading.
Z,= vertical intensity of earth's magnetic field at place of second deviation reading.

The values of horizontal and vertical intensity (H and Z) can be obtained from
H.O. charts No. 1701 and 1702, respectively.

The constant K represents a mass of vertical soft iron (the c rod) causing deviation.
From the intersection of the curve of figure 721, B, and a horizontal line through the
value of constant K, draw a vertical line to the bottom scale, which shows the required
length of Flinders bar.

If some length of Flinders bar was in place when the two deviation readings were
made, enter the graph of figure 721, B, with this length and determine the corresponding
value of K. Call this K, and that obtained by computation K,. Algebraically add
K, and K, to determine the value of K to use for finding the total length of Flinders
bar required. If the Flinders bar is forward of the compass, K, is negative (—), and
if aft of the compass, K: is positive (+). In the computation of K», both Z, and Z? are
positive in north magnetic latitude and negative in south magnetic latitude. Also, d
and d, are positive if deviation is east on magnetic heading east in north latitude or
magnetic heading west in south latitude. Tf either the heading or direction of tbe
deviation is reversed, the sign of d; or d; is negative. If both are reversed, the sign is
positive. If the value of K is negative, the Flinders bar should be installed forward of
the compass, and if positive, it should be installed aft.

Example.—The deviation of a magnetic compass of a ship on heading magnetic
east is I? E at New York (H 0.170, Z 0.539) and 9%E at Panama (H 0.311, Z 0.260).
The shielding factor is 0.8.

Required.— The correct length of Flinders bar if (1) no Flinders bar is in place

during observations, (2) six inches of Flinders bar is in place forward of the compass
during observations.

Solution.—

(en DG ENE
0.260—0.539

=(—) 0.133
K,=0
K =K,+K, =(—) 0.133

COMPASS ERROR 183

From figure 721, B, the correct amount of Flinders bar is 22 inches. Since the
amount used must be a multiple of % inch, the amount to use is 21% inches. Since K
is negative, the bar should be installed forward of the COMPASS.

(2) From figure 721, B, the value of K, corresponding to six inches of Flinders bar
is 0.009. The value is negative because the bar is forward of the compass. Therefore,
K,+K.=(—) 0.133+ (—) 0.009=(—) 0.142. From figure 721, B, the total amount of
Flinders bar required is 24 inches, which should be installed forward of the compass.

Answers.—(1) 21% inches of Flinders bar installed forward of the compass, (2) 24
inches of Flinders bar installed forward of the compass.

When the length of Flinders bar is determined in this way, accurate results can be
expected only if the vessel is magnetically unchanged between deviation readings.

Lord Kelvin suggested the following rule for improving the adjustment for co-
efficient B if no better method is available:

Remove the deviation observed on magnetic east or west headings by means of fore-and-
aft B magnets when the vessel has arrived at places of weaker vertical magnetic field, and
by means of Flinders bar when it has arrived at places of stronger vertical magnetic field,
whether in the northern or southern hemisphere.

After a number of applications of this rule following alternate passage from weaker
to stronger fields and then stronger to weaker fields, the amount of Flinders bar should
be very nearly correct.

722. Adjustment for deviation due to induced magnetism in symmetrical hori-
zontal soft iron.—That part of horizontal soft iron which is symmetrically arranged
with respect to the compass can be considered equivalent to two rods extending through
the compass, one in a fore-and-aft direction (— a rod) and the other in an athwartship
direction (—e rod). The deviation caused by both of these rods is quadrantal, but of
opposite sign. If both rods were equally effective in causing deviation, they would
cancel each other and no deviation would result on any heading. In most vessels,
however, the athwartships iron dominates, and deviation due to all horizontal soft iron
can generally be considered to be that which would result from a single (—)e rod.
In figure 722a the deviation resulting from such a rod is shown for various magnetic
headings in any latitude. There is no deviation on any cardinal heading, but the direc-
tive force is weakened on heading magnetic east or west. The maximum deviation
occurs on intercardinal headings by compass, being easterly in the northeast and south-
west quadrants, and westerly in the other two quadrants. This is coefficient D devia-
tion. In figure 722a the headings shown on the compass card are the magnetic headings
of the vessel. Their offset from the lubber’s line shows the direction and relative
magnitude of deviation.

— The field causing this deviation is neutralized by installing two masses of soft iron
abeam of the compass, on opposite sides and equidistant from its center. Such iron
is usually in the form of hollow spheres or cylinders, called quadrantal correctors.
These can be moved in or out in an athwartship direction along brackets on the sides of
the binnacle.

Quadrantal correctors act as (+) e parameters which neutralize the (—) e parameter
of the athwartshipsiron. As shown in figure 722b, the portion of the coro ACE adjacent
to the compass is always of opposite polarity to the deflecting force. The amount of
the correction can be adjusted by moving the correctors toward or away from the com-
pass card. If the inboard limit of travel is reached without fully removing the devia-
tion, larger correctors are needed. If overcorrection occurs at the outboard limit, mallar
correctors are needed. A single corrector can be used, but this produces an unbalanced
field which is less desirable than a balanced one. In general, large correctors ata greater
distance are preferable to small correctors close up because there is less mutual induction

184 COMPASS ERROR

between the correctors if they are widely separated. In the rare case when quadrantal
deviation is westerly on heading northeast (coefficient D is negative, the fore-and-aft
horizontal soft iron predominating), the quadrantal correctors should be mounted
fore-and-aft on the binnacle. |

Figure 722c shows the approximate amount of deviation correction to be expected
from correctors of various sizes, shapes, and distance from the center of a standard

FIGURE 722a.— Deviation caused by induced magnetism in symmetrical horizontal soft iron.

Navy 7%-inch compass. The data apply to either the athwartships or fore-and-aft
position.

Like the Flinders bar (art. 720), the quadrantal correctors should be handled
carefully, and checked from time to time to see if they have acquired permanent mag-
netism. The test can be made by rotating each corrector through 180? without altering
its distance from the center. If the compass heading changes, the correctors have
acquired permanent magnetism which can be removed by tapping with a hammer when

COMPASS ERROR 185

the blue pole is toward the north, or by removing the spheres, heating them to a dull
red, and permitting them to cool slowly.

723. Adjustment for deviation due to induced magnetism in asymmetrical hori-
zontal soft iron.—If the horizontal soft iron is not arranged symmetrically with respect
to the compass, resulting in an effective pole which is on neither the fore-and-aft nor
athwartships axis through the compass, quadrantal deviation with its maximum values

ths
SO

FIGURE 722b.— Adjustment for symmetrical horizontal soft iron.

on cardinal headings (coefficient Æ) results. Constant deviation (coefficient A) may
also be caused by this arrangement. Either coefficient E or Ais due to a combination of
parameters. l l ir

For a centerline compass on a ship of conventional construction, any deviation due
to induced magnetism in asymmetrical horizontal soft iron is small, and many installa-
tions make no provision for neutralizing the effect. However, some binnacles SE
provided with a pair of E-links, which are bars that can be attached to the side brackets
to permit the quadrantal correctors to be slewed somewhat with respect to the com-

186 COMPASS ERROR

pass. When this has been done, the horizontal axis through the correctors and the
compass makes an angle with the athwartship axis of the compass. Mta

After a compass has been adjusted, any remaining constant deviation due to
magnetic coefficient A is likely to be very small. If such deviation exists, its cause is
likely to be chiefly mechanical. If a compass is used primarily for determining the
heading (as a steering compass), all constant deviation can be removed by realignment
of the binnacle so as to rotate the lubber's line by the required amount. However, if à
compass is to be used for observing bearings or azimuths, only the mechanical A-error
should be removed in this manner. This is because such readings are taken on the face
of the card itself, and are therefore not affected by misaiignment of the lubber’s line.
The two components of constant deviation can be separated in the following manner:
Measure the deviation on various headings by means of bearings or azimuths (art. 1428).
This includes only magnetic coefficient A. Then measure the deviation on various
headings by means of the lubber’s line, comparing the heading by compass with the
magnetic heading determined
by pelorus or gyro compass.
This includes the combined
effect of magnetic and mechani-
cal coefficient A deviation. The
difference between the two
values is the mechanical coeffi-
cient A. For a properly adjusted
compass the magnetic coefficient
A deviation is so small that pro-

QUADRANTAL CORRECTION IN DEGREES

= =>
Note: These are

vision is not made forits removal.
724. Heeling error.—All of
the effects discussed previously

| 4
approxima'e corrections of a standard compass.
Different needle arrays will alter the results somewhat.

refer to a vessel on an even keel.
When the vessel heels, conditions

9" 10” 11" TAn 13" 14” T5 à M :
POSITION OF SPHERE CENTER— INCHES FROM CENTER are altered. Deviation which
OF COMPASS

now appears, or the change of
deviation from that when the
vessel was on an even keel, is
called heeling error. Fora con-
stant angle of heel and a steady heading, this error remains essentially unchanged.
However, it tends to increase as the heel becomes greater, and to reverse sign as the heel
changes from one side to another. "Therefore, if a vessel is rolling or pitching, the
compass tends to oscillate. "This increases the difficulty of reading the compass.

The cause of heeling error is the displacement of the permanent and induced
magnetic fields with respect to the compass. Figure 724 shows a vessel heeled to star-
board on heading magnetic north or south, in north magnetic latitude. The vessel was
constructed in north magnetic latitude. On an even keel the vertical parameter R
of permanent magnetism for a centrally located compass is direetly below the compass,
with the blue pole nearer the compass. When the vessel is heeled as shown at A, the
blue pole is to port of the compass, causing deviation toward that side. A vertical rod
of soft iron below the compass (parameter k) exerts a similar influence, as shown at B.
An athwartship horizontal rod through the compass has no deviating effect while the
vessel is on an even keel, but when it heels as shown in figure 724, the vertical com-
ponent of the earth's field causes the port end to acquire a blue pole and the starboard
end a red pole (parameter e), as shown at C. Each of the three causes shown in figure 724
results in a blue pole being established on the port or high side of the vessel. This causes

Quadrantal sphere corrections on Navy standard
7%" compass. H=180 M. G.

FIGURE 722c.— Effect of various quadrantal correctors.

COMPASS ERROR 187

A B

FIGURE 724.— Effect of heel.

the red north ends of the compass magnets to be attracted to this side. If the heading
is magnetic north, the deviation is westerly, and if magnetic south, itis easterly. This
effect is offset somewhat by the changed magnetic field surrounding the quadrantal
correctors. On heading magnetic east or west, these components have no deviating
effect, but the directive force of the compass is strengthened or weakened. When the
vessel pitches, the effects described for north-south and east-west headings are reversed.
On a heading other than a cardinal direction (magnetic) the effect is some combination
of the two. The magnetic situation varies not only with the heading, but also with the
magnetic latitude and the magnetic history of the vessel.

Although heeling error is due in part to permanent magnetism and in part to
induced magnetism, the induced magnetism generally exerts the greater influence. The
most effective method of neutralizing this effect would be to attack each parameter
separately. This would require the placement of soft iron above the compass. Since this
would not be a convenient arrangement, the condition is improved by placing a vertical
permanent magnet, called a heeling magnet, centrally below the compass, and adjusting
its height until the error is minimized. In north magnetic latitude, the red end is placed
uppermost in most installations. As the vessel proceeds to lower magnetic latitudes,
parameter R becomes less effective in producing deviation because of the stronger
directive force due to the horizontal component of the earth's magnetic field. Para-
meters k and e become weaker because of decreased intensity of the vertical component
of the earth's field, and the strengthening of the horizontal component also reduces
their effect. "Therefore, the heeling magnet requires readjustment as the magnetic
latitude changes. As the vessel approaches the magnetic equator, the heeling magnet
should be lowered. After the vessel crosses the magnetic equator, it may be necessary
to invert the heeling magnets, so that the opposite end is uppermost. A change in the
setting of the heeling magnet may introduce deviation on headings of compass east or
west because of altered induction between the heeling magnet and the Flinders bar.
This should be removed by means of the fore-and-aft (B) magnets in the trays below
the compass.

If adjustment for heeling error is made when the vessel is tied up or at anchor,
it is best done by listing the vessel on a northerly or southerly heading, and adjusting
the heeling magnet until the reading of the compass is restored to what it was before
the vessel heeled. If the adjustment is made at sea, the vessel should be placed on a
heading of compass north or south. If there is little rolling, the vessel can be listed
and the compass reading restored, as at dockside. If the vessel rolls moderately on
this heading, the heeling magnet should be placed at that height at which oscillation
of the compass card is minimum. If the setting for minimum oscillation is different
on north and south headings, the mean position should be used. Any yawing of the
vessel should be considered when reading the compass under rolling conditions.

The approximate position of the heeling magnet can be determined by means of

188 COMPASS ERROR

an instrument known as a heeling adjuster or a vertical force instrument, a form of dip
needle. This consists of a small magnet balanced about a horizontal axis by means
of a small adjustable weight. A scale indicates the distance of the weight from the
axis. The instrument is taken ashore and balanced at a place where the earth’s field
is undisturbed, the magnet being in a magnetic north-south direction, approximately.
The instrument is then taken aboard ship, the compass removed from its binnacle,
and the heeling adjuster installed in its place. The weight is set to a distance equal
to the distance determined ashore, multiplied by A, the shielding factor (art. 721).
The heeling magnet is then moved up or down until the magnet of the instrument is
level. This should be approximately the correct setting. "This method is used prin-
cipally when the listing of a vessel is difficult or impractical.

725. Soft iron correctors and nearby magnets.— The soft iron correctors used in com-
pass adjustment are near enough to the compass magnets and the magnets used in
compass adjustment to be influenced by them.

The Flinders bar acquires a certain amount of induced magnetism from the fields
of the heeling magnet and the fore-and-aft (B) corrector magnets. The approximate
amount of deviation caused by induced magnetism from the heeling magnet of a 7%-
inch compass when H —0.165 is shown in figure 725. Because of such induced mag-
netism, the “drop-in” method of determining the amount of Flinders bar is not accurate.
By this method, Flinders bar lengths are added until the compass reading changes by the
required amount. Better adjustment is achieved by using the required amount of Flin-
ders bar and removing any remaining deviation on east-west headings by means of the fore-
and-aft magnets. The principal reason that it is preferable to use a larger number of
magnets at a distance from the compass than a smaller number near it, is that the former
arrangement produces less induced magnetism in the Flinders bar and quadrantal correc-
tors. If the Flinders bar length is changed, the deviation on headings of magnetic east
and west should be checked, and any needed adjustment made by means of fore-and-aft
magnets. When all correctors have been put in place, their positions relative to each
other are constant. Therefore, the Flinders bar acts as a permanent magnet, and the
resulting deviation is semicircular (coefficient B). The Flinders bar may also intro-
duce a small amount of quadrantal deviation (coefficient D), its action being somewhat
like that of a quadrantal corrector placed in the fore-and-aft axis of the compass.

a o
o o

DEVIATION

|

|
JUL

|

|

£

Ei

| /

pH

Ð

/

HÆ
ARE
HE
"n
i

dram
EIEEFMEBEI
HE

POSITION OF HEELING MAGNET

FIGURE 725.—Deviation due to inductive effect of heeling magnet on Flinders bar.

COMPASS ERROR 189

The quadrantal correctors acquire induced magnetism from the fields of the fore-
and-aft (B) magnets, the athwartship (C) magnets, and the compass magnets. The
magnetism acquired from the B and C magnets is semicircular (coefficient B from the
B magnets, and coefficient C from the C magnets), and that acquired from the field of
the compass magnets is quadrantal (coefficient D). The semicircular deviation is
minimized by keeping the B and C magnets as far away from the quadrantal correctors
as practicable, and any deviation that does exist is removed by means of these magnets.
The quadrantal deviation is removed by means of the quadrantal correctors themselves.
The compass magnets of most modern compasses have little effect upon the quadrantal
correctors.

Because of the interaction between the various correctors, it is good practice to
insert the required amount of Flinders bar, and to install the quadrantal correctors
and heeling magnet at their approximate positions before adjusting the compass. If
a radical change is subsequently made in any of these adjustments, the settings of the
B and C magnets should be checked and altered if necessary.

Analysis of Deviation

726. Nature and purpose of analysis.—An analysis consists of determining the
approximate value of each of the six coefficients, and studying the results. The purpose
of the analysis is to give the compass adjuster an understanding of the magnetic prop-
erties of the vessel. This provides the basis for the approximate placement of the
various correctors, and suggests possibilities for further refinement in the adjustment.
Without an analysis, compass adjustment is a morc-or-less mechanical process. Fewer
mistakes are likely to be made by the person who understands the nature of the magnetic
field he seeks to neutralize.

727. The analysis.— The first step in an analysis is to record the deviation on each
cardinal and intercardinal heading by the compass to be analyzed. For the purpose of
analysis, easterly deviation is considered positive (+), and westerly deviation negative
(—). Approximate values of the various coefficients are:

Coefficient A—mean of deviation on all headings.

Coefficient B—mean of deviation on headings 090? and 270°, with sign at 270°
reversed.

Coefficient C—mean of deviation on headings 000° and 180°, with sign at 180°
reversed.

Coefficient D—mean of deviation on intercardinal headings, with signs at headings
135° and 315° reversed.

Coefficient E—mean of deviation on cardinal headings, with signs at 090° and 270°
reversed.

Coefficient J—change of deviation for a heel of 1° while the vessel heads 000° by
compass. It is considered positive if the north end of the compass card is drawn
toward the low side, and negative if toward the high side. rou

Example.—A. magnetic compass which has not been adjusted has deviation on
cardinal and intercardinal compass headings as follows:

Compass heading Deviation Compass heading Deviation
000° SW 180° 8°0 E
045° 34°0 E 2254 125 W
090° 31°0 E 2107 2970 W
155^ 13°5 E SL 3620 W

On heading compass north the deviation is 1325 W when the vessel heels 10° to star-

board.
Required —The approximate value of each coefficient.

190

COMPASS ERROR

Solution.— À " o 90 195— 90?0— 36°20
PE ndo Sf :5— 29: O
?04-29?0 3
BL (4) 30°0
Hg 2 geg å
O= ana) 428
inr = ler E 6°0 o
p=?4-0 13 - 54-3 (4+) 1898
PIE EL A NE 191
8132542195 road,
Ja (—) 122

Answers.—A (+) 223, B (+) 30%0, C
On any compass heading (CH) the
alone is:
Coefficient A:
Coefficient B:
Coefficient C:
Coefficient D:
Coefficient E:
Coefficient J:

(—) 4:8, D (+) 1378, E (+) 1*1, J (—) 122.
deviation (d) from each coefficient acting

d,= 4

da=B sin CH
dc=C cos CH
dp=D sin 20H
dg— E cos 2CH
dy=J cos CH.

For a vessel on an even keel, the total deviation on any compass heading is the algebraic
sum of the deviation due to each of the first five coefficients:

d=d, +ds+dc+dp--de= A+ B sin CH LO cos CH+ D sin 2CH+E cos 2CH.

For the compass of the example given above, the deviation due to each component,

and the total, on various headings is:

CH A B C D E d
|

000 | +2.3 00 ES 0.0 | +11 = ad
DIS, rat +7.8 | —46 +69 | +10 | 413.4
030 | -F2:3 7] 15:05 442. 4- CR
045 E E212 pi sa E 58 00 | +33.9
060: 1.2.8 14) «26,031 TEE ka A
0758 | +23 | +29.0 | —12 +6.9 | —1.0 | 36.0
090 | 25 | 30.0 0. 0 Con em BET
10508 gar o Bn —69 | —L0 | 4246
120 |. --2.8. «4-26. 0.1522. 4. 1| = 12:0: ee
138 "T" 2 ao Mira QUNM TS 00 | +13.1
150 | 42.3 | 15:0] 44910219 0 oo 0
165.4 c2 d +7.8 | +46 TO +410 +8. 8
180 | +23 0.0 318-48 0.0 | I +8. 2
ISES —7.8 | +46 +6.9 | +10 +7.0
210 F285 velns a 153070 n +4, 1
225 | +23 | —21.2« kg p ende 228 0. 0 GER
2408) +23 "1960-49 4 ROO —9. 9
2554 |. 2.3 jex-29 09] Seo + 639 pal 810 | CC
2/0. ln 189.3 194300 0. 0 TO 171 —28. 8
285^ +25 || O59 0 E —6:9" 11.0 11358
300 ie +23 ]"52:26.0 415-2 4 NE 120 0 o
815 |. 2.3 iy S21. 2 VN e 0.0. Ne OSI
330 (2.89 | 18.0" 249 MS r
345 |) 49.3 RE AG —69 | +10 | —16.0

COMPASS ERROR 191
COMPASS HEADINGS
000° 045° 090° 135° 180° 225° 270°

315° 360°

409 E

AU Deviation
30°E À

Coefficient A `

B SS RS:
Abit rozā ntE
Coefficient C

DEVIATION

10°W

Coefficient D

20°W ete

30°W

40°W

FIGURE 727.—Coefficients and total deviation of an unadjusted magnetic compass.

The various components and the total deviation are shown in graphical form
in figure 727. Since the various coefficients are only approximated by the method
given above, the curve of total deviation found in this way should not be expected to
coincide exactly with a curve drawn from values found by measurement on the various
headings.

The shapes of the curves of figure 727 are typical of those of an unadjusted compass
of a large steel ship. However, an analysis of the results indicates the following:

Coefficient A is normally negligible. The presence of more than 2° of constant
error indicates an abnormal condition which should be discovered and corrected. If
the vessel has been in service for some time without major structural change, and no
misalignment of the lubber’s line of the compass or the pelorus or gyro compass used
for measuring deviation has been noted previously, it is probable that a mistake has
been made in determining the azimuth or bearing used for establishing deviation.

Coefficient F is normally negligible for a compass located on the center line of the
vessel. This vessel has an excessive amount, which should be corrected by slewing the
quadrantal correctors, using an Ē-link.

192 COMPASS ERROR

Since deviation is east on heading 090° and west on 000°, it is probable that the
blue pole of the vessel's permanent field is on the port bow.

The compass being unadjusted, no Flinders bar is in place, and the large B de-
viation on heading 090° is a combination of deviation from induced magnetism in
vertical soft iron and that due to the permanent magnetism of the vessel. Since the
deviation on heading 270° is nearly the same as that on 090°, but of opposite sign, ad-
justment on one of these headings should result in nearly correct adjustment on the
other. Since some B and C deviation occurs on intercardinal headings, while no D
deviation occurs on cardinal headings, adjustment for B and C should be made before
that for final D adjustment.

A second analysis made after adjustment may reveal possibilities for further
refinement in the adjustment.

If heeling error is measured on any heading other than compass north or south,
the value of coefficient J can be found by means of the formula:

d=J cos CH
Ted gë de.
converted to cos CH
ge J=d sec CH.

If HE is the total observed change of deviation (heeling error), and 2 is the angle of
heel in degrees (for relatively small angles), the formula becomes

; HE = CH
If heeling error is sought, the formula becomes

HE-J5 cos CH.

Adjustment Procedure

728. Preliminary steps.—Efficient and accurate adjustment is preceded by cer-
tain preliminary steps best made while a vessel is tied up or at anchor.

The magnetic environment of the compass should be carefully inspected. Stray
magnetic influences such as those caused by tools, direct current electric appliances,
personal equipment (such as keys, pocketknives, or steel belt buckles), nylon clothing,
etc., should be eliminated. Permanently installed equipment of magnetic material
(such as cargo booms, boat davits, cranes, or guns) should be placed in the positions `
they normally occupy at sea. The degaussing coils should be secured by the revers-
ing process (art. 743) if this has not already been done.

The compass itself should be checked carefully for bubbles, and to be sure it is
centered on the vertical axis of the binnacle. If it is, and the vessel is on an even keel,
there is no change of reading as the heeling magnet is raised and lowered in its tube.
An adjustment should be made to the gimbal rings if the compass is off center. There
should be no play in the position of the compass once it is centered.

The lubber's line, too, should be checked to be sure it is in line with the longitudinal
axis of the vessel. This can be done by sighting on the jackstaff if the compass is on the
center line. If it is not, a batten might be erected at a distance from the center line
equal to the distance from the center of the compass to the centerline. Another way
is to determine the distance from the compass to the center line and from this point to
the jackstaff. The first distance divided by the second is the natural tangent of the

COMPASS ERROR 193

angle at the compass between the line of sight to the jackstaff and the line of sight
through the lubber’s line. If the compass is in an exposed position where bearings can
be taken, and the true heading is known, the observed relative bearing of a distant
object can be compared with that obtained by careful measurement on the chart. If
the vessel is at anchor or underway, the method explained in article 723 can be used.

If a pelorus or gyro compass or repeater is to be used in determining deviation of
the compass, its lubber's line should be checked in the same manner, or by comparing
a relative bearing of a distant object taken by two instruments, the lubber's line of
one having previously been checked. If a gyro compass is to be used, it is checked to
see that it is synchronized with a repeater. With accurate synchronization, any
error in one will also be present in the other. The speed and latitude adjustments of
the gyro compass should be checked carefully.

All devices to be used in the adjustment should be checked to see that they are on
hand and in good condition. The trays for B and C permanent magnets, the quad-
rantal correctors, and heeling magnet should be checked for freedom of motion. The
Flinders bar and quadrantal correctors should be checked for permanent magnetism.
The correct amount of Flinders bar should be placed in its tube. The quadrantal
correctors should be placed in their approximate positions, being centered if no better
information is available. The heeling magnet is generally placed with the red end
uppermost in north magnetic latitude, and the blue end uppermost in south magnetic
latitude. If no better information is available, the heeling magnet should be placed
near the bottom of the tube.

Plans for the actual adjustment should be made carefully. A suitable time and
location should be selected. If landmarks are to be used, suitable ones should be
selected to provide the information desired. Areas of heavy traffic should be avoided.
If azimuths of the sun are to be used, a time should be selected when the sun will not
be too high in the sky for suitable observation. A curve of magnetic azimuths (art.
731) should be made, and just before adjustment begins a comparing watch should be
checked and set, if possible, to correct time. Local variation should be checked care-
fully, and corrected for date, if necessary. Any necessary recording and work forms
should be made up. Each person to participate in the adjustment should be instructed
regarding the general plan and his specific duties.

729. Underway procedure.—When everything is in order and the vessel has ar-
rived at its adjusting area, final adjustment can begin. Trim should be normal, and
the vessel free from list, so that no heeling error is present.

All adjustment headings should be magnetic. Compass headings can be used,
but this results in a slight turn being required every time an adjustment is altered.
Also, the coefficients are not completely separated unless the vessel is on magnetic
headings.

Turns to each new heading should be made slowly, swinging slightly beyond the
desired heading before steadying on it. If steering is by gyro, the gyro error should
be checked on each heading if time and facilities permit. The vessel should remain
on each heading for at least two minutes before the deviation is determined or an
adjustment made, to permit the compass card to come to rest and the magnetic condi-
tion of the vessel to become settled. If observations are made before the vessel’s
magnetism becomes settled, the reading will be incorrect by an amount called the
Gaussin error.

Adjustments should be carried out in the correct order, as follows:

1. Steady on magnetic heading 090° (or 270°) and adjust the fore-and-aft perma-
nent magnets until the compass heading coincides with the magnetie heading, thus

194 COMPASS ERROR

removing all coefficient B on this heading. Use magnets in pairs, from the bottom up,
with the trays at the lowest point of travel. When overcorrection occurs, remove the
two highest magnets and raise the trays until all deviation has been removed. If two
magnets overcorrect, use a single magnet. It is not necessary to determine in ad-
vance which direction the red ends should occupy, for a mistake will be immediately
apparent by an increase in the deviation. | |

2. Steady on magnetic heading 180° (or 000°) and adjust the athwartship perma-
nent magnets until the compass heading coincides with the magnetic heading, thus
removing all coefficient C on this heading. Use the same technique as in step 1.

3. Steady on magnetic heading 270° (090° if 270° was used in step 1) and remove
half the deviation with the fore-and-aft magnets. |

4. Steady on magnetic heading 000° (180° if 000° was used in step 2) and remove
half the deviation with-the athwartship magnets. d

5. Steady on any intercardinal magnetic heading and adjust the position of the
quadrantal correctors until the compass heading coincides with the magnetic heading,
thus removing all coefficient D on this heading. Leave the quadrantal correctors at
equal distances from the compass.

6. Steady on either intercardinal magnetic heading 90° from that used in step 5
and remove half the deviation by adjusting the positions of the quadrantal correctors,
leaving them at equal distances from the compass.

7. Secure all correctors in their final positions and record their number, size, posi-
tions, and orientation, as appropriate, on the bottom of the deviation table form (if a
standard form such as that shown in fig. 710 is used).

8. Swing ship for residual deviation. That is, determine the remaining deviation
on a number of headings at approximately equal intervals. Every 15° is preferable,
but if the maximum deviation is small, every 45° (cardinal and intercardinal headings)
may suffice.

9. If the vessel has degaussing, energize the degaussing coils and repeat the
swing.

10. Make a deviation table (art. 710) for each condition (degaussing off and on),
giving values for headings at 15° intervals if the maximum deviation is large (more than
about 2°), or at 45° intervals if the maximum deviation is small. Record values to the
nearest half degree.

If preferred, the adjustment may be started on a north or south heading, thus
reversing steps 1 and 2 and also 3 and 4.

With patience and skill, the readings can be made at exact headings. However,
if some of the headings are off slightly during the swing, this need not invalidate the
results. The exact headings should be recorded, and the deviation determined for
these values. The results can then be plotted on cross-section paper with the deviation
being one coordinate and the heading the other. The deviation at each heading to be
recorded can then be read from the curve. This is good practice even when readings
are made at exact headings, for if any large errors have been made, the fact will be
immediately apparent. Also, such a curve may be of assistance in making an analysis.
If a reason cannot be found for any marked irregularity in the curve, readings might be
made again at the headings involved.

The deviation of all compasses aboard the vessel can be determined from a single
swing if the heading by each compass is recorded at the moment the magnetic direction
is noted. If deviation of one compass is determined by means of a magnetic bearing or
azimuth (arts. 733-735), the readings of this compass can then be used to establish the
magnetic headings for determining the deviation of each other compass (art. 732).

COMPASS ERROR 195

Compass adjustment is best made when the sea is relatively smooth, so that steady
headings can be steered, and heeling error is absent. The setting of the heeling magnet
can be checked later, preferably at the next time that the vessel is on a north or south
heading and rolling moderately.

An analysis of deviation can be made either before or after adjustment. If this
reveals an excessive amount of A (constant) deviation, the source of the error should
be found and corrected (art. 723), if mechanical or mathematical. If an appreciable
amount of Æ deviation is present, E-links should be used and the spheres slewed. This
is particularly to be anticipated for compasses which are not on the center line.

The procedure outlined above is for initial adjustment aboard a new or radically
modified vessel. Deviation on the heading being used for navigation should be checked
from time to time and any important differences from the values shown on the deviation
table should be investigated. At sea, it is good practice to compare the magnetic and
gyro compasses at intervals not exceeding half an hour. The error of one or both of these
compasses should be checked twice a day when means are available. In pilot waters
deviation checks should be made as convenient opportunities present themselves.

Whenever there is reason to question the accuracy of the deviation table, the ship
should be swung at the first opportunity and a new table made up if there are significant
changes in the old one. Suitable occasions for swinging ship would be after a deviation
check indicates a significant error or after any event that might result in changes in the
magnetic field of the vessel (art. 712). Intervals of swing should not exceed three
months even when there is no reason to question the accuracy of the deviation table.

If a swing indicates the presence of large maximum deviation, the compass should
be readjusted. Unless there is reason to change it, the Flinders bar length should remain
the same. Other adjustments are altered as needed, none of the correctors being re-
moved at the beginning of adjustment. Whenever the vessel crosses the magnetic
equator, the opportunity should be used to check the deviation on magnetic headings
east and west. Any adjustment needed should be made by means of the fore-and-aft
(B) magnets. Upon crossing the magnetic equator, the heeling magnet should be
inverted.

The Flinders bar and quadrantal correctors should be checked for permanent
magnetism at intervals of about a year, or oftener if such magnetism is suspected.

Finding the Deviation

730. Placing a vessel on a desired magnetic heading.—As indicated in article 729,
compass adjustment is best made with the vessel on magnetic headings. The compass
being adjusted cannot be used for placing the vessel on a desired magnetic heading
because its deviation is unknown, and is subject to change during the process of adjust-
ment. A number of methods are available, including use of (1) another magnetic
compass of known deviation, (2) a gyro compass, (3) bearing of a distant object, and
(4) azimuth (art. 1428) of a celestial body.

Magnetic compass. The deviation at the desired magnetic heading is determined
from the deviation table for that compass, and applied to the magnetic heading to
determine the equivalent compass heading. |

Example 1.— It is desired to place a vessel on magnetic heading east, using the
standard compass. The deviation table for this compass is shown in figure 710.
Degaussing is off.

Required.—Heading per standard compass (psc). |

Solution.—From figure 710 the deviation on heading 090? magnetic with degaussing

196 COMPASS ERROR

off is found to be 225E. Therefore, the equivalent compass heading 1s 090° —2°5=
087:5.

Answer.—Hpse 08795. h

Gyro compass. The variation is applied to the desired magnetic heading, to deter-
mine the equivalent true heading. Any gyro error is then applied to determine the
equivalent gyro heading. This is the method commonly used by vessels equipped with
a reliable gyro compass. |

Example 2.—It is desired to place a vessel on magnetic heading north, using the
gyro compass. The variation in this area is 6° W, and the gyro error is TU

Required.—Heading per gyro compass (pgc). NA

Solution.—The equivalent true heading is 000? —6?—354?. The gyro heading is
354% 193535

Answer.—Hpge 353°.

Bearing of distant object. If a vessel remains within a small area during compass
adjustment, the bearing of a distant object is essentially constant. The required
distance of the object in miles is found by multiplying the cotangent of the maximum
tolerable error by the radius in miles of the maneuvering circle. Thus, if the maximum
error that can be tolerated is 025 (cotangent 114.6), and the vessel can be maneuvered
within 200 yards (0.1 mile) of a fixed position such as a buoy, the object selected should
be at least 114.6X0.1=11.5 miles away. The 200-yard limit is within radial lines
centered at the distant object and tangent to a circle having a radius of 200 yards and
its center at the center of the maneuvering area. Thus, a vessel has considerable
maneuvering space along the line of sight, but very limited room across this line. How-
ever, it is not necessary that the vessel stay within the required area, but only that it
be there when readings are made. Thus, if the center of the area is marked by a buoy,
the vessel might steady on each heading while still some distance away, and note the
required readings as the buoy is passed. In this way, a small radius may be practical
even for a large vessel.

The object selected should be conspicuous and should have a clearly defined
feature of small visible width upon which to observe bearings. The object having been
selected, its true bearing from the center of the maneuvering area should be measured
on the chart. To this, the variation at the center of the maneuvering area should be
applied to determine the equivalent magnetic bearing. The desired magnetic heading
should be set at the lubber’s line of the pelorus, and the far vane set at the magnetic
bearing of the distant object. The vessel should then be maneuvered until the object
is in line with the vanes.

Example 3.—It is desired to place a vessel on magnetic heading northeast in an
area where the variation is 4° E. The true bearing of a distant object is 219°.

Requred.—The setting of the pelorus.

Solution.—Set 045° at the lubber’s line, and set the far vane at 219°—4°—215°.

If preferred, 000? can be set at the lubber's line, and the far vane at the relative
bearing, 170° (magnetic bearing minus desired magnetic heading). If a gyro repeater or
a magnetic compass is used instead of a pelorus, the true (or magnetic) bearing should
be converted to the equivalent gyro (or compass) bearing.

If the distant object selected is not charted, or the position of the vessel is not
known accurately, the approximate magnetic bearing of the object can be determined -
by measuring its compass bearing on each cardinal and intercardinal compass heading,
and finding the mean of these readings. The value so determined will be incorrect
by the amount of any constant deviation (coefficient gin

Eixample 4.—The compass bearings of a distant object are as shown below.

COMPASS ERROR 197

Required.—The magnetic bearing of the object, assuming no constant deviation

(coefficient 4).

Solution.—

CH CB
000 324. 8
045 22097
090 3126
135 306. 8
180 304. 9
225 310. 8
270 3162
S15 320.0
sum 2516. 8

mean 314.6

Answer.—MB 31476.

Azimuth of celestial body. The true azimuth of the celestial body selected should
be computed (arts. 2125-2127) for the time of observation. The magnetic variation
should then be applied to determine the equivalent magnetic azimuth. The desired
magnetic heading should then be set at the lubber’s line of the pelorus, and the far
vane set at the magnetic azimuth of the celestial body. The vessel should then be
maneuvered until the body is in line with the vanes.

Example 5.—It is desired to place a vessel on magnetic heading west in an area
where the variation is 17° W, and at a time when the computed true azimuth of the
sun is 098°.

Requred.—The setting of the pelorus.

Solution.—Set 270? at the lubber’s line, and set the far vane at 098? 4-17? —115?.

If preferred, 000° can be set at the lubber’s line, and the far vane at the relative
azimuth (magnetic azimuth minus desired magnetic heading). If a gyro repeater or
a magnetic compass is used instead of a pelorus, the true (or magnetic) azimuth should
be converted to the equivalent gyro (or compass) azimuth.

731. Curve of magnetic azimuths.—During the course of compass adjustment
and swinging ship, a magnetic direction is needed many times, either to place the
vessel on desired magnetic headings or to determine the deviation of the compass
being adjusted. If a celestial body is used to provide the magnetic reference, the
azimuth is continually changing as the earth rotates on its axis. Frequent and numerous
computations can be avoided by preparing, in advance, à table or curve of magnetic
azimuths. True azimuths at frequent intervals are computed by any of the methods
of computation discussed in chapters XX and XXI. The variation at the center of
the maneuvering area is then applied to determine the equivalent magnetic azimuths.
These are plotted on cross-section paper, with time as the other argument, using any
convenient scale. A curve is then faired through the points.

Points at intervals of half an hour (with a minimum of three) are usually sufficient
unless the body is near the celestial meridian and relatively high in the sky, when
additional points are needed. If the body crosses the celestial meridian, the direction
of curvature of the line reverses.

Unless extreme accuracy is required, the Greenwich hour angle and declination
can be determined for the approximate mid time, the same value of declination used
for all computations, and the Greenwich hour angle considered to increase 15? per hour.

An illustration of a curve of magnetic azimuths of the sun is shown in figure 731.
This curve is for the period 0700-0900 zone time on May 31, 1958, at latitude 23?09:5 N,

198 COMPASS ERROR

078*

077° H

DEIER EI CERE aaa ca mala
crearla aloja ER ET ES CS
GAEL AE Aa

076* H

075°

074 H-

MAGNETIC AZIMUTH

073°

a E TESTE
072° f

071°

070°

ZONE TIME

FIGURE 731.—Curve of magnetic azimuths.

COMPASS ERROR 199

longitude 822241 W, about a mile north of Battery No. 5, Havana, Cuba. The
variation in this area is 2°47’ E. At the midtime, the meridian angle of the sun is
66°46°9 E, and the declination is 21%3/3 N. Azimuths were computed by H.O.
Pub. No. 260 (art. 2126) at half-hour intervals, as follows:

Zone time Meridian angle Declination Latitude d
Q u h m o o o /

0700 81 46.9 E (5 27.1 E) 21.9 N 23:2*/N 1 06950
0730 T4 16.9 R"(4*5771 E) 21.9 N 23.2:N* 071 57
0800 66 46.9 E (4 27.1 E) 21.9 N 23.2 N 074 06
0830 SOSO UNS 57.1'B) 21.9 N 23.2 N 076 08
0900 51 46.9 E (3 27.1 E) 21.9 N 23.2 N 078 07

This curve was constructed on the assumption that the vessel would remain in
approximately the same location during the period of adjustment and swing. If the
position changes materially, this should be considered in the computation.

732. Deviation by magnetic headings.—If the vessel is placed on a magnetic
heading by any of the methods of article 730, compass deviation on that heading is the
difference between the magnetic heading and the compass heading. If the compass
heading is less than the magnetic heading, deviation is easterly, if the compass heading
is greater than the magnetic heading, deviation is westerly.

Example.—A vessel is being maneuvered to determine the deviation of the magnetic
steering compass on cardinal and intercardinal headings. The gyro compass, which
has an error of 0°5 W, is used for placing the vessel on each of the magnetic headings.
Variation in the area is 27°5 E.

Required.—Deviation on each magnetic heading, using the compass headings
given below:

Solution.—

MH V TH GE Hpgc CH Dev.

000 27.0 10 027.5 0.5 W 028 009.3 0.3 W
045 2775 U) 072.5 0.5 W 073 046.1 He
090 216516 11725 0.5 W 118 093.6 3.6 W
135 2750 TH 162.5 0.5 W 163 136.7 PW
180 205 E 207.5 0.5 W 208 179.6 0.4 E
225 220110 252.5 0.5 W 253 223.8 1.2 E
270 24.0 Iu 297.5 0.5 W 298 266.5 3.5 E
315 27.51 342.5 0.5 W 343 313.2 1.8 E

733. Deviation by magnetic bearing or azimuth.—Deviation can be found by
comparing a magnetic bearing or azimuth with one measured by compass. The
magnetic direction can be obtained as explained in articles 730-731. If the compass
direction is less than the magnetic direction, deviation is easterly; if the compass direc-
tion is greater than the magnetic direction, deviation is westerly. This method is
used for determining deviation on a given compass heading. The equivalent magnetic
heading can be determined by applying the deviation thus determined. | If this method
is used for swinging ship, the values can be plotted as explained in article 729. For a
well-adjusted compass, the deviation may be so small that the compass headings can be
considered magnetic headings, without introducing significant errors.

Example.—The standard compass of a vessel has been adjusted, and the vessel is
to be swung for residual deviation during the period and for the place for which the
curve of magnetic azimuths of figure 731 has been constructed.

200 COMPASS ERROR

Required —Find the deviation on each heading given below, at the times indicated.
Solution.—
CH Time Cin MZn Deviation

e h m 8 o
000 7 35 20 073.2 072.4 0.8W
045 (4412102 074.0 072.8 1.2W
090 7 50 15 074.2 073.4 0.8 W
135 7 57 36 074.0 073.9 0.1 W
180 8 04 44 073.7 074.4 0.7E
225 S10 710 073.5 074.8 1.3E
270 8 16 33 074.3 075.2 0.9E
315 8 24 51 075.8 075.7 0.1 W

The magnetic azimuth (MZn) is determined from figure 731, and the deviation from
compass azimuth (CZn) and magnetic azimuth.

734. Deviation by a range is a special case of deviation by magnetic bearing.
Two objects appearing in line, one behind the other, constitute a range. Range
markers are established in many places to mark important channels, the extremities
of measured miles, etc. In addition, numerous good ranges occur naturally, as when
a lighthouse is in line with a tank, or a tower with a chimney. The true direction
of such a range can be determined by measurement on the chart, and variation applied
to determine the equivalent magnetic direction. In the case of a natural range, the
objects should preferably be at least an inch apart as they appear on the chart, to
minimize any plotting errors.

A range is superior to the bearing of a single object because it provides a critical
indication of when the vessel is in the correct position to take a reading. The vessel
crosses the range on various compass headings. At each crossing, the compass bearing
of the range is observed, and also the compass heading. It is well to use two ranges
nearly 90° apart, if available, because of the difficulty of crossing at small angles.

Example.—A vessel maneuvering to adjust its compass in the Lower Bay of New
York Harbor finds the true direction of the range between West Bank Light and
Coney Island Light to be 032%. The variation in this area is 1192W. The vessel steams
across the range on various compass headings, noting the compass direction of the range
at the times of crossing, as shown below.

Required.—The deviation on each compass heading indicated.

Solution.— he magnetic bearing of the range is 032? 4- 11?2—043?2.

CH MB Range CB Range Devtation
[0] o

o o

000 043.2 032.9 10.3 E
045 043.2 023.7 19.5 E
090 043.2 031.9 LESCH
135 043.2 044.2 1.0 W
180 043.2 048.5 5.9 W
225 043.2 051.0 7.8 W
270 043.2 055.6 12.4 W
315 043.2 049.8 6.6 W

The analysis of these results (art. 727) indicates a constant error of 120E. The

mean compass bearing is 042°2, differing from the correct magnetic bearing by the
amount of the constant error.

Ranges are widely used to check the deviation on the heading in use as a vessel

COMPASS ERROR 201

proceeds through pilot waters. In this manner several checks can be made without
advance preparation as a vessel enters or leaves port. ia
) 735. Deviation by reciprocal bearings.—Another method of using magnetic bear-
ings is by means of a compass on the beach. This method is particularly useful when
no suitable distant object or range is available, or where it may not be practical e
remain close to a given bearing line. G |

A reliable compass is taken ashore to a location which is free from maenetic dis-
turbance. If the location is not marked by a conspicuous object, such ESA beacon
flagpole, prominent tree, etc., a temporary marker should be erected. A staff with
a flag or bunting should be adequate. The marker should be of sufficient size and nature
to be conspicuous at the vessel. At suitable visual or radio signals from the vessel
bearings are observed simultaneously aboard the vessel and ashore. The bearings of
the vessel observed by the shore compass are magnetic. The reciprocals of these can
be considered magnetic bearings of the shore station from the vessel. The bearings
measured aboard the vessel are compass bearings. The difference is deviation. To
avoid confusion in the sequence of bearings, the time of each bearing is recorded.
Timepieces should be synchronized before the start of observations. -

Erample.—Simultaneous bearings are observed by a shore compass and the
standard compass aboard a vessel, as shown below.

Required.—The deviation of the standard compass on each heading.

Solution.—
MB of MB of shore CB of shore
CH Time vessel position position Deviation
000 112 507 127 lā 10 W
045 1120 309 129 13 2 W
090 1126 312 132 130 2E
135 1018 296 116 113 3 E
180 1029 295 115 109 6 E
225 1039 288 108 096 12 E
270 1052 288 108 113 5W
315 1104 280 109 115 6W

mean 118 TIS

The analysis of these results indicates no constant deviation. This is further in-
dicated by the fact that the means of the bearings aboard and ashore are equal.

Adjustment by Defiector

736. Principles involved.—As indicated in article 713, the magnetic field of a
vessel causes deviation of a magnetic compass, and also alters its directive force,
strengthening it on some headings and weakening it on others. The purpose of com-
pass adjustment is to neutralize the effect of the vessel's magnetic field on the compass.
If this is done completely, all deviation is removed, and the directive force is the same
on all headings. "The usual procedure, described earlier in this chapter, is to adjust by
reducing or eliminating the deviation. By the deflector method, the various correctors
are adjusted until the directive force is the same on all cardinal headings. Deviation
is then a minimum.

The relative directive force on various headings is determined by means of an in-
strument called a deflector. Actual measurement is of the setting of the instrument
when the compass card has been rotated or “deflected” through 90? under certain
standard conditions. The units are arbitrary “deflector units" which are used only

for comparison with readings on other headings.

202 COMPASS ERROR

The deflector method provides a quick adjustment with only four headings being
needed, without need for bearings, azimuths, or comparison with other compasses. It
is easy to use. However, it is not as thorough as the method described in article 729,
and should not be used when the usual method is available. The deflector method
makes no provision for determination of coefficient A (art. 716), the amount of Flinders
bar needed, the setiing of the heeling magnet, or the residual deviation. Coefficient
E can be determined, but is usually ignored. The method has never been popular in
the United States. It offers little or no advantage for a vessel equipped with a reliable
gyro compass.

737. Adjustment by deflector—The preliminary steps of adjustment are the
same as indicated in article 728, omitting those relating to peloruses and other com-
passes. Preparations having been completed, the adjustment should be carried out as
follows:

1. Steady on heading 000° (or 180°) by the compass being adjusted. Note the
heading by another compass and keep the vessel on this heading, steering by means of `
the second compass. Put the deflector in place over the first compass, and deflect
the compass card 90°. Record the reading on the deflector scale, and remove the
deflector.

2. Steady on heading 090° (or 270°) by the compass being adjusted, and follow
the procedure of step 1.

3. Steady on heading 180° (000° if 180° was used in step 1) by the compass being
adjusted, and determine the deflector reading by the procedure of step 1. Leave the
deflector in place and set it to the mean of the readings on headings 000° and 180°.
Adjust the fore-and-aft permanent magnets until the deflection is 90°. This corrects
for coefficient B, and the deflector readings on compass headings 000° and 180° should
now be the same. Remove the deflector.

4. Steady on heading 270° (090° if 270° was used in step 2) by the compass being
adjusted, and determine the deflector reading by the procedure of step 1. Leave the
deflector in place and set it to the mean of the readings on headings 090° and 270°.
Adjust the athwartship permanent magnets until the deflection is 90°. This corrects
for coefficient C, and the deflector readings on compass headings 090° and 180° should
now be the same.

5. Without changing the heading, set the deflector to the mean of the N-S and
E-W means. Adjust the quadrantal correctors until the deflection is 90°. This cor-
rects for coefficient D, and the deflector readings on all cardinal headings should be the
same. Remove the deflector.

Adjustment is now complete. It can be checked by repeating the five steps, a
procedure which is particularly recommended if the difference between deflector
readings on opposite headings is more than ten units. If means are available, and time
permits, the vessel should be swung for residual deviation. If preferred, a heading of
east or west can be used, reversing steps 1 and 2 and also steps 3 and 4.

This method is particularly useful when a quick adjustment is needed following
some change that affects the magnetic environment of the compass. Å

738. The Kelvin deflector was developed in Great Britain by Sir William Thomson
(Lord Kelvin). It consists essentially of two permanent magnets hinged like a pair
of dividers, with opposite poles at the hinge. The magnets are mounted vertically over
the center of the compass, with the hinged end on top. The separation of the lower
ends can be varied by means of a screw. The amount of separation, indicated by a
scale and vernier drums, is the reading used in the adjustment.

The deflecting force increases as the separation becomes greater. When the
deflector is in place over the compass, the blue pole is in line with the north (red) end

COMPASS ERROR 203

of the compass magnets, as indicated by a pointer. As the deflecting magnets are ro-
tated around the vertical axis of the instrument, the compass card rotates in the same
direction, but at a slower rate. The separation is adjusted until the rotation of the
instrument is 170° when the deflection of the compass card is 90°. These are the
standard conditions under which readings are made.

The Kelvin type deflector, which provides adjustment to an accuracy of 2° to 3°,
is used on many British merchant vessels. Deflectors are seldom used on British
Navy vessels.

739. The De Colong deflector was developed in Russia, and is standard equipment
on naval vessels of the USSR. It provides an accuracy of 0?5 to 1?0. Essentially,
this instrument consists of two horizontal magnets which are perpendicular to each
other. The small magnet is held in a fixed position close to the compass card. The
large magnet is mounted in a small tray which can be moved up and down along a
vertical spindle mounted over the center of the compass. The red end of this magnet
is placed toward the north. When it is positioned so that the directive force is exactly
neutralized, the small magnet causes the compass card to be deflected 90°. The
height of the large magnet is the deflector reading, the scale being on the vertical
spindle, and the index on the movable tray.

Provision is made for mounting the large magnet vertically, to measure the vertical
force of the magnetic field at the compass. A separate scale is provided for this purpose.
Additional magnets are generally provided for use near the magnetic equator, where the
vertical intensity is very small.

In practice, a separate deflector is provided for each compass, and they are not
interchangeable. By the addition of an auxiliary scale, the instrument could be made
usable for any compass.

Degaussing Compensation

740. Degaussing.—As indicated in article 712, a steel vessel has a certain amount
of permanent magnetism in its “hard” iron, and induced magnetism in its “soft” iron.
Whenever two or more magnetic fields occupy the.same space, the total field is the vector
sum (art. O18) of the individual fields. Thus, within the effective region of the field
of a vessel, the total field is the combined total of the earth’s field and that due to the
vessel. Consequently, the field due to earth's magnetism alone is altered or distorted
due to the field of the vessel. This is indicated by a tendency of the lines of force to
crowd into the metal of the vessel (art. 703), as shown in figure 741a.

Certain mines and other explosive devices are designed to be triggered by the
magnetic influence of a vessel passing near them. It is therefore desirable to
reduce to a practical minimum the magnetic field of a vessel. One method of doing
this is to neutralize each component by means of an electromagnetic field produced by
direct current of electricity in electric cables installed so as to form coils around the
vessel. A unit sometimes used for measuring the strength of a magnetic field is the
gauss. The reduction of the strength of a magnetic field decreases the number of gauss
in that field. Hence, the process is one of degaussing the vessel.

When a vessel's degaussing coils are energized, the magnetic field of the vessel is
completely altered. This introduces large deviation in the magnetic compasses.
This is removed, as nearly as practicable, by introducing at each compass an equal
and opposite force of the same type—one caused by direct current in a coil—for each
component of the field due to the degaussing currents. This is called compass com-
pensation. When there is a possibility of confusion with compass adjustment to
neutralize the effects of the natural magnetism of the vessel, the expression degaussing
compensation is used. Since the neutralization may not be perfect, a small amount

204 COMPASS ERROR

of deviation due to degaussing may remain on certain headings. This is the reason
for swinging ship twice—once with degaussing off and once with 1t on—and having
two separate columns in the deviation table (fig. 710). k ;

741. A vessel's magnetic signature.—A simplified diagram of the distortion of the
earth's magnetic field in the vicinity of a steel vessel is shown in figure 741a. The
strength of the field is indicated by the spacing of the lines, being stronger as the lines
are closer together. If a vessel passes over a device for detecting and recording the
strength of the magnetic field, a certain pattern is traced, as shown in figure 741b.
Since the magnetic field of each vessel is different, each has a distinctive trace, known
as its magnetic signature. The simplified signature shown in figure 741b is one that
might result from an uncomplicated field such as that shown in figure 741a.

Several degaussing stations have been established to determine magnetic signatures
and recommend the currents needed in the various degaussing coils. Since a vessel's
induced magnetism varies with heading and magnetic latitude, the current settings of
the coils which neutralize induced magnetism need to be changed to suit the conditions. -
A "degaussing folder" is provided each vessel to indicate the changes, and to give
other pertinent information.

A vessel's permanent magnetism changes somewhat with time and the magnetic
history of the vessel. "Therefore, the information given in the degaussing folder should
be checked from time to time by a return to the magnetic station.

742. Degaussing coils.—For degaussing purposes, the total field of the vessel is
divided into three components: (1) vertical, (2) horizontal fore-and-aft, and (3) hori-
zontal athwartships. The positive directions are considered downward, forward, and
to port, respectively. "These are the normal directions for a vessel headed north or
east in north latitude. Each component is opposed by a separate degaussing field just
strong enough to neutralize it. Ideally, when this has been done, the earth's field
passes through the vessel smoothly and without distortion. The opposing degaussing
fields are produced by direct current flowing in coils of wire. Each of the degaussing
coils is placed so that the field it produces is directed to oppose one component of the
ship's field.

The number of coils installed depends upon the magnetic characteristies of the
vessel, and the degree of safety desired. "The ship's permanent and induced magnetism
may be neutralized separately so that control of induced magnetism can be varied as
heading and latitude change, without disturbing the fields opposing the vessel's perma-
nent field. The principal coils employed are the following:

Main (M) coil. The M-coil is placed horizontal, and completely encircles the
vessel, usually at or near the water line. Its function is to oppose the vertical compo-
nent of the vessel's permanent and induced fields combined. Generally the induced
field predominates. Current in the M-coil is varied or reversed according to the change
of the induced component of the vertical field with latitude. |

Forecastle (F) and. quarterdeck (Q) coils. The F- and Q-coils are placed horizontal
just below the forward and after thirds (or quarters), respectively, of the weather deck.
The designation “Q” for quarterdeck is reminiscent of the days before World War II
when the “quarterdeck” of naval vessels was aft along the ship's quarter. These coils,
in which current can be individually adjusted, remove much of the fore-and-aft compo-
nent of the ship's permanent and induced fields. More commonly, the combined F-
and Q-coils consist of two parts; one part the FP- and QP-coils, to take care of the
permanent fore-and-aft field, and the other part, the FI- and Q7-coils, to neutralize
the induced fore-and-aft field. Generally, the forward and after coils of each type are
connected in series, forming a split-coil installation and designated FP-PQ coils and
FI-QI coils. Current in the FP-QP coils is generally constant, but in the FJ-Q7 coils

COMPASS ERROR 205

FIGURE 741a.— Simplified diagram of distortion of earth's magnetic field in the vicinity of a steel
vessel.

MAGNETIC
INTENSITY

FIGURE 741b.—Simplified signature of vessel of figure 741a.

206 COMPASS ERROR

is varied according to the heading and magnetic latitude of the vessel. In split-coil
installations, the coil designations are often contracted to P-coil and I-coil.

Longitudinal (L) coil. Better control of the fore-and-aft components, but at greater
installation expense, is provided by placing a series of vertical, athwartships coils along
the length of the ship. It is the field, not the coils, which is longitudinal. Current in
an L-coil is varied as with the FJ-Q/ coils. It is maximum on north and south head-
ings, and zero on east and west headings.

Athwartship (A) coil... The A-coil is in a vertical fore-and-aft plane, thus producing
a horizontal athwartship field which neutralizes the athwartship component of the
vessel's field. In most vessels, this component of the permanent field is small and can
be ignored. Since the A-coil neutralizes the induced field, primarily, the current 1s
changed with magnetic latitude and with heading, being maximum on east or west
headings, and zero on north or south headings. :

The strength and direction of the current in each coil is indicated and adjusted
at a control panel which is normally accessible to the navigator. Current may be `
controlled directly by rheostats at the control panel or remotely by push buttons which
operate rheostats in the engine room.

Since degaussing fields oppose the vessel's fields, the positive directions of the
degaussing fields are upward, aft, and to starboard. For positive fields in M, F, FI,
FP, Q, QI, and QP coils, current flows forward on the starboard side of the vessel;
and the north end of a small compass placed above any of these coils is deflected out-
board. For a positive field in the L-coil, current flows upward on the starboard side,
and the north end of a compass is deflected aft when placed below an upper, athwart-
ship portion of the coil. For a positive field in the A-coil, current in the upper, fore-
and-aft portion flows aft, and the north end of a compass is deflected to starboard
when placed below this portion of the coil. The FI-QI coils are generally connected
so that the field in the F7-coil is negative when that in the Q/-coil is positive.

Appropriate values of the current in each coil are determined at a degaussing sta-
tion, the various currents being adjusted until the vessel’s signature is made as flat
as possible. Recommended current values and directions for all headings and mag-
netic latitudes are set forth in the vessel’s degaussing folder. This document is nor-
mally retained by the navigator, whose responsibility it is to see that the recom-
mended settings are maintained whenever the degaussing system is energized.

743. Securing the degaussing system.—Unless the degaussing system is prop-
erly secured, residual magnetism may remain in the metal of the vessel. During de-
gaussing compensation and at other times, as recommended in the degaussing folder,
the “reversal” method is used. The steps in the reversal process are as follows:

1. Start with maximum degaussing current used since the system was last
energized.

2. Decrease current to zero and increase it in the opposite direction to the same
value as in step 1.

3. Decrease the current to zero and increase it to three-fourths maximum value
in the original direction.

4. Decrease the current to zero and increase it to one-half maximum value in
the opposite direction.

5. Decrease the current to zero and increase it to one-fourth maximum value in
the original direction. i

6. Decrease the current to zero and increase it to one-eighth maximum value in
the opposite direction.

7. Decrease the current to zero and open switch.

COMPASS ERROR 207

744. Magnetic treatment of vessels.—In some instances, the degaussing can be
made more effective by changing the magnetic characteristics of the vessel by a process
known as deperming. k Heavy cables are wound around the vessel in an athwartship
direction, forming vertical loops around the longitudinal axis of the vessel. The loops
are run beneath the keel, up the sides, and over the top of the weather deck at closely-
spaced equal intervals along the entire length of the vessel. Predetermined values of
direct current are then passed through the coils. When the desired magnetic charac-
teristics have been acquired, the cables are removed.

i A vessel which does not have degaussing coils, or which has a degaussing system
which is inoperative, can be given some temporary protection by a process known as
flashing. A horizontal coil is placed around the outside of the vessel and energized
with large predetermined values of direct current. When the vessel has acquired a
vertical field of permanent magnetism of the correct magnitude and polarity to reduce
to a minimum the resultant field below the vessel for the particular magnetic latitude
involved, the cable is removed. This type protection is not as satisfactory as that
provided by degaussing coils because it is not adjustable for various headings and
magnetic latitudes, and also because the vessel's magnetism slowly readjusts itself
following treatment.

During magnetic treatment it is a wise precaution to remove all magnetic com-
passes and Flinders bars from the vessel. Permanent adjusting magnets and quad-
rantal correctors are not materially affected, and need not be removed. If for any
reason it is impractical to remove a compass, the cables used for magnetic treatment
should be kept as far as practical from it.

745. Degaussing compensation.—The magnetic fields created by the degaussing
coils would render the vessel's magnetic compasses useless unless compensated. This
is accomplished by subjecting the compass to compensating fields along three mutually
perpendicular axes. These fields are provided by small compensating coils adjacent
to the compass. In nearly all installations, one of these coils, the heeling coil, is hori-
zontal and on the same plane as the compass card. Current in the heeling coil is ad-
justed until the vertical component of the total degaussing field is neutralized. The
other compensating coils provide horizontal fields perpendicular to each other. Cur-
rent is varied in these coils until their resultant field is equal and opposite to the hori-
zontal component of the degaussing field. In early installations, these horizontal fields
were directed fore-and-aft and athwartships by placing the coils around the Flinders
bar and the quadrantal spheres. Compactness and other advantages are gained by
placing the coils on perpendicular axes extending 045%-225 and 315°-135° relative
to the heading. A frequently used compensating installation, called the type “K,”
is shown in figure 745. It consists of a heeling coil extending completely around the
top of the binnacle, four “intercardinal” coils, and three control boxes. The inter-
cardinal coils are named for their positions relative to the compass when the vessel is
on a heading of north, and also for the compass headings on which the current in the
coils is adjusted to the correct amount for compensation. The NE-SW coils operate
together as one set, and the NW-SE coils operate as another. One control box is
provided for each set, and one for the heeling coil.

The compass compensating coils are connected to the power supply of the de-
gaussing coils, and the currents passing through the compensating coils are adjusted
by series resistances so that the compensating field is equal to the degaussing field.
Thus, a change in the degaussing currents is accompanied by a proportional change
in the compensating currents. Each coil has a separate winding for each degaussing

circuit it compensates.

208 COMPASS ERROR

Degaussing compensation is carried out while the vessel is moored at the ship-
yard where the degaussing coils are installed. This is usually done by personnel of
the yard, using the following procedure:

1. The compass is removed from its binnacle and a dip needle is installed in its
place. The M-coil and heeling coil are then energized, and the current in the heeling
coil is adjusted until the dip needle indicates the correct value for the magnetic latitude
of the vessel. The system is then secured by the reversing process.

2. The compass is restored to its usual position in the binnacle. By means of
auxiliary magnets, the compass card is deflected until the compass magnets are parallel
to one of the compensating coils
or set of coils used to produce
a horizontal field. The com-
pass magnets are then perpen-
dicular to the field produced `
by that coil. One of the de-
gaussing circuits producing a
horizontal field, and its com-
pensating winding, are then
energized, and the current in
the compensating winding .is
adjusted until the compass
reading returns to the value it
had before the degaussing circuit
was energized. The system is
then secured by the reversing
process. The process is re-
peated with each additional
circuit used to create a hori-
zontal field. The auxiliary
magnets are then removed.

3. The auxiliary magnets
are placed so that the compass
magnets are parallel to the
other compensating coils or set
of coils used to produce a hori-
zontal field. The procedure of
step 2 is then repeated for each _
circuit producing a horizontal
field.

FIGURE 745.— Type “K” degaussing compensation When the vessel gets under

installation. way, it proceeds to a suitable
i maneuvering area. The vessel
is then headed so that the compass magnets are parallel first to one compensating
coil or set of coils and then the other, and any needed adjustment is made in the com-
pensating circuits to reduce the error to a minimum. The vessel is then swung for
residual deviation, first with degaussing off and then with degaussing on, and the
correct current settings for each heading at the magnetic latitude of the vessel. From
the values thus obtained, the “DG OFF” and “DG ON” columns of the deviation table
(fig. 710) are filled In. If the results indicate satisfactory compensation, a record is
made of the degaussing coil settings and the resistances, voltages, and currents in the
compensating coil circuits. The control boxes are then secured.

COMPASS ERROR 209

Under normal operating conditions, the settings need not be changed unless changes '
are made in the degaussing system, or unless an alteration is made in the amount of
Flinders bar or the setting of the quadrantal correctors. However, it is possible for a
ground to occur in the coils or control box if the circuits are not adequately protected
from sea water or other moisture. If this occurs, it should be reflected by a change in
deviation with degaussing on, or by a decreased installation resistance. Under these
conditions, compensation should be carried out again. If the compass is to be needed
with degaussing on before the ship can be returned to a shipyard where the com-
pensation can be made by experienced personnel, the compensation should be made at
sea on the actual headings needed, rather than by deflection of the compass needles by
magnets. More complete information related to this process is given in H.O. Pub.
No. 226 and the degaussing folder.

If a vessel has been given magnetic treatment, its magnetic properties have been
changed. This necessitates readjustment of each magnetic compass. This is best
delayed for several days to permit stabilization of the magnetic characteristics of the
vessel. If this cannot be delayed, the vessel should be swung again for residual deviation
after a few days. Degaussing compensation should not be made until after compass
adjustment has been completed.

Problems

711a. Fill in the blanks in the following:

ING! V MC D EC CE
(1) 105 15E — 5W — =
Ø) = — 4E 215 14E
@ = 12W = = 067 7W
(4) 156 — 166 = 160 Er
(5) 222 = 216 3W ast xt
(6) 009 x 357 = — 10E
(7) — 2W = 6E 015 Æ
CSR = 210 == 214 LW

Answers.—(1) MC 090°, CC 095°, CE 10°E; (2) TC 229°, V 10°E, MC 219°; (3)
TC 060°, MC 072°, D 5°E; (4) V 10°W, D 6?E, CE 4°W; (5) V 6? E, CC 219°,
CE 3°E; (6) V 12? E, D 2? W, CC 359°; (7) TC 019°, MC 021°, CE 4? E; (8) TC 213^,
hee LE, [D 4% W: mal ap

711b. A vessel is on course 150? by compass in an area where the variation is 19° E.
The deviation is as shown in figure 710. Degaussing is on.

Required.—(1) Deviation.

(2) Compass error.

(3) Magnetic heading.

(4) True heading.

Answers.—(1) D 1°E, (2) CE 20? E, (3) MH 151°, (4) TH 170°.

711c. A vessel is on course 055° by gyro and 041° by magnetic compass. The gyro
error is 19 W. The variation is 15° E.

Required.—The deviation on this heading.

Answer.—D 2? W.

711d. A vessel is on course 177? by gyro. The gyro error is 0.5E. A beacon bears
088? by magnetic compass in an area where variation is 11^ W. The deviation is as

shown in figure 710, degaussing off.

210 COMPASS ERROR

Required.—The true bearing of the beacon.

Answer.—TB 076°.

721a. A magnetic compass is adjusted on the magnetic equator, without any
Flinders bar being used. The residual deviation on heading 090° magnetic is 1° E.
Some days later, at latitude 37° N, dip 70°, the deviation on heading 090° is 12? W.

Required.—The length and location of Flinders bar required to restore a residual
deviation of 1? E (using fig. 721, A) if the magnetic properties of the vessel are unchanged.

Answer.—Fifteen inches of Flinders bar forward of the compass.

721b. The deviation of a magnetic compass of a vessel on heading 270° magnetic `
is 22E at Sydney, Australia (south magnetic latitude) and 12? W at Seattle, Wash.
(north magnetic latitude). At Sydney, H—0.258 and Z—0.51. At Seattle, H —0.188
and Z=0.53. The shielding factor is 0.9.

Required.—The length of Flinders bar to use if (1) no Flinders bar is in place
during observations, (2) 12 inches of Flinders bar is in place forward of the compass dur-
ing observations.

Answers.—(1) 8% inches (8.5 inches by computation) of Flinders bar aft of the
compass, (2) nine inches (8.8 inches by computation) of Flinders bar forward of the
compass.

727. A magnetic compass which has not been adjusted has deviation on cardinal
and intercardinal compass headings as follows:

Compass heading Deviation Compass heading Deviation
000 2.0 E 180 6.0 E
045 20.5 E 225 5.5 W
090 18.5 E 270 22.0 W
135 8.0 E 315 23:5 W

On heading compass north the deviation is 620 W when the vessel heels 7° to starboard.

Required.—(1) The approximate value of each coefficient.

(2) The total deviation to be expected on compass heading 300°, with the vessel
on an even keel.

(3) Heeling error on compass heading 060°, with a heel of 10°.

Answers.—(1) A (+)0°5, B (+)20°2, C (—)2?0, D (+)7°6, E (+)2°9, J (—)1?1;
(2) d 26°0 W; (3) HE 575.

730a. It is desired to place a vessel on magnetic heading west, using the magnetic
steering compass. The deviation table for this compass is shown in figure 710. De-
gaussing is on.

Required.—Heading per steering compass (p stg c).

Answer.—Hp stg c 272°.

730b. It is desired to place a vessel on magnetic heading south, using the gyro
compass. The variation in this area is 12? E, and the gyro error is 095 E.

Required. —Heading per gyro compass.

Answer.—Hpge 19125.

730c. It is desired to place a vessel on magnetic heading southeast in an area
where the variation is 6? W. The true bearing for a distant object is 047?.

Required.—(1) The magnetic bearing of the object.

(2) The relative bearing of the object when the vessel is on the desired magnetic
heading.

Answers.—(1) MB 058°, (2) RB 278°.

COMPASS ERROR 211

730d. The compass bearings of a distant object are as follows:

CH CB CH CB
000 358 180 002
045 dodi 295 006
090 351 270 012
185 353 815 009

Required.—The magnetic bearing of the object, assuming no constant deviation
(coefficient 4).

Answer.—MB 001°.

730e. It is desired to place a vessel on magnetic heading east in an area where the
variation is 13? E, and at a time when the computed true azimuth of the sun is 218°.

Required.—(1) The magnetic azimuth of the sun.

(2) The relative azimuth when the vessel is on the desired magnetic heading.

(3) The azimuth by a magnetic compass having deviation as shown in figure 710
(DG on).

(4) The azimuth by a gyro compass having a gyro error of 1° W.

Answers.—(1) MZn 205°, (2) RZn 115°, (3) CZn 202°, (4) Znpge 219°.

732. A vessel is being maneuvered to determine the residual deviation of a magnetic
compass. The gyro compass, which has an error of 1° E, is used for placing the vessel on
the magnetic headings indicated below. Variation in the area is 728 W. The following
readings are obtained:

MH GA MH CH
000 000.0 180 180.1
045 044.1 225 225.8
090 088.5 270 271.4
135 134.2 315 315.9
Required.—Gyro heading and deviation on each magnetic heading.
Answers.—
MH Hpgc Dev. MH Hpgc Dev.
000 351.2 0.0 180 171.2 0.1 W
045 036.2 0.9 E 225 216.2 0.8 W
090 081.2 1.5 E 270 261.2 1.4 W
135 126.2 0.8 E 315 306.2 0.9 W

733. A vessel is being swung for residual deviation during the period and at the
place for which the curve of magnetic azimuths of figure 731 has been constructed.
The following readings are obtained:

CH Time CZn CH Time CZn
o h m s o o D kai A o
000 150913907 3.4 180 S n, dd (m
045 On Be aes 229 3 Z9 10) se
090 810455 119 270 SPTP

135 8 11 01 74.0 315 Seo alee WZ

212 COMPASS ERROR

Required.—Deviation on each compass heading.

Answers.— a?
CH Deviation CH Deviation
000 0.1 E 180 0.0
045 1.3 E 225 1227 VV:
090 2.6 E 270 2.8 W
135 0.9 E SS 0.8 W

734. A vessel being swung for residual deviation crosses a range on various compass
headings as indicated below, the compass bearing of the range being observed at each
crossing. The true direction of the range is 255°. The variation in the vicinity is 2495 E.

CH CB CH CB
000 230.3 180 230.6
045 228.7 225 232.4
090 227.4 270 233.8
135 228.0 315 232.3
Required.—Deviation on each compass heading.
Ánswers.—
CH Deviation CH Deviation
000 0.2 E 180 0.1 W
045 1.8 E 225 1.9 W
090 3.1 E 270 3.3 W
135 Sech 315 1.8 W

735. Bearings of a vessel are taken by means of a compass ashore, and simultaneous
bearings of the shore position are taken from the vessel, as follows:

CB of CB of

shore MB of shore MB of
CH position vessel CH position vessel
000 020 198 180 003 184
045 013 189 i 225 009 194
090 004 174 270 013 204
135 001 172 315 017 205

Required.—(1) Deviation on each heading.
(2) The value of coefficient A.

Answers.—

(1)
CH Deviation CH Deviation
000 2 W 180 1E
045 4 W 225 5E
090 10 W 270 11 E
135 9W 315 8E

(2) Coefficient A is zero.

CHAPTER VIII

DEAD RECKONING

801. Introduction.—Dead reckoning (DR) is the determination of position by
advancing a known position for courses and distances. It is reckoning relative to
something stationary or “dead” in the water, and hence applies to courses and speeds
through the water. Because of leeway due to wind, inaccurate allowance for compass
error, imperfect steering, or error in measuring speed, the actual motion through the
water is seldom determined with complete accuracy. In addition, if the water itself
is in motion, the course and speed over the bottom differ from those through the water.
It is good practice to use the true course steered and the best determination of measured
speed, which is normally speed through the water, for dead reckoning. Hence, geo-
graphically, a dead reckoning position is an approximate one which is corrected from
time to time as the opportunity presents itself. Although of less than the desired
accuracy, dead reckoning is the only method by which a position can be determined
at any time and therefore might be considered basic navigation, with all other methods
only appendages to provide means for correcting the dead reckoning. The prudent
navigator keeps his direction- and speed- or distance-measuring instruments in top
condition and accurately calibrated, for his dead reckoning is no more accurate than
his measurement of these elements.

If a navigator can accurately assess the disturbing elements introducing geo-
graphical errors into his dead reckoning, he can determine a better position than that
established by dead reckoning alone. This is properly called an estimated position
(EP). It may be established either by applying an estimated correction to a dead
reckoning position, or by estimating the course and speed being made good over the
bottom. The expression “dead reckoning” is sometimes applied loosely to such reckon-
ing, but it is better practice to keep this “estimated reckoning” distinct from dead
reckoning, if for no other reason than to provide a basis for evaluating the accuracy
of one’s estimates. When good information regarding current, wind, etc., is available,
it should be used, but the practice of applying corrections based upon information of
uncertain accuracy is, at best, questionable, and may introduce an error. Estimates
should be based upon judgment and experience. Positional information which is
incomplete or of uncertain accuracy may be available to assist in making the estimate.
However, before adequate experience is gained, one should be cautious in applying
corrections, for the estimates of the inexperienced are often quite inaccurate.

Dead reckoning not only provides means for continuously establishing an ap-
proximate position, but also is of assistance in determining times of sunrise and sunset,
the celestial bodies available for observation, the predicted availability of electronic
aids to navigation, the suitability and interpretation of soundings for checking position,
the predicted times of making landfalls or sighting lights, estimates of arrival times, and
in evaluating the reliability and accuracy of position-determining information. Be-
cause of the importance of accurate dead reckoning, a careful log is kept of all courses
and speeds, times of all changes, and compass errors. These may be recorded directly
in the log or first in a navigator’s notebook for later recording in the log, but whatever
the form, a careful record is important. | ; :

Modern navigators almost invariably keep their dead reckoning by plotting directly

on the chart or plotting sheet, drawing lines to represent the direction and distance of
213

214 DEAD RECKONING

travel and indicating dead reckoning and estimated positions from time to time.
This method is simple and direct. Large errors are often apparent as inconsistencies
in an otherwise regular plot. Before the advent of power vessels, when frequent course
and speed changes were common, and when charts were sometimes of questionable
accuracy, it was common practice to keep the dead reckoning mathematically by one,
or a combination, of the “sailings” (arts. 811-825). Except for great-circle sailing,
and occasionally composite and Mercator sailings, these are of little more than historical
interest to modern navigators, other than those of small boats. vi

In determining distance run in a given time, one may find table 19 useful. Similar
information is given in a somewhat different form in an auxiliary table in H.O. Pub.
No. 214.

802. Plotting position ow the chart.—A position is usually expressed in units of
latitude and longitude, generally to the nearest 0*1, but it may be expressed as bearing
and distance from a known position, such as a landmark or aid to navigation.

To plot a position on a Mercator chart, or to determine the coordinates of a point
on such a chart, proceed as follows:

To plot a position when its latitude and longitude are known: Mark the given latitude
on a convenient latitude scale along a meridian, being careful to note the unit of the
smallest division on the scale. Place a straightedge at this point and parallel to a
parallel of latitude (perpendicular to à meridian). Holding the straightedge in place,
set one point of a pair of dividers at the given longitude on the longitude scale at
the top or bottom of the chart (or along any parallel) and the other at à convenient
printed meridian. Without changing the spread of the dividers, place one point on
the same printed meridian at the edge of the straightedge, and the second point at the
edge of the straightedge in the direction of the given longitude. This second point is
at the given position. Lightly prick the chart. Remove first the straightedge and
then the dividers, watching the point to be sure of identifying it. Make a dot at the
point, enclose it with a small circle or square as appropriate (art. 805), and label it.
If the dividers are set to the correct spread for longitude before the latitude is marked,
one point of the dividers can be used to locate the latitude and place the straightedge,
if one is careful not to disturb the setting of the dividers.

To determine the coordinates of a point on the chart: Place a straightedge at the given
point and parallel to a parallel of latitude. Read the latitude where the straightedge
crosses a latitude scale. Keeping the straightedge in place, set one leg of a pair of
dividers at the given point and the other at the intersection of the straightedge and a
convenient printed meridian. Without changing the spread of the dividers, place one
end on a longitude scale, at the same printed meridian, and the other point on the
scale, in the direction of the given point. Read the longitude at this second point.

Several variations of these procedures may suggest themselves. That method
which seems most natural and is least likely to result in error should be used.

803. Measuring direction on the chart.—Since the Mercator chart, commonly used
by the marine navigator, is conformal (art. 302), directions and angles are correctly
represented. It is customary to orient the chart with 0009 (north) at the top; other
directions are in their correct relations to north and each other.

As an aid in measuring direction, compass roses are placed at convenient places on
the chart or plotting sheet. A desired direction can be measured by placing a straight-
edge along the line from the center of a compass rose to the circular graduation repre-
senting the desired direction. "The straightedge is then in the desired direction, which
may be transferred to any other part of the chart by parallel motion, as by parallel
rulers or two triangles (art. 603). The direction between two points is determined by
transferring that direction to a compass rose. If a drafting machine (art. 606) or some

DEAD RECKONING 215

form of plotter (art. 605) or protractor (art. 604) is used, measurement can be made
directly at the desired point, without using the compass rose.

Measurement of direction, whether or not by compass rose, can be made at any
convenient place on a Mercator chart, since meridians are parallel to each other and a
line making a desired angle with any one makes the same angle with all others. Such
a line isa rhumb line, the kind commonly used for course lines, except in polar regions.
For direction on a chart having nonparallel meridians, measurement can be made at
the meridian involved if the chart is conformal, or by special technique if it is not
conformal. Explanation of the former is given in article 2511. The only nonconformal
chart commonly used by navigators is the gnomonic, and instructions for measuring
direction on this chart are usually given on the chart itself.

Compass roses for both true and magnetic directions may be given. A drafting
machine can be oriented to any reference direction—true, magnetic, compass, or grid.
When a plotter or protractor is used for measuring an angle with respect to a
meridian, the resulting direction is true unless other than true meridians are used.
For most purposes of navigation it is good practice to plot true directions only, and to
label them in true coordinates.

804. Measuring distance on the chart.—The length of a line on a chart is usually
measured in nautical miles, to the nearest 0.1 mile. For this purpose it is customary to
use the latitude scale, considering one minute of latitude equal to one nautical mile.
The error introduced by this assumption is not great over distances normally measured.
It is maximum near the equator or geographical poles. Near the equator a ship travel-
ing 180 miles by measurement on the chart would cover only 179 miles over the earth.
Near the pole a run of 220 miles by chart measurement would equal 221 miles over the
earth.

Since the latitude scale on a Mercator chart expands with increased latitude, meas-
urement should be made at approximately the mid latitude. For a chart covering a
relatively small area, such as a harbor chart, this precaution is not important because
of the slight difference in scale over the chart. On such charts a separate mile scale
may be given, and it may safely be used over the entire chart. However, habit is
strong, and mistakes can probably be avoided by always using the mid latitude.

For long distances the line should be broken into à number of parts or /egs, each
one being measured at its mid latitude. The length of a line that should be measured
in a single step varies with latitude, decreasing in higher latitudes. No realistic nu-
merical value can be given, since there are too many considerations. With experience
a navigator determines this for himself. On the larger scale charts this is not a problem
because the usual dividers used for this purpose will not span an excessively long
distance.

In measuring distance, the navigator spans with his dividers the length of the line
to be measured and then, without altering the setting, transfers this length to the
latitude scale, carefully noting the graduations so as to avoid an error in reading.
This precaution is needed because of the difference from chart to chart. In measuring
a desired length along a line, the navigator spans this length on the latitude scale
opposite the line and then transfers his dividers to the line, without changing the setting.
For a long line the navigator sets his dividers to some convenient distance and steps
off the line, counting the number of steps, multiplying this by the length of the step,
and adding any remainder. If the line extends over a sufficient spread of latitude to
make scale difference a factor, he resets his dividers to the scale for the approximate
mid latitude of each leg. The distance so measured is the length of the rhumb line.

For measuring distance on a nearly-constant-scale chart, such as the Lambert
conformal, the mid-latitude precaution is usually unnecessary. Such charts generally

216 DEAD RECKONING

have a mile scale independent of the latitude scale. On a gnomonic chart a special
procedure is needed, and this is usually explained on the chart. i i |

805. Plotting and labeling the course line and positions.— Course is the intended
horizontal direction of travel. A course line is a line extending in the direction of the
course. From a known position of the ship the course line is drawn in the direction
indicated by the course. It is good practice to label all lines and points of significance
as they are drawn, for an unlabeled line or point can easily be misinterpreted later.
Any simple, clear, logical, unambiguous system of labels is suitable. "The following
is widely used and might well be considered standard.

Label a course line with direction and speed. Above the course line place a capital
C followed by three figures to indicate the course steered. It is customary to label
and steer courses to the nearest whole degree, although they are generally computed to
the nearest 0?1. "The course label should indicate true direction, starting with 000? at
true north and increasing clockwise through 360%. Below the course line, and under
the direction label, place a capital S followed by figures representing the speed in
knots. Since the course is always given in degrees true and the speed in knots, it 1s
not necessary to indicate the units or the reference direction (fig. 805).

A point to be labeled is enclosed by a small circle in the case of a fix (an accurate
position determined without reference to any former position) or dead reckoning

position, and by a small square
in the case of an estimated po-
R sition. It is labeled with the
S S F time, usually to the nearest
H
Brenner tE minute, and the nature of the
S15 position (FIX, EP, DR). Time
Figure 805.—A course line with labels. 1s usually expressed in four fig-
ures without punctuation, on a
24-hour basis (art. 1903). Zone time (art. 1907) is usually used, but Greenwich
mean time (art. 1907) may be employed. A course line is a succession of an infinite
number of dead reckoning positions. Only selected points are labeled.

The labels of a line are placed along the line, and those of a point are at an angle
to the line.

806. Dead reckoning by plot.—As a vessel clears a harbor and proceeds out to sea,
the navigator obtains one last good fix while identifiable landmarks are still available.
This is called taking departure, and the position determined is called the departure.
Piloting (ch. IX) comes to an end and the course is set for the open sea. The course
line is drawn and labeled, and some future position is indicated as a DR position.
The number of points selected for labeling depends primarily upon the judgment and
individual preference of the navigator. It is good practice to label each point where
a change of course or speed occurs. If such changes are frequent, no additional points
need be labeled. With infrequent changes, it is good practice to label points at some
regular interval, as every two hours. From departure, the dead reckoning plot con-
tinues unbroken until a new well-established position is obtained, when both DR and
fix are shown. The fix serves as the start of a new dead reckoning plot. Although
estimated positions are shown, it is generally not good practice to begin a new DR
at these points.

A typical dead reckoning plot is shown in figure 806, indicating procedures both
when there are numerous changes of course and speed and when there is a long con-
tinuous course. It is assumed that no fix is obtained after the initial one at 0800 on
September 8. Note that course lines are not extended beyond their limits of usefulness.
One should keep a neat plot and leave no doubt as to the meaning of each line and

$

DEAD RECKONING 217

69 W 68 °W
67° S
42°N = W 66 W 65°W
21 DR vi
pie Se Da e 42 N
1230 DR g-T- SD amt
IN
S 71500 DR
& 0915 DR Bis SR
o/o
_ 1700 DR
ve j-
ala «1800 DR
(01524 1100 DR
1015 DR O s) a i!
41°N T
41°N
å 1700 DR G
E
Os 1600 DRS
E 1500 DRS
- 1400 DRS
o / 0100 DR
40 N E L 1300 DRS j (Sept. 9)- 40? N
E
B 1200 DRS
D 0200 DR
E 1100 DRS
STA Ø 0300 DR
H 1000 DR ©
ISS `
: 0400 DR Ø
1
en? mei 39°N
jo O: o
69 W 68° W 67 °W 66° W 65'W

FIGURE 806.—A typical dead reckoning plot.

marked point. A neat, accurate plot is the mark of a good navigator. The plot should
be kept extended to some future time. A good navigator is always ahead of his ship.
In shoal water or when near the shore, aids to navigation, dangers, etc., it is customary
to keep the dead reckoning plot on a chart. A chart overprinted with loran or other
electronic position lines may be used at a considerable distance from shore. But on
the open sea, with only dead reckoning and celestial navigation available, it is good
practice to use a plotting sheet (art. 323).

807. Current.—Water in essentially horizontal motion over the surface of the
earth is called current. The direction in which the water is moving is called the set,
and the speed is called the drift. In navigation it is customary to use the term “cur-
rent” to include all factors introducing geographical error in the dead reckoning, whether
their immediate effects are on the vessel or the water. When a fix is obtained, one as-
sumes that the current has set from the DR position at the same time to the fix, and
that the drift is equal to the distance in miles between these positions, divided by the
number of hours since the last fix. This is true regardless of the number of changes
of course or speed since the last fix.

218 DEAD RECKONING

If set and drift since the last fix are known, or can be estimated, a better position
can be obtained by applying a correction to that obtained by dead reckoning. This
is conveniently done by drawing a straight line in the direction of the set for a distance
equal to the drift multiplied by the number of hours since the last fix, as shown in figure
805. The direction of a straight line from the last fix to the EP is the estimated course
made good, and the length of this line divided by the time is the estimated speed made
good. These estimated values are sometimes called the course of advance (COA)
and speed of advance (SOA), respectively. The course and speed actually made good
over tbe ground are then called the course over the ground (COG) and speed over the
ground (SOG), respectively.

If a current is setting in the same direction as the course, or its reciprocal, the
course over the ground is the same as that through the water. The effect on the speed
can be found by simple arithmetic. If the course and set are in the same direction,
the speeds are added; if in opposite directions, the smaller is subtracted from the larger.
This situation is not unusual when a ship encounters a tidal current while entering or
leaving port. If a ship is crossing a current, solution can be made graphically by
vector diagram (arts. O17, O18) since velocity over the ground is the vector sum of
velocity through the water and velocity of the water. Although distances can be used,
it is generally easier to use speeds.

Example 1.—A ship on course 080°, speed ten knots, is steaming through a current
having an estimated set of 140% and drift of two knots.

Required.—Estimated course and speed made good.

Course steered OT i
Speed Through

Course Made Good 089
Speed Made Good 11.2

FIGURE 807a.—Finding course and speed made good through a current.

A

Solution (fig. 807a).—(1) From A, any convenient point, draw AB, the course and
speed of the ship, in direction 080°, for a distance of ten miles.
(2) From B draw BC, the set and drift of the current, in direction 140°, for a
distance of two miles.
(3) The direction and length of AC are the estimated course and speed made good.
Determine these by measurement.
Answers.—Estimated course made good 089°, estimated speed made good 11.2 kn.
If it is required to find the course to steer at a given speed to make good a desired
course, plot the current vector from the origin, A, instead of from B.
Example 2.—The captain desires to make good a course of 095° through a current
having a set of 170° and a drift of 2.5 knots, using a speed of 12 knots.
Required.—The course to steer and the speed made good.
Solution (fig. 807b).—(1) From A, any convenient point, draw line AB extending
in the direction of the course to be made good, 095°.
(2) From A draw 40, the set and drift of the current.
(3) Using C as a center, swing an arc of radius CD, the speed through the water
(12 knots), intersecting line AB at D.
(4) Measure the direction of line CD, 083°5. This is the course to steer.
(5) Measure the length AD, 12.4 knots. This is the speed made good.

DEAD RECKONING 219

Course To M

ake
Speed Made wed 088

Good ] 24

5
Course To Steer 083.
LA: Speed Through Water 12

Figure 807b.—Finding the course to steer at a given speed to make good a given
course through a current.

Answers.— Course to steer 08325, speed made good 12.4 kn.

If it is required to find the course to steer and the speed to use to make good a
desired course and speed, proceed as follows:

Example 3.— The captain desires to make good a course of 265? and a speed of 15
knots through a current having a set of 185? and a drift of three knots.

Required.—The course to steer and the speed to use.

Course To Make Good 265
ed To Make Good 15

Course To Steer 276
Speed Through Water 14.8

FIGURE 807c.—Finding the course to steer and the speed to use to make good a given course
and speed through a current.

Solution (fig. 807c).—(1) From A, any convenient point, draw AB in the direction
of the course to be made good, 265°, and for a length equal to the speed to be made
good, 15 knots.

(2) From A draw AC, the set and drift of the current.

(3) Draw a straight line from C to B. The direction of this line, 276°, is the
required course to steer; and the length, 14.8 knots, is the required speed.

Answers.—Course to steer 276°, speed to use 14.8 kn.

Such vector solutions can be made to any convenient scale and at any convenient
place, such as the center of a compass rose, an unused corner of the plotting sheet, a
separate sheet, or directly on the plot.

808. Leeway is the leeward motion of a vessel due to wind. It may be expressed
as distance, speed, or angular difference between course steered and course through the
water. However expressed, its amount varies with the speed and relative direction of
the wind, type of vessel, amount of freeboard, trim, speed of the vessel, state of the
sea, and depth of water. If information on the amount of leeway to be expected under
various conditions is not available for the type vessel involved, it should be determined
by observation. When sufficient data have been collected, suitable tables or graphs
can be made for quick and convenient estimate. The accuracy of the information
should be checked whenever convenient, and corrections made when sufficient evidence
indicates the need.

Leeway is most conveniently applied by adding its effect to that of current and
other elements introducing geographical error in the dead reckoning. It is customary
to consider the combined effect of all such elements as current, and to make allowance

220 DEAD RECKONING

for this as explained in article 807. In sailing ship days it was common practice to 3
consider leeway in terms of its effect upon the course only, and to apply it as a correction
in the same manner that variation and deviation are applied. While this method has
merit even with power vessels, it is generally considered inferior to that of considering
leeway as part of current.

809. Automatic dead reckoning.—Several types of devices are in use for per-
forming automatically all or part of the dead reckoning. Perhaps the simplest is the
automatic course recorder, which provides a graphical record of the various courses
steered. In its usual form this device is controlled by the gyro compass, and so
indicates gyro courses.

Dead reckoning equipment receives inputs from the compass, usually the gyro
compass, and a mechanical log or engine revolution counter. It determines change in
latitude and longitude, the latter by first determining departure and then mechanically
multiplying this by the secant of the latitude. The device is provided with counters
on which latitude and longitude can be set. As the vessel proceeds, the changes are
then mechanically added to or subtracted from these readings to provide a continuous,
instantaneous indication of the dead reckoning position. The navigator or an assistant
reads these dials at intervals, usually each hour, and records the values in a notebook.
Most models of dead reckoning equipment are provided, also, with a tracer for keeping
a graphical record of dead reckoning in the form of a plot by moving a pencil or pen
across a chart or plotting sheet. This part of the device is called a dead reckoning
tracer. Whatever the form, dead reckoning equipment is a great convenience, partic-
ularly when a ship is maneuvering. However, such mechanical equipment is subject
to possible failure. The prudent navigator keeps a hand plot and uses the dead reck-
oning equipment as a check. In navigation it is never wise to rely upon a single method
if a second method is available as a check.

If it were possible to measure, with complete accuracy, the direction and distance
traveled with respect to the earth, an accurate geographical position could be known at
all times. Several methods of doing so have been suggested, and while developments
along these lines relate principally to aircraft and guided missiles, it is possible that
from these or other developments may come some method suitable for shipboard use.
The two methods most prominently suggested are (1) Doppler and (2) inertial. By the
Doppler method one or more beams of radiant energy are directed downward at an
angle. The return echo from the bottom is of a slightly different frequency due to the
motion of the craft. The amount of the change, or Doppler, is proportional to the
speed. By proper selection of beams, it is possible to measure speed in a lateral direction
as well as in a forward direction. Distance can be determined by mechanical or elec-
tronic integration of these measurements, and this can be converted into position.
By the inertial method, accelerometers measure the acceleration in various directions,
and by double integration this is converted to distance, from which position can be
determined. Either of these methods can provide considerable accuracy over a period
of several hours, but since the error increases with time, they are not yet suitable for
general shipboard use over long distances.

l 810. Dead reckoning by computation.—Dead reckoning involves the determina-
tion of position by means of course and distance from a known position. A closely
related problem is that of finding the course and distance from one point to another.
Although both of these problems are customarily solved by plotting directly on the
chart, it occasionally becomes desirable to solve by computation, usually by logarithms
(arts. 010-015) or traverse table (art. 812). The various methods of solution are

DEAD RECKONING 221

collectively called the sailings. Computation should be carried to the precision shown
in the examples, even though this in some instances exceeds the usable precision, and
sometimes the accuracy. Å

811. The sailings.—In the solution of problems involved in the sailings, the
following quantities are used:

1. Latitude (L). The latitude of the point of departure is designated Lı; that of
the point of arrival or the destination, L»; mid latitude, Lm; latitude of the vertex of a
great circle, Ly; and latitude of any point on a great circle, Ly.

2. Difference of latitude (l).

3. Meridional parts (M). The meridional parts of the point of departure are
designated M,, and of the point of arrival or the destination, M».

4. Meridional difference (m).

5. Longitude (X). The longitude of the point of departure is designated X; that
of the point of arrival or the destination, M; of the vertex of a great circle, Ay; and of
any point on a great circle, Xx.

6. Difference of longitude (DLo).

7. Departure (p).

8. Course or course angle (Cn or C).

9. Distance (D).

The various kinds of sailings are:

1. Plane sailing. The earth, or that part traversed, is regarded as a plane surface.
A single course and distance, difference of latitude, and departure are the only items
involved. Hence, the method provides solution for latitude of the point of arrival,
but not for longitude of this point, one of the spherical sailings being needed for this
problem. Because of the basic assumption that the earth is flat, this method should
not be used for distances of more than a few hundred miles.

2. Traverse sailing combines the plane sailing solutions when there are two or
more courses.

3. Parallel sailing is the interconversion of departure and difference of longitude
when a vessel is proceeding due east or due west. This was a common occurrence when
the sailings were first employed several hundred years ago, but only an incidental
situation now.

4. Middle- (or mid-) latitude sailing involves the use of the mid latitude for
converting departure to difference of longitude when the course is not due east or due
west.

5. Mercator sailing provides a mathematical solution of the plot as made on a
Mercator chart. It is similar to plane sailing, but uses meridional difference and differ-
ence of longitude in place of difference of latitude and departure, respectively.

6. Great-circle sailing involves the solution of courses, distances, and points
along a great circle between two points, the earth being regarded as a sphere.

7. Composite sailing is a modification of great-circle sailing to limit the maximum
latitude.

In addition, meridian sailing might be added to this list to cover the special
case of a vessel following a course of due north or due south (true). However, no
solution is needed for this case because there is no departure or difference of longitude,
and the distance is considered equal to the difference of latitude in minutes. The
true course is 000° or 180°. de

Except for great-circle sailing and the great-circle part of composite sailing, the
various problems normally arising under the sailings can be solved (1) by plane trigo-
nometry, either using natural functions (tab. 31) or logarithms (tabs. 32 and 33);

222 DEAD RECKONING

(2) by traverse table (tab. 3), or (3) graphically. For the graphical solution, cross-
section paper is helpful. The triangle of each method is drawn, and the parts are meas-
ured. Solution by computation is most accurate.

In the mathematical solution of navigational problems, the use of standard work
forms is desirable to provide orderly computations and to minimize errors. This
subject is further discussed in appendix Q, which gives recommended forms for many
of the common problems of navigation.

Great-circle sailing and occasionally composite sailing and Mercator sailing are
the only ones commonly used, except by small-boat navigators.

812. Traverse tables, such as table 3, providing a solution for any plane right
triangle, can be used in the solution of the usual problems encountered in any of the
sailings except great-circlé and composite. A separate table is given for each degree
of course if the lower line of column headings is used, and for each degree of latitude

if the upper line of column headings is used. For
intermediate values interpolation should be made be-
P2 tween tables. The main part of each table involves
solution for the various sides of a plane triangle.
The auxiliary table to the right of each main table
provides a tabulated solution for the course. The
manner Of using the table in specific problems is
illustrated in the examples given in the explanations

of the various sailings.
813. Plane sailing.—In plane sailing the figure
R formed by the meridian through the point of de-
parture, the parallel through the point of arrival, and
the course line is considered a plane right triangle.
This is illustrated in figure 813, in which P, and P;
C are the points of departure and arrival, respectively.
The course angle and the three sides are as labeled.

From this triangle:

l h p p
cos C=5 sin C= tan C=ī
P; From the first two of these formulas the following
Brong 813 The plane sailing relationships can be derived:
triangle.

¿=D cos C D=} sec C p=D'"sm.C

The usual problems solved by plane sailing are: (1) given the course and distance,
find the difference of latitude and the departure; and (2) the reverse of this. It is good
practice to label /, N or S, and p, E or W, to aid in identification of the quadrant of the
course. Logarithmic and traverse table solutions are illustrated in the following
examples:

Example 1.—A vessel steams 188.4 miles on course 005°.

Required.—(1) Difference of latitude, (2) departure.

Solution.— By computation:

D 188.4 mi. log 2.27508 log 2.27508
C 005° l cos 9.99834 l sin 8.94030
(D) e Enger log 2.27342 ==,

(2) p 16.4 mi. E log 1.21538

DEAD RECKONING 223

By traverse table:

mim l p
100.0 99.6 8.7
80.0 79.7 7.0
8.0 8.0 0.7
0.4 0.4 0.0
188.4 (1) 187.7N (2) 16.4 E

Example 2.—A ship has steamed 136.6 miles north and 203.1 miles west.
Required.—(1) Course, (2) distance.
Solution.—By computation:

p 203.1 mi.W log 2.30771

l 136/6N log (—) 2.13545 log 2.13545

C N56%04/6W l tan 0.17226 l sec 0.25330
(2) D 244.8 mi. log 2.38875

(1) Cn 303°9
By traverse table:

p 203.1 mi.W log 2.30771 l D (303°) D (304°)
l 136/6N log (—) 2.13545 100.0 183.6 178.8
p=1 1.487 log 0.17226 30.0 55.1 53.6
C N56°1W 6.0 11.0 10.7
(1) Cn 303°9 0.6 181 TNT
(2 D 244.9 mi. 186.6 2508 2443

In the solution, the navigational form (art. O11) is used, with the basic quantity
being on the left, and related information on the same line. "Thus, 2.27508 is the
logarithm (“log”) of 188.4, and 9.99834 is the logarithmic cosine (7 cos") of 5°.

The labels (N, S, E, W) of l, p, and C are determined by noting the direction of
motion or the relative positions of the two places.

In the solution of example 2 by traverse table, it is first necessary to solve for p=-/.
If this is done by logarithms, as shown above, the solution is similar to that by compu-
tation, with one additional step. Solution for p+/ can be made by any method, or
course can be found as shown in the first solution, and this value used for entering the
traverse table to determine the distance.

The distance in the traverse table solution is found by interpolation between the
values for 303? and 304°.

When the course is near 090° or 270°, the solution of C to the nearest 071 only, as by
traverse table, may introduce a large error in distance.

814. Traverse sailing.—A traverse is a series of courses, or a track consisting of a
number of course lines, as might result from a sailing vessel beating into the wind.
Traverse sailing is the finding of a single equivalent course and distance. If the effect
of an estimated current is to be considered, the set is treated as an additional course,
the drift times the number of hours involved being used as the distance. If direction
and distance from some point, such as a lighthouse, other than the point of departure
is desired, the bearing of the point of departure from the selected position is used as the
first course and the distance between these points as the first distance.

Solution is usually made by means of the traverse tables, the distance to the north
or south and that to the east or west on each course being tabulated, the algebraic
sum of difference of latitude and departure being found, and the result being converted

to course and distance.

224 DEAD RECKONING

Example —A ship steams as follows: course 158°, distance 15.5 miles; course
135°, distance 33.7 miles; course 259°, distance 16.1 miles; course 293°, distance 39.0
miles; course 169°, distance 40.4 miles.

Required.—Equivalent single (1) course, (2) distance.

Solution.—Solve for each leg as in example 1, article 813. Tabulate the answers

as follows:
Course Dist. N S E W
9 má. má. má. ma. má.
158 NOTO 14.4 5.9
1355 DONI 23.8 23.8
259 bon! 3.0 15.8
293 39.0 152 35.9
169 40.4 39.7 "Te.
15.2 80.9 37.4 ESO
(1) (2) 15.2 57
192.3 612 65.7 14.3

Convert 1 65/78, p 14.3 mi.W to equivalent single course and distance as shown
in example 2, article 813.

815. Parallel sailing consists of the interconversion of departure and difference of
longitude. It is the simplest form of spherical sailing (other than meridional sailing).
The formulas for these transformations are:

DLo=p sec L p=DLo cos L

When solution is made by table 3, enter the table for the latitude and use the
upper line of column headings.

Example 1.—The DR latitude of a ship on course 090° is 49?40:2 N.

Required.—The change in longitude if the ship steams for 136.4 miles.

Solutien.—B computation:

p 136.4 mi. E log 2. 13481

L 49°40/2 N l sec 0. 18897

DLo 210/8E log 2. 32378

DLo 3%30/8 E
By traverse table:

p DLo (499) DLo (50°)

100.0 152. 4 155. 6

30.0 45. 7 46. 7

6.0 9 9. 3

0. 4 0. 6 0. 6

136. 4 207. 8 2125

DLo for L 49%40/2 N: 210/7—39?30/7 E.

Example 2.— The DR latitude of a ship on course 270° is 37°50/1S.
steams on this course until the longitude changes 4°33/5W.

Required.—The distance steamed.

Solution.—By computation:

The ship

DLo 273/5W log 2. 43696
[530950415 l cos 9. 89751
p 216.0 mi.W log 2. 33447

DEAD RECKONING 225

By traverse table:

DLo p (37°) p (389)
200. 0 159. 7 157. 6
70. 0 55. 9 55.9
3.0 214 Op di
Ds 0. 4 0.4
21359 218. 4 215. 6

p for L 37?50:18: 216.1 mi.W.

The labels (E or W) of p and DLo agree with the direction of motion.

816. Middle-latitude sailing, popularly called mid-latitude sailing, combines plane
sailing and parallel sailing. Plane sailing is used to find difference of latitude and
departure when course and distance are known, or vice versa. Parallel sailing is
used to interconvert departure and difference of longitude, the middle or mean latitude
(Lm) being used. If a course line crosses the equator, that part on each side (the
north latitude and south latitude portions, respectively) should be. solved separately.

This sailing, like most elements of navigation, contains certain simplifying approxi-
mations which produce answers somewhat less accurate than those yielded by more
rigorous solutions. For ordinary purposes, however, the results are more accurate
than the navigation of the vessel using them. From time to time suggestions have
been made that a correction be applied to eliminate the error introduced by assuming
that the meridians of the point of departure and of the destination converge uniformly
(as the two sides of a plane angle), rather than as the sine of the latitude (approximately).
The proposed correction usually takes the form of some quantity to be added to or
subtracted from the middle latitude to obtain a ‘‘corrected middle latitude” for use in
the solution. Tables giving such a correction have been published for both spherical
and spheroidal earths. However, the actual correction is not a simple function of the
middle latitude and the difference of longitude, as assumed, because the basic formulas
of the sailing are themselves based upon a sphere, rather than a spheroid. Hence, the
use of such a correction is misleading, and may introduce more error than it eliminates.
The use of any correction is not considered justified; if highly accurate results are re-
quired, a different method should be used.

Example 1.—A vessel steams 1,253.4 miles on course 070? from lat. 15?17:4 N, long.
$51°37 18 E.

Required.—(1) Latitude and (2) longitude of the point of arrival.

Solution.—B computation:

[DETZ59-4 mm log 3.09809 log 3.09809
C 070? l cos 9.53405 l sin 9.97299
l 428.7 N log 2.63214 Ee
p 1177.8 mi. E log 3.07108
Lm 18%51/8N l sec 0.02397
DLo 1244'7 E log 3.09505
IX 515917^4N T5 359 T1042 N
AAN xl 334.4 N
(1) L; 22926'1N Lm 18°51/8 N
` 151°37/8 E
DLo 20%44'7E

(2) M

172922! 5E

226 DEAD RECKONING

By traverse table:

D l p
1000.0 342.0 940.0
200.0 68.4 187.9
50.0 17.1 47.0
3.0 1.0 DES
0.4 0.1 0.4
1253.4 428.6 1178.1
I, 15917'4N L, 15°17/4N
| 7908'6N Xl 3°34/3N p DLo(18?) DLo(19?)
(DI m9292650N Lm 18%51/7N 1000.0 1051.0 1058.0
100.0 105.1 105.8
Mm 151°37/8E 70.0 73.6 74.0
DLo 20°45/3E DLo 1245/3 8.0 8.4 8.5
(25172223 (1 0.1 0.1 0.1

1178.1 1238.2 1246.4

Example 2.—A vessel at lat. 8248/95, long. 895313 W is to proceed to lat. 17%06'9 S,
long. 104951. 6 W.
Required.—(1) Course, (2) distance.

Solution.—By computation:

Lu 848/98 ^, 89?53:3W
L, 17%06/9 S Ae 104516 W
| 818/08 DLo 14%58/3W
Xl 409/05 DLo 898:3 W
Lm. 12%57:95
DLo 898:3 W log 2.95342
Lm 12%57/9 S8 l cos 9.98878
p 875.4 mi. W log 2.94220
l 498/08 log (—) 2.69723 log 2.69723
C S 60219 W l tan 0.24497 l sec 0.30586
(2) D 1007.1 mi. log 3.00309

(1) Cn 240%4

By traverse table:

L, 8%48/98 X 89°53/3 W
I, 1790610 S M 104°51'6 W ` DLo p(129) p(13°)
| 8718'0S DLo 14%58'3 W 800.0 782.5 779.5
4 l 4°09/0S DLo 898/3 90.0 88.0 87.7
Lm 12%57'9 S 8.0 7.8 7.8
0.3 0.3 0.3
898.3 878.6 875.3
p 875.4 mi. W log 2.94221 l D(240°) D(241°)
l 498'0S log (—) 2.69723 400.0 800.0 825.1
H= 1.758 log 0.24498 90.0 180.0 185.6
C S 6094 W 8.0 16.0 16.5
(1) Cn 240% 0.0 0.0 0.0

(2) D 1008.5 mi. 498.0 996.0 1027.2

DLo

FIGURE 817.— Mercator sailing

relationships.

DEAD RECKONING 227

The labels (N, S, E, W) of J, p, DLo, and C are
determined by noting the direction of motion or the
relative positions of the two places.

When the course is near 090% or 2709, the solu-
tion of C to the nearest 021 only, as by traverse table,
may introduce a large error in distance.

817. Mercator sailing problems are solved
graphically when measurement is made on a Mercator
chart. Graphical solution can also be made as
shown in figure 817. The lower part is identical with
the plane sailing triangle, figure 813. For mathe-
matical solution the formulas of Mercator sailing are:

D=l sec C

l=D cos C DLo=m tan C

Another formula sometimes of use is:
_0XDLo
Piri

Solution can be made by computation or by traverse
table.

Example 1.—A ship at lat. 322147 N, long. 66?28:9 W is to head for Chesapeake
Lightship, lat. 36587 N, long. 75%42/2 W.
Required.—(1) Course, (2) distance.

Solution.—By computation:

L, 32%14/7 N
Le 36?58:7 N
l 4?44:0N
l 284:0N

DLo 553/3W
m 3435.7

C N 58%09/1 W

l 284/0 N
(2) D 538.2 mi.
(1) Cn 30178

By traverse table:
Ti 9291477 N
L» 36%58'7 N
| 4°44/0N
| 284'0N

DLo 553/3 W

m 343.7

DLo=m 1.610
C N 5822 W

(1) Cn 30178
(2) D 539.0 mi.

M, 2033.3 A, 66?28:9 W
M 2377.0 M 75942:2 W
m 343.7 DLo 9%13/3W
DLo 55313 W
log 2.74296
log (—) 2.53618
l tan 0.20678 l sec 0.27764
log 2.45332
log 2.73096
M, 2033.3 ^; 6628:9 W
M; 2377.0 20015 BEAT
Moots... DLo 921343 W
DLo ` 553:3 W
2.74296 l D (301°) D (302°)
log (—) 2.53618 200.0 388.3 377.4
0.20678 80.0 155.3 151.0
4.0 7.8 7.5
0.0 0.0 0.0
284.0 551.4 535.9

228

DEAD RECKONING

Example 2.—A ship at lat. 75°31/7N, long. 79%08!7 W, in Baffin Bay, steams

263.5 miles on course 155°.

Required.—(1) Latitude and (2) longitude of point of arrival.
Solution.—By computation:

D 263.5 mi. log 2.42078
C 155° l cos 9.95728 l tan 9.66867
| 238/88 log 2.37806
m 846.3 log 2.92752
DLo 394'6E log 2.59619
L, 75°31/7N M; 7072.4 X, 79%08/7 W
| 3°58/8S DLo 6°34/6E
(IIS ON M, 6226.1 (2) Az 72934 I
m 846.3
By traverse table:
D l m DLo
200.0 181.3 800.0 373.0
60.0 54.4 40.0 18.6
3.0 DU 6.0 2.8
0.5 0.5 0.6 0.3
263.5 238.9 846.6 394.7
DIN M, 7072.4 X, 79°08/7 W
l 3°58'9S DLo 6%34'7E
(DIET IN M, 6225.8 (2) da 72°34/0 W
m 846.6

The labels (N, S, E, W) of /, DLo, and C are determined by noting the direction
of motion or the relative positions of the two places.

If the course is near 090° or 270°, a small error in C introduces a large error in DLo.
The solution for C to the nearest 0?1 only, as by traverse table, may introduce a large error
in distance if the course is near 090° or 270°.

818. Rhumb lines and great circles.—The principal advantage of a rhumb line
is that it maintains constant true direction. A ship following the rhumb line between
two places does not change true course. A rhumb line makes the same angle with all
meridians it crosses and appears as a straight line on a Mercator chart. It is adequate
for most purposes of navigation, bearing lines (except long ones, as those obtained by
radio) and course lines both being plotted on a Mercator chart as rhumb lines, except
in high latitudes. The equator and the meridians are great circles, but may be consid-
ered special cases of the rhumb line. For any other case, the difference between the
rhumb line and the great circle connecting two points increases (1) as the latitude
increases, (2) as the difference of latitude between the two points decreases, and (3) as
the difference of longitude increases. It becomes very great for two places widely
separated on the same parallel of latitude far from the equator.

A great circle is the intersection of the surface of a sphere and a plane through the
center of the sphere. It is the largest circle that can be drawn on the surface of the
sphere, and is the shortest distance, along the surface, between any two points on the
sphere. Any two points are connected by only one great circle unless the points are
antipodal (180° apart on the earth), and then an infinite number of great circles passes
through them. Thus, two points on the same meridian are not joined by any great
circle other than the meridian, unless the two points are antipodal. If they are the

DEAD RECKONING 229

poles, all meridians pass through them. Every great circle bisects every other great
circle. Thus, except for the equator, every great circle lies half in the northern hemi-
sphere and half in the southern hemisphere. Any two points 180° apart on a great
circle have the same latitude numerically, but contrary names, and are 180° apart in
longitude. The point of greatest latitude is called the vertex. For each great circle
there is one of these in each hemisphere, 180° apart. At these points the great circle
is tangent to a parallel of latitude, and hence its direction is due east-west. On each side
of these vertices the direction changes progressively until the intersection with the
equator is reached, 90° away, where the great circle crosses the equator at an an gle equal
to the latitude of the vertex. As the great circle crosses the equator, its change in
direction reverses, again approaching east-west, which it reaches at the next vertex.

On a Mercator chart a great circle appears as a sine curve extending equal distances
each side of the equator. The rhumb line connecting any two points of the great
circle on the same side of the equator is a chord of the curve, being a straight line nearer
the equator than the great circle. Along any intersecting meridian the great circle
crosses at a higher latitude than the rhumb line. If the two points are on opposite
sides of the equator, the direction of curvature of the great circle relative to the rhumb
line changes at the equator. The rhumb line and great circle may intersect each other,
and if the points are equal distances on each side of the equator, the intersection takes
place at the equator.

819. Great-circle sailing is used when it is desired to take advantage of the shorter
distance along the great circle between two points, rather than to follow the longer
rhumb line. The arc of the great circle between the points is called the great-circle
track. If it could be followed exactly, the destination would be dead ahead throughout
the voyage (assuming course and heading were the same). The rhumb line appears
the more direct route on a Mercator chart because of chart distortion. The great
circle crosses meridians at higher latitudes, where the distance between them is less.

The decision as to whether or not to use great-circle sailing depends upon the
conditions. The saving in distance should be worth the additional effort, and of
course the great circle should not cross land, or carry the vessel into dangerous waters
or excessively high latitudes. A slight departure from the great circle or a modification
called composite sailing (art. 825) may effect a considerable saving over the rhumb line
track without leading the vessel into danger. If a fix indicates the vessel is a consider-
able distance to one side of the great circle, the more desirable practice often is to
determine a new great-circle track, rather than to return to the original one.

Since a great circle is continuously changing direction as one proceeds along it, no
attempt is customarily made to follow it exactly, except in polar regions (ch. XXV).
Rather, a number of points are selected along the great circle, and rhumb lines are
followed from point to point, taking advantage of the fact that for short distances a
great circle and a rhumb line almost coincide.

The number of points to use is a matter of personal preference, a large number
of points providing closer approximation to the great circle but requiring more frequent
change of course. As a general rule, each 5% of longitude is a convenient length.
Legs of equal length are not provided in this way, but this is not objectionable under
normal conditions.

If a magnetic compass is used, the variation for the middle of the leg is usually
used for the entire leg. In some areas the change in variation and the change in course
due to convergence of the meridians are in opposite directions and of about the same
magnitude. In these areas the same magnetic course can be used for relatively
long distances. The change of deviation with change of heading may also be a

consideration.

230 DEAD RECKONING

The problems of great-circle sailing can be solved by (1) chart (art. 820), (2)
conversion angle (art. 821), (3) computation (art. 822), (4) table (art. 823), (5) graph-
ically, or (6) mechanically. Of these, (5) and (6) are but graphical or mechanical
solutions of (3). They usually provide solution only for initial course and the distance,
and are not in common use.

820. Great-circle sailing by chart.—Problems of great-circle sailing, like those of
rhumb line sailing, are most easily solved by plotting directly on a chart. For this
purpose the U. S. Navy. Hydrographic Office publishes a number of charts on the
gnomonic projection (art. 317), covering the principal navigable waters of the world.
On this projection any straight line is a great circle, but since the chart is not conformal
(art. 302), directions and distances cannot be measured directly, as on a Mercator
chart. An indirect method is explained on each chart.

The usual method of using a gnomonic chart is to plot the great circle and, if it
provides a satisfactory track, to determine a number of points along the track, using
the latitude and longitude scales in the immediate vicinity of each point. These
points are then transferred to a Mercator chart or plotting sheet and used as a succession
of destinations to be reached by rhumb lines. The course and distance for each leg is
determined by measurement on the Mercator chart or plotting sheet. This method
is illustrated in figure 820, which shows a great circle plotted as a straight line on a
gnomonic Chart and a series of points transferred to a Mercator chart. The arrows
represent corresponding points on the two charts. The points can be plotted directly
on plotting sheets without the use of a small-scale chart, but the use of the chart pro-
vides a visual check to avoid large errors, and a visual indication of the suitability of
the track.

Since gnomonic charts are normally used only because of their great-circle prop-
erties, they are often popularly called great-circle charts.

ZE

eet
TTL

50°

Figure 820.—Transferring great-circle points from a gnomonic chart to a Mercator chart.

DEAD RECKONING 231

A projection on which a straight line is approximately a great circle can be used
in place of a gnomonic chart with negligible error. If such a projection is conformal
as in the case of the Lambert conformal (art. 314), measurement of course and distales
of each leg can be made directly on the chart, as explained in article 2511.

Some great circles are shown on pilot charts and certain other charts, together
with the great-circle distances. Where tracks are recommended on charts ok in sailing
directions, it is good practice to follow such recommendations.

821. Great-circle sailing by conversion angle.—The direction of the great circle
at the point of departure is called the initial great-circle course, and its direction at the
destination is called the final great-circle course. The difference between the initial
great-circle course and the single rhumb line course is called conversion angle. This
is usually about half the difference between initial and final great-circle courses.

Conversion angles for difference of longitude to 120°, sufficient for virtually all
situations in which great-circle sailing is likely to be used by ships, are given in table 1.
To use the table, measure the rhumb line course on a Mercator chart (or compute it
by Mercator or mid-latitude sailing) and apply the conversion angle to find the initial
great-circle course. The sign of the correction can
be determined by means of the tabulation at the
bottom of the table. With a little practice, one
can determine the sign mentally by remembering
that the great-circle course always lies nearer the
pole (in the hemisphere of the point of departure)
than the rhumb line course, except for those values
given in italics. P

The use of the conversion angle as taken directly q ;
from the table results in a course line tangent to the Pronet E O o
great circle (as plotted on a Mercator chart) and
hence one that carries the vessel to higher latitudes than the great circle. To convert
this to the corresponding chord, as in great-circle sailing by chart, divide the conversion
angle by the number of legs, and subtract this value from the tabulated conversion
angle before applying the correction to the rhumb line course. At the end of each leg
make a new solution, using the position of the vessel as the point of departure.

This method does not indicate the suitability of the route unless the entire solution
is made in advance and the results plotted on a chart.

Approximate values of conversion angle can be found by the formula:

sin Lm tan % DLo
cos Kl

Conversion

A

D

tan conversion angle=

if both points are on the same side of the equator. For small differences of latitude,
cos X | can be considered 1 without introducing a significant error. The tangent of
a small angle equals, approximately, the angle itself (in radians). Therefore, for small
values of DLo and / (up to 15° to 20°) the formula can be simplified:

conversion angle— X DLo sin Lm.

This formula can be solved graphically (fig. 821). Draw any line PA, and from E
draw PB making an angle with PA equal to Lm. Along PB measure % DLo, letting
any convenient linear unit equal 1°. From C, the point thus found, draw CD per-
pendicular to PA. The length of CD in the units used for % DLo is the conversion
angle in degrees. Conversion angle can also be determined by table 3, using mid
latitude as course, 4 DLo as D, and conversion angle as p. The value found by
formula, however solved, may not be accurate for large differences of latitude.

232 DEAD RECKONING

822. Great-circle sailing by computation.—In figure 822, 1 is the point of departure,

2 the destination, P the pole nearer 1, 1XV2 the great circle through 1 and 2, V the

vertex, and X any point on the great circle. The ares P1, PX, PV, and P2 are the

colatitudes of points 1, X, V, and 2, respectively. If 1 and 2 are on opposite sides of
the equator, P2 is 90? + L,. The length of arc 1-2 is the great-circle distance between

1 and 2. Arcs 1-2, P1, and P2 form a spherical triangle. The angle at 1 is the initial

great-circle course from 1 to 2, that at 2 the supplement of the final great-circle course

(or the initial course from 2 to 1), and that at P the DLo between 1 and 2.
Great-circle sailing by computation usually involves solution for the initial great-

circle course; the distance; latitude and longitude, and sometimes the distance, of the

vertex; and the latitude and longitude of various points (X) on the great circle. The

computation for initial course and the distance involves solution of an oblique spherical
triangle, and any method of solving such a
triangle can be used. If 2 is the geo-
graphical position (GP) of a celestial body
(the point at which the body is in the
zenith), this triangle is solved in celestial
navigation, except that 90?— D (the alti-
tude) is desired instead of D. The solu-
tion for the vertex and any point X
usually involves the solution of right
spherical triangles.

Í Although various formulas can be
used, haversine formulas are considered |
most suitable for determining initial
course and the distance, as these avoid

Nūrs s f Y | the ambiguity that may arise through the
X= E kt S use of trigonometric functions which do

not indicate the quadrant in which the

FIGURE 822.—The navigational triangle of great- answer lies. In the formulas given below,

circle sailing. the subscripts refer to the points indi-

cated in figure 822. All terms without

subscripts are from 1 to 2, D, and DLo, are from 1 to V, and D,, and DLo,, are

from V to X. Other quantities can be computed by interchanging 1 and 2 in figure

822 and using the same formulas. The following formulas are suitable for great-circle
sailing by computation:

hav D = hav DLo cos L, cos L,+hav l
which may be written hav D = hav 0+hav l (where hav ¢=hav DLo cos L, cos L»)
hav C = sec L, ese D [hav coL;—hav (D ~ coL,)]
COS. Ls — COS sin ©
sin DLo, = cos C csc L,
sin D, = cos L, sin DLo,
tan L, = cos DLo,, tan L,

Example.—A ship is proceeding from Manila to Los Angeles. The captain wishes
to use great-circle sailing from lat. 12%45'2 N, long. 124°20/1 E, off the entrance to
San Bernardino Strait, to lat. 33°48/8 N, long. 120?07:1 W, five miles south of Santa
Rosa Island.

Required.—(1) The initial great-circle course.

(2) The great-circle distance.

DEAD RECKONING 233

(3) The latitude and longitude of the vertex.
(4) The distance from the point of departure to the vertex.

(5) The latitude and longitude of points at DLo intervals of 12° each side of the
vertex.

Solution.—
^; 124°20/1E D 103°05/9
^. 120°07/1 W coL, 7791478
DLo 115%32/8E l hav 9.85468 D=coL, 25951'1
Ly; °12°45/2N l cos 9.98915 lsec 0.01085
La; 33?48:8N l cos 9.91953
front tae tu l hav 9.76336 n hav 0.57991
181219034 GIN n hav 0.03340
D 103%05'9 n hav 0.61331 l ese 0.01145
coli, 56°1172 n hav 0.22175
D=coL, 25°5171 n hav(—) 0.05004
n hav 0.17171 l hav 9.23480
(1) Cn 050?3 C N50%19/3E l hav 9.25710
(2) D 6185.9 mi.
Ly 12°45/2N l cos 9.98915 l cos 9.98915
C N50%19/3E l sin 9.88629 l cos 9.80514
KO) IM 4192172.N l cos 9.87544 l ese 0.17999
(3 A, 160°34'4W DLo, 75%05/5 E (sin 9.98513 [ sin 9.98513
D, 70%28'5 l sin 9.97428
(4 D, 4228.5 mi.
Do, 129001 0 24°00/0 36°00/0 48°00/0 60%00/0 72°00/0
i cos DLo,: 9.99040 9.96073 9.90796 9.82551 9.69897 9.48998
(tan L, 9.94457 9.94457 9.94457 9.94457 9.94457 9.94457
l tan L, 9.93497 9.90530 9.85253 9.77008 9.64354 9.43455
Co), 40%43/6N 38?48/1N 9599742. IN 30?29/8N 23%45:2N 15°12/9N
Owe 172°34/4 W 175925:/6. E 163°25/6E 151925/6B 139°25/6E 127?25'6 E
(5) Az 148°34/4 W 136°34/4 W 124?34/4W — =

CoL, is always 90° — L,. CoL, is 90% — L, if L, and L, are of same name, and
90° + L, if of contrary name.

D ~ coL, is always the numerical difference between D and col.

C is labeled N or S to agree with L, and E or W to agree with DLo. This is not
the same as in rhumb line sailings. In great-circle sailing.L; may be south of Li, yet
the initial course may have a northerly component.

L, is always numerically equal to or greater than L, or Lo.

If C is less than 90°, the nearer vertex is toward Lo; but if C is greater than 90°,
the nearer vertex is in the opposite direction.

DLo, and D, of the nearer vertex are never greater than 90°. However, when
L, and L; are of contrary name, the other vertex, 180° away, may be the preferable
one to use in the solution for various points along the great circle if it is nearer the
mid point of the great circle.

The vertex nearer L; has the same name (N or S) as Ly.

L, has the same name (N or S) as L, if DLo,, is less than 90°, but the opposite
name if DLo,, is greater than 90°. |

The great circle is a symmetrical curve about the vertex. Hence, any given DLo
can be applied to X, in both directions (E and W) to find two points having the same

234 DEAD RECKONING

latitude. However, if whole degrees of ^; are desired, different E and W intervals are
neéded unless A, is a whole degree or an exact half degree.

Only those points on the portion of the great circle between the point of departure
and destination are recorded. | ob

The following formulas are sometimes useful in great-circle sailing:

sin C=sin DLo cos L, ese D

This offers a simpler solution than the haversine formula, but unless L; is of the same
name and equal to or greater than Ly, it leaves doubt as to whether C is less or greater |
than 90°.

cos C=sin L, sin DLo,

This offers an even simpler solution, but has the same limitations as those given above.
Further, it requires a knowledge of the position of the vertex. It is particularly useful
in determining the direction of the great circle at any given point along the circle.

sin L,=sin L, cos D,,
sin DLo,,=sec L, sin Das

These formulas are useful for finding points at approximately equal distances, along the
great circle, from the vertex, should this be considered more desirable than finding points
of equal DLo. The method of selecting the longitude (or DLo,;) and determining the
latitude at which the great circle crosses the selected meridian provides shorter legs in
higher latitudes and longer legs in lower latitudes, where the difference between the —
great circle and rhumb line is smaller. In using these formulas, D,, is expressed in
degrees. If it is greater than 90° (5,400 miles), L, is of contrary name to L,, and
DLo,, is greater than 90°.

cos DLo,,=tan L, cot L,

This formula is useful in determining the longitude (or DLo,;) at which the great circle
crosses selected parallels of latitude. If L, is of contrary name to L,, DLo,, is greater
than 90°. This formula is also used in composite sailing (art. 825).

823. Great-circle sailing by table.—Although tables designed to facilitate the
computations of great-circle sailing have been published, no such table is in common use
today. However, any method of solving the astronomical triangle of celestial naviga-
tion can be used for solving great-circle sailing problems. When such an adaptation is
made, the point of departure replaces the assumed position of the observer, the destination
replaces the geographical position of the body, difference of longitude replaces meridian
angle, initial course angle replaces azimuth angle, and great-circle distance replaces
zenith distance (90°—altitude). Therefore, any table of azimuths (f the entering
values are meridian angle, declination, and latitude) can be used for determining initial
great-circle course. H.O. Pubs. Nos. 208, 211, 214, 249, 260, and 261 are examples of
tables that can be used for this purpose. Tables which provide solution for altitude,
such as H.O. Pubs. Nos. 208, 211, 214, and 249, can be used for determining great-
circle distance. The required distance is 90°—altitude (90°-+ negative altitudes).

In inspection tables such as H.O. Pubs. Nos. 214, 249, 260, and 261, the given
combination of L;, L;, and DLo may not be tabulated. In this case reverse the name of
L, and use 180—DLo for entering the table. The required course angle is then 180°
minus the tabulated azimuth, and distance is 90° plus the altitude. If neither com-

DEAD RECKONING 235

bination can be found, solution cannot be made by that method. By interchanging
Lı and Ls, one can find the supplement of the final course angle.

Solution by table often provides a rapid approximate check, but accurate results
usually require triple interpolation (art. P4). Inspection tables do not provide solution
for points along the great circle, and therefore are of limited usefulness.

An example of the use of H.O. Pub. No. 214 for great-circle sailing is given as
example 8, near the front of each volume.

824. Altering a great-circle track to avoid obstructions.—Great-circle sailing
cannot be used unless the great-circle track is free from obstructions. It does not
start until one clears the harbor and takes his departure (art. 806), and often ends near
the entrance to the destination. However, islands, points of land, or other obstructions
may prevent the use of great-circle sailing over the entire distance. One of the prin-
cipal advantages of solution by great-circle chart is that the presence of any obstruc-
tions is immediately apparent.

Often a relatively short run by rhumb line is sufficient to reach a point from which
the great-circle track can be followed. Where a choice is possible, the rhumb line
selected should conform as nearly as practicable to the direct great circle.

If the great circle crosses a small island, one or more legs may be altered slightly,
or perhaps the drift of the vessel will be sufficient to make any planned alteration
unnecessary. The possible use of the island in obtaining an en route fix should not be
overlooked. If a larger obstruction is encountered, as in the case of the Aleutian
Islands on a great circle from Seattle to Yokohama, some judgment may be needed in
selecting the track. It may be satisfactory to follow a great circle to the vicinity of the
obstruction, one or more rhumb lines along the edge of the obstruction, and another
great circle to the destination. Another possible solution is the use of composite sailing
(art. 825), and still another the use of two great circles, one from the point of departure
to a point near the maximum latitude of unobstructed water, and the second from this
point to the destination.

It is sometimes desirable to alter a great-circle track to avoid unfavorable winds
or currents. The shortest route is not always the quickest.

Whatever the problem, a great-circle chart can be helpful in its solution.

825. Composite sailing.—When the great circle would carry a vessel to a higher
latitude than desired, a modification of great-circle sailing, called composite sailing,
may be used to good advantage. The composite track consists of a great circle from
the point of departure and tangent to the limiting parallel, a course line along
the parallel, and a great circle tangent to the limiting parallel and through the
destination.

Solution of composite sailing problems is most easily made by means of a great-
circle chart. Lines from the point of departure and the destination are drawn tangent
to the limiting parallel. The coordinates of various selected points along the composite
track are then measured and transferred to a Mercator chart, as in great-circle sailing
(art. 820).

Composite sailing problems can also be solved by computation. For this purpose
the last formula of article 822 is used:

cos DLo,,=tan L, cot Ly.

In the computation, the point of departure and the destination are used succes-

sively as point X. j
Example.—A ship leaves Baltimore, bound for Bordeaux (Royan), France. The

captain desires to use composite sailing from lat. 36%57:7 N, long. 75°42:2 W, one mile

236 DEAD RECKONING

south of Chesapeake Lightship, to lat. 45%39/1 N, long. 1?29:8 W, near the entrance to
Grande Passe de l'Ouest, limiting the maximum latitude to 47? N.

Required.—(1) The longitude at which the limiting parallel is reached. (2) The
longitude at which the limiting parallel should be left.

Solution.—
I5 90954 7N [ tan 9.87651
La 45°39/1N l tan 0.00988
L, 47%00/0N l cot 9.96966 l cot 9.96966
DLo,, 45°26/1E l cos 9.84617 Ix ng
DLo,, 17*27:0 W l cos 9.97954

(1) X4 302161 W
(2) Xj, 18%56'8 W

Composite sailing applies only when the vertex lies between the point of departure
and the destination.

The remainder of the problem is one of solving the two great circles by great-
circle sailing and the east-west portion by parallel sailing. Since both great circles
have vertices at the same parallel, computation for C, D, and DLo, can be made by
considering them parts of the same great circle with L,, Ly, and L, as given and DLo=
DLo,;--DLo,;, The total distance is the sum of the great-circle and parallel distances.
In finding X; be careful to apply DLo,, to the correct vertex and in the correct direction.

Problems

806a. Draw a small area plotting sheet by either method explained in article 324,
covering the area between latitude 32°-34°N and longitude 118°-122°W. Plot
the following points:

A L 35°49'1N C L 33?38'0N
^ 120?52:0W A 118386 W
B L 32%17/4N Ds di 3293040 N
A 121?28:0W A 118%36:2W

Required.—(1) The bearings of B, C, and D from A.

(2) The course and distance of A, B, and C from D.

Answers.—(1) Bas 198°5, Bac 09525, Bap 124°; (2) Cos 304°, Dp4 138.8 mi Cop
26405 Do, 145.7 mi One 3588 D, D 67:5 T

806b. Use the plot of problem 806a. A ship starts from A at 1200, and steams as
follows:

Time Course Speed
DE
1500 240° 15 kn.
1800 240° 17 kn.
2000 1255 20 kn.
9300 090° 20 kn.
o
0500 015 10 kn.

Plot and label the dead reckoning course line and DR positions.

Required.—(1) The dead reckoning position of the ship at 0500.

(2) The bearing and distance of D from the 2300 DR position.

(3) The course and distance from the 0500 DR position to C.

(4) Estimated time of arrival (ETA), to the nearest minute, at Cif the ship proceeds
directly from the 0500 DR position at 20 knots.

DEAD RECKONING 234

Answers.—(1) 0500 DR: L 33%35/1N, 119°35/8W; (2) B 096°, D 66.0 mi.;
(3) C 086°, D 48.1 mi.; (4) ETA 0724.

807a. A ship on course 120°, speed 12 knots, is steaming through a current having
a set of 350° and a drift of 1.5 knots.

Required.—Course and speed made good.

Answers.—Course made good 114°, speed made good 11.1 kn.

807b. The captain desires to make good a course of 180° through a current having
a set of 090° and a drift of two knots, using a speed of 11 knots.

Required.—The course to steer and the speed made good.

Answers.—Course to steer 190°5, speed made good 10.8 kn.

807c. The captain desires to make good a course of 325° and a speed of 20 knots
through a current having a set of 270° and a drift of one knot.

Required.—The course to steer and the speed to use.

Answers.—Course to steer 327°, speed to use 19.4 kn.

813a. A vessel steams 117.3 miles on course 214°.

Required.—(1) Difference of latitude, (2) departure, by plane sailing.

Answers.—(1) 1 97:28, (2) p 65.6 mi. W.

813b. A steamer is bound for a port 173.3 miles south and 98.6 miles east of the
vessel’s position.

Required.—(1) Course, (2) distance, by plane sailing.

Answers.—(1) C 150?4; (2) D 199.4 mi. by computation, 199.3 mi. by traverse table.

814a. A ship steams as follows: course 359°, distance 28.8 miles; course 006°,
distance 16.4 miles; course 266%, distance 4.9 miles; course 144°, distance 3.1 miles;
course 333°, distance 35.8 miles; course 280°, distance 19.3 miles.

Required.—(1) Course, (2) distance, by traverse sailing.

Answers.—(1) C 33494, (2) D 86.1 mi.

814b. A lightship bears 020°, distant 3.4 miles from a ship standing out to sea at
a speed of 12 knots. The ship steams on the following courses for the times indicated:
course 090? for 18”, course 114° for 1^12", course 070° for 3^45", course 095° for 54”,
course 050° for 36™. The navigator estimates that during this entire time the ship
has been in a current having a set of 315° and a drift of 0.5 knot.

Required.—The bearing and distance of the estimated position from the lightship,
by traverse sailing.

Answers.—B 080°3, D 73.0 mi. by computation, 73.1 mi. by traverse table.

815a. The 1530 DR position of a ship is lat. 44%36/3N, long. 31?18:3W. The
ship is on course 270°, speed 17 knots.

Required.—The 2000 DR position, by parallel sailing.

Answer.—2000 DR: L 44936/3N, ^ 33?05:7 W.

815b. The captain of the ship of problem 815a desires to change course when the
ship arrives at long. 38?00:0 W.

Required.—Estimated time of arrival (ETA) at the turning point, by parallel
sailing.

Answer.—ETA 0819 the following day.

816a. A vessel steams 263.3 miles on course 340? from lat. 16?32:28, long. 1%04:4 E.

Required.—(1) Latitude and (2) longitude of the point of arrival, by middle-
latitude sailing.

Answer.—By computation or traverse table: (1) L 12?24:85, (2) ^ 0?28:6 W.

816b. A vessel leaves lat. 45°00/0 N, long. 15020070 W and arrives at lat. 38%18.7 N,
long. 137?14:6 W. |

Required.—(1) Course made good, (2) distance made good, by middle-latitude

sailing.

238 DEAD RECKONING

Answers. —(1) C 125°1; (2) D 698.6 mi. by computation, 697.9 mi. by traverse
table.

816c. A vessel is at lat. 1908/35, long. 175%24/5E. It steams at 13.5 knots on
course 075° for 22:15". Twenty-four hours after that it is at lat. 0?06:6 S, long.
174°20'0 W.

Required.—(1) Latitude and (2) longitude of the point of arrival after 22^15";
(3) course and (4) distance made good during the last 24 hours of steaming; and (5)
course and (6) distance made good over entire period, by middle-latitude sailing.

Answers.—(1) L 0%09/5N by computation, 0%09/4N by traverse table; (2)
^ 179?45:3W; (3) C 092°8; (4) D 325.7 mi. by computation, 338.3 mi. by traverse
table; (5) C 084°3; (6) D 618.5 mi. by computation, 625.6 mi. by traverse table.

817a. A ship at lat. 33?53:3S, long. 18°23/1E, leaving Cape Town, heads for
Ambrose Lightship, lat. 40°27/1N, long. 73°49/4 W.

Required.—(1) Course and (2) distance, by Mercator sailing.

Answers.—(1) C 310°9; (2) D 6,811.5 mi. by computation, 6,812.8 mi. by traverse
table. Compare these answers with those of problem 822, the great-circle sailing
solution between the same . points.

817b. A ship at lat. 15°03!7 N, long. 151?26/8 E steams 57.4 miles on course 035°.

Required.—(1) Latitude and (2) longitude of the point of arrival, by Mercator
sailing.

Answers.—(1) L 15°50!7 N, 1 152%00/7E.

821. Point A is at lat. 35?24:2 N, long. 125%02/6 W. Point B is at lat. 41°09/2N,
long. 147°22'6E.

Reguired.—The conversion angle from A to B (1) by table 1, (2) by complete for- `
mula, (3) by construction; (4) rhumb line course by Mercator sailing; (5) initial great-
circle course (using table 1, conversion angle); (6) chord course for first leg, if there are
to be 17 legs (using table 1, conversion angle).

Answers.—Conversion angle (1) 29?8, (2) 30?7, (3) 27?1, (4) Cn 27478, (5)
Cn 3046, (6) Cn 30298.

822. A ship leaves Cape Town bound for New York City. The captain decides
to use great-circle sailing from lat. 33%53:3 S, long. 18°23/1 E (near Green Point Light)
to Ambrose Lightship, lat. 40°27/1 N, long. 73°49/4 W.

Required.—(1) The initial great-circle course.

(2) The great-circle distance.

(3) The latitude and longitude of both vertices.

(4) The distance from the point of departure to each vertex.

(5) The latitude and longitude of points on the great circle at longitude 15° E and
at each 5° of longitude thereafter to longitude 70° W.

Answers.—(1) O 304°5. (2) D 6,762.7 mi. (3) L,46%49/4S, 1, 69°18/8E; L, 46949/4
N,X,110%41'2W. (4) D 2,407.5 mi. to eastern hemisphere vertex, 8,392.5 mi. to western
hemisphere vertex. (5) L; 33°53/3S, 1, 18°23/1E (point of departure); L, 31%52/28,
^, 15%00:0E; L, 28%32/58, 2, 1020070 0-41 2474177 5; Amo 0000 127 20?37:88,
Az 0?00:0; Le 16%04/58, Az 5?00:0W; L, 11?10/8S, ^, 10%00"0W; L, 6?0177 S, \,15°00/0
W; Lz 0543198, A. 20?00:0 W; L, 4°35/0N, X, 259000 W; L, 9°47/2N, A, 3090070 W;
L, 14°45/7N, A, 35?00:0W; L, 19°25/0N, 1, 40200 10W 214112884 1L SINS 3 45?00:0W;
1222789929 4X2 50%00:0 W; L, 30°59/8N, ^, 55%00:0 W; L, 34%01/7N, àz 60000 W;
Tz 36°40°1N, Az 65?00:0 W; L, 38°56/6N, dX, 70000 W; L» 40%27'1N, Ae 73%49'4 W
(destination).

825. A ship is to steam from Valparaiso, Chile, to Wellington, New Zealand.
The captain wishes to use composite sailing from lat. 32%58/08, long. 71°41! 2W, off

Punta Angeles Light, to lat. 42°00/ OS, long. 175°00/0E, near Cape Palliser, limiting
the maximum latitude to 50°S

DEAD RECKONING 239

-Required.—(1) The longitude at which the limiting parallel is reached.

(2) The longitude at which the limiting parallel should be left.

(3) The initial great-circle course.

(4) The total distance.

(5) The latitude and longitude of points along the great circles at intervals of 10°
of DLo from the vertices.

Answers.—(1) Ae 128%42'9W. (2) 4,144904'3 W. (3) C 230?0. (4) D 5,024.6 mi.
(5) Lı 32?58:08, X, 71?41:2W (point of departure); L, 3727/28, A, 78°42/9W; L,
42923168, A, 8842.9 W; L, 45%54'3S, 1, 9842/0 W; L, 48?14'28, A, 108%42'9 W;
L, 49234718, N, 118%42'9 W; Le 50°00/0S, Ae 12894279 W (first vertex); Ly: 50%00'0S,
Moz 144?04:3 W (second vertex); L, 49?34/18, A, 154?04'3W ; L, 48?14'2 S, X, 164?04:3
W; L, 45?54:38, Az 174%04'3 W; L, 42°23/6S, N, 175%55'7 E; Le 4200/05, X 1750010
E (destination).

CHAPTER IX

PILOTING

General

901. Introduction.—On the high seas, where there is no immediate danger of
grounding, navigation is a comparatively leisurely process. Courses and speeds are
maintained over relatively long periods, and fixes are obtained at convenient intervals.
Under favorable conditions a vessel might continue for several days with no positions
other than those obtained by dead reckoning, or by estimate, and with no anxiety on
the part of the captain or navigator. Errors in position can usually be detected and
corrected before danger threatens.

In the vicinity of shoal water the situation is different. Frequent or continuous
positional information is usually essential to the safety of the vessel. An error which
at sea may be considered small, may in pilot waters be intolerably large. Frequent
changes of course and speed are common. The proximity of other vessels increases
the possibility of collision. Navigation under these conditions is called piloting or
pilotage.

No other form of navigation requires the continuous alertness needed in piloting.
At no other time is navigational experience and judgment so valuable. The ability
to work rapidly and to correctly interpret all available information, always keeping
“ahead of the vessel," may mean the difference between safety and disaster.

In piloting, positions are commonly obtained by reference to nearby landmarks,
or the bottom. Advancements in electronics have provided additional aids which are of
particular value in piloting, and have extended the range of piloting techniques far
to sea.

902. Preparation for piloting.—Because the time element is often of vital im-
portance in piloting, adequate preparation is important. Long-range preparation
includes the acquisition of a thorough knowledge of the methods and techniques of
piloting, and the organization and training of those who will assist in any way. This
includes the steersman, who will be granted less tolerance in straying from the prescribed
course than when farther offshore.

The more immediate preparation includes a study of the charts and publications
of the area to familiarize oneself with the channels, shoals, tides, currents, aids to
navigation, etc. One seldom has time to seek such information once he is proceeding
in pilot waters. The more detailed preparation required for leaving or entering port
is given in chapter XXIII.

Position

903. Lines of position.—As in electronic and celestial navigation, piloting makes
extensive use of lines of position. Such a line is one on some point of which the vessel
may be presumed to be located, as a result of observation or measurement. It may be
highly reliable, or of questionable accuracy. Lines of position are of great value, but
one should always keep in mind that they can be in error because of imperfections in
instruments used for obtaining them and human limitations in those who use the
instruments and utilize the results. The extent to which one can have confidence in
various lines of position is a matter of judgment acquired from experience.

240

PILOTING 241

A line of position might be a straight line (actually a part of a great circle), an
arc of a circle, or part of some other curve such as a hyperbola (art. O34). An ap-
propriate label should be placed on the plot of a line of position at the time it is drawn,
to avoid possible error or confusion. A label should include all information essential
for identification, but no extraneous information. The labels shown in this volume are
recommended.

904. Bearings.—A bearing is the horizontal direction of one terrestrial point from
another. It is usually expressed as the angular difference between a reference direction
and the given direction. In navigation, north is generally used as the reference direc-
tion, and angles are measured clockwise through 360°. It is customary to express all
bearings in three digits, using preliminary zeros where needed. Thus, north is 000°
or 360°, a direction 7? to the right of north is 007°, east is 090°, southwest is 225°, etc.

For plotting, true north is used as the reference direction. A bearing measured
from this reference is called a true bearing (TB). A magnetic, compass, or grid
bearing (MB. CB, or GB) results from using magnetic, compass, or grid north, respec-
tively, as the reference direction. This is similar to the designation of courses. In the
case of bearings, however, one additional reference direction is often convenient. This
is the heading of the ship. A bearing expressed as angular distance from the heading is
called a relative bearing (RB). It is usually measured clockwise through 360°, but
for some purposes it is more conveniently measured either clockwise or counterclockwise
through 180°, and designated right or left, respectively. A relative bearing may be
expressed in still another way, as indicated in figure 904. Except for dead ahead and
points at 45° intervals from it, this method is used principally for indicating directions
obtained visually, without precise measurement. An even more general indication of
relative bearing may be given by such directions as “ahead,” “on the starboard bow,”
“on the port quarter,” “astern.” The term abeam may be used as the equivalent of
either the general “on the beam" or, sometimes, the more precise “broad on the beam."
Degrees are sometimes used instead of points to express relative bearings by the system
illustrated in figure 904. However, if degrees are used, a better practice is to use the
360° or 180? system. Thus, a relative bearing of “20% forward of the port beam" is
better expressed as “290%,” or “70? left."

True, magnetic, and compass bearings are interconverted by the use of variation
and deviation, or compass error, in the same manner as courses. Interconversion of
relative and other bearings is accomplished by means of the heading. If true heading
is added to a relative bearing, true bearing results (RB+TH=TB). If magnetic,
compass, or grid heading (MH, CH, GH) is added to relative bearing, the correspond-
ing magnetic, compass, or grid bearing is obtained.

A bearing line extending in the direction of an observed bearing of a charted object
is one of the most widely used lines of position. If one knows that an identified
landmark has a certain bearing from his vessel, the vessel can only be on the line at which
such a bearing might be observed, for at any other point the bearing would be different.
This line extends outward from the landmark, along the reciprocal of the observed
bearing. Thus, if a lighthouse is east of a ship, that ship is west of the lighthouse.
lf a beacon bears 156°, the observer must be on a line extending 156°+180°=336°
from the beacon. Since observed bearing lines are great circles, this relationship is
not strictly accurate, but the error is significant only where the great circle departs
materially from the rhumb line, as in high latitudes (ch. XXV).

Bearings are obtained by compass, gyro repeater, pelorus, alidade, radar, etc.
One type of bearing can be obtained by eye without measurement. When two objects
appear directly in line, one behind the other, they are said to be “in range,” and together
they constitute a range. For accurately charted objects, a range provides the most

242 PILOTING

accurate line of position obtainable, and one of the easiest to observe.

Tanks, steeples,
towers, cupolas, etc., sometimes form natural ranges. A navigator should be familiar

with prominent ranges in his operating area, particularly those which can be used to

mark turning points, indicate limits of shoals, or define an approach heading or let-go
point of the anchorage of a naval vessel.

So useful is the range in marking a course
that artificial ranges, usually in the form of two lighted beacons, have been installed

in line with channels in many ports. A vessel proceeding along the channel has only

3
= c Q >
M es ss E
92. er S Ded SS ey»
ta KA 29 Ahead TE ŠŠ S$
20127 Po ee S SB»
SS 2? ve ES
E L Db SN S
2 One O PS N
^, Ke % X S S (N
Yp "ër SMS
O, 4. S oe
re Sa Ing «R RS
Point B iz S qe? A
O, S YA
"Port pāra y RAN "s
eam gat

0,

Int Forya,, d 1 Point Forward ^

ort Beam Wee UE das a ad of Starboat Be
Broad on Broad on
Port Beam um A

rA. Starboard Beam
i 1 Point
Ab,
port Beam Starboard aft
pat Beam
as N 2p,
SS oin
V ot S" Serbog y Ada
DNO R Oy,
RSS ar
a et

Se, 12
Ugo, DA
S 4. ty n OF
bud P &
J Š % o K
M $ o a 2
S Le gI w
% 3 dëi ¿En DIAS S fundo ^S
éi Fes Bi E ee mM
= E S UÁstem VERS H9. 5 A
seu = S esas Mim eM
& = E oes 2 a
GE 2 >
s 4
z

FIGURE 904.—One method of expressing relative bearings.

to keep the beacons in range to remain in the center of the channel. If the farther
beacon (customarily the higher one) appears to “open out” (move) to the right of the
forward (lower) beacon, one knows that he is to the right of his desired course line.
Similarly, if it opens out to the left, the vessel is off course to the left.

It is good practice to plot only a short part of a line of position in the vicinity of

the vessel, to avoid unnecessary confusion and to reduce the chart wear by erasure.
Particularly, one should avoid the drawin

g of lines through the chart symbol indicating
the landmark used. In the case of a range, a straightedge is placed along the two

objects, and the desired portion of the line is plotted. One need not know the numerical

PILOTING 243

value of the bearing represented by the line. However, if there is any doubt as to the
identification of the objects observed, the measurement of the bearing should prove
useful.

A bearing line is labeled with the time above the line, and the bearing below the
line. A range is labeled with the time only.

905. Distance.—If a vessel is known to be a certain distance from an identified
point on the chart, it must be somewhere on a circle with that point as the center and
the distance as the radius. An arc of the circle can be drawn and labeled with the
time above the line and the distance below the line.

Distances are obtained by radar, range finder, stadimeter, synchronized sound and
radio signals, synchronized air and water sounds, vertical sextant angles (table 9), etc.
If vertical sextant angles are used, measurement should be made from the top of the
object to the visible sea horizon, if it is available. If measurement is made to a water
line not vertically below the top of the object, a problem may be encountered because
distance from table 9 is to the point vertically below the top of the object, while the
distance used for entering table 22 to determine dip short of the horizon is to the water
line. Generally, any differences in these two distances can be determined from the
chart. This problem may, in some cases, be avoided by decreasing the height of eye
sufficiently to bring the horizon between the observer and the object.

906. The fix.—A line of position, however obtained, represents a series of possible
positions, but not a single position. However, if two simultaneous, nonparallel lines
of position are available, the only position that satisfies the requirements of being on
both lines at the same time is the intersection of the two lines. This point is one form
of fix. Examples of several types of fix are given in the illustrations. In figure 906a
a fix is obtained from two bearing lines. The fix of figure 906b is obtained by two
distance circles. Figure 906c illustrates a fix from a range and a distance. In figure
906d a bearing and distance of a single object are used.

Some consideration should be given to the selection of objects to provide a fix.
It is essential, for instance, that the objects be identified. The angle between lines of
position is important. The ideal is 90°. If the angle is small, a slight error in measur-

Figure 906a.—A fix by two bearing lines. Figure 906b.—A fix by two distances.

244 PILOTING

ing or plotting either line results in a relatively large error in the indicated position.
In the case of a bearing line, nearby objects are preferable to those at a considerable
distance, because the linear (distance) error resulting from an angular error increases
with distance. Thus, an error of 1° represents an error of about 100 feet if the object
is one mile distant, 1,000 feet if the object is ten miles away, and one mile if the object
is 60 miles from the observer.

Another consideration is the type of object. Lighthouses, spires, flagpoles, etc.,
are good objects because the point of observation is well defined. A large building,
most nearby mountains, a point of land, etc., may leave some reasonable doubt as to
the exact point used for observation. If a tangent is used (fig. 906a), there is a pos-
sibility that a low spit may extend seaward from the part observed. A number of
towers, chimneys, ete., close together require careful identification. A buoy or a
lightship may drag anchor and be out of position. Most buoys are secured by a
single anchor and so have a certain radius of swing as the tide, current, and wind change.

Although two accurate nonparallel lines of position completely define a position,
if they are taken at the same time, an element of doubt always exists as to the accuracy
of the lines. Additional lines of position can serve as a check on those already obtained,
and, usually, to reduce any existing error. If three lines of position cross at a common
point, or form a small triangle, it is usually a reasonable assumption that the position is
reliable, and defined by the center of the figure. However, this is not necessarily so,
and one should be aware of the possibility of an erroneously indicated position. Some-

R.TR.Q
N

N

© TR.
MON.O
1527 FIX
1033 FIX
1)
FiaunE 906c.—A fix by a range and FIGURE 906d.—A fix by distance and bear-

distance. ing of single object.

times an error can be identified. For instance, if several fixes obtained by bearings on
three objects produce triangles of about the same size, one might reasonably suspect
a constant error in the observation of the bearings, particularly if the same instrument
1s used for all observations, or in the plotting of the lines. If the application of a
constant error to all bearings results in a point, or near-point fix, the navigator is usually
justified in applying such a correction. This situation is illustrated in figure 906e
where the solid lines indicate the original plot, and the broken lines indicate each line
of position moved 3° in a clockwise direction. If different instruments are used for
observation, one of them might be consistently in error. This might be detected by
altering all bearings observed by that instrument by a fixed amount and producing good
fixes. However, one seldom has time for much experimentation of this kind while
piloting. If an error is suspected, such experiments might better be conducted while

PILOTING 24 5

bx Indicated Fix

FicurE 906e.—Adjusting a fix for inaccurate bearings.

at anchor or moored alongside a pier. Underway, other instruments, such as radar,
or another method, such as that explained in article 907, might better be used.

Lines of position obtained by observation of bearings or distances can be used
with lines of position obtained in any other manner, as by radio direction finder, loran,
celestial navigation, etc. If an object such as a buoy is passed close aboard, a fix is
obtained without plotting. Similarly, there should be no doubt as to the position of a
vessel which is observed to be midway between two channel buoys a short distance
apart.

907. Horizontal angles.—A fix may be obtained by means of the difference in
bearing of several objects. If a constant error is present in the instrument used for
measuring directions, it will not be reflected in the difference between bearings. There-
fore, the differences may be more accurate than the bearings. Horizontal sextant
angles, however, are usually the most accurate source of such information.

Customarily, two angles are obtained on three objects. These angles are then
plotted from a single point on a sheet of transparent material, or set on a mechanical
device called a three-arm protractor (fig. 4011c) in United States usage and a station
pointer in British terminology. The three lines or arms are then fitted to the chart
by trial and error until all three pass through the objects used for observation. The
observer is then at the common intersection of the three lines. This method provides
accurate results unless the three objects lie on or near a circle which passes through
the observer. The best way to avoid this is to select objects nearly in a straight line,
a group with the center one nearer than the other two, or objects so widely separated
that the angle between the two end ones approaches or exceeds 180°.

Because of its high accuracy, this method is frequently used in hydrographic
surveying (ch. XLI). It has fallen into virtual disuse in the ordinary course of navi-

246 PILOTING

gation because of the convenience and reliability of other methods. However, it may
be used when a position of greater than normal accuracy is required, as for finding
the position of letting go an anchor. Simultaneous angles are required for accurate
results. These are customarily obtained by two observers, each with a sextant. Ifa
single observer is available, he first observes the angle changing more slowly, then the
other, and then makes a second observation of the first angle. The average of the
two readings of the first angle is used with the second angle.

908. Nonsimultaneous observations.—For fully accurate results, observations
made to fix the position of a moving vessel should be made simultaneously, or nearly
so. On a slow-moving vessel, relatively little error is introduced by making several
observations in quick succession. A wise precaution is to observe the objects more
nearly ahead or astern first, since these are least affected by the motion of the observer.
For more accurate results, all readings but the last can be repeated in reverse order,
and the mean of each pair used. Thus, if three bearings (on objects A, B, and C)
are to be used, five readings can be taken, as follows: A, B, C, B, A. The two B .
readings are averaged, and also the two A readings. The time of the C reading is
considered the time of all readings. Approximately equal intervals should elapse
between readings. An indication of the error introduced by not observing this precau-
tion is the fact that at ten knots & vessel moves 1,000 feet in one minute. At 20 knots,
this distance is doubled. If the angle between lines of position is small, and the earlier
bearings are of objects near the beam, the position indicated by the fix might be in
error by more than the motion of the vessel, particularly if the objects on which later
bearings are taken are abaft those of earlier bearings.

Sometimes it is not possible or desirable to make simultaneous or nearly simul-
taneous observations. Such a situation may arise, for instance, when a single object
is available for observation, or
when all available objects are
on nearly the same or recipro-
cal bearings, and there is no
means of determining distance.
Under such conditions, a period
of several minutes or more
may be permitted to elapse
between observations to provide
lines of position crossing at suit-
able angles. When this occurs,
the lines can be adjusted to a
common time to obtain a run-
ning fix. Refer to figure 908a.
A ship is proceeding along a
coast on course 020?, speed 15
knots.. At 1505 lighthouse ZL
bears 310°. If the line of posi-
tion is accurate, the ship is
somewhere on it at the time of
observation. Ten minutes later
the ship will have traveled 2.5
miles in direction 020°. If the
ship was at A at 1505, it will
be at A’ at 1515. However, if
Figure 908a.—Advancing a line of position. the position at 1505 was B, the

PILOTING 247

position at 1515 will be B’. A

similar relationship exists be-

tween C and C’, D and D', E ©
and E”, ete. Thus, if any point
on the original line of position is
moved a distance equal to the
distance run, and in the direc-
tion of the motion, aline through
this point, parallel to the origi-
nal line of position, represents
all possible positions of the ship
at the later time. This process
is called advancing a line of
position. The moving of a line
back to an earlier time is called
retiring a line of position.

The accuracy of an ad-
justed line of position depends
not only upon the accuracy of
the original line, but also upon
the reliability of the information
used in moving the line. A
small error in the course made
good has little effect upon the
accuracy of a bearing line of
an object near the beam, but
maximum effect upon the bear-
ing line of an object nearly ahead or astern. Conversely, the effect of an error in speed
is maximum upon the bearing line of an object abeam. The opposite is true of circles
of position. The best estimate of course and speed made good should be used in
advancing or retiring a line of position.

If there are any changes of course or speed, these should be considered, for the
motion of the line of position should reflect as accurately as possible the motion of the
observer between the time of observation and the time to which the line is adjusted.
Perhaps the easiest way to do this is to measure the direction and distance between
dead reckoning or estimated positions at the two times, and use these to adjust some
point on the line of position. This method is shown in figure 908b. In this illustration
allowance is made for the estimated combined effect of wind and current, this effect
being plotted as an additional course and distance. If courses and speeds made good
over the ground are used, the separate plotting of the wind and current effect is not
used. In the illustration, point A is the DR position at the time of observation, and
point B is the estimated position (the DR position adjusted for wind and current) at
the time to which the line of position is adjusted. Line A’B’ is of the same length
and in the same direction as line AB.

Other techniques may be used. The position of the object observed may be ad-
vanced or retired, and the line of position drawn in relation to the adjusted position.
This is the most satisfactory method for a circle of position, as shown in figure 908c.
When the position of the landmark is adjusted, the advanced line of position can be
laid down without plotting the original line, which need be shown only if it serves a
useful purpose. This not only eliminates part of thé work, but reduces the number of
lines on the chart, and thereby decreases the possibility of error. Another method is

FIGURE 908b.—Advancing a line of position with a change
in course and speed, and allowing for current.

248 PILOTING

FIGURE 908c.—Advancing a circle of position.

to draw any line, such as a perpendicular, from the dead reckoning position at the time
of observation to the line of position. A line of the same length and in the same direc-
tion, drawn from the DR position or EP at the time to which the line is adjusted, locates
a point on the adjusted line, as shown in figure 908d. If a single course and speed is
involved, common practice is to measure from the intersection of the line of position
and the course line. If the dividers are set to the distance run between bearings
and placed on the chart so that one point is on the first bearing line and the other point
is on the second bearing line, and the line connecting the points is parallel to the course
line, the points will indicate the positions of the vessel at the times of the bearings.

An adjusted line of position is labeled the same as an unadjusted one, except that
both the time of observation and the time to which the line is adjusted are shown, as
in the illustrations of this article and article 909. Because of additional sources of
error in adjusted lines of position, they are not used when satisfactory simultaneous
lines can be obtained.

309. The running fix.—As stated in article 908, a fix obtained by means of lines of
position taken at different times and adjusted to a common time is called a running fix.
In piloting, common practice is to advance earlier lines to the time of the last observation.
Figure 909a illustrates a running fix obtained from two bearings of the same object.
In figure 909b the ship changes course and speed between observations of two objects.
A running fix by two circles of position is shown in figure 909c.

When simultaneous observations are not available, a running fix may provide the
most reliable position obtainable. The time between observations should be no longer
than necessary, for the uncertainty of course and distance made good increases with
time.

The errors applicable to a running fix are those resulting from errors of the indi-
vidual lines of position. However, a given error may have quite a different effect upon

PILOTING 249

the fix than upon the line of position. Consider, for example, the situation of an
unknown head current. In figure 909d a ship is proceeding along a coast, on course
250°, speed 12 knots. At 0920 lighthouse A bears 190°, and at 0930 it bears 143°.
If the earlier bearing line is advanced a distance of two miles (ten minutes at 12 knots)
in the direction of the course, the running fix is as shown by the solid lines. However
if there is a head current of two knots, the ship is making good a speed of only ten ssi,
and in ten minutes will travel a distance of only 1% miles. If the first bearing line is
advanced this distance, as shown by the broken line, the actual position of the ship is
at B. This is nearer the beach than the running fiz, and therefore a dangerous situation.
A following current gives an indication of position too far from the object. Therefore, if
a current parallel to the course (either head or following) is suspected, a minimum
estimate of speed made good will result in a possible margin of safety. If the second
bearing is of a different object, a mazimum estimate of speed should be made if the second
object is on the same side and farther forward, or on the opposite side and farther aft,
than the first object was when observed. All of these situations assume that danger
is on the same side as the object observed first. If there is either a head or following
current, a series of running fixes based upon a number of bearings of the same object
will plot in a straight line parallel to the course line, as shown in figure 909e. The
plotted line will be too close to the object observed if there is a following current, and
too far out if there is a head current. The existence of the current will not be apparent
unless the actual speed over the ground is known. The position of the plotted line
relative to the dead reckoning course line is not a reliable guide.

A current oblique to the course will result in an incorrect position, but the direction
of the error is indeterminate. In general, the effect of a current with a strong head or
following component is similar to that of a head or following current, respectively. The
existence of an oblique current, but not its amount, can be detected by observing and

1518 DR 1527 ER

Kë
e
1527
DR
N
e
1505 9
DR ` y
Ò o
u
9

Figure 908d.—Advancing a line of position by its relation
to the dead reckoning.

250

PILOTING

0405-0414
090

FIGURE 909a.—A running fix by two bearings on the same
object.

1233 DR

O
CUP

1215 DR

Ficure 909b.—A running fix with a change of course and speed be-

tween observations on separate landmarks,

251

PILOTING

0758R FIX

FIGURE 909c.—A running fix by two circles of position.

0930 Actual
Position

O,

Q

INS
LAG

Ficure 909d.—Effect of a head current on a running fix.

252 PILOTING

plotting several bearings of the same object. The running fix obtained by advancing 4
one bearing line to the time of the next one will not agree with the running fix obtained
by advancing an earlier line. Thus, if bearings A, B, and C are observed at five-minute
intervals, the running fix obtained by advancing B to the time of C will not be the same
as that obtained by advancing A to the time of C, as shown in figure 909f.

Whatever the current, the direction of the course made good (assuming constant
current) can be determined. On the chart, plot the various bearing lines. (fig. 909g,
left). Draw a straight line on a piece of transparent material, and along it mark off
the distances run (using any assumed speed) between bearings (fig. 909g, right). If
transparent material is not available, mark off the distances along the edge of a piece

x

FIGURE 909e.—A number of running fixes with a following current.

of paper. By trial and error, fit the distances to the bearing lines on the chart, so that
each mark falls on its bearing line (fig. 909h). The direction of the line is the vourse
being made good. Its distance from the track is in error by an amount proportional
to the ratio of the speed being made good to the speed assumed for the solution. If a
good fix (not a running fix) is obtained at some time before the first bearing for the
running fix, and the current has not changed, the track can be determined by drawing
a line from the fix, in the direction of the course made good. The intersection of the
track with any of the bearing lines is an actual position.

The current can be determined whenever a dead reckoning position and fix are
available for the same time. The direction from the dead reckoning position to the fix
is the set of the current. The distance between these two positions, divided by the
time (expressed in hours and tenths) since the last fix, is the drift of the current in
knots. For accurate results, the dead reckoning position must be run up from the
previous fix without any allowance for current. Any error in either the dead reckoning

PILOTING 253

Occ.

Conflicting Running Fixes at 1540

FiGURE 909f.—Detecting the existence of an oblique current, by a series of
running fixes.

020

Fiaure 909g.—Preparing to determine the course made good.

254 PILOTING

position (such as poor steering,
unknown compass error, inaccu-
rate log, wind, etc.) or the fix
will be reflected in the deter-
mination of current. When the
dead reckoning position and fix
are close together, a relatively
small error in either may in-
troduce a large error in the
apparent set of the current.

910. Solution without a
plot.—A running fix can be
obtained by utilizing the mathe-
matical relationships involved. .
Refer to figure 910. A ship
steams past landmark D. At `
any point A a bearing of D is
observed and expressed as de-
grees right or left of the course
(a relative bearing if the ship is
on course). Atsome later time,
at B, a second bearing of D is observed and expressed as before. At C the landmark is -
broad on the beam. "The angles at A, B, and C are known, and also the distance run be-
tween points. The various triangles could be solved by trigonometry (app. O) to find
the distance from D at any bearing. Distance and bearing provide a fix.

Table 7 provides a quick and easy solution. The table is entered with the differ-
ence between the course and first bearing (angle BAD in fig. 910) along the top of the table,
and the difference between the
course and second bearing
(angle CBD) at the left of the
table. For each pair of angles
listed, two numbers are given.
To find the distance from the
landmark at the time of the
second bearing (BD), multiply
the distance run between bear-
ings by the first number from
table 7. To find the distance
when the object is abeam (CD),
multiply the distance run be-
tween A and B by the second
number from the table. If the
run between bearings is exactly
one mile, the tabulated values
are the distances sought.

Example.—A ship is steaming
on course 050%, speed 15 knots.
At 1130 a lighthouse bears 024°,
and at 1140 it bears 359°.

Figure 909h.— Determining the course made good.

Figure 910.— Triangles involved in a running fix.

PILOTING 255

Required.—(1) Distance from the light at 1140.

(2) Distance from the light when it is broad on the port beam.

ai (fig. OMASE) The difference between the course and the first bearing
(0509-0249) is 26°, and the difference between the course and the second bearing
(050? + 360? —359?) is 51°.

(2) From table 7 the two numbers (factors) are 1.04 and 0.81, found by
interpolation.

(3) The distance run between bearings is 2.5 miles (10 minutes at 15 knots).

(4) The distance from the lighthouse at the
time of the second bearing is 2.5 1.04=2.6 miles.

(5) The distance from the lighthouse when it is
broad on the beam is 2.5X0.81=2.0 miles.

Answers.—(1) D 2.6 mi., (2) D 2.0 mi. H

Certain combinations of angles provide quick
mental solution without the need for table 7. If
the second difference (angle CBD) is double the
first difference (angle BAD), triangle BAD is isos-
celes (art. O28), with equal angles at A and D.
Therefore side AB (the run) is equal to side BD
(the distance off at the time of the second bearing).
This is called doubling the angle on the bow. If
the first angle is 45% and the second 90%, the dis-
tance run equals the distance when broad on the
beam. These are called bow and beam bearings.
If the first angle is 63°5 and the second 90°, the dis-
tance off when abeam is about twice the distance
run. If the angles are 71°5 and 90°, the distance
off when abeam is about three times the distance
run. If the first angle is 22°5 and the second 45°,
the distance at which the object will be passed abeam
is about 7/10 of the distance run between bearings.
If the angles are 22°5 and 26°5, the distance abeam
will be about 7/3 of the distance run. If the angles
are 30° and 60°, the distance of the object when
abeam will be about 7/8 of the distance run between
bearings. If the two angles are such that their natu-
ral cotangents differ by unity, the distance abeam A
will be equal approximately to the distance run Figure 911a.—A danger bearing.
between bearings. Some combinations having ap-
proximately this relationship are 22?—34?, 25°-41°, 27°-46°, 32°-59°, and 40?-799?.

If either the course or speed is in error, the result will be inaccurate.

911. Safe piloting without a fix.—A fix or running fix is not always necessary to
insure safety of the vessel. Ifa ship is proceeding up a dredged channel, for instance,
the only knowledge needed to prevent grounding is that the ship is within the limits of
the dredged area. This information might be provided by a range in line with the
channel. A fix is not needed except to mark the point at which the range can no longer
be followed with safety. Such a point is usually marked by a buoy.

Under favorable conditions a danger bearing might be used to insure safe passage
past a shoal or other danger. Refer to figure 91la. A vessel is proceeding along a
coast, on course line AB. A shoal is to be avoided. A line HX is drawn from light-
house H, tangent to the outer edge of the danger. As long as the bearing of light His

> UJ

Course line

256 PILOTING

less than XH, the danger bearing, the vessel is in safe water. An example is YH, no
part of the bearing line passing through the danger area. Any bearing greater than
XH, such as ZH, indicates a possible dangerous situation. If the object is passed on
the port side, the safe bearing is less than the danger bearing, as shown in figure 911a.
If the object is passed on the starboard side, the danger bearing represents the mini-
mum bearing, safe ones being greater. To be effective, a danger bearing should not
differ greatly from the course, and the object of which bearings are to be taken should
be easily identifiable and visible over the entire area of usefulness of the danger bearing.
A margin of safety might be provided by drawing line HX through a point a short

o
=
w
e
=
=>
o
o

Fīcune 911b.—Horizontal danger angles.

distance off the danger. If a natural or artificial range is available as a danger bearing,
it should be used.

A vessel proceeding along a coast may be in safe water as long as it remains &
minimum distance off the beach. "This information may be provided by any means
available. One method useful in avoiding particular dangers is the use of a danger
angle. Refer to figure 911b. A ship is proceeding along a coast on course line AB,
and the captain wishes to remain outside a danger D. Prominent landmarks are
located at M and N. A circle is drawn through M and N and tangent to the outer
edge of the danger. If X is a point on this circle, angle MXN is the same as at any
other point on the circle (except that part between M and N). Anywhere within the
circle the angle is larger and anywhere outside the circle it is smaller. Therefore, any
angle smaller than MXN indicates a safe position and any angle larger than MXN
indicates possible danger. Angle MXN is therefore a maximum horizontal danger

PILOTING 257

angle. A minimum horizontal danger angle is used when a vessel is to pass inside
an offlying danger, as at D’ in figure 911b. In this case the circle is drawn through M
and N and tangent to the inner edge of the danger area. The angle is kept larger than
MYN. Ifa vessel is to pass between two danger areas, as in figure 911b, the horizontal
angle should be kept smaller than MXN but larger than MYN. The minimum danger
angle is effective only while the vessel is inside the larger circle through M and N.
Bearings on either landmark might be used to indicate the entering and leaving of the
larger circle. A margin of safety can be provided by drawing the circles through
points a short distance off the dangers. Any method of measuring the angles, or
difference of bearing of M and N, can be used. Perhaps the most accurate is by
horizontal sextant angle. If a single landmark of known height is available, similar
procedure can be used with a vertical danger angle between top and bottom of the
object. In this case the charted position of the object is used as the center of the circles.

A vessel may sometimes be kept in safe water by means of a danger sounding.
The value selected depends upon the draft of the vessel and the slope of the bottom.
It should be sufficiently deep to provide adequate maneuvering room for the vessel to
reach deeper water before grounding, once the minimum depth is obtained. In an
area where the shoaling is gradual, a smaller margin of depth can be considered safe
than in an area of rapid shoaling. Where the shoaling is very abrupt, as off Point
Conception, California, no danger sounding is practical. It is good practice to promi-
nently mark the danger sounding line on the chart. A colored pencil is useful for
this purpose.

If it is desired to round a point marked by a prominent landmark, without ap-
proaching closer than a given minimum distance, this can be done by steaming until
the minimum distance is reached and then immediately changing course so as to
bring the landmark broad on the beam. Frequent small changes of course are then
used to keep the landmark near, but not forward of, the beam. This method is not
reliable if the vessel is being moved laterally by wind or current.

An approximation of the distance off can be found by noting the rate at which the
bearing changes. If the landmark is kept abeam, the change is indicated by a change
of heading. During a change of 57°5, the distance off is about the same as the distance
run. Fora change of 28°5, the distance is about twice the run; for 19? it is about three
times the run; for 14°5 it is about four times the run; and for 11°5 it is about five times
the run. Another variation is to measure the number of seconds required for a change
of 16°. The distance off is equal to this interval multiplied by the speed in knots and
divided by 1,000. That is, D= Bier where D is the distance in nautical miles, S is
the speed in knots, and t is the time interval in seconds. This method can also be used
for straight courses (with bearings 8° forward and abaft the beam), but with somewhat
reduced accuracy.

912. Soundings.—The most important use of soundings is to determine whether
the depth is sufficient to provide a reasonable margin of safety for the vessel. For this
reason, soundings should be taken continuously in pilot waters. A study of the chart
and the establishment of a danger sounding (art. 911) should indicate the degree of
safety of the vessel at any time.

Under favorable conditions, soundings can be a valuable aid in establishing the
position of the vessel. Their value in this regard depends upon the configuration of
the bottom, the amount and accuracy of information given on the chart, the type and
accuracy of the sounding equipment available aboard ship, and the knowledge and skill
of the navigator. In an area having a flat bottom devoid of distinctive features, or in an

258 PILOTING

area where detailed information is not given on the chart, little positional information
can be gained from soundings. However, in an area where depth curves run roughly
parallel to the shore, a sounding might indicate distance from the beach. In any area
where a given depth curve is sharply defined and relatively straight, 1t serves as a line
of position which can be used with other lines, such as those obtained by bearings of
landmarks, to obtain a fix. The 100-fathom curve at the outer edge of the con-
tinental shelf might be crossed with a line of position from celestial observation or
loran. The crossing of a sharply defined trench, ridge, shoal, or flat-topped seamount.
(a guyot) might provide valuable positional information.

In any such use, identification of the feature observed is important. In an area
of rugged underwater terrain, identification might be difficult unless an almost con-
tinuous determination of position is maintained, for it is not unusual for a number of
features within a normal radius of uncertainty to be similar. If the echo sounder
produces a continuous recording of the depth, called a bottom profile, this can be `
matched to the chart in the vicinity of the course line. If no profile is available,
a rough approximation of one can be constructed as follows: Record a series of sound-
ings at short intervals, the length being dictated by the scale of the chart and the ex-
isting situation. For most purposes the interval might be each minute, or perhaps
each half-mile or mile. Draw a straight line on transparent material and, at the scale
of the chart, place marks along the line at the distance intervals at which soundings
were made. For this purpose the line might be superimposed over the latitude scale
or a distance scale of the chart. At each mark record the corresponding sounding.
Then place the transparency over the chart and, by trial and error, match the recorded
soundings to those indicated on the chart. Keep the line on the transparency parallel
or nearly parallel to the course line plotted on the chart. A current may cause some
difference between the plotted course line and the course made good. Also, speed over
the bottom might be somewhat different from that used for the plot. This should be
reflected in the match. This method should be used with caution, because it may be
possible to fit the line of soundings to several places on the chart.

Exact agreement with the charted bottom should not be expected at all times.
Inaccuracies in the soundings, tide, or incomplete data on the chart may affect the
match, but general agreement should be sought. Any marked discrepancy should be
investigated, particularly if it indicates less depth than anticipated. If such a dis-
crepancy cannot be reconciled, the wisest decision might well be to haul off into deeper
water or anchor and wait for more favorable conditions or additional information.

913. Most probable position (MPP).—Since information sufficient to establish
an exact position is seldom available, the navigator is frequently faced with the problem
of establishing the most probable position of the vessel. If three reliable bearing lines
cross at a point, there is usually little doubt as to the position, and little or no judgment
is needed. But when conflicting information or information of questionable reliability
is received, a decision is required to establish the MPP. At such a time the experience
of the navigator can be of great value. Judgment can be improved if the navigator
will continually try to account for all apparent discrepancies, even under favorable
conditions. If a navigator habitually analyzes the situation whenever positional
information is received, he will develop judgment as to the reliability of various types
of information, and will learn something of the conditions under which certain types
should be treated with caution.

When complete positional information is lacking, or when the available information
is considered of questionable reliability, the most probable position might well be
considered an estimated position (EP). Such a position might be determined from a
single line of position, from a line of soundings, from lines of position which are some-

PILOTING 259

what inconsistent, from a dead reckoning position with a correction for current or
wind, etc.

Whether the most probable position is a fix, running fix, estimated position, or
dead reckoning position, it should be kept continually in mind, together with jū
estimate of its reliability. The practice of continuing a dead reckoning plot from one
good fix to another is advisable, whether or not information is available to indicate a
most probable position differing from the dead reckoning position, for the DR plot pro-
vides an indication of current and leeway. A series of estimated positions may not be
consistent because of the continual revision of the estimate as additional information
isreceived. However, it is good practice to plot all MPP’s, and sometimes to maintain
a separate EP plot based upon the best estimate of course and speed being made good
over the ground, for this should furnish valuable information to indicate whether the
present course is a safe one.

Aids to Navigation

914. Kinds of aids.—When piloting, a navigator is concerned primarily with the
position of his vessel relative to nearby land, shoals, and other dangers. It is natural,
therefore, that he make extensive use of landmarks, which are conspicuous objects,
structures, or lights serving as indicators for guidance or warning of a craft. Such an
object visible from a distance to seaward is called a seamark. Either type of mark may be
called a daymark if useful only during daylight, or a nightmark if useful primarily during
darkness. A natural or artificial mark used to assist a vessel in avoiding a particular
hazard may be called a clearing mark. If an uncharted landmark is discovered,
its position might be established from available information or by triangulation
(art. 4110) from known positions, and plotted on the chart for future use. A perma-
nent feature might well be reported to the appropriate government charting agency.

A mark established by man, to serve as a landmark, is called an aid to navigation.
This should not be confused with the expression navigational aid, which includes,
in addition to aids to navigation, such items as instruments, charts, tables, etc. The
principal aids to navigation are:

Lighthouse, a structure exhibiting a major light designed to serve as an aid to
navigation. Lighthouses vary in appearance because of location, relative importance,
the type of soil upon which they are constructed, prevalence of violent storms, back-
grounds against which they are seen, distances the lights are to be seen, etc. Some
are located on land, and some in the water. Figure 914 illustrates several typical light
structures. The type of structure and its coloring assist in daylight identification.
There are about 400 lighthouses in United States waters, being located along all coasts,
the Great Lakes, and many of the inland waterways.

Beacon. In a general sense, a beacon is anything serving as a signal or indication,
either for guidance or warning. However, as a distinctive type of aid to navigation,
a beacon is either a fixed aid (not a floating one) or an unlighted aid (sometimes called
a daybeacon). As thus defined, a lighthouse is a beacon. However, the term “beacon”
is generally applied particularly to secondary fixed structures, whether lighted or not.
There are about 15,000 beacons of this type in United States waters.

Lightship, a distinctively marked vessel anchored or moored at a charted point,
to serve as an aid to navigation. By night it displays a characteristic masthead light
and a less brilliant light on the forestay. The forestay indicates the direction in which
the vessel is headed, and hence the direction of the current (or wind), since lightships
head into the wind or current. By day a lightship displays the International Code
signal of the station when requested, or if an approaching vessel does not seem to
recognize it. The name of the station is painted in large letters on the side of the

260 PILOTING

MASONRY STRUCTURE CYLINDRICAL TOWER SQUARE
HOUSE ON CYLINDRICAL BASE

NW

PANA,
SEI)

ES — UY Ghi
CYLINDRICAL CAISSON STRUCTURE SKELETON IRON STRUCTURE

FIGURE 914.—Typical light structures.

PILOTING 261

vessel. All lightships except Lake Huron Lightship have red hulls; white lettering and
superstructure; and buff masts, lantern galleries, ventilators, and stacks. Relief light-
ships have the same coloring, but carry the name “Relief.” Lake Huron Lightship
has a black hull. A lightship may be equipped with certain auxiliary devices such as
a fog signal, submarine sound signal, and radiobeacon. When under way or off station
a lightship displays the lights and sounds the signals prescribed by the rules of the
road, and flies the International Code signal flags “PO,” signifying that it is not then
serving as an aid to navigation. It does not then show or sound any of the signals
of a lightship. A lightship is the floating equivalent of a lighthouse. Most U. S.
lightships eventually will be replaced by structures similar to Texas towers.

Buoy, a floating object, other than a lightship, moored to the bottom as an aid to
navigation. There are many different types of buoys to serve different purposes.
Buoys are the most numerous aid to navigation, about 20,000 unlighted and 3,000
lighted buoys being maintained by the United States Coast Guard alone.

Any lighted aid to navigation may be called a light.

Along the coasts of the United States, and in the Great Lakes (United States
side) most aids to navigation are installed and maintained by the United States Coast
Guard. Along certain rivers they are under the control of other government agencies,
notably the Corps of Engineers of the United States Army. A number of privately
maintained aids are in use. An example of such aids are lights at the ends of privately
owned piers.

915. Lights.—A light extends the use of various aids to navigation to periods of
darkness. If such a light is to serve its purpose, the user must be able to distinguish
it from the general background of shore lights, and to determine which navigational
light it is. That is, one must be able to identify the light. For this purpose each
light is given a distinctive sequence of light and dark periods, and in some cases a
distinctive color, or color sequence. These features are called the characteristics of
the light (fig. 915). No two lights are given the same characteristics if they are so
located that one migbt be mistaken for the other.

The U.S. Coast Guard publishes a Light List in five volumes: two volumes for
the Atlantic coast and Gulf of Mexico, and one volume each for the Pacific coast and
islands, Great Lakes, and Mississippi River system. The U.S. Navy Hydrographic
Office publishes seven Lists of Lights giving characteristics of lights of foreign waters
and the principal lights along the coasts of the United States. Characteristics are
also indicated on charts. The letter W indicates a white light, R a red light, and G
a green light. Other colors are not used by the United States Coast Guard. If no
color indication is given, a light is white. Colors are produced by glass shades
or screens. The period of a light is the time required for one complete sequence of
characteristics.

Some lights provide bearing indication by a system of light sectors, different
colors being exhibited in the various sectors. As an observer crosses the boundary
between sectors, he can note the change of color. The boundaries are indicated in
the light lists and by broken lines on charts. The bearings given in these indications
are those of the light as observed at a distance, not the direction outward from the
light. In general, red sectors are used to indicate obstruction areas. In using light
sectors to determine bearing, one should remember that the line of demarcation is not
always sharply defined, and that when haze or smoke is present, a white light might
have a reddish hue.

916. Visibility of lights.—Usually a navigator wants to know not only the identity
of a light, but also the area in which he might reasonably expect to observe it. His
track is planned to take him within range of lights which can prove useful during

262 PILOTING

Symbols and meaning

Illustrati . Lights which Phase description
a kr Lights which do | ¿how color

not change color riti

EY Alt.=Alternat-| A continuous steady

ing. light.

F. Fl. = Fixed |Alt. F. Fl.=Al-| A fixed light varied at

and flashing. ternating fixed regular intervals by
and flashing. a flash of greater
brilliance.

F.Gp.Fl. = Fixed |Alt. F. Gp. Fl. | A fixed light varied at
and group =Alternating regular intervals by
flashing. fixed and groups of 2 or more

group flashing flashes of greater
brilliance.

Fl. =Flashing---- |Alt. Fl. Alter-| Shows a single flash at
nating flash- regular intervals, the
ing. duration of light al-

ways being less than

the duration of dark-
ness. Shows not
more than 30 flashes

per minute.

Gp. Fl.=Group . Gp. Fl.=| Shows at regular inter-

flashing. Alternating vals groups of 2 or
group flash-| more flashes.
Ing.

QS Flom Quicks [EAS Shows not less than
flashing. 60 flashes per min-

ute.

"GEI Na In eee a ee Shows quick flashes
terrupted for about 4 sec-
quick flash- onds, followed by a
ing. dark period of

about 4 seconds.

S-L. Fl.2Short- | ---------2----. Shows a short flash of
long flashing. about 0.4 second,

followed by a long
flash of 4 times
that duration.

Occ. = Occulting c A light totally eclipsed
ternating oc- at regular inter-
culting. vals, the duration

of light always

equal to or greater
than the duration
of darkness.

Eë Ocie cga d Et e A light with a group
Group occult- of 2 or more eclipses
at regular intervals.

EUM

ing.

Light colors used and abbreviations: W= white, R=red, G — green.

Figure 915.— Light characteristics.

periods of darkness. If lights are not sighted within a reasonable time after prediction,
a dangerous situation may exist, requiring resolution or action to insure safety of the
vessel.

The area in which a light can be observed is normally a circle with the light as
the center, and the range of visibility as the radius. However, on some bearings the
range may be reduced by obstructions. In this case the obstructed arc might differ
with height of eye and distance. Also, lights of different colors may be seen at different
distances. This fact should be considered not only in predicting the distance at which
a light can be seen, but also in identifying it. The condition of the atmosphere has
a considerable effect upon the distance at which lights can be seen. Sometimes lights
are obscured by fog, haze, dust, smoke, or precipitation which may be present at the
light, or between it and the observer, but not at the observer, and possibly unknown

PILOTING 263

to him. There is always the possibility of a light being extinguished. In the case of
unwatched lights, this condition might not be detected and corrected at once. During
periods of armed conflict, certain lights might be deliberately extinguished if they are
considered of greater value to the enemy than to one's own vessels.

On a dark, clear night the range of visibility is limited primarily in two ways:
(1) luminosity and (2) curvature of the earth. A weak light cannot normally be
expected to be seen beyond a certain range, regardless of the height of eye. This
distance is called luminous range. Light travels in almost straight lines, so that an
observer below the visible horizon of the light should not expect to see the light,
although the loom extending upward from the light can sometimes be seen at greater
distances. "Table 8 gives the distance to the horizon at various heights. The tabu-
lated distances assume normal refraction. Abnormal conditions might extend this
range somewhat (or in some cases reduce it). Hence, the geographic range, as the
luminous range, is not subject to exact prediction at any given time.

The geographic range depends upon the height of both the light and the observer,
as shown in figure 916. In this illustration a light 150 feet above the water is shown.
At this height, the distance to the horizon, by table 8, is 14.0 miles. Within this
range the light, if powerful enough and atmospheric conditions permit, is visible regard-
less of the height of eye of the observer (if there is no obstruction). Beyond this
range, the visibility depends upon the height of eye. Thus, by table 8 an observer
with height of eye of five feet can see the light on his horizon if he is 2.6 miles beyond
the horizon of the light, or a total of 16.6 miles. For a height of 30 feet the distance
is 14.0+6.3 = 20.3 miles. If the height of eye is 70 feet, the geographic range is
14.0+9.6 = 23.6 miles.

The range of important lights is given in the light lists, and also on the charts.
The tabulated or charted range is for mean high water and a height of eye of 15 feet, and
because of various uncertainties is given only to the nearest whole mile. Where the
luminous range is less than the charted range, the shorter distance is given. This fact
is not indicated. Therefore, in predicting the range at which a light can be seen, one
should first determine the geographic range and compare this with the charted range.

|
|
|
|
|
|

/
2.6»

m
e

FIGURE 916.— Geographie range of visibility of a light.

264 PILOTING

This is done by adding 4.4 miles (the distance to the horizon at a height of 15 feet) to
the value from table 8 for the height of the light. If this value approximates the
charted range, one is generally safe in assuming that the charted range is the geographic
range. The predicted range is then found by adding the distance to the horizon for
both the light and the observer, as indicated above, or, approximately, by taking the
difference between 4.4 and the distance for the height of eye of the observer (a constant
for any given height) and adding this value to the charted range (subtracting if the
height of eye is less than 15 feet). In making a prediction, one should keep in mind
the possibility of the luminous range being between the charted range and the predicted
range. The power of the light should be of some assistance in identifying this
condition.

If one is approaching a light, and wishes to predict the time at which it should be
sighted, he first predicts the range. It is then good practice to draw a circle indicating
the limit of visibility. The point at which the course line crosses the circle of visibility |
is the predicted position of the vessel at the time of sighting the light. "The predicted
time of arrival at this point is the predicted time of sighting the light. The direction
of the light from this point is the predicted bearing at which the light should be sighted.
Conversion of the true bearing to a relative bearing is usually helpful in sighting the
light. The accuracy of the predictions depends upon the accuracy of the predicted
range, and the accuracy of the predicted time and place of crossing the circle of visi-
bility. If the course line crosses the circle of visibility at a small angle, a small lateral
error in track may result in a large error of prediction, both of bearing and time. "This
is particularly apparent if the vessel is farther from the light than predicted, in which
case the light might be passed without being sighted. Thus, if a light is not sighted
at the predicted time, the error may be on the side of safety. However, such an in-
terpretation should not be given unless confirmed by other information, for there is
always the possibility of reduced range of visibility, or of the light being extinguished.

When a hght is first sighted, one might determine whether it is on the horizon by
immediately reducing the height of eye by several feet, as by squatting or changing
position to a lower height. If the light disappears, and reappears when the original
height is resumed, it is on the horizon. This process is called bobbing a light. If a
vessel has considerable vertical motion due to the condition of the sea, a light sighted
on the horizon may alternately appear and disappear. This may lead the unwary to
assign faulty characteristics and hence to err in its identification. "The true character-
istics should be observed after the distance has decreased, or by increasing the height
of eye of the observer.

917. Buoys.—The primary functions of buoys are to delineate channels, indicate
shoals, mark obstructions, and warn the mariner of danger.

The prineipal types of buoys used by the United States are illustrated in figure
917, and described as follows: |

Can, à buoy built up of steel plates, in the shape of an ordinary cylindrical “tin”
can.

Nun, a buoy built up of steel plates, the above-water portion being in the shape
of a truncated cone.

Spar, a large log, trimmed, shaped, and appropriately painted. Some spar buoys
of the same shape are constructed of steel.

Bell, a steel float surmounted by a short skeleton tower in which the bell is located.
Older bell buoys are sounded by the motion of the buoys in the sea. In newer types
the bells are struck by compressed gas or electrically operated hammers. A gong buoy

is similar to a bell buoy, but instead of a bell it has a set of gongs, each of which has a
distinctive tone.

PILOTING 265

Whistle, a steel float sur-

mounted by a small tower
in which a whistle is located.
Older whistle buoys are sounded ati”
by the motion of the sea. In
some newer buoys a trumpet
is sounded electrically.

Lighted, a steel float sur-
mounted by a skeleton tower CAN SPAR
with the light at the top. En-
ergy for the light is provided by
electric batteries or a tank of
acetylene gas, located in the
metal float.

Combination, a buoy hav-
ing more than one means of BELL WHISTLE
conveying intelligence, as a
lighted bell buoy or lighted
whistle buoy.

Some unlighted buoys are
fitted with reflectors to assist
in their location and identi-
fication by searchlight at night.
The colors of the reflectors
have the same significance as
those of lights. Radar re-
flectors are fitted to some E
buoys to increase the strength miele BRINE) mue
of the returned signal. A buoy
may be equipped with a marker FIGURE 917.—Principal buoy types used by United States.
radiobeacon.

Most maritime countries use either the lateral system of buoyage or the cardinal
system, or both. In the lateral system, used on all navigable waters of the United
States, the coloring, shape, numbering, and lighting of buoys indicate the direction to
a danger relative to the course which should be followed. In the cardinal system the
coloring, shape, and lighting of buoys indicate the direction to a danger relative to the
buoy itself. The color, shape, lights, and numbers of buoys in the lateral system as
used by the United States are determined relative to a direction from seaward. Along
the coasts of the United States, the clockwise direction around the country is arbitrarily
considered to be the direction “from seaward." Some countries using the lateral
system have methods of coloring their buoys and lights opposite to that of the United
States. Appendix J treats this subject in greater detail.

In United States waters the following distinctive system of identification is used:

Red nun buoys mark the right side of channels for an inbound vessel, and obstruc-
tions which should be kept to starboard. They have even numbers which increase
from seaward.

Black can buoys mark the left side of channels for an inbound vessel, and obstruc-
tions which should be kept to port. They have odd numbers which increase from
seaward.

Red and black horizontally banded buoys mark junctions or bifurcations of channels,
or an obstruction that can be passed on either side. The color (red or black) of the

—_— ee

—

266 PILOTING

top band and the shape (nun or can) indicate the side on which the buoy should be
passed by a vessel proceeding along the principal channel.

Black and white vertically striped buoys mark the center of a channel and should
be passed close aboard. These “mid-channel buoys” may be either nuns or cans.

In fairways and channels solid red or solid black buoys have numbers. Others
may have letter designations. Along channels certain numbers may be omitted to
maintain the approximate sequence on both sides of the channels.

Lights. Red lights are used only on red buoys and buoys with a red band at the
top, green lights are used only on black buoys and buoys with a black band at the top.
White lights are used without any color significance. Lights on red and black buoys,
if not fixed, are always regularly flashing or regularly occulting. Quick flashing lights
are used when a light of distinct cautionary significance is desired, as at a sharp turn
or constriction in the channel. Interrupted quick flashing lights are used on red and
black horizontally banded buoys. White short-long flashing lights are used on black
and white vertically striped buoys.

Special purpose buoys. White buoys mark anchorages. Yellow buoys mark quar-
antine anchorages. White buoys with green tops are used in dredging and survey
operations. Black and white horizontally banded buoys mark fish net areas. Yellow
and black vertically striped buoys mark seadromes. White and orange banded, either
horizontally or vertically, are used for special purposes.

Wreck buoys are generally placed on the seaward or channel side, as near the wreck
as conditions permit. The possibility of the wreck having shifted position due to sea
action since the buoy was placed should not be overlooked.

Station buoys, are placed close to some lightships and important buoys to mark
the position if the regular aid is not at the assigned position. Such buoys are colored
and numbered the same as the regular aid, lightship station buoys having the letters
“LS” above the initials of the station.

Buoys are secured by anchor, and swing in a circle of small radius as the current
changes. In this respect, they are inferior to fixed aids for position fixing. They may
be shifted, carried away, capsized, or sunk. Lighted buoys may be extinguished and
sound buoys may not function.

Dates shown in light lists for seasonal buoys are approximations which vary with
local conditions.

918. Fog signals.—Any sound-producing device may serve as a fog signal to warn
the mariner of danger or to assist him in establishing the position of his vessel. If a
fog signal is to be fully effective for the second of these functions, the mariner must
be able to recognize it as a fog signal and to know from what point it is sounded.
Bells, whistles, etc., which are sounded by action of the sea are erratic in operation
and positive identification is not always possible. At most lighthouses and lightships
fog signals are operated by mechanical means, providing a definite sequence of sounds
and silent periods resembling the characteristics of lights. The sequence, stated in the
light list, is an aid to identification. The distinctive sound of each ir of signal
apparatus is helpful in this respect. About 600 fog signals are maintained by the
United States Coast Guard. These are of the following types:

Bell, sounded by means of a hammer actuated by hand, descending weight, com-
pressed gas, or electricity. ;

Diaphone, a device producing sound by means of a
actuated by compressed air.
followed by a lower pitch.

i A slotted reciprocating piston
Two-tone” diaphones produce a blast with a high pitch

PILOTING 267

Diaphragm horn, a device producing sound by means of a disk diaphragm vibrated
by compressed air, steam, or electricity. Duplex or triplex units produce simultaneous
sounds of different pitch, resulting in a chime signal.

Reed horn, a device producing sound by means of a steel reed vibrated by
compressed air.

Siren, a device producing sound by means of either a disk or a cup-shaped rotor
actuated by compressed air, steam, or electricity.

Whistle, producing sound by compressed air or steam emitted through a circular
slot into a cylindrical bell chamber.

Radiobeacons, radar, and other electronic aids to navigation can be of considerable
assistance to a vessel equipped to use them.

Tides and Currents

919. Tidal effects.—The daily rise and fall of the tide, with its attendant flood
and ebb of tidal current, is familiar to every mariner. He is aware, also, that at high
water and low water the depth of water is momentarily constant, a condition called
stand. Similarly, there is a moment of slack water as a tidal current reverses direction.
As a general rule, the change in height or the current speed is at first very slow, increasing
to a maximum about midway between the two extremes, and then decreasing again.
If plotted against time, the height of tide or speed of a tidal current takes the general
form of a sine curve. Sample curves, and more complete information about causes,
types, and features of tides and tidal currents, are given in chapter XXXI. Ocean
(nontidal) currents are discussed in chapter XXXII. The present chapter is con-
cerned primarily with the application of tides and currents to piloting, and predicting
the tidal conditions that might be encountered at any given time.

Although tides and tidal currents are caused by the same phenomena, the time
relationship between them varies considerably from place to place. For instance, if
an estuary has a wide entrance and does not extend far inland, the time of maximum
speed of current occurs at about the mid time between high water and low water.
However, if an extensive tidal basin is connected to the sea by a small opening, the
maximum current may occur at about the time of high water or low water outside the
basin, when the difference in height is maximum.

The height of tide should not be confused with depth of water. For reckoning
tides a reference level is selected. Soundings shown on the largest scale charts are the
vertical distances from this level to the bottom. At any time the actual depth is this
charted depth plus the height of tide. In most places the reference level is some form
of low water. But all low waters at a place are not the same height, and the selected
reference level is seldom the lowest tide that occurs at the place. When lower tides
occur, these are indicated by a negative sign. Thus, at a spot where the charted depth is
15 feet, the actual depth is 15 feet plus height of tide. When the tide is three feet, the
depth is 15+3=18 feet. When it is (—)1 foot, the depth is 15—1=14 feet. It is
well to remember that the actual depth can be less than the charted depth. In an area
where there is a considerable range of tide (the difference between high water and low
water), the height of tide might be an important consideration in using soundings
to assist in determining position, or whether the vessel is in safe water.

One should remember that heights given in the tide tables are predictions, and that
when conditions vary considerably from those used in making the predictions, the
heights shown may be considerably in error. Heights lower than predicted are par-
ticularly to be anticipated when the atmospheric pressure is higher than normal, or
when there is a persistent strong offshore wind. Along coasts where there is a large

268 PILOTING

inequality between the two high or two low tides during a tidal day the height predictions
liable than elsewhere.

i ens bi encountered in pilot waters is due primarily to tidal action, but
other causes are sometimes present. The tidal current tables give the best prediction
of total current, regardless of cause. The predictions for a river may be considerably
in error following heavy rains or a drought. The effect of current is to alter the course
and speed made good over the bottom (art. 807). Due to the configuration of land (or
shoal areas) and water, the set and drift may vary considerably over different parts of a
harbor. Since this is generally an area in which small errors in position of a vessel are
of considerable importance to its safety, a knowledge of predicted currents can be
critical, particularly if the visibility is reduced by fog, snow, etc. if the vessel is pro-
ceeding at reduced speed, the effect of current with respect to distance traveled is
greater than normal. Strong currents are particularly to be anticipated in narrow
passages connecting larger bodies of water. Currents of more than five knots are
encountered from time to time in the Golden Gate at San Francisco. Currents of more
than 13 knots sometimes occur at Seymour Narrows, British Columbia.

In straight portions of rivers and channels the strongest currents usually occur in
the middle, but in curved portions the swiftest currents (and deepest water) usually
occur near the outer edge of the curve. Countercurrents and eddies may occur on
either side of the main current of a river or narrow passage, especially near obstructions
and in bights.

In general, the range of tide and the speed of tidal current are at a minimum upon
the open ocean or along straight coasts. The greatest tidal effects are usually en-
countered in rivers, bays, harbors, inlets, bights, etc. A vessel proceeding along a
coast can be expected to encounter stronger sets toward or away from the shore while
passing an indentation than when the coast is straight.

920. Predictions of tides and currents to be expected at various places are pub-
lished annually by the U. S. Coast and Geodetic Survey. These are supplemented
by nine sets of Tidal Current Charts, each set consisting of 12 charts, one for each hour
of the tidal cycle. On these charts the set of the current at various places in the area is
shown by arrows, and the drift by numbers. Since these are average conditions, they
indicate in a general way the tidal conditions on any day and during any year. They
are designed to be used with the tidal current tables (except those for New York Harbor,
which are used with the tide tables). These charts are available for Boston Harbor,
Narragansett Bay to Nantucket Sound, Long Island Sound and Block Island Sound,
New York Harbor, Delaware Bay and River, Tampa Bay, San Francisco Bay, Puget
Sound (northern part), and Puget Sound (southern part). Current arrows are some-
times shown on nautical charts. These represent average conditions and should not
be considered reliable predictions of the conditions to be encountered at any given time.
When a strong current sets over an irregular bottom, or meets an opposing current,
ripples may occur on the surface. These are called tide rips. Areas where they occur
frequently are shown on charts.

Usually, the mariner obtains tidal information from tide and tidal current tables.
However, if these are not available, or if they do not include information at a desired
place, the mariner may be able to obtain locally the mean high water lunitidal interval
or the high water full and change. The approximate time of high water can be found by
adding either interval to the time of transit (either upper or lower) of the moon (art.
2104). Low water occurs approximately % tidal day (about 6"12%) before and after
the time of high water. The actual interval varies somewhat from day to day, but

approximate results can be obtained in this manner. Similar information for tidal
currents (lunicurrent interval) is seldom available.

PILOTING 269

921. Tide tables for various parts of the world are published in four volumes by the
U.S. Coast and Geodetic Survey. Each volume is arranged as follows:

Table 1 contains a complete list of the predicted times and heights of the tide for
each day of the year ata number of places designated as reference stations.

| Table 2 gives differences and ratios which can be used to modify the tidal informa-
tion for the reference stations to make it applicable to a relatively large number of
subordinate stations.

Table 8 provides information for use in finding the approximate height of the tide
at any time between high water and low water.

Table 4 is a sunrise-sunset table at five-day intervals for various latitudes from
76? N to 60%S (40°S in one volume).

Table 5 provides an adjustment to convert the local mean time of table 4 to zone or
standard time.

Table 6 (two volumes only) gives the zone time of moonrise and moonset for each
day of the year at certain selected places.

Table 7 gives certain astronomical data. In the two volumes not having moon-
rise-moonset tables, this is table 6.

Extracts from tables 1, 2, and 3 for the East Coast of North and South America
are given in appendix T. Before the edition having predictions for 1958, the arrange-
ment of tables 1 and 2 were somewhat different than shown.

922. Tide predictions for reference stations.—The first page of appendix T is the
table 1 daily predictions for New York (The Battery) for the first quarter of 1958.
As indicated at the bottom of the page, times are for Eastern Standard Time (+5 zone,
time meridian 75° W). Daylight saving time is not used. Times are given on the
24-hour basis. The tidal reference level for this station is mean low water.

For each day, the date and day of week are given, and the time and height of each
high and low water are given in chronological order. Although high and low waters
are not labeled as such, they can be distinguished by the relative heights given immed-
lately to the right of the times. Since two high tides and two low tides occur each tidal
day, the type of tide at this place is semidiurnal (art. 3105). The tidal day being
longer. than the civil day (because of the revolution of the moon eastward around the
earth), any given tide occurs later from day to day. Thus, on Saturday, March 22,
1958, the first tide that occurs is the lower low water (—0.3 foot at 0333). The follow-
ing high water (lower high water) is 4.1 feet above the reference level (a 4.4 foot rise
from the preceding low water), and occurs at 0929. This is followed by the higher
low water (—0.2 feet) at 1540, and then the higher high water of 4.4 feet at 2143.
The cycle is repeated on the following day with variations in height, and later times.

Because of later times of corresponding tides from day to day, certain days have
only one high water or only one low water. Thus, on January 9 high tides occur at
1051 and 2329. The next following high tides are at 1146 on January 10 and 0024 on
January 11. Thus, only one high tide occurs on January 10, the previous one being
shortly before midnight on the ninth, and the next one occurring early in the morning
of the eleventh, as shown.

923. Tide predictions for subordinate stations.—The second page of appendix T
is a page of table 2 of the tide tables. For each subordinate station listed, the following
information is given: h

Number. The stations are listed in geographical order and given consecutive
numbers. At the end of each volume an alphabetical listing is given, and for each
entry the consecutive number is shown, to assist in finding the entry in table 2.

Place. The list of places includes both subordinate and reference stations, the

latter being given in bold type.

270 PILOTING

Position. The approximate latitude and longitude are given to assist in locating
the station. The latitude is north or south, and the longitude east or west, depending
upon the letters (N, S, E, W) next above the entry. These may not be the same as
those at the top of the column.

Differences. The differences are to be applied to the predictions for the reference
station shown in bold capitals next above the entry on the page. Time and height differ-
ences are given separately for high and low waters. Where differences are omitted,
they are either unreliable or unknown.

The time difference is the number of hours and minutes to be applied to the time
at the reference station to find the time of the corresponding tide at the subordinate
station. This interval is added if preceded by a plus sign (+), and subtracted if
preceded by a minus sign (—). Special conditions occurring at a few stations are
indicated by footnotes on the applicable pages. In some instances, the corresponding
tide falls on a different daté at reference and subordinate stations.

Height differences are shown in a variety of ways. For most entries separate
height differences in feet are given for high water and low water. These are applied
to the height given for the reference station. In many cases a ratio is given for either
high water or low water, or both. The height at the reference station is multiplied
by this ratio to find the height at the subordinate station. For a few stations, both a
ratio and difference are given. In this case the height at the reference station is first
multiplied by the ratio, and the difference is then applied. An example is given in
each volume of tide tables. Special conditions are indicated in the table or by footnote.
Thus, a footnote on the second page of appendix T indicates that “Values for the
Hudson River above George Washington Bridge are based upon averages for the six
months May to. October, when the fresh-water discharge is a minimum.”

Ranges. Various ranges are given, as indicated in the tables. In each case this
is the difference in height between high water and low water for the tides indicated.

Example.—List chronologically the times and heights of all tides at Yonkers,
(No. 1581) on January 10, 1958.

Solution.—

Date January 10, 1958

Subordinate station Yonkers

Reference station New York

High water time difference (+) 1509»

Low water time difference (OS

High water height difference (—) 0.7 ft.

Low water height difference 0.0 ft.

New York Yonkers

HW 2329 (9th) 4.4 ft. 0038 SWELL
LW 0525 (—) 0.6 ft. 0635 (—) 0.6 ft.
HW 1146 4.6 ft. 1255 3.9 ft.
LW 1758 (—) 0.8 ft. 1908 (—) 0.8 ft.

924. Finding height of tide at any time.—Table 3 of the tide tables provides means
for determining the approximate height of tide at any time. It is based upon the
assumption that a plot of height versus time is a sine curve (art. 040). Instructions

)

vg ght of tide at Yonkers (No. 1581) at 1000 on January 10,

PILOTING 271

Solution. —The given time is between the low water at 0635 and the high water
at 1255 (sample ot art. 923). Therefore, the tide is rising. The duration of rise is
12557 06356 20”. The range of tide is 3.9—(—0.6) —4.5 feet. The given time
is 2 55 before high water, the nearest tide. Enter the upper part of the table with
duration of rise 6*20”, and follow the line horizontally to 2157” (the nearest tabulated
value to 255"). Follow this column vertically downward to the entry 2.0 feet in
the line for a range of tide of 4.5 feet. This is the correction to be applied to the nearest
tide. Since the nearest tide is high water, subtract 2.0 from 3.9 feet. The answer,
1.9 feet, is the height of tide at the given time.

Answer.—Ht. of tide at 1000, 1.9 ft.

Interpolation in this table is not considered justified.

It may be desired to know at what time a given depth of water will occur. In
this case, the problem is solved in reverse.

Example 2.—The captain of a vessel drawing 22 feet wishes to pass over a tempo-
rary obstruction near Days Point, Weehawken (No. 1571), having a charted depth of 21
feet, passage to be made during the morning of January 10, 1958.

Required.—The earliest time after 0800 that this passage can be made, allowing
a safety margin of two feet.

Solution.—The least acceptable depth of water is 24 feet, which is three feet more
than the charted depth. Therefore, the height of tide must be three feet or more. At
the New York reference station a low tide of (—) 0.6 foot occurs at 0525, followed
by a high tide of 4.6 feet at 1146. At Days Point the corresponding low tide is (—) 0.6
foot at 0548, and the high tide is 4.4 feet at 1210. The duration of rise is 6"22™, and
the range of tide is 5.0 feet. The least acceptable tide is 3.0 feet, or 1.4 feet less than
high tide. Enter the lower part of table 3 with range 5.0 feet and follow the horizontal
line until 1.5 feet is reached (the nearest tabulated value to 1.4 feet). Follow this
column vertically upward until the value of 2^19" is reached on the line for a duration
of 620” (the nearest tabulated value to 622%). The minimum depth will occur
about 2119” before high water, or at about 0951.

Answer.—A depth of 24 feet occurs at 0951.

If the range of tide is more than 20 feet, half the range (one third if the range is
greater than 40 feet) is used to enter table 3, and the correction to height is doubled
(trebled if one third is used).

A diagram for a graphical solution is given in figure 924. Eye interpolation can
be used if desired. The steps in this solution are as follows:

1. Enter the upper graph with the duration of rise or fall. This is represented
by a horizontal line.

2. Find the intersection of this line and the curve representing the interval from
the nearest low water (point 4).

3. From A, follow a vertical line to the sine curve of the lower diagram (point B).

4. From B, follow horizontally to the vertical line representing the range of tide
(point C).

5. Using C, read the correction from the series of curves.

6. Add (algebraically) the correction of step 5 to the low water height, to find the
height at the given time.

The problem illustrated in figure 924 is similar to that of example 1 given above.
The duration of rise is 62257, and the interval from low water is 5523". The range of
tide is 6.1 feet. The correction (by interpolation) is 5.7 feet. If the height of the pre-
ceding low tide is (—)0.2 foot, the height of tide at the given time is (—)0.2+5.7=5.5
feet. To solve example 2 by the graph, enter the lower graph and find the intersection
of the vertical line representing 5.0 feet and the curve representing 3.6 feet (the. mini-

272 PILOTING

Duration of rise or fall, in hours

men
o

m
I

curves)

(

Height in feet above LOW water

0 2 4 6 "a" "19 odium A SIE
Range of tide in feet

FIGURE 924.—Graphical solution for height of tide at any time.

PILOTING 273

mum acceptable height above low water). From this point follow horizontally to the
sine curve, and then vertically to the horizontal line in the upper figure representing the
duration of rise of 6^22", From the curve, determine the interval 4*10". The earliest
time is about 4^10" after low water, or at about 0958.

925. Tidal current tables are somewhat similar to tide tables, but the coverage is
less extensive, being given in two volumes. Each volume is arranged as follows:

Table 1 contains a complete list of predicted times of maximum currents and slack,
with the velocity (speed) of the maximum currents, for a number of reference stations.

Table 2 gives differences, ratios, and other information related to a relatively large
number of subordinate stations.

Table 3 provides information for use in finding the speed of the current at any time
between tabulated entries in tables 1 and 2.

Table 4 gives the number of minutes the current does not exceed stated amounts,
for various maximum speeds.

Table 5 (Atlantic Coast of North America only) gives information on rotary tidal
currents.

Each volume contains additional useful information related to currents. Extracts
from the tables for the Atlantic Coast of North America are given in appendix U.
Before the edition having predictions for 1958, the arrangement of tables 1 and 2 were
somewhat different than shown.

926. Tidal current predictions for reference stations.—The extracts of appendix
U are for The Narrows, New York Harbor. Times are given on the 24-hour basis, for
meridian 75° W.

For each day, the date and day of week are given, with complete current information.
Since the cycle is repeated twice each tidal day, currents at this place are semidiurnal.
On most days there are four slack waters and four maximum currents, two of them
floods (f) and two of them ebbs (e). However, since the tidal day is longer than the
civil day, the corresponding condition occurs later from day to day, and on certain
days there are only three slack waters or three maximum currents. At some places,
the current on some days runs maximum flood twice, but ebb only once, a minimum
flood occurring in place of the second ebb. The tables show this information.

As indicated by appendix U, the sequence of currents at The Narrows on Wednes-
day, February 26, 1958, is as follows:

0000 Flood current, 8” after maximum velocity (speed).

0300 Slack, ebb begins.

0625 Maximum ebb of 1.6 knots, setting 160°.

1019 Slack, flood begins.

1217 Maximum flood of 1.1 knots, setting 340°.

1512 Slack, ebb begins.

1840 Maximum ebb of 1.5 knots, setting 160°.

2216 Slack, flood begins.

2400 Flood current, 42™ before maximum velocity (speed).

Only one maximum flood occurs on this day, the previous one having occurred 8
minutes before the day began, and the following one predicted for 42 minutes after the
day ends. .

927. Tidal current predictions for subordinate stations.—For each subordinate
station listed in table 2 of the tidal current tables, the following information is given:

Number. The stations are listed in geographical order and given consecutive num-
bers, as in the tide tables (art. 923). At the end of each volume an alphabetical listing
is given, and for each entry the consecutive number is shown, to assist in finding the

entry in table 2.

274 PILOTING

Place. The list of places includes both subordinate and reference stations, the
latter being given in bold type. i i ME k

Position. The approximate latitude and longitude are given to assist in locating
the station. The latitude is north or south and the longitude east or west as indi-
cated by the letters (N, S, E, W) next above the entry. The current given 1s for the
center of the channel unless another location is indicated by the station name.

Time difference. Two time differences are tabulated. One is the number of hours
and minutes to be applied to the tabulated times of slack water at the reference station
to find the times of slack waters at the subordinate station. The other time difference
is applied to the times of maximum current at the reference station to find the times of
the corresponding maximum current at the subordinate station. The intervals, which
are added or subtracted in accordance with their signs, include any difference in time
between the two stations, so that the answer is correct for the standard time of the subor-
dinate station. Limited application and special conditions are indicated by footnotes.

Velocity (speed) ratios. Speed of the current at the subordinate station 1s found
by multiplying the speed at the reference station by the tabulated ratio. Separate
ratios may be given for flood and ebb currents. Special conditions are indicated
by footnotes.

As indicated in appendix U, the currents at Chelsea Docks (No. 1005) can be found
by adding 1°30™ for slack water and 1"40" for maximum current to the times for The
Narrows, and multiplying flood currents by 0.9 and ebb currents by 1.2. Applying
these to the values for Wednesday, February 26, 1958, the sequence is as follows:

0000 Flood current, 1°32™ before maximum velocity (speed).

0132 Maximum flood of 1.4 knots, setting 010°.

0430 Slack, ebb begins.

0805 Maximum ebb of 1.9 knots.

1149 Slack, flood begins.

1357 Maximum flood of 1.0 knots, setting 010°.

1642 Slack, ebb begins.

2020 Maximum ebb of 1.8 knots.

2346 Slack, flood begins.

2400 Flood current, 14” after slack.

928. Finding speed of tidal current at any time.—Table 3 of the tidal current
tables provides means for determining the approximate velocity (speed) at any time.
Instructions for its use are given below the table, which is reproduced in appendix U.

Example 1.—Find the speed of the current at Chelsea Docks at 1500 on February
26, 1958.

Solution.—The given time is between the maximum flood of 1.0 knots at 1357 and
the slack at 1642 (art. 927). The interval between slack and maximum current (1642
— 1357) is 245", The interval between slack and the desired time (1642—1500) is 1542™,
Enter the table (A) with 2*40" at the top, and 1"40" at the left side (the nearest tabulated
values to 2°45" and 1"42", respectively), and find the factor 0.8 in the body of the
table. The approximate speed at 1500 is 0.8X1.0=0.8 knot, and it is flooding.

Answer.—Speed 0.8 kn.

It may be desired to determine the period during which the current is less (or
greater) than a given amount. "Table 4 of the tidal current tables can be used to de-
termine the period during which the speed does not exceed 0.5 knot.
speeds, and for mere accurate results under some conditions, table 3 of the tidal current
tables can be used, solving by reversing the process used in example 1.

Example 2.—During what period on the evening of February 26, 1958, does the
ebb current equal or exceed 1.0 knot at Chelsea Docks?

For greater

PILOTING 275

Solution. —The maximum ebb of 1.8 knots occurs at 2020. This is preceded by a
slack at 1642, and followed by the next slack at 2346. The interval between the earlier
slack and the maximum ebb is 3°38, and the interval between the ebb and following
slack is 3:26". The desired factor is 13-06. Enter table A with 3°40™ (the nearest
tabulated value to 3°38™) at the top, and follow down the column to 0.6 (midway
between 0.5 and 0.7). At the left margin the interval between slack and the desired
time is found to be 1"30" (midway between 1*20% and 140"). Therefore, the current
becomes 1.0 knot at 1642--1^30"— 1812. Next, enter table A with 3-20" (the nearest
tabulated value to 3*26") at the top, and follow down the column to 0.6. Follow this
line to the left margin, where the interval between slack and desired time is found to
be 1520". "Therefore, the current is 1.0 knot or greater until 2346—1°20"=2226. If
the two intervals between maximum current and slack were nearest the same 20%
interval, table A would have to be entered only once.

Answer.—The speed equals or exceeds 1.0 knot between 1812 and 2226.

929. Current diagrams.—A current diagram is a graph showing the speed of the
current along a channel at different stages of the tidal current cycle. The current
tables include such diagrams for Boston Harbor; Vineyard and Nantucket Sounds (one
diagram); East River, New York; New York Harbor; Delaware Bay and River (one
diagram); Chesapeake Bay; South San Francisco Bay; and North San Francisco Bay.
The diagram for New York Harbor is reproduced in appendix U.

On this diagram each vertical line represents a given instant identified in terms
of the number of hours before or after slack at The Narrows. Each horizontal line
represents a distance from Ambrose Channel Entrance, measured along the usually-
traveled route. The names along the left margin are placed at the correct distances
from Ambrose Channel Entrance. "The current is for the center of the channel opposite
these points. "The intersection of any vertical line with any horizontal line represents
a given moment in the current cycle at a given place in the channel. If this inter-
section is in a shaded area, the current is flooding; if in an unshaded area, it is ebbing.
The speed in knots can be found by interpolation (if necessary) between the numbers
given in the body of the diagram. The given values are averages. To find the value
at any given time, multiply the speed found from the diagram by the ratio of mazi-
mum speed of the current involved to the maximum shown on the diagram, both values
being taken for The Narrows. If the diurnal inequality is large, the accuracy can be
improved by altering the width of the shaded area to fit conditions. The diagram
covers 1% current cycles, so that the right-hand third is a duplication of the left-hand
third.

If the current for a single station is desired, table 1 or 2 should be used. The
current diagrams are intended for use in either of two ways: First, to determine a
favorable time for passage through the channel. Second, to find the average current
to be expected during any passage through the channel. For both of these uses a
number of “speed lines” are provided. When the appropriate line is transferred to the
correct part of the diagram, the current to be encountered during passage 1s indicated
along the line.

Example.—During the morning of January 10, 1958, a ship is to leave Pier 83 at
W. 42nd Ste and proceed down the bay at ten knots.

Required —(1) Time to get underway to take maximum advantage of a favorable
current, allowing 15 minutes to reach mid channel.

(2) Average speed over the bottom during passage down the bay.

Solution.—(1) Transfer the line (slope) for ten knots southbound to the diagram,
locating it so that it is centered on the unshaded ebb current section between W. 42nd

276 PILOTING

St. and Ambrose Channel Entrance. This line crosses a horizontal line through W.
42nd St. about one-third of the distance between the vertical lines representing three
and two hours, respectively, after ebb begins at The Narrows. The setting is not
critical. Any time within about half an hour of the correct time will result in about the
same current. Between the points involved, the entire speed line is in the ebb current
enert Table 1 indicates that on the morning of January 10 ebb begins at The Narrows
at 0050. Two hours forty minutes after ebb begins, the time is 0330. Therefore, the
ship should reach mid channel at 0330. It should get underway 15 minutes earlier,
at 0315. k l

(3) To find the average current, determine the current at intervals (as every two
miles), add, and divide by the number of entries.

Distance Current
18 11,2
16 1.4
14 1.9
12 185
10 2.0

8 1.9
6 Īsās
4 1.2
2 1.4
0 152
sum 14.8

The sum of 14.8 is for ten entries. The average is therefore 14.8--10=1.5 knots.

(4) This value of current is correct only if the ebb current is an average one.
From table 1 the maximum ebb involved is 2.2 knots. From the diagram the maximum
value at The Narrows is 2.0 knots. Therefore, the average current found in step (3)
should be increased by the ratio 2.2+2.0=1.1. The average for the run is therefore
1.5X1.1=1.6 knots. Speed over the bottom is 10+1.6=11.6 knots.

Answers.—(1) T 0315, (2) S 11.6 kn.

In the example, an ebb current is carried throughout the run. If the transferred
speed line had been partly in a flood current area, all ebb currents (those increasing
the ship's speed) should be given a positive sign (+), and all flood currents a negative
sign (—). A separate ratio should be determined for each current (flood or ebb), and
applied to the entries for that current. In Chesapeake Bay it is not unusual for an
outbound vessel to encounter three or even four separate currents during passage down
the bay. Under the latter condition, it is good practice to multiply each current taken
from the diagram by the ratio for the current involved.

If the time of starting the passage is fixed, and the current during passage is
desired, the starting time is identified in terms of the reference tidal cycle. The
speed line is then drawn through the intersection of this vertical time line and the
horizontal line through the place. The average current is then determined in the same
manner as when the speed line is located as described above.

Miscellaneous

930. Allowing for turning characteristics of vessel.—When
necessary (as in an area where maneuvering space is limited, when a
is approached, or when steaming in formation with other ships),

precise piloting is
specified anchorage
the turning char-

PILOTING ké

acteristics of the vessel should be consid-
ered. That is, a ship does not complete
a turn instantaneously, but follows a
curve the characteristics of which depend
upon the vessel's length, beam, underwater
contour, draft, etc. From the moment
the rudder is put over until the new
course is reached, the vessel moves a cer-
tain distance in the direction of the origi-
nal course. This distance is called ad-
vance. The distance the vessel moves
perpendicular to the original course line
during the turn is called transfer. These
terms are illustrated in figure 930a. The
amount of advance and transfer for a
given vessel depends primarily upon the
amount of rudder used and the angle
through which the ship is to be turned.
The speed of the vessel has little ef-
fect. Allowance for advance and trans-
fer is illustrated in the following example.

' «se
te- — Transfer -- gina eL

H Inte, 1 ^
End of Turn

t<—_— Advance —— ——&
|
E

-«-Start of Turn

Original Course

FIGURE 930a.— Advance and transfer.

Example (fig. 930b).—A ship proceeding on course 100? is to turn 60? to the left
to come on a range which will guide it up a channel. For a 60? turn and the amount
of rudder used, the advance is 920 yards and the transfer is 350 yards.

Figure 930b.—Allowing for advance and transfer.

278 PILOTING

Required.—The bearing of flagpole “FP.” when the rudder is put over.

Solution.—(1) Extend the original course line, AB.

(2) At a perpendicular distance of 350 yards, the transfer, draw a line A’B’
parallel to the original course line AB. The point of intersection, C, of A’B’ with the
new course line (located by the range) is the place at which the turn is to be completed.

(3) From C draw a perpendicular, CD, to the original course line, intersecting it
at D.

(4) From D measure the advance, 920 yards, back along the original course line.
This locates E, the point at which the turn should be started.

(5) The direction of “FP.” from E, 058°, is the bearing when the turn should be
started.

Answer.—B 058°.

931. Anchoring.—If a vessel is to anchor at a predetermined point, as in an as-
signed berth, an established procedure should be followed to insure accuracy of placing
the anchor. In the case of naval vessels, it is desired that the error not exceed ten yards.
This requires a high order of navigational accuracy. Several procedures have been
devised. The following is representative (fig. 931).

_ 2000

© S'PIPE

CHY.

FIGURE 931.—Anchoring.

PILOTING 279

The position selected for anchoring is located on the chart. The direction of
approach is then determined, considering limitations of land, shoals, other vessels, etc.
Where conditions permit, the approach should be made heading into the current or,
if the wind has a greater effect upon the vessel, into the wind. It is desirable to ap-
proach from such direction that a prominent object, or preferably a range, is available
dead ahead to serve as a steering guide. It is also desirable to have a range or promi-
nent object near the beam at the point of letting go the anchor. If practicable a
straight approach of at least 500 yards should be provided to permit the vessel to
steady on the required course. The track is then drawn in, allowing for advance and
transfer during any turns.

Next, a circle is drawn with the selected position of the anchor as the center, and
with a radius equal to the distance between the hawsepipe and pelorus, alidade, etc.,
used for measuring bearings. The intersection of this circle and the approach track,
point A, is the position of the vessel (bearing-measuring instrument) at the moment
of letting go. A number of arcs of circles are then drawn and labeled as shown in figure
931. The desired position of the anchor is the common center of these arcs. The
selected radii may be chosen at will. Those shown in figure 931 have been found to
be generally suitable. In each case the distance indicated is from the small circle.
Turning bearings may also be indicated.

During the approach to the anchorage, fixes are plotted at frequent intervals, the
measurement and plotting of bearings going on continuously, usually to the nearest
half or quarter degree. The navigator advises the captain of any tendency of the vessel
to drift from the desired track, so that adjustments can be made. The navigator
also keeps the captain informed of the distance to go, to permit adjustment of the speed
so that the vessel will be nearly dead in the water when the anchor is let go.

At the moment of letting go, the position of the vessel should be determined as
accurately as possible, preferably by two simultaneous horizontal sextant angles, or
by simultaneous or nearly simultaneous bearings of a number of prominent landmarks.

A number of variations may suggest themselves. One occasionally mentioned is
as follows: An inverted compass rose (0? at south) is placed around each landmark used.
A thumb tack with an attached thread is inserted at the symbol of two landmarks. One
observer continually notes the bearing of each object. Alternately they call out the
bearings. The navigator takes one thread in each hand and maintains a slight strain.
As each bearing is called out, he adjusts the appropriate thread by means of the reverse
compass rose. The point of intersection of the two threads is the position of the vessel.
By this means the ship can be “walked in" to the anchorage. This method is particu-
larly to be recommended when one landmark is on each bow.

The exact procedure to use depends upon local conditions, number and training
of available personnel, equipment, and personal preference of individuals concerned.
Whatever the procedure, it should be carefully planned, and any needed advance
preparations should be made early enough to avoid haste and the attendant danger of
making a mistake. Teamwork is important. Each person involved should under-
stand precisely what is expected of him.

932. Piloting and electronics.—Many of the familiar electronic aids to navigation
are used primarily in piloting. The radio direction finder provides bearings through
fog and at greater distance from the aids. Distance finding stations provide distances
which might not otherwise be available. The sonic depth finder provides frequent or
continuous soundings. Radar provides bearings, distances, and information on the
location and identity of various targets. Some of the longer range systems such as
loran, consol, and Decca extend piloting techniques far to sea, where nearness of shoals
and similar dangers is not a problem. Electronic aids, whether applicable primarily
to piloting or to other forms of navigation, are discussed in part three (chs. X-XIII).

280 PILOTING

933. Practical piloting.—In pilot waters, navigation is primarily an art. It is
essential that the principles explained in this chapter be mastered and applied in-
telligently. From every experience the wise navigator acquires additional knowledge
and improves his judgment. The mechanical following of a set procedure should not
be expected to produce satisfactory results always.

While piloting, the successful navigator is somewhat of an opportunist, fitting his
technique to the situation at hand. If a vessel is steaming in a large area having
relatively weak currents and moderate traffic, like Chesapeake Bay, fixes may be
obtained at relatively long intervals, with a dead reckoning plot between. In a narrow
channel with swift currents and heavy traffic, like the East River between Manhattan
and Long Island, New York City, an almost continuous fix is needed. In such an
area the navigator may draw the desired track on the chart and obtain fixes every
few minutes, or even seconds, directing the vessel back on the track as it begins to drift
to one side.

If the navigator is to traverse unfamiliar waters, he studies the chart, sailing direc-
tions or coast pilot, tide and tidal current tables, and light lists to familiarize himself with
local conditions. The experienced navigator learns to interpret the signs around him.
The ripple of water around buoys and other obstructions, the direction and angle of
tilt of buoys, the direction at which vessels ride at anchor, provide meaningful informa-
tion regarding currents. The wise navigator learns to interpret such signs when the
position of his vessel is not in doubt. When visibility is poor, or available information
is inconsistent, the ability developed at favorable times can be of great value.

With experience, a navigator learns when a danger angle or danger bearing is useful,
and what ranges are reliable and how they should be used. However familiar one is
with an area, he should not permit himself to become careless in the matter of timing
lights for identification, plotting his progress on a chart, or keeping a good recent position.
Fog sometimes creeps in unnoticed, obscuring landmarks before one realizes its presence.
A series of frequent fixes obtained while various aids are visible provides valuable
information on position and current.

Practical piloting requires a thorough familiarity with principles involved and
local conditions, constant alertness, and judgment. A study of avoidable groundings
reveals that in most cases the problem is not lack of knowledge, but failure to use or
interpret available information. Among the more common errors are:

1. Failure to obtain or evaluate soundings.

2. Failure to identify aids to navigation.

3. Failure to use all available navigational aids.
4. Failure to correct charts.

E Failure to adjust a magnetic compass or maintain an accurate table of cor-
rections.

6. Failure to apply deviation, or error in its application.
7. Failure to apply variation, or to allow for change in variation.

8. Failure to check gyro and magnetic compass readings at frequent and regular
intervals.

9. Failure to keep a dead reckoning plot.
10. Failure to plot information received.
11. Failure to properly evaluate information received.
12. Poor judgment.
13. Failure to do own navigating (following another vessel).

14. Failure to obtain and use information available on charts and in various
publications.

PILOTING 281

15. Poor ship organization.
16. Failure to “keep ahead of the vessel.”
Further discussion on practical piloting is given in chapter XXIII.

Problems

904. The navigator of a vessel on gyro course 214? obtains a relative bearing on &
lighthouse of 86? left. The gyro error is 1? W, deviation of the standard compass is
3? W, and variation is 139 E.

Required.—The (1) gyro, (2) true, (3) standard-compass, and (4) magnetic
bearings of the lighthouse.

Answers.—(1) Bpgc:128?, (2) TB 127°, (3) CB 117°, (4) MB 114°.

Problems 906a-909g, 911a-911c, and 916b are based upon the following fictitious
aids to navigation, which can be plotted on a large-scale plotting sheet (art. 324) or a clear
part of a coast chart for the appropriate latitude. Thelatitude range of these problems
is from 40°20’N to 40°40’N. Approach charts to New York include this range.
The longitude range is from 164°20’W to 164°40’W. In these problems the gyro
compass is the reference for all courses and bearings, and it is considered to be without
error.

Latitude Longitude
Jones Point Light 40206 N 164°20'5 W
Parker Point Light 4023:7 N 164?21:2 W
Point Carlson Light 40°22'0 N 164°28'3 W
North Baker Range Light 40?33:9 N 164?38:2 W
South Baker Range Light 40?31:5 N 164%34!7 W
Hanford Mid-channel Buoy 40229 N 164%34/1 W
Water tower 40362 N 164279 W
West Bank Lightship 40395 N 164?20:3 W
Cupola 40°25'4 N 164°2173 W

906a. A navigator of a vessel on course 075? observes Jones Point Light to bear
56?right at the same time an assistant observes Parker Point Light to bear 46° left.

Required.—The fix at the time of the bearings.

Answer.—Fix: L 40%21/9N, X 164?22:5 W.

906b. A vessel under way in fog obtains simultaneous radar ranges (distances) on
Point Carlson Light bearing southerly (3.0 miles) and Parker Point Light (5.5 miles).

Required.—The fix at the time of the distance measurements.

Answer.—Fix: L 40%25'0 N, A 164?28:2 W.

906c. A vessel under way with the Baker Range dead ahead observes Point Carlson
Light broad on the port beam.

Required.—The fix at the time Point Carlson Light is abeam..

Answer.—Fix: L 40?24/9 N, ^ 164?25:0 W.

906d. The navigator of a vessel on course 110? measures the vertical sextant
angle between the top of Point Carlson Light and the horizon at the same time the light
bears dead ahead. The top of the light is 230 feet above the water and the sextant
angle is 0218/3. The height of eye of the observer is 30 feet. There is no IC:

Required.—The fix at the time the angle is measured.

Answer.—Fix: L 40%24/4N, 4 164?37:0 W.

906e. A vessel is under way with the Baker Range dead ahead. The South Baker
Range Light is 5.0 miles off by radar.

Required.—The fix at the time of measurement.

282 PILOTING

Answer.—Fix: L 40%28/2N, ^ 164?29:8 W.

906f. A southbound vessel passes Hanford Mid-channel Buoy close aboard at 0327.

Required.—The fix at this time.

Answer.—Fix: L 40?22:9 N, A 164%34!1 W.

907a. Using horizontal sextant angles, a navigator measures the angle between
South Baker Range Light and Point Carlson Light to be 54°14’. At the same time
an assistant measures the angle between Parker Point Light and Point Carlson Light
to be 25°04’.

Required.—The fix at the time of observation.

Answer.—Indeterminable because the three lights and the vessel are all located
on the circumference of the same circle.

907b. Using horizontal sextant angles, a navigator measures the angle between
South Baker Range Light and Point Carlson Light to be 85°45’. At the same time an
assistant measures the angle between Parker Point Light and Point Carlson Light to
be 35°10’.

Required.—The fix at the time of observation.

Answer.—Fix: L 40%31/6N, X 164?27:6 W.

908. About 0229 the navigator of a vessel observes the following bearings:

Jones Point Light 150?
Point Carlson Light 263?
Parker Point Light 020?
Point Carlson Light 266?
Jones Point Light 154?

The time intervals between bearings are approximately equal. The bearing on
Parker Point Light is obtained at 0229.

Required.—(1) The bearings to plot for an 0229 fix.

(2) The 0229 fix.

Answers.—(1) Jones Point Light, B 152°; Point Carlson Light, B 264%”; Parker
Point Light, B 020%. (2) 0229 fix: L 40%22/5N, x 164°21/8 W.

909a. A vessel is underway on course 071?, speed 15.0 knots. At 1150 the water
tower bears 051°. At 1200 the tower bears 009°.

Required.—The 1200 running fix.

Answer.—1200 R fix: L 40%34/9N, ^ 164°28/2 W.

909b. At 1205 the vessel of problem 909a changes course to 047?, and at 1210 the
water tower bears 270°.

Required. —The 1210 running fix, by advancing the 1200 bearing line and crossing
it with the 1210 bearing line.

Answer.—1210 R fix: L 40%36/2N, A 164°25/4 W.

909c. Under way in fog, a vessel on course 188°, speed 5.0 knots, passes west of

the West Bank Lightship and at 0613 it is 1.2 miles off by distance finding signals. At
0622 the distance is 1.8 miles.

Required.—The 0622 running fix.
Answer.—0622 R fix: L 40?38'1N, ^ 164°21/8 W.

909d. The navigator of a vessel on course 052°, speed 13.5 knots, observes Point
Carlson Light bearing 079° at 2117.

Required.—The distance off when abeam if Point Carlson Light is abeam at (1)
2126, (2) 2129, (3) 2132.

Answers.—(1) D 1.1 mi., (2) D 1.4 mi., (3) D 1.7 mi.

909e. The navigator of a vessel on course 000° observes South Baker Range Light
bearing 324° at 0551 and 270° at 0600.

PILOTING 283

Required.—The distance off when abeam if the vessel is making good (1) 15.0 kn.,
(2) 16.0 kn., (3) 17.0 kn.

Answers.—(1) D 1.6 mi., (2) D 1.8 mi., (3) D 1.9 mi.

909f. The navigator of a vessel obtains bearings on West Bank Lightship, as follows:
033° at 1423, 021° at 1435, 010° at 1443.

Required.—The course being made good over the ground.

Answer.—COG 073°.

909g. A vessel on course 214°, speed 14.0 knots, fixes its position at latitude
40^33:0 N, longitude 164?21:5 W at 1200. At 1254 a second fix places the vessel at
latitude 40%22'0 N, longitude 164?32/5 W.

Regutred.—The set and drift of the current during the run.

Answers.—Set 249°, drift 1.6 kn.

910a. The navigator of a vessel steaming at 17 knots observes the following pairs
of relative bearings on different landmarks and seamarks as indicated :

Relative Relative

Time Object bearing Time Object bearing

GU Gab A A 3182 (Se 1913924 Q 330
1258 A 2929 1350 C 303°

(2) 1306 B 040° (4) 1401 D 281°
1321 B 059° 1452 D 2514

Reguired.—In each case, the distance off at the time of the second bearing, and the
distance when abeam, using table 7.

Answers.—
Object Dist. at 2nd bearing Dist. abeam
(1) A 9.2 8.5
(2) B 8.3 T. 1
(3) C Dir 4.8
(4) D 34.8 34.0

910b. A vessel is steaming on course 193° at 20 knots. The following true bearings
are observed on the objects indicated:

True True

Time Object Bearing Time Object Bearing

(1) 0800 A 229° (4) 0912 D 21555
0836 A 265° 0927 D 238°
(2) 0840 B 238° (5) 0929 E 2002
0855 B 283° 0954 E DOGS
(3) 0855 C 25675 (6) 0959 F 2038
0906 C 283? 1031 F DE

Required.—Without plotting, and without the use of table 7, determine the dis-
tances off A, B, D, and E at the time of the second bearing, and the distances off B, C,
D, E, and F when abeam.

Answers.— |
Object Dist. at 2nd bearing Dist. abeam
(1) A 12.0 =
(2) B 5.0 520
(3) C = TB
(4) D 5.0 3.5
(5) E 8.3 7.3
(6) F = 10; 7

284 PILOTING

911a. Two shoals to the south of South Baker Range Light are marked by buoys.
The positions of the buoys are reported to be unreliable because of the recent passage of
a storm. At the narrowest point in the channel the position of the danger Mab egi on
each side is lat. 40925/5 N, long. 164°37/2 W; and lat. 40°25:7N, long. 164?35:6 W.

Reguired.—The maximum and minimum danger bearings on South Baker Range
Light to clear the shoals.

Answers.—B 018° and B 007°. e

911b. A vessel is to pass along the coast north of Parker Point and inside a sub-
merged rock a short distance offshore. In this area the five-fathom curve (the danger
sounding) is farthest offshore at lat. 40%24:5N, long. 164°22'3W. The closest safe
approach to the rock is at lat. 40%24:4 N, long. 164%22.9 W.

Required.—The maximum and minimum horizontal sextant angles between
Parker Point Light and the prominent cupola to the north of it which will permit safe
passage between the five-fathom curve and the rock.

Answers.—Danger angles: 92? and 68?.

911c. A vessel steaming at 13.0 knots has West Bank Lightship abeam at 0311,
and immediately begins a course change to keep the lightship broad on the beam. At
0316 the change in heading is noted.

Required.—(1) Distance off if the heading change is 19?.

(2) Distance off if the heading change is 16?.

Answers.—(1) D 3.2 mi., (2) D 3.9 mi.

916a. A lookout at a height of eye of 55 feet observes a flashing light on the horizon.
The light is timed and identified as a navigational light 117 feet above sea level.

Required.—The distance of the vessel from the light when it is first observed.

Answer.—D 20.9 mi.

916b. The light of Hanford Mid-channel Buoy is located 11 feet above sea level
and has a charted range of 6 miles. At 0207 a vessel on course 221°, speed 15 knots,
passes West Bank Lightship abeam, 0.9 mile to starboard. The height of eye on the
bridge is 48 feet.

Required.—(1) The distance at which the navigator, on the bridge, can expect
to see the buoy light in clear weather with good visibility.

(2) The time and bearing at which the light should be sighted.

Answers.—(1) D 6.0 mi., (2) T 0302, B 202°.

916c. A navigational light 120 feet above sea level has a charted range of
17 miles.

Required.—The distance at which an observer at a height of eye of 60 feet can expect
to see the light.

Answer.—D 17 to 21.4 mi., depending upon the luminous range of the light.

920. The mean high water lunitidal interval at a certain port is 2217”.

Required.—The approximate times of each high and low water on a day when
the moon transits the local meridian at 1146.

Answers.—HW at 0139 and 1403, LW at 0751 and 2015.

922. List chronologically the times and heights of all tides at New York (The
Battery) on February 11, 1958.

Answer. —
Time Tide Height
0157 HW 4.5 ft.
0831 LW (—) 0.1 ft.
1423 HW 3.9 ft.

2049 LW (—) 0.1 ft.

PILOTING 285

923. List chronologically the times and heights of all tides at Castle Poi
: t
Hoboken, N. J. (No. 1569) on March 18, 1958. t odd

Answer.—
Time Tide Height
0113 LW (—) 0.3 ft.
0723 HW 4.4 ft.
1336 LW (>) 04. 11.
1945 HW 4.3 ft.

924a. Find the height of tide at Union Stock Yards, New York (No. 1573) at
0600 on February 6, 1958.

Answer.—Ht. of tide at 0600, 0.3 ft.

924b. The captain of a vessel drawing 24 feet wishes to pass over a temporary
obstruction near Bayonne, N. J. (No. 1555) having a charted depth of 22 feet, passage
to be made during the evening of March 5, 1958.

Required.—The earliest and latest times that the passage can be made, allowing
a safety margin of two feet.

Answers.—Earliest time 1806, latest time 2148.

926. Determine the sequence of currents at The Narrows on January 8, 1958.

Answer.—

0000 Ebb current, 56? after slack.
0222 Maximum ebb of 2.3 knots.
0543 Slack, flood begins.

0821 Maximum flood of 2.2 knots.
1135 Slack, ebb begins.

1454 Maximum ebb of 2.5 knots.
1828 Slack, flood begins.

2051 Maximum flood of 1.9 knots.
2357 Slack, ebb begins.

2400 Ebb current, 3? after slack.

927. Determine the sequence of currents at Highlands Bridge, Shrewsbury River
(No. 1083) on January 5, 1958.
Answer.—

0000 Ebb current, 22™ before maximum velocity (speed).
0022 Maximum ebb of 2.7 knots.

0351 Slack, flood begins.

0628 Maximum flood of 3.3 knots, setting 170°.

0940 Slack, ebb begins.

1302 Maximum ebb of 3.0 knots.

1644 Slack, flood begins.

1855 Maximum flood of 2.6 knots, setting 170°.

2150 Slack, ebb begins.

2400 Ebb current, 1°11™ before maximum velocity (speed).

928a. Find the speed of the current at Bear Mountain Bridge (No. 1029) at 0900

on February 19, 1958.
Answer.—Speed 0.5 kn.
928b. At about what time during the morning of February 3, 1958, does the flood

current northwest of The Battery (No. 1001) reach a speed of 1.0 knot?
Answer.—T 0525.

286 PILOTING

929. A vessel arrives at Ambrose Channel Entrance two hours after flood begins
at The Narrows on the morning of February 16, 1958.

Required.—(1) The speed through the water required to take fullest advantage of
the flood tide in steaming to Chelsea Docks.

(2) The average current to be expected.

(3) Estimated time of arrival off Chelsea Docks.

Answers.—(1) S 9 kn., (2) S 1.4 kn., (3) ETA 0608.

930. A vessel on course 337° begins a 90° turn at half right rudder when a buoy
is close aboard. When the heading is 067°, the buoy bears 192°, distant 1225 yards
by radar.

Required.—Advance and transfer.

Answers.—Advance ,1,000 yards, transfer 712 yards.

931. In the solution of this problem, a plotting sheet covering the area between
latitudes 40?29/35" N and 40°30/25” N, and longitudes 164?19'35" W and 164?20'50" W
will be needed. The plotting sheet or chart used for other problems of this chapter
will be suitable if the scale is adjusted so that one graduation equals 50 feet (two
graduations equal one second of arc).

A vessel in convoy receives orders to anchor in lat. 40°29’50” N, long. 164°20’25” W.
After studying the chart, the navigator and captain select two landmarks to use as
reference points in making the approach. Landmark A is located at lat. 40°29’40” N,
long. 164?20'50" W; landmark B at lat. 40?30'20" N, long. 164°20’30”W. It is
decided that the approach will be made with landmark A dead ahead. The gyro
repeater to be used in taking bearings is located 200 feet abaft the hawsepipes.

Reguired.—(1) The course during approach. The bearings of landmark B when
there are (2) 1,000 yards, (3) 600 yards, (4) 400 yards, (5) 200 yards, (6) 100 yards,
(7) 0 yards (the let-go point) to go, assuming the vessel keeps landmark 4 dead ahead.

Answers.—(1) C 24275, (2) B 29575, (3) B 314?0, (4) B 325?5, (5) B 33725,
(6) B 343?5, (7) B 34995.

PART THREE

ELECTRONIC NAVIGATION

PART THREE

ELECTRONIC NAVIGATION

CHAPTER X. Radio Waves

CHAPTER XI. Electronics and Navigation
CHAPTER XII. Direction and Distance by Electronics

CHAPTER XIII. Hyperbolic Systems

289
304
313
333

CHAPTER X

RADIO WAVES

1001. Source of radio waves.—All matter is made up of tiny particles called atoms.
Each atom has a central nucleus composed principally of subatomic particles called
protons and neutrons. One or more electrons revolve around the nucleus in orbits
resembling those of planets around the sun (art. 1407). The number and arrangement
of the particles constituting an atom of each element of matter determine the properties
of that element. Electrons, each having a mass of only about 1/1,840 that of a proton
or neutron, are kept in their orbits principally by means of an attractive electrical force,
each electron carrying one negative “charge” and each proton one positive “charge.”
Like charges repel and unlike charges attract. This electrical attraction is additional
to the gravitational attraction existing between all particles in the universe. The
neutron is electrically neutral.

Under suitable conditions, some electrons become detached from their atoms.
An excess or deficiency of electrons in a nonconductor is called static electricity. A
substance which provides a path for electron movement with relatively little resistance
is called a conductor. A flow of electrons along such a conductor constitutes an electric
current, although the current direction is conventionally considered to be opposite
to the direction of flow of the electrons. A direct current flows continuously in the
same direction. If the strength of the current varies rhythmically but does not change
direction, the current is said to be pulsating. If the direction of flow periodically re-
verses, an alternating current results.

In addition to its electrical and gravitational forces, a moving electron is accom-
panied by a magnetic force. As long as the flow is steady, the magnetic force is con-
stant. If a conductor is in the region of influence or field of magnetism, there is no
noticeable effect unless the strength of the field is changing, or relative motion exists
between the conductor and the field, when an induced current flows in the conductor.
The extent to which a substance has electrons free to move under suitable influence
determines its value as a conductor. One which offers great resistance to such flow is
called an insulator.

In a suitable electrical system, an electric. charge creates a magnetic field which
builds up to a maximum. If the electric current is then discontinued, the magnetic
field collapses. This change in the strength of the magnetic field induces an electric
current in the conductor, but in the opposite direction to the original current. This
current creates a new magnetic field, and the cycle repeats. Thus, an alternating
current is produced, the strength increasing to a maximum in one direction, decreasing
to zero, increasing to a maximum in the opposite direction, and again decreasing to zero
to start a new cycle. This cycle is repeated many times each second, the number
depending upon the characteristics of the system. Such a system is called an os-
cillating circuit.

A relatively small amount of energy is dissipated as heat in overcoming the resist-
ance of the circuit. The remainder continues to oscillate between electric and magnetic
fields. The build-up and collapse of each field occurs at about the speed of light, which
is approximately 186,000 statute miles (300,000,000 meters) per second. If a relatively
long period of time is available for the cycle to occur, the energy is fully transferred
before the next step occurs. However, if the cycle is speeded until the time needed

289

290 RADIO WAVES

for each field to build up or collapse is more than about one-half cycle, some of the
energy becomes detached and is radiated into space, through which it travels at about
the speed of light. This electromagnetic radiation, having both: electrical and magnetic
properties, is known as radio waves, if of a frequency suitable for radio communication.
1002. Radio wave terminology.—The build-up and collapse of the electric
and magnetic fields are proportional to the sine of the portion of the cycle completed,
as shown in figure 1002. This representation has led to the use of the term “wave”
when referring to electromagnetic propagation. The highest point on the curve (in
the direction considered positive) is the crest, and the lowest point the trough. Either
point may be called the peak, considered positive or negative if a distinction is desired.
The displacement of a peak from zero is called the amplitude. The forward side of
any wave is called the wave front. For a nondirectional antenna each wave proceeds
outward as an expanding sphere (or hemisphere).
One cycle is a complete sequence of values, as from crest to crest. The distance
traveled by the energy during one cycle is the wave length, usually expressed in metric
units (meters, centimeters,
1 CYCLE etc.). The number of cycles
ilā WAVE LENGTH | | repeated during unit time (usu-
ally one second) is the fre-
AMPLITUDE quency. This is given in cycles
per second (cps), kilocycles per
second (kc), megacycles per
second (mc), or occasionally
kilomegacycles per second
(kmc). A kilocycle is 1,000
cycles, a megacycle is 1,000,000

Crest

FIELD STRENGTH
ao Æ

Trough

ES aa ul cycles, and a kilomegacycle is
DISTANCE 1,000,000,000 cycles. Wave
FrauRE 1002.— Radio wave terminology. length and frequency are in-

versely proportional. The
approximate value of either may be found by dividing 300,000,000 by the other
quantity, if wave length is expressed in meters and frequency in cycles per second.
Thus, if the frequency is 1,500 kilocycles per second (1,500,000 eps), the wave

length is on 39200 meters. If the wave length is ten centimeters (0.1 meter),
the frequency is about 200, 0:000. 3.900,000,000 cycles per second or three kilomega-

cycles (usually expressed as 3,000 megacycles). A more precise value for the speed of
propagation in air is 299,708,000 meters per second. This is equivalent to 186,230
statute miles, or 161,829 nautical miles, per second. "The exact value varies slightly
with density of the medium through which the wave travels, and frequency. The
speed in à vacuum is a little more than that in air.

The phase of a wave is the amount by which the cycle has progressed from a speci-
fied origin. For most purposes it is stated in circular measure, a complete cycle being
considered 360?. Generally, the origin is not important, principal interest being the
phase relative to that of some other wave. Thus, two waves having crests one-fourth
cycle apart are said to be 90° “out of phase." If the crest of one wave occurs at the
trough of another, the two are 180? out of phase.

1003. Electromagnetic spectrum.— The entire range of electromagnetic radiation
frequencies is called the electromagnetic spectrum. "The range of frequencies suitable
for radio transmission, called the radio spectrum, extends from ten kilocycles per second

RADIO WAVES 291

.to 300,000 megacycles per second, approximately. For convenience, it is divided into
a number of bands, as shown in table 1003. Below the radio spectrum, but overlap-
ping it, is the audio frequency band, extending from 20 to 20,000 cycles per second,
approximately. This is the range of frequencies that can be heard by the human
ear. Above the radio spectrum are heat and infrared, the visible spectrum (light in
its various colors), ultraviolet, X-rays, gamma rays, and cosmic rays. These are in-
cluded in table 1003. Waves shorter than one meter are sometimes called microwaves.

Band RRS Range of frequency Range of wave length

Audio frequency AF 20 to 20,000 cps 15,000,000 to 15,000 m
Radio frequency RF 10 ke to 300,000 me 30,000 m to 0.1 cm

Very low frequency VLF 10 to 30 ke 30,000 to 10,000 m

Low frequency LF 30 to 300 ke 10,000 to 1,000 m

Medium frequency MF 300 to 3,000 ke 1,000 to 100 m

High frequency HF 3 to 30 me 100 to 10 m

Very high frequency VHF 30 to 300 me 10 to 1 m

Ultra high frequency UHF 300 to 3,000 me 100 to 10 cm

Super high frequency SHF 3,000 to 30,000 me 10 to 1 em

Extremely high frequency| EHF 30,000 to 300,000 me 1 to 0.1 cm
Heat and infrared * 106 to 3.95 105 mc 0.03 to 7.6 X 1075 em
Visible spectrum * 3.9X 108 to 7.9 X 10% mc 7.6X 1075 to 3.8 10-5 cm
Ultraviolet * 7.9 X108 to 2.3 X 101% me | 3.8X 1075 to 1.3X 107% cm
X-rays * 2.0X10? to 3.0 1013 me | 1.5X 10-5 to 1.0 X 10% em
Gamma rays * 2.3X 1012to 3.0X 104 me | 1.3X107 to 1.0X 10-71 cm
Cosmic rays * >4.8X 10% me KOA DA qn

* Values approximate.
Table 1003.—Electromagnetic spectrum.

1004. Polarization.—As indicated in article 1001, radio waves have both electrical
and magnetic properties. The two fields are conceived as having direction associated
with the orientation of the vibrations. The direction of the electric component of the
field is called the polarization of the electromagnetic field. Thus, if the electric com-
ponent is vertical, the wave is said to be “vertically polarized," and if horizontal,
‘horizontally polarized.” A wave traveling through space may be polarized in any
direction. One traveling along the surface of the earth is always vertically polarized
because the earth, a conductor, short-circuits any horizontal component. The magnetic
field and the electrical field are always mutually perpendicular.

1005. Reflection.—When radio waves strike a surface, they are reflected in the
same manner as light waves, if conditions are favorable. Radio waves of all frequencies
are reflected by the surface of the earth. The strength of the reflected wave depends
upon grazing angle (the angle between the incident ray and the horizontal), type of po-
larization, frequency, reflecting properties of the surface, and divergence of the reflected
ray. Lower frequency results in greater penetration. At very low frequencies usable
radio signals can be received some distance below the surface of the sea.

A change of phase takes place when a wave is reflected from the surface of the
earth. The amount of the change varies with the conductivity of the earth and the
polarization of the wave, reaching a maximum of 180? for a horizontally polarized
wave reflected from sea water (considered to have infinite conductivity). When
direct waves (those traveling from transmitter to receiver in a relatively straight line,
without reflection) and reflected waves arrive at a receiver, the total signal is the vector
sum of the two. If the signals are in phase, they reinforce each other, producing a
stronger signal. If there is a phase difference, the signals tend to cancel each other,
the cancellation being complete if the phase difference is 180? and the two signals
have the same amplitude. This interaction of waves is called wave interference. A

292 RADIO WAVES

phase difference may occur because of the change of phase of a reflected wave, or
because of the longer path followed by it. The second effect decreases with greater
distance between transmitter and receiver, for under these conditions the difference
in path lengths is smaller. At lower frequencies there is no practical solution to
interference caused in this way. For VHF and higher frequencies the condition can
be improved by elevating the antenna, if the wave is vertically polarized. Also,
interference at higher frequencies can be more nearly eliminated because of the
ereater ease of beaming the signal to avoid reflection.

Reflections may also occur from mountains, trees, and other obstacles. Such
reflection is negligible for lower frequencies, but becomes more prevalent as frequency
increases. In radio communication it can be reduced by using directional antennas,
but this solution is not always available for navigational systems.

Various reflecting surfaces occur in the atmosphere. At high frequencies, reflec-
tions take place from rain. At still higher frequencies, reflections are possible from
clouds, particularly rain clouds. Reflections may even occur at a sharply defined
boundary surface between air masses, as when warm, moist air flows over cold, dry
air. When such a surface is roughly parallel to the surface of the earth, radio waves
may travel for greater distances than normal. A somewhat similar condition is
described in article 1006. The principal source of reflection in the atmosphere is the
ionosphere (arts. 1007, 1008).

1006. Refraction of radio waves is similar to that of light waves (art. 1613).
Thus, as a signal passes from air of one density to that of a different density, the direc-
tion of travel is altered. The principal cause of refraction in the atmosphere is the
difference in temperature and pressure occurring at various heights and in different
air masses.

Refraction occurs at all frequencies, but at those below 30 mc the effect is small as
compared with ionospheric effects (art. 1008), diffraction (art. 1009), and absorption
(art. 1010). At higher frequencies, refraction in the lower layer of the atmosphere
extends the radio horizon to a distance about 15 percent greater than the visible
horizon. The effect is the same as if the radius of the earth were about one-third
greater than it is, and there were no refraction.

Sometimes the lower portion of the atmosphere becomes stratified with horizontal
layers of air having certain characteristics, resulting in nonstandard temperature and
moisture changes with height. If there is a marked temperature inversion (art. 3815)
or a sharp decrease in water vapor content with increased height, a horizontal radio
duct may be formed. High frequency radio waves traveling horizontally within the
duct are refracted to such an extent that they remain within the duct, following the
curvature of the earth for phenomenal distances. This is called super-refraction.
Maximum results are obtained when both transmitting and receiving antennas are
within the duct. There is a lower limit to the frequency affected by ducts. It varies
from about 200 mc to more than 1,000 me.

At night, surface ducts may occur over land due to cooling of the surface. At sea,
surface ducts about 50 feet thick may occur at any time in the trade wind belt. Surface
ducts 100 feet or more in thickness may extend from land out to sea when warm air from
the land flows over the cooler ocean surface. Elevated ducts from a few feet to more
than 1,000 feet in thickness may occur at elevations of 1,000 to 5,000 feet, due to the
settling of a large air mass. This is a frequent occurrence in Southern California and
certain areas of the Pacific Ocean.

Refraction effects associated with the ionosphere are discussed in article 1008.

A bending in the horizontal plane occurs when a ground wave (art. 1008) crosses a
coast at an oblique angle. This is due to a marked difference in the conducting and

RADIO WAVES 293

reflecting properties of the land and water over which the wave travels. The
effect is known as coastal refraction or land effect. _

1007. The ionosphere.—Since an atom normally has an equal number of negatively
charged electrons and positively charged protons, it is electrically neutral. An ion
is an atom or group of atoms which has become electrically charged, either positively
or negatively, by the loss or gain of one or more electrons.

Loss of electrons may occur in a variety of ways. In the atmosphere, ions are
usually formed by collision of atoms with rapidly moving particles, or by the action of
cosmic rays or ultraviolet light. In the lower portion of the atmosphere, recombination
soon occurs, leaving a small percentage of ions. In thin atmosphere far above the surface
of the earth, however, atoms are widely separated and a large number of ions may be
present. The region of numerous positive and negative ions and unattached electrons
is called the ionosphere. The extent of ionization depends upon the kinds of atoms
present in the atmosphere, the density of the atmosphere, and the position relative to
the sun (time of day and season). After sunset, ions and electrons recombine faster
than they are separated, decreasing the ionization of the atmosphere.

An electron can be separated from its atom only by the application of greater
energy than that holding the electron. Since the energy of the electron depends
primarily upon the kind of an atom of which it is a part, and its position relative to the
nucleus of that atom, different kinds of radiation may cause ionization of different
substances.

In the outermost regions of the atmosphere the density is so low that oxygen
exists largely as separate atoms, rather than combining as molecules as it does nearer
the surface of the earth. At great heights the energy level is low and ionization from
solar radiation isintense. Thisis known asthe F layer. Above this level the ionization
decreases because of the lack of atoms to be ionized. Below this level it decreases
because the ionizing agent of appropriate energy has already been absorbed. During
daylight, two levels of maximum F ionization can be detected, the F, layer at about
125 statute miles above the surface of the earth, and the F, layer at about 90 statute
miles. At night, these combine to form a single F layer.

At a height of about 60 statute miles the solar radiation not absorbed by the F
layer encounters, for the first time, large numbers of oxygen molecules. A new maximum
ionization occurs, known as the E layer. The height of this layer is quite constant, in
contrast with the fluctuating F layer. At night the E layer becomes weaker, sometimes
completely disappearing.

Below the E layer a weak D layer forms at a height of about 45 statute miles, where
the incoming radiation encounters ozone (Os) for the first time. The D layer is the
principal source of absorption of HF waves, and of reflection of LF and VLF waves
during daylight.

1008. The ionosphere and radio waves. —When a radio wave encounters a particle
having an electric charge, it causes that particle to vibrate. The vibrating particle
absorbs electromagnetic energy from the radio wave and reradiates it. The net effect
is a change of polarization and an alteration of the path of the wave. That portion of
the wave in a more highly ionized region travels faster, causing the wave front to tilt
and the wave to be directed toward a region of less intense ionization.

Refer to figure 1008a, in which a single layer of the ionosphere is considered. Ray
1 enters the ionosphere at such an angle that its path is altered, but it passes on through
and proceeds outward into space. As the angle with the horizontal decreases, a critical
value is reached where the ray (2) is bent or reflected back toward the earth. As the
angle is still further decreased, as at 3, the return to earth occurs at a greater distance

from the transmitter.

994 RADIO WAVES

A wave reaching a receiver by way of the ionosphere is called a sky wave. This
expression is also appropriately applied to a wave reflected from an air mass boundary.
In common usage, however, it is generally associated with the ionosphere. The wave
which travels along the surface of the earth is called a ground wave. At angles greater
than the critical angle, no sky-wave signal is received. Therefore, there is a minimum
distance from the transmitter at which sky waves can be received. This is called the
skip distance, shown in figure 1008a. If the ground wave extends out for less distance
than the skip distance, a skip zone occurs, in which no signal is received.

The critical radiation angle depends upon the intensity of ionization, and the fre-
quency of the radio wave. As the frequency increases, the angle becomes smaller. At
frequencies greater than about 30 mc virtually all of the energy penetrates through or is
absorbed by the ionosphere. "Therefore, at any given receiver there is à maximum
usable frequency if sky waves are to be utilized. The strongest signals are received
at or slightly below this frequency. There is also a lower practical frequency beyond
which signals are too weak to be of value. Within this band the optimum frequency

Distance

FiGURE 1008a.—The effect of the ionosphere on radio waves.

can be selected to give best results. It cannot be too near the maximum usable frequency
because this frequency fluctuates with changes of intensity within the ionosphere.
During magnetic storms the ionospheric density decreases. The maximum usable
frequency decreases, and the lower usable frequency increases. The band of usable
frequencies is thus narrowed. Under extreme conditions it may be completely elim-
inated, isolating the receiver and causing a radio blackout.
Sky-wave signals reaching a given receiver may arrive by any of several paths
de shown in figure 1008b. A signal which undergoes a single reflection is called d
one-hop” signal, one which undergoes two reflections witb a ground reflection between
is called a “two-hop” signal, etc. A “multihop” signal undergoes several reflections
The layer at which the reflection occurs is usually indicated, also, as “one hop E »
“two hop F,” etc. Å pe
Because of the different paths and phase changes occurring at each reflection, the
various signals arriving at a receiver have different phase relationships. Sud the
density of the ionosphere is continually fluctuating, the strength and phase relation-
ships of the various signals may undergo an almost continuous change. Thus, the
various signals may reinforce each other at one moment and cancel ku Other = the
next, resulting in fluctuations of the strength of the total signal received. This is

RADIO WAVES 295

called fading. This phenomenon may also be caused by interaction of components
within a single reflected wave, or changes in its strength due to changes in the reflecting
surface, Tonospheric changes are associated with fluctuations in the radiation received
from the sun, since this is the principal cause of ionization. Signals from the F layer
> aig ad erratic because of the rapidly fluctuating conditions within the layer
itself.

The maximum distance at which a one-hop-E signal can be received is about
1,400 miles. At this distance the signal leaves the transmitter in approximately a
horizontal direction. A one-hop-F signal can be received out to about 2,500 miles.
At low frequencies ground waves extend out for great distances.
| A sky wave may undergo a change of polarization during reflection from the
ionosphere, accompanied by an alteration in the direction of travel of the wave. This is

` GROUND
REFLECTION

FIGURE 1008b.— Various paths by which a sky wave signal might be received.

called polarization error. Near sunrise and sunset, when rapid changes are occurring
in the ionosphere, reception may become erratic and polarization error a maximum.
This is called night effect.

1009. Diffraction.—When a radio wave encounters an obstacle, its energy is re-
flected or absorbed, causing a shadow beyond the obstacle. However, some energy
does enter the shadow area because of diffraction. This is explained by Huygens”
principle, which states that every point on the surface of a wave front is a source of
radiation, transmitting energy in all directions ahead of the wave. No noticeable effect
of this principle is observed until the wave front encounters an obstacle, which inter-
cepts a portion of the wave. From the edge of the obstacle, energy is radiated into
the shadow area, and also outside of the area. The latter interacts with energy from
other parts of the wave front, producing alternate bands in which the secondary radi-
ation reinforces or tends to cancel the energy of the primary radiation. Thus, the
practical effect of an obstacle is a greatly reduced signal strength in the shadow area,

206 RADIO WAVES

OBSTACLE

a
=
TRANSMITTER O<
Pr
===
7 $

FIGURE 1009.—Diffraction.

and a disturbed pattern for a short distance outside the shadow area. This is illus-
trated in figure 1009.

The amount of diffraction is inversely proportional to the frequency, being greatest
at very low frequencies.

1010. Absorption and scattering.—The amplitude of a radio wave expanding out-
ward through space varies inversely with distance. "That is, it gets weaker with in-
creased distance. The decrease of strength with distance is called attenuation. Under
certain conditions the attenuation is greater than in free space.

A wave traveling along the surface of the earth loses a certain amount of energy
to the earth. The wave is diffracted downward and absorbed by the earth. Asa
result of this absorption, the remainder of the wave front tilts downward, resulting in
further absorption by the earth. Attenuation is greater over a surface that is a poor
conductor. Relatively little absorption occurs over sea water, which is an excellent
conductor at low frequencies, and low frequency ground waves travel great distances
over waiter.

A sky wave suffers an attenuation loss in its encounter with the ionosphere. The
amount depends upon the height and composition of the ionosphere, as well as the
frequency of the radio wave. Maximum ionospheric absorption occurs at about
1,400 ke.

In general, atmospheric absorption increases with frequency,
at SHF and EHF. At these frequencies, attenuation is further i

due to reflection by oxygen, water vapor, water droplets, and r

being a problem only
ncreased by scattering
ain in the atmosphere.

RADIO WAVES 297

| 1011. Noise.—Unwanted signals in a receiver are called interference. The inten-
tional production of such interference to obstruct communication is called jamming.
Unintentional interference is called noise.

Noise may originate within the receiver. Hum is usually the result of induction
from neighboring circuits carrying alternating current. Microphonic noise is the result
of vibration of elements in an electron tube. Irregular crackling or sizzling sounds
may be caused by poor contacts or faulty components within the receiver. Electron
movement in normal components causes some noise. This source sets the ultimate
limit of sensitivity (art. 1018) that can be achieved in a receiver. It is the same at
any frequency.

Noise originating outside the receiver may be either man-made or natural. Man-
made noises originate in electrical appliances, motor and generator brushes, ignition
systems, and other sources of sparks which transmit electromagnetic signals that are
picked up by the receiving antenna.

Natural noise is caused principally by discharge of static electricity in the atmos-
phere. This is called atmospheric noise, atmospherics, or static. An extreme example
is a thunderstorm. An exposed surface may acquire a considerable charge of static
electricity. This may be caused by friction of water or solid particles blown against
or along such a surface. It may also be caused by splitting of a water droplet which
strikes the surface, one part of the droplet acquiring a positive charge and the other
a negative charge. These charges may be transferred to the surface. The charge
tends to gather at points and ridges of the conducting surface, and when it accumulates
to a sufficient extent to overcome the insulating properties of the atmosphere, it dis-
charges into the atmosphere. Under suitable conditions this becomes visible and is
known as St. Elmo's fire, which is sometimes seen at mastheads, the ends of yardarms, etc.

Atmospheric noise occurs to some extent at all frequencies, but decreases with
higher frequencies. Above about 30 mc it is not generally a problem.

Since most of the noise occurs at low frequencies, it travels great distances and the
accumulation may reach troublesome proportions at these frequencies, particularly
during the summer in mountainous regions.

1012. Antenna characteristics.—Antenna design and orientation have a marked
effect upon radio wave propagation. For a single-wire antenna, strongest signals are
transmitted along the perpendicular to the wire, and virtually no signal in the direction
of the wire. For a vertical antenna, the signal strength is the same in all horizontal
directions. Unless the polarization undergoes à change during transit, the strongest
signal received from a vertical transmitting antenna occurs when the receiving antenna is
also vertical.

For lower frequencies the radiation of a radio signal takes place by interaction
between the antenna and the ground. For a vertical antenna, efficiency increases with
greater length of the antenna. For a horizontal antenna, efficiency increases with
greater distance between antenna and ground. Near-maximum efficiency is attained
when this distance is one-half wave length. This is the reason for elevating low fre-
quency antennas to great heights. However, at the lowest frequencies, the required
height becomes prohibitively great. At 10 ke it would be about eight nautical miles
for a half-wave-length antenna. Therefore, lower frequency antennas are inherently
inefficient. This is partly offset by the greater range of a low frequency signal of the
same transmitted power as one of higher frequency. | | |

At higher frequencies, the ground is not used, both conducting portions being
included in a dipole antenna. Not only can such an antenna be made efficient, but 16
can also be made sharply directive, thus greatly increasing the strength of the signal
transmitted in a desired direction.

298 RADIO WAVES

The power received is inversely proportional to the square of the distance from the
transmitter, assuming there is no attenuation due to absorption or scattering.

1013. Range.—The range at which a usable signal is received depends upon the
power transmitted, the sensitivity of the receiver, frequency, route of travel, noise level,
and perhaps other factors. For the same transmitted power, both the ground-wave and
sky-wave ranges are greatest at the lowest frequencies, but this is somewhat offset by
the lesser efficiency of antennas for these frequencies. At higher frequencies, only direct
waves are useful, and the effective range is greatly reduced. Attenuation, skip distance,
ground reflection, wave interference, condition of the ionosphere, atmospheric noise
level, and antenna design all affect the distance at which useful signals can be received.

1014. Frequency and radio wave propagation.—Frequency is an important con-
sideration in radio wave propagation, as indicated previously. The following summary
indicates the principal effects associated with the various frequency bands, starting
with the lowest and progressing to the highest usable radio frequency.

Very low frequency (VLF, 10 to 30 kc). For a given transmitted power, sky-wave
signals travel tremendous distances, the ionosphere being most effective in reflecting
waves of the lowest frequency. Diffraction is also maximum. However, because of
the long wave length, large antennas are needed, and even these are inefficient, permit-
ting radiation of relatively small amounts of power. Relatively little energy is reflected
by the ground or other obstacles. Magnetic storms have little effect upon transmission
because of the efficiency of the ionosphere in reflecting VLF waves. During such
storms, VLF signals may constitute the only source of radio communication over great
distances. However, interference from atmospheric noise may be troublesome. Sig-
nals may be received below the surface of the sea.

Low frequency (LF, 30 to 300 kc). As frequency is increased to the LF band, the
ionosphere becomes less efficient as a reflector, diffraction decreases, ground losses
increase, and range for a given power output falls off rapidly. However, this is partly
offset by more efficient transmitting antennas, which can be made of a size practical
for use aboard ship. The LF band is useful for radio direction finding (art. 1202) and
ground-wave transmission over medium distances.

Medium frequency (MF, 300 to 3,000 kc). Ground waves provide dependable
service, but the range for a given power is reduced greatly, varying from about 400
miles at the lower portion of the band to about 15 miles at the upper end for a trans-
mitted signal of one kilowatt. These values are influenced, however, by the power of
the transmitter, the directivity and efficiency of the antenna, and the nature of the
terrain over which signals travel. Elevating the antenna to obtain direct waves may
improve the transmission. At the lower frequencies of the band, sky waves are avail-
able both day and night. As the frequency is increased, ionospheric absorption increases
to a maximum at about 1,400 kc. At higher frequencies the absorption decreases,
permitting increased use of sky waves. Since the ionosphere changes with the hour,
season, and sunspot cycle, the reliability of sky-wave signals is variable. By careful
selection of frequency, one can obtain ranges of as much as 8,000 miles with one kilowatt
of transmitted power, using multihop signals. However, the frequency selection is
critical. If it is too high, the signals penetrate the ionosphere and are lost in space.
If it is too low, signals are too weak. In general, sky-wave reception is equally good by
day or night, but lower frequencies are needed at night. The standard broadcast band
for commercial stations (535 to 1,605 ke) and the authorized frequencies for loran (art.
1302) are in the MF band.

High frequency (HE, 3 to 30 me). As with higher medium frequencies, the ground-
wave range of HF signals is limited to a few miles, but the elevation of the antenna may
increase the direct-wave distance of transmission. Also, the height of the antenna

RADIO WAVES 299

nes Los an important effect upon sky-wave transmission because the antenna has an

image" within the conducting earth. The distance between antenna and image is
related to the height of the antenna, and this distance is as critical as the distance be-
tween elements of an antenna system. Maximum usable frequencies (art. 1008) fall
generally within the HF band. By day this may be 10 to 30 mc, but during the night
it may drop to eight to ten mc. The HF band is widely used for ship-to-ship and ship-
to-shore communication.

Very high frequency (VHF, 30 to 300 mc). Communication is limited primarily
to the direct wave, or the direct wave plus a ground-reflected wave. Elevating the
antenna to increase the distance at which direct waves can be used results in increased
distance of reception, even though some wave interference between direct and ground-
reflected waves is present. Diffraction is much less than with lower frequencies, but
is most evident when signals cross sharp mountain peaks or ridges. Under suitable
conditions, reflections from the ionosphere are sufficiently strong to be useful, but
generally they are unavailable. "There is relatively little interference from atmospheric
noise in this band. Reasonably efficient directional antennas are possible with VHF.
The VHF band is much used for communication with aircraft and for radio aids to air
navigation. "The first television and FM channels were within this band.

Ultra high frequency (UHF, 300 to 3,000 mc). Sky waves are not used in the UHF
band because the ionosphere is not sufficiently dense to reflect the waves, which pass
through it into space. Ground waves and ground-reflected waves are used, although
there is some wave interference. Diffraction is negligible, but the radio horizon extends
about 15 percent beyond the visible horizon, due principally to refraction. Reception
of UHF signals is virtually free from fading and interference by atmospheric noise.
Sharply directive antennas can be produced for transmission in this band, which is
coming into wider use for television and other line-of-sight transmission.

Super high frequency (SHF, 3,000 to 30,000 mc). There are no sky waves in the
SHF band, transmission being entirely by direct and ground-reflected waves. Diffrac-
tion and interference by atmospheric noise are virtually nonexistent. Highly efficient,
sharply directive antennas can be produced. Thus, transmission in this band is similar
to that of UHF, but with the effects of shorter waves being greater. Reflection by
clouds, water droplets, dust particles, etc., increases, causing greater scattering, in-
creased wave interference, and fading. At the upper end of the band, absorption in
the atmosphere increases as the frequency approaches that of molecular motion. Use
of this baud is largely experimental.

Extremely high frequency (EHF, 30,000 to 300,000 mo). The effects of shorter
waves are more pronounced in the EHF band, transmission being free from wave
interference, diffraction, fading, and interference by atmospherie noise. Only direct
and ground-reflected waves are available. Scattering and absorption in the atmosphere
are pronounced and may produce an upper limit to the frequency useful in radio com-
munication. The EHF band is a region of experimentation.

1015. Regulation of frequency use.—While the characteristics of various fre-
quencies are important to the selection of the most suitable one for any given purpose,
these are not the only considerations. Confusion and extensive interference would
result if every user had complete freedom of selection. Some form of regulation is
needed. The allocation of various frequency bands to particular uses is a matter of
international agreement. Within the United States the Federal Communications
Commission has responsibility for authorizing use of particular frequencies. In some
cases a given frequency is allocated to several widely separated transmitters, but only
under conditions which minimize interference, as during daylight hours. Interference
between stations is further reduced by the use of channels, each of a narrow band of

300 RADIO WAVES

frequencies. That is, assigned frequencies are separated by an arbitrary band of
frequencies that are not authorized for use. In the case of radio aids to navigation,
ship communications, etc., bands of several channels are allocated, permitting selection
of band and channel by the user.

1016. Kinds of radio transmission.—A series of waves transmitted at constant
frequency and amplitude is called a continuous wave (CW). This cannot be heard
except at the very lowest radio frequencies, when it may produce, in a receiver, an
audible hum of high pitch. get, Ag i

Although a continuous wave may be used directly, as in radio direction finding
(art. 1202) or Decca (art. 1309), it is more commonly modified in some manner. This

CARRIER AMPLITUDE MODULATED

m aie | E

CARRIER FREQUENCY MODULATED
WAVE WAVE

SAME INFORMATION TRANSMITTED BY
AMPLITUDE AND FREQUENCY MODULATED WAVES

Figure 1016a.—Amplitude modulation (upper figure) and frequency
modulation (lower figure) by the same modulating wave.

is called modulation. When this occurs, the continuous wave serves as a carrier wave
for information. Any of several types of modulation may be used.

In amplitude modulation (AM) the amplitude of the carrier wave is altered in
accordance with the amplitude of a modulating wave, usually of audio frequency, as
shown in figure 1016a. In the receiver the signal is demodulated by removing the
modulating wave and converting it back to its original form. This form of modulation
is widely used in voice radio, as in the standard broadcast band of commercial
broadcasting.

If the frequency instead of the amplitude is altered in accordance with the amplitude
of the impressed signal, as shown in figure 1016a, frequency modulation (FM) occurs.
This is used for FM broadcasts and the sound portion of television broadcasts.

RADIO WAVES 301

Pulse modulation (PM) is somewhat different, there being no impressed modulating
wave. In this form of transmission, very short bursts of carrier wave are transmitted
separated by relatively long periods of “silence,” during which there is no transmission:
This type of transmission, illustrated in figure 1016b, is used in some common radio
navigational aids, including radar (art. 1208) and loran (art. 1302).

i NO TRANSMISSION | NO TRANSMISSION il

Figure 1016b.—Pulse modulation.

1017. Transmitters.—A radio transmitter consists essentially of (1) a power supply
to furnish direct current, (2) an oscillator to convert direct current into radio-frequency
oscillations (the carrier wave), (3) a device to control the generated signal, (4) an
amplifier to increase the output of the oscillator. For some transmitters a microphone
is needed with a modulator and final amplifier to modulate the carrier wave. In addi-
tion, an antenna and ground (for lower frequencies) are needed to produce electromag-
netic radiation. These components are illustrated diagrammatically in figure 1017.

Microphone Da Antenna

A i NIA
Amplifier Modulator

ml

—

Oscillator R F Amplifier

Em

Ground =
Power Supply E

Figure 1017.—Components of a radio transmitter.

1018. Receivers.—When a radio wave passes a conductor, a current is induced
in that conductor. A radio receiver is a device which accepts the power thus generated
in an antenna, and transforms it into usable form. It should be able to select signals
of a single frequency (actually a narrow band of frequencies) from among the many
which may reach the receiving antenna. If necessary, the receiver should be able to
demodulate the signal, and always it should provide adequate amplification. The
output of a receiver may be presented audibly by earphones or loud speaker; or visually
on a dial, cathode ray tube (art. 1019), counter, or other display. Thus, the useful
reception of radio signals requires three components: (1) an antenna, (2) a receiver,
and (3) a display unit.

Radio receivers differ mainly in (1) frequency range, the range of frequencies to
which they can be tuned; (2) selectivity, the ability to confine reception to signals of
the desired frequency and avoid others of nearly the same frequency; (3) sensitivity,
the ability to amplify a weak signal to usable strength against a background of noise;
(4) stability, the ability to resist drift from conditions or values to which set; and (5)
fidelity, the completeness with which the essential characteristics of the original signal
are reproduced. Receivers may have additional features such as an automatic fre-
quency control, automatic noise limiter, etc.

302 RADIO WAVES

Some of these characteristics are interrelated. For instance, if a receiver lacks
selectivity, signals of a frequency differing slightly from those to which the receiver
is tuned may be received. This condition is called spillover, and the resulting inter-
ference is called cross talk. If the selectivity is increased sufficiently to prevent spill-
over, it may not permit receipt of a great enough band of frequencies to obtain the
full range of those of the desired signal. Thus, the fidelity may be reduced.

1019. The cathode ray tube is a useful device for presenting certain types of
information. This tube, with its associated controls, is often called an oscilloscope,
or scope for short. In television receivers it is usually called the picture tube.

The essential components of a cathode ray tube are shown in figure 1019. At the
left is a cathode which serves as a source of electrons. In this usage it is called an
electron gun. The electrons are collected and focused into a beam by a focusing
anode, and then speeded up by an accelerating anode. If there were no other con-
trols, the beam of electrons would travel the remainder of the length of the tube and
strike the enlarged, curved surface of the tube face at its center, approximately. The
inside of the face is coated with a material known as a phosphor (such as zinc sul-

FACE

GRID VERTICAL DEFLECTION PLATES

CATHODE

ELECTRON

- EMT | o "ud e - BEAM

FOCUSING ANODE HORIZONTAL
ACCELERATING ANODE DEFLECTION PLATES

Figure 1019.—A cathode ray tube.

phide or calcium sulphide) which becomes luminous (phosphorescent) where a beam of
electrons impinges upon it. If the beam is sharply focused, a dot of light appears at
the point of impact.

By means of the vertical deflection plates, the beam is bent upward or downward.
This is accomplished by impressing electric charges on these plates. The beam, being
negatively charged, is repelled by the negative plate and attracted by the positive
plate. If an alternating current is used, the strength and polarity of the electric
charge on each plate changes continually, causing the beam to be deflected alternately
up and down. This results in vertical motion of the spot of light on the face of the
tube. If the motion is sufficiently rapid, a vertical line appears on the face of the
tube. This is true not only because of the persistency of vision within the eye, but
also because the tube face does not immediately fade when the stream of electrons is
moved to another point. This visible line is called a trace, and the motion of the dot
in producing it, a sweep. A horizontal trace can be made by means of the horizontal
at acai plates which operate in a manner similar to that of the vertical deflection
plates.

If both sets of plates are energized at the same time, the spot of light can be moved
to various places on the face of the tube. If two alternating currents are properly
synchronized, the spot can be made to trace repeatedly some pattern, such as a sine

RADIO WAVES 303

wave. It is generally desirable to have one trace repeated in accordance with a pre-
arranged plan, having the deflection such that motion in one direction across the
face of the tube is relatively slow, and that in the opposite direction is very fast, so
that the return of the spot to a starting point is almost instantaneous. Such a return
is called flyback, and the faint trace that may be visible is called a retrace. The
position of the spot along the trace can be used as a measurement of elapsed time
since the spot was at some reference point. This is usually accomplished by having
a received signal impress a momentary charge on the other set of deflecting plates,
causing a deflection of the trace as the spot is momentarily moved to one side of the
line; or by causing the reeeived signal to intensify the spot, causing it to glow brighter.

By suitable controls, the trace can be divided into two or more parts, made to
rotate, or take any of a great variety of motions and shapes.

In a dark trace tube the spot appears dark on a lighter background.

The cathode ray tube has many applications in electronic navigational equipment.

References

International Hydrographic Bureau. Radio Aids to Maritime Navigation and Hydrog-
raphy. 2d ed. International Hydrographic Bureau Special Publication 39.
Monaco, 1965.

Reintjes, J. F., and Coate, G. T. Principles of Radar. 3d ed. M. I. T. Radar
School. New York, McGraw-Hill, 1952.

Schelkunoff, S. A., and Friis, H. T. Antenna Theory and Practice. New York, Wiley,
1952.

Sheingold, A. Fundamentals of Radio Communication. New York, Van Nostrand,
1951.

Terman, F. E. Radio Engineers’ Handbook. New York, McGraw-Hill, 1943.

U.S. Department of Commerce. Jonospheric Radio Propagation. National Bureau
of Standards Monograph 80. Washington, U.S. Govt. Print. Off., 1965.

U.S. Department of the Navy. Elements of Electricity and Radio. NAVSHIPS
900,012. Washington, 1944.

CHAPTER XI
ELECTRONICS AND NAVIGATION

1101. Electronics is the science and technology relating to the emission, flow, and
effects of electrons in a vacuum or through a semiconductor such as a gas, and to
systems using devices in which this action takes place. The widest use of electronics
is in radio in its various forms. However, by the definition given above, electronics
may be used in a secondary sense in a great many devices which are otherwise unrelated
to radio.

1102. Use of electronics in navigation.—The expression “electronic navigation”
may imply a distinct type of navigation comparable to celestial navigation, piloting,
and dead reckoning. However, the use of electronics by the navigator is nearly
always in one of these fields, although it is true that piloting techniques have been
extended far from shore.

In celestial navigation, electronics is used for transmission of radio time signals
to ships at sea, permitting the frequent checking of chronometers. A more direct
application is the radio sextant. If the body is above the horizon, this instrument can
measure altitudes of the sun and moon through an overcast or in clear weather, day or
night. With further development, it may be possible to use this instrument for measure-
ment of altitudes of other celestial bodies.

In piloting, electronics has its widest application. In addition to the various
radio aids commonly associated with navigation, electronics is used in the echo sounder
(art. 619), sonar (art. 1108), and sofar (art. 1313).

In dead reckoning, electronics is used in some devices for automatically determin-
ing dead reckoning position. These may be essentially recording or indicating devices,
or instruments for measuring speed and direction, as well as indicating the results of
the measurements (art. 809).

In addition to these applications of electronics to navigation, radio communication
is helpful to the mariner. Weather maps and other information may be sent by fac-
simile (art. 3828). Various navigational warnings are broadcast, as well as weather
and ice reports and predictions, distress information, and even medical advice. In-
formation concerning the various services available is given in H.O. Pubs. Nos. 117-A
and 117-B, Radio Navigational Aids, and in 118-A and 118-B, Radio Weather Aids.

The use of electronics for direct determination of positional information is related
primarily to measurement of direction and measurement of distance or difference in
distance.

1103. Direction measurement at the receiving site is accomplished by means of a
directional antenna. Nearly all antennas have some directional properties, but in
the usual antenna used for radio communication, these properties are not sufficiently
critical for navigational use.

A widely used directional antenna is in the form of a loop. Suppose a transmitted
radio signal encounters such a loop oriented in the direction of travel of the radio
signal, as shown in figure 1103a. If the diameter of the loop is half the wave length,
the crest of one wave arrives at one side of the loop at the same time that the trough
arrives at the opposite side, as shown. Thus, the currents induced in the two sides
reinforce each other, causing maximum output from the antenna. A short time later,

as the wave continues to move past the antenna, the crest reaches the other side of the
304

ELECTRONICS AND NAVIGATION 305

loop, and a new trough reaches the ap-
proach side. A maximum current now
flows in the opposite direction. There-
fore, with the antenna in this orientation,
an alternating current flows in the loop.
If the loop diameter is less than half a
wave length, the current is less than
maximum.

If the antenna is rotated 90%, the al-
ternate crests and troughs arrive at both
sides at the same time, tending to cause
currents to flow in opposite directions around the loop. Under these conditions
the two parts cancel each other, resulting in zero antenna output. This condition is
called a null.

As the antenna is rotated, its output varies with the angle relative to the direction
of motion of the radio signal. This condition is illustrated in figure 1103b. The
length of a line from the center to the outer edge of the shaded area represents the
strength of the antenna output at that bearing, relative to the direction of motion of
the radio wave. Thus, when it is in line, with either side of the loop toward the approach-
ing signal, the output is maximum, and at 90? it is minimum. Since the change with
bearing is most rapid near the region of minimum
signal, this is the portion used for determination of
direction.

Because of the characteristics of the simple
loop antenna, a 180° ambiguity exists. That is,
a signal approaching from either of two directions
180° apart would cause the same antenna output.
This ambiguity can be resolved by using a vertical
sense antenna in connection with a loop. The
output from this wire, if the direction of motion of
the signal is horizontal, is the same in all directions.
Therefore, the polar diagram of its output is a circle,
with the same polarity in all directions. If this
output is exactly equal to the maximum of the
loop, it will cancel the output from one side and
double that from the other, since the polarity in the
two sides is opposite. The resulting diagram of
antenna output is shown in figure 1103c. With this
arrangement, a single minimum exists, permitting
the determination of which of the two reciprocal
bearings is correct, thereby removing,the ambiguity.
The loop antenna is then used for making the
reading. This is the type of equipment commonly
used with a radio direction finder (art. 1202).

Two variations of the loop antenna are also
used in radio direction finders. In one of these,
the crossed loop type, two loops are rigidly mounted
in such manner that one is rotated 90° with respect
to the other. The relative output of the two an-
tennas is related to the orientation of each with

Figure 1103a.—Principle of the loop antenna.

oļu
SE
CIS

180

FicGureE 1103b.—Polar diagram of
output of loop antenna.

306 ELECTRONICS AND NAVIGATION

o

O
00
"i

FIGURE 1103c.—Polar diagram of output of loop antenna with vertical sense
antenna.

respect to the direction of travel of the radio wave, and is measured by a device
called a goniometer. This is the type antenna used in an automatic direction finder.
In the other variation, the rotating loop type, a single loop is kept in rapid ro-
tation by means of a motor. The antenna output is shown on a cathode ray tube, and
the resulting display shows

the direction of the signal.

With higher frequencies,

for which a dipole antenna is

INCOMING used, a different method of

PARABOLIC RADIO achieving directional proper-
REFLECTOR WAVES ties is employed. The anten-
na is placed at the focus of a

reflecting parabola (art. O34).

Incoming parallel beams are

all reflected to the antenna,

Fong 1103d.— Principle of the parabolic reflector. which receives a concentra-

tion of energy, as shown in

figure 1103d. When the parabola is turned away from the approaching signal, little or

no signal is received. The effectiveness of such an arrangement increases with higher
frequency, for which an efficient antenna decreases in size, approaching a single

point. This type antenna is used for radar (art. 1208), and the ramark beacon
(art. 1210) depends upon it.

ELECTRONICS AND NAVIGATION 307

1104. Directional transmission.—The simple loop antenna, with or without a
vertical sensing antenna, can be used for transmitting signals. The polar diagram
of the strength of the transmitted signal is similar to that of the output of a receiving
antenna, as shown in figure 1103b or figure 1103c.

Where it is desired to maintain the same direction or directions of transmission,
permanent large installations can be made and properly designed for maximum effi-
. eiency at the frequency used. This is called an Adcock antenna, which is similar in
principle to the loop except that it is not connected across the top.

For higher frequencies, the parabolic reflector is used to produce a beam of radio
energy. The effect is similar to that of a searchlight.

Various combinations of antennas and phase relationships are used to produce
patterns of signals serving as a navigational system. Some of these are discussed in
articles 1105 and 1106.

1105. Radio tracks.—A track defined by radio may be called a “radio track.”
One of the simplest methods is to use two Adcock antennas placed 90% with respect
to each other. As shown in figure 1105,
one antenna can be used to produce a “fig-
ure 8” pattern with its axis in a north- íð
south direction, and a second one to pro-
duce a similar pattern in an east-west
direction. If each antenna transmits a
characteristic signal, the lines along
which these two signals are received with
equal intensity represent radio tracks.
This system, used in the radio ranges (art.
1207) which for many years constituted
the primary guidance along the federal
airways of the United States, has a 90°
ambiguity. The directions of the tracks
can be altered by changing the orienta- E
tion of the antennas, or by changing the Bas
phases of the signals from the two antennas.

A variation of this system is the use prcung 1105.— Radiation pattern of two Adcock
of three or more antennas equally spaced antennas rotated 90° with respect to each other.
along a straight line, the distance be-
tween consecutive antennas being three wave lengths. By a combination of amplitudes
and phase shifts, a series of equisignal tracks are produced. This system, known
as elektra, was used by the Germans during the early part of World War II. It was
the predecessor of the German sonne and British consol systems (art. 1206).

At higher frequencies, radio tracks can be provided by parabolic reflectors. The
disadvantage of such a system is that virtually no signal is received unless one is
almost directly in line with the beam.

Although ships have occasionally used radio tracks, particularly the four-course
radio ranges, such systems have been designed primarily for use by aircraft. Simple
track guidance, as here described, has been largely replaced by rotating beacons pro-
viding multiple track guidance. quh. i

1106. Rotating beacons may be used to provide an indication of direction without
actual direction measurement at the receiver. In the earliest installations, a directional
antenna was mounted on a vertical axis and rotated slowly at uniform speed. When
a distinctive phase of the pattern, such as a null, passed through a reference direction
(usually true or magnetic north), a nondirectional signal was transmitted. When this

308 ELECTRONICS AND NAVIGATION

signal was received, a stopwatch was started. The elapsed time from this moment
until the distinctive phase was received was an indication of the direction of the re-
ceiver from the transmitter.

In later installations the antenna remains stationary and the radiation pattern is
caused to rotate. In the vortac ranges (art. 1207) used for air navigation with respect
to the federal airways, two signal patterns are transmitted by VHF antennas similar
in principle to the Adcock antenna. The pattern of one remains fixed, and that of
the other rotates. The result is a change of phase with direction. Along the refer-
ence direction (magnetic north) from the transmitter the signals are in phase. The
phase difference along any other radial is constant. The receiver measures the phase
difference and indicates the direction on a dial. The receiver is also provided with a
knob for selecting a desired phase difference (direction) and a pointer to indicate
whether the craft should go right or left to reach the desired radial.

With three antennas in line, as in the elektra system, rotation is accomplished by
slowly shifting the phase of the current in the two outer antennas. This, in combina- `
tion with periodic reversal of the direction of the current, produces alternate sectors of
dot and dash signals. During the cycle of operation, the patterns rotate so that a
portion of each pattern sweeps past the receiver. The relative number and order of
dots and dashes is an indication of direction when referred to a table or special chart for
interpretation. However, identical readings can be obtained in a number of sectors.
A radio direction finder bearing, dead reckoning position, or other positional information
can be used to resolve the ambiguity. As developed by the Germans, this system
was known as sonne. The British further developed the system under the name
consol (art. 1206). The American development is known as consolan. :

1107. Speed measurement can be accomplished electronically by utilizing th
Doppler principle. A beam of electromagnetic energy can be transmitted from
a moving craft. If this energy strikes an obstacle and some of the energy returns as an
echo, it will have a slightly different apparent frequency because of the motion of the
transmitter. The difference is proportional to the speed in the direction of the beam.
If the beam is directed ahead or astern, the speed of the craft is indicated. If two
beams are used with a fixed angle between them, and the two rotated about a vertical
axis until both readings are the same, direction of motion can also be measured. In
this case the measured speed is a fixed proportion of the actual speed. Thus,
Doppler navigation (art. 809) is a dead reckoning system, since it provides measure-
ment of both speed and direction of motion. "This method is particularly applicable
to aircraft.

Another method of measuring speed and direction of motion is by inertial naviga-
tion (art. 809). By this principle, fore-and-aft and athwartship accelerations are
measured and automatically integrated once to provide a measurement of speed in each
direction, and a second time to provide an indication of distance.

Since both Doppler and inertial systems provide dead reckoning information, their
errors are cumulative, tending to increase with time.

1108. Distance measurement.—Since the speed of travel of radio waves is nearly
constant, the time of travel between two points is directly proportional to the distance
between the points. Therefore, it provides a possible method of determining distance
if a means is available for measuring very small intervals of time. Considering the
Reni waves as 186,230 statute miles per second, or 983,294,400 feet per second,

Á = ravels sia I 983 feet in one-millionth of a second. This small unit is
ion S a microsecond (us). About 6.18 us are needed for a wave to travel one nautical

If signals are transmitted from a known point at established times, as every second

ELECTRONICS AND NAVIGATION 309

of GMT, and the time of reception at a second point is measured, the difference between
the two times ls an indication of distance. Such a system requires clocks that can be
kept synchronized to a very small unit of time, perhaps one microsecond.

Another method is to measure a time interval by means of a cathode ray tube
(art. 1019). The reference or starting time needed for measurement of the interval is
commonly provided by originating the signal at or near the receiving antenna. The
signal travels to the “target” and back, the time required for the round trip being
measured. This is the principle of radar (art. 1208). In primary radar, a reflected
signal or echo is returned. In secondary radar, the transmitted signal serves as an
interrogator to trigger a transponder, which immediately (or after a known delay)
transmits a return signal. This is the principle of shoran (art. 1213), hiran (art. 1213),
electronic position indicator (art. 1213), distance measuring equipment used with
vortac (art. 1207), and racons (art. 1210).

In order to utilize this principle, it is necessary to be able to transmit very short
bursts or “pulses” of energy. Otherwise, the return signal would be lost in the stronger
outgoing signal. This is accomplished by means of pulse modulation (art. 1016),
which permits transmission of signals during a period as short as a fraction of a micro-
second, if needed.

Distance through the water is measured in a similar manner, using sound waves.
The short bursts of energy, usually in the ultrasonic range above audible frequencies,
are produced electronically. Because of the much slower speed of sound waves, as
compared with radio signals, the lengths of the individual pulses are correspondingly
greater, and simpler means are generally used for measuring the time interval. This
principle is used in sonar (from sound navigation and ranging) to measure horizontal
distances, and in echo sounders (art. 619) to measure vertical distances. The term
“sonar” is sometimes used in a general sense to include echo sounders.

Another method of measuring distance electronically is by comparison of the phase
difference between signals derived from two continuous wave transmissions of different
frequency. A transmitter and a receiver are located at each of the points between which
distance is to be measured. At each station the interaction between the transmitted
and received signals produces signals of two additional frequencies, called beat frequen-
cies, equal to the sum and difference, respectively, of the two signals. If one of these
additional signals is transmitted from one station to the other and compared with the
corresponding signal there, the phase difference is an indication of distance. If the
distance between the stations is changing, a Doppler effect occurs, permitting measure-
ment of speed. This is the operating principle of pure-range Raydist (art. 1214).

Distance can also be measured by a combination of radio and sound signals.
Simultaneous signals are transmitted by radio and by sound, either through the air or
through the water. The difference in speed is so great that the travel time of the radio
signal can be considered zero. Thus, the time interval between reception of the radio
and sound signals is an indication of distance. This method is used only over relatively
short distances, where the distance in nautical miles can be considered equal to the
elapsed time in seconds divided by 1% if the sound travels through water, and by 5%
if it travels through air. This was the first electronic method of determining distance
and is still utilized in a number of distance finding stations (art. 1205). The method is
sometimes used by surveyors, who have a special beacon for this purpose. The finding
of distance by this beacon is called radio acoustic ranging (RAR), further discussed
in article 1205.

1109. Distance-difference measurement.—If synchronized signals from two sta-
tions are transmitted, the difference in distance from the stations can be measured,
either by means of the elapsed time interval between the arrival of the two signals, or

310 ELECTRONICS AND NAVIGATION

by measurement of the phase difference between the signals. Tf beat frequencies are
used, synchronization may not be needed. A E Së

Refer to figure 1109. Let M and S be two stations. Synchronization is achieved
by letting the signals of M, the master, control those of S, the slave. Circles Mi,
M2, M3, etc., are units of distance from M; and circles S1, S2, S3, etc., are units of
distance from S. If both signals are transmitted at the same instant, they will arrive
together at any point along a line equidistant from the two stations. "This center line
is the perpendicular bisector of the base line joining the two stations. On a sphere,
both center line and base line are great circles.

The center line is the zero time difference line. Tf the M signal arrives at some
point before the S signal, the time difference can be found by subtracting the M signal
travel time (or distance) from the S signal travel time (or distance). If a line is drawn
through all intersections at which units of distance from S are greater by one than those
from M (S8, M7; S7, M6; S6, M5; etc.), a curve is formed, as shown at “+1” in figure
1109. A similar curve labeled “—1” is formed if all points at which units of distance
from S are less by one than those from M (M8, S7; M7, S6; etc.) are connected. The
minus sign indicates that the M signal arrives (—)1 time unit before the S signal,
or S-M=(—)1. On a plane surface, such curves are hyperbolas (art. O34) because
they connect points of equal difference of distance between two fixed points. On a
sphere, such curves are called spherical hyperbolas. On the spheroidal earth they are
not plane hyperbolas, and differ somewhat from spherical hyperbolas.

Other, more sharply curving hyperbolas are formed by connecting lines of greater
time (distance) difference, as at (+)2, (—)2, (+)3, (—)3, etc. The maximum difference
occurs along the base line extensions beyond the transmitters. This difference depends
upon the distance between stations. A pattern of all positive readings can be obtained
by delaying the start of the S signal until the M signal is received at S, or longer.
Suppose the S signal is transmitted ten units after the M signal. The M signal for a
base line six units long will already have traveled four units beyond S when the S signal
leaves the transmitter. Therefore, the reading along the base line extension from S is
(+)4, or ten more than shown in figure 1109. By the time the S signal arrives at the
master transmitter, the M signal will be at ten (the delay) plus six (the number of
units between M and S) units, or 16 units away. Therefore, the reading along the
base line extension beyond M is 10+6=(+)16. Similarly it can be shown that all
other readings are also increased by (+) 10.

Each hyperbola becomes more nearly a straight line (great circle) as distance from
the base line increases. At a distance from the center of the base line of five times the
length of the base line, the departure of the hyperbola from a great circle becomes
very small. For a “long” base line of several hundred miles, as in loran (art. 1302),
the lines are considered curves over their entire length. Thisis also true of a “medium”
base line as used in gee (art. 1308), Decca (art. 1309), Lorac (art. 1310), and hyperbolic
Raydist (art. 1311), which are not used over such an extensive area. If the base line
is very short, as in sonne and consol (art. 1312), the system 1s considered directional
rather than hyperbolic, beyond a distance of a few miles from the station.

Each hyperbola is a line of position. Accuracy of such a system is greatest along
the base line, where the hyperbolas are most closely spaced. As the distance between
consecutive lines increases, the accuracy decreases, being so low along the base line
extensions that use of this part of the pattern is normally avoided.

A hyperbolic system has the disadvantage of requiring two stations for a single
family of lines of position. „This can be partly overcome by using a series or chain
of stations, so that each station except the end ones operates with the station on either
side to form an intersecting lattice of position lines. This method is used with loran

ELECTRONICS AND NAVIGATION

a

te

Í

FiGuRE 1109.—A family of hyperbolic lines of position.

312 ELECTRONICS AND NAVIGATION

(art. 1302). With Decca (art. 1309), a central master operates with three slaves sur-
rounding it. Another disadvantage of a hyperbolic system is the need for computation
of points along the hyperbolas. These points are computed in advance and tabulated,
or plotted and connected by curves on special charts. This task is not normally
performed by the user, but it does add to the cost of the system.

An advantage of a hyperbolic system is that it may not require transmission from
the craft, an important consideration in time of war.

Hyperbolic lines of position may also be established by means of sound signals.
Such a system, called sofar, is described in article 1313.

References

Hall, J. S. Radar Aids to Navigation. M. I. T. Radiation Laboratory Series. New
York, McGraw-Hill, 1947.

Reintjes, J. F., and Coate, G. T. Principles of Radar. 3rd ed. M. I. T. Radar
School. New York, McGraw-Hill, 1952.

Schelkunoff, S. A., and Friis, H. T. Antenna Theory and Practice. New York, Wiley,
1952.

Terman, F. E. Radio Engineers’ Handbook. New York, McGraw-Hill, 1943.

U. S. Department of the Navy. Radar System Fundamentals. NAVSHIPS 900,016
and 900,017. Washington, 1944.

CHAPTER XII
DIRECTION AND DISTANCE BY ELECTRONICS

1201. Introduction.—Many systems have been proposed to utilize the various
techniques described in chapter XI. Only the more prominent ones put to practical
use are discussed in this chapter and the following one.

1202. Radio direction finder (RDF).—The type radio direction finder commonly
used aboard ship consists essentially of a loop antenna (art. 1103) that can be turned
in any direction around a vertical axis, and some kind of indicator. In its usual form,
the indicator consists of a compass rose with a pointer pivoted at its center. The
pointer is so oriented to the antenna that it points toward the direction from which
the signal is coming when the null is received. If the compass rose is oriented with
0° in line with the ship's head, the usual orientation in a permanent installation,
measured directions are relative bearings. In many permanent installations, there is a
course input from the gyro compass so that approximately true bearings are measured.

Radio bearings may be taken on any received radio signal within frequency range
of the receiver. At many locations radiobeacons are provided for this purpose. "Their
locations and identifying signals are shown on the chart by appropriate symbol (app.
K) and the abbreviation “R. Bn.", and are tabulated in H.O. Pub. No. 117, Radio
Navigational Aids. When bearings are taken on other stations, one should be careful
to determine the location of the transmitting antenna from which the signal is coming.
This may not always be the same as a receiving antenna associated with the same
station, and the signal may possibly be rebroadcast from another station.

Along some foreign coasts direction finder stations are provided to obtain bearings,
upon request, and transmit the information to the vessel requesting it. These stations
are indicated on the chart by the letters “R.D.F.”, and listed in H.O. Pub. No. 117.

1203. Errors of radio bearings.— Bearings obtained by radio direction finder are
subject to certain errors, as follows:

Quadrantal error. When radio waves arrive at a receiver, they are influenced
somewhat by the environment, resulting in an erroneous indication of direction. Aboard
ship this is a function of the relative bearing, normally being maximum for bearings
broad on the bow and broad on the quarter. Its value for various bearings can be
determined, and a calibration table made. "The usual method of calibration is to obtain
a series of simultaneous radio and visual bearings on a transmitter. This may be done
while a ship swings at anchor, or more quickly by steaming in a circle within sight of
a transmitter. Another method, when two ships are available, is for the second ship to
transmit while circling the first. Naval vessels sometimes use this method while both
ships are underway, proceeding between ports. A vector diagram solution, usually
on a maneuvering board (art. 1212), can be used to determine the courses and speeds
of the maneuvering vessel. Metal booms, cranes, etc., should be in their normal
positions during calibration. If their positions are changed when the radio direction
finder is used, an error may be introduced.

Coastal refraction. As indicated in article 1006, a radio wave crossing a coast
line at an oblique angle undergoes a change of direction due to difference in conducting
and reflecting properties of land and water. This is sometimes called land effect. It
is avoided by not using, or regarding as of doubtful accuracy, bearings of waves which
cross a shore line at an oblique angle. If the transmitter is near the coast, negligible

313

314 DIRECTION AND DISTANCE BY ELECTRONICS

error is introduced because of the short distance the waves travel before undergoing
refraction. )

Polarization error. As indicated in article 1008, the direction of travel of radio
waves may undergo an alteration during the confused period near sunrise or sunset,
when great changes are taking place in the ionosphere. This error is sometimes called
night effect. The error can be minimized by averaging several readings, but any radio
bearings taken during this period should be considered of doubtful accuracy.

Reciprocal bearings. Unless a radio direction finder has a vertical sensing wire
(art. 1103), there is a possible 180 ambiguity in the reading. If such an error is
discovered, one should take the reciprocal of the uncorrected reading, and apply the
correction for the new direction. If there is doubt as to which of the two possible
directions is the correct one, one should wait long enough for the bearing to change
appreciably and take another reading. The transmitter should draw aft between
readings. If the reciprocal is used, the station will appear to have drawn forward.
A reciprocal bearing furnished by a direction finder station should not be used because
the quadrantal error is not known, either on the given bearing or its reciprocal.

In general, good radio bearings should not be in error by more than 2°. However,
conditions vary considerably, and skill is an important factor. By practicing fre-
quently when results can be checked by visual observation or by other means, one can
develop skill and learn to what extent radio bearings can be relied upon under various
conditions. Bearings taken ashore should be of slightly greater accuracy than those
taken aboard ship. Shore stations indicate bearings of doubtful accuracy. These
stations should not be asked to estimate the size of the probable error.

1204. Using radio bearings.—A bearing obtained by radio, like one determined
in any other manner, provides means for establishing a line of position. By heading
in the direction from which the signal is coming, one can proceed toward, or home on,
the transmitter. In thick weather one should avoid heading directly toward the
source of radiation unless he has reliable information to indicate that he is some dis-
tance away. In 1934 the Nantucket Lightship was rammed and sunk by a ship
homing on its radiobeacon.

Radio waves, like light, travel along great circles. Except in high latitudes,
visual bearings can usually be plotted as straight lines on a Mercator chart, without
significant error. Radio bearings, however, are often observed at such positions with
respect to the transmitter that the use of a rhumb line is not satisfactory. Under
these conditions it is customary to apply the conversion angle (art. 821) as a correction
to the observed angle, to find the equivalent rhumb line. Such a correction is not
needed when a bearing is plotted on a gnomonic chart or one on which a straight line
is a good approximation of a great circle. In other situations, a correction may be
necessary.

If the transmitter and receiver are on the same meridian, or are both on the equator
no correction as needed because rhumb lines and great circles coincide under these
conditions. The size of the correction increases with degree of departure from these
conditions, and with greater distance between transmitter and receiver.

Conversion angles are given in table 1. This table is used to convert great circle
to rhumb line directions or vice versa as in great circle sailing, radio, and consol bearings
varu ākā 1 VIE is not BUS than 4?5, and the mid latitude

tter and 10t more than 85°, the first part of the table should
be used. The simplifying assumptions used in the computation of this part of the
table do not introduce a significant error within the limits of the table.
PM ON the correction can be determined by referring to the rules given at the

j ^ page of table 1. These follow from the fact that the great circle is

DIRECTION AND DISTANCE BY ELECTRONICS 315

NORTHERN HEMISPHERE

Great Circje Great Circle

Á + TRANSMITTER — N

RECEIVER RECEIVER
WEST OF E REGUATOR es EAST OF
TRANSMITTER TRANSMITTER

\ — TRANSMITTER + /

S e e

Great Circle Great Circle

SOUTHERN HEMISPHERE

FIGURE 1204.— Sign of conversion angle correction to radio bearings.

nearer the pole than the rhumb line. It can be visualized by means of a simple sketch,
as shown in figure 1204.

Example.—The DR position of a ship is lat. 42%15/2N, long. 9%48/6W. A
radio bearing is taken on Cabo Montedor Light Station, at lat. 41?45'00" N, long.
8?52/20" W. "The reading, corrected for calibration error, is 12525.

Reguired.—The equivalent rhumb line bearing.

Solution.— Latitude Longitude
Receiver 42%15/2N 9°48'6W
Transmitter TIO45 0 NSESSS52 SV)
Difference 9012 5679 —:0-9
Mid latitude 42?0
Correction (+) 0?3 (from table 1)
Great-circle bearing 12575
Rhumb line bearing J 125?8

Answer.—B 12518.

Radio bearings are plotted and labeled as any other bearing line (art. 904). If it is
desired to indicate the nature of the bearing, the word “radio” might be added to the
label, preferably below the line. Since radio bearings are generally somewhat less
accurate than visual bearings, and often are observed at greater distances, positions
obtained by them are generally considered of insufficient accuracy to be termed fixes,
and so are usually considered estimated positions (art. 913). However, judgment
should govern the reliance to be placed upon such positional information. A series
of such positions may provide the basis for elimination of random errors, giving a
reliable fix unless systematic errors (art. 2903) are present.

Some navigators estimate or assume a probable error (usually of +2° unless
conditions suggest another value) and plot lines on each side of the bearing line to
indicate the probable area within which the vessel is presumed to be located.

Radio bearings furnished by a direction finder station have been corrected for
known errors at the receiver, but not for conversion angle. The latter should be
applied by the user.

1205. Distance finding stations.—At some locations a radio signal is synchronized
with a sound signal which may be transmitted through either air or water. The

316 DIRECTION AND DISTANCE BY ELECTRONICS

travel time of the radio signal is negligible compared to that of the sound signal. Con-
sequently, the difference in time between reception of the two signals is proportional
to the distance from the station. The distance in nautical miles is equal to the number
of seconds of time interval divided by 5% if the sound travels through air, or by 1% if
through water (or multiplied by 0.18 or 0.8, respectively). The distance so found is
from the origin of the sound signal, which might differ somewhat from that of the radio
signal. The distance may be in error by as much as ten percent.

A light, portable, floating beacon, designed for use primarily in surveying, transmits
radio signals through the air when triggered by a suitable sound signal. Determination
of distance by the use of such a beacon is called radio acoustic ranging (RAR).

1206. Consol is a long-range, short-base-line, hyperbolic system operating in the
250-350 ke frequency range. The three antennas constituting a station are spaced
at intervals of about three wave lengths. Beyond a distance of about 25 miles from
the center station the lines of position can be considered great circles with negligible
error. In use, the system is considered a directional one, the hyperbolic portion of
the lines not being used.

The radiation pattern of each station consists of alternate sectors of dot and dash
signals, the sectors averaging 15? in width. During the “keying” cycle of 30 or 60
seconds, this pattern rotates, the equisignal between dots and dashes moving through
one sector. During this period, 60 signals (either dots or dashes) are transmitted. At
any point along the dividing bearing between sectors at the beginning of the cycle, 60
dots or 60 dashes should be received. Along any other bearing line the count of 60 is
distributed between the two types of signal. The relative number of each, and their
order, is related to the bearing of the receiver.

The total count is generally less than 60 because the dot and dash sectors overlap,
one type signal gradually fading as the other becomes stronger. The equisignal
boundary is the line along which both signals are of equal intensity and neither can be
distinguished. Several signals may be lost during passage of this sector. The number
of signals lost (60 minus the actual count) should be distributed equally between the
dots and dashes. If the difference is an odd number, the smaller correction should be
applied to the count received first, because the ear can generally follow a fading signal
to a lower degree of contrast than it can detect the first signal of a new series. This is
particularly true when dots are received first. Thus, if the count is 25 dots and 30
dashes, the total is 55, and 5 signals have been lost in the equisignal sector. The
corrected count is 25+2—27 dots, and 30+3=33 dashes.

The great-circle bearing corresponding to the count is determined by referring
to H.O. Pubs. Nos. 117-A and 117-B, a separate table being given for the dot and
dash sectors of each station. If plotting is to be done on a Mercator chart, the con-
version angle correction should be applied using the table given in H.O. Pubs. Nos.
117-A and 117-B. Table 1 may also be used; however, the entering arguments of
transmitter and receiver must be reversed. Special charts showing the lines or gradua-
tions have been prepared by some foreign countries.

The time of observation of a consol line of position is the moment at which
the equisignal is heard.

Under favorable conditions, the coverage area for a consol station extends outward
for about 1,000 to 1,200 miles by day, and 1,200 to 1,500 miles by night, over water.
Over land, Si at any time that the noise level is high, these ranges may be reduced
materially. The accuracy varies considerably over the pattern. Directionally, it is
RA along the great circle through the center antenna and perpendicular to the
ine of antennas. At an angle of 60° to this perpendicular, the accuracy drops to a
A EE usable value. Therefore, there is a usable sector of about 120? on each side
oí the line of antennas, with an unusable sector of about 60° at each end of this line.

DIRECTION AND DISTANCE BY ELECTRONICS 317

In terms of distance, the greatest angular error occurs within the range in which sky
waves and ground waves mingle, between about 250 and 400 miles from the station.

As a very general rule, for 95 percent of the time when ground waves are received,
the error over water is not more than about one-third degree along the perpendicular,
increasing to about twice this value at an angle of 60% to the perpendicular. In terms
of miles, this is about one mile error for each 180 miles from the station along the
perpendicular, and each 90 miles along the bearing line 60% from the perpendicular.
For sky waves these values are about doubled, and when sky waves and ground waves
are near the same amplitude, the error may be considerably larger. These values refer
to single observations. The error is generally reduced by taking the average of several
readings. On many occasions a good dead reckoning position is more reliable than a
position obtained by consol. However, the method is valuable when the position is
considerably in doubt, and is a useful check to prevent gross errors by other methods.
Tf the position is so seriously in doubt that the sector is uncertain, a bearing by radio
direction finder should resolve the ambiguity.

A reading cannot be made oftener than once every one or two minutes, depending
upon the cycle of operation. Each 30- or 60-second “keying cycle” is followed by a
period of equal length, during which a continuous tone and identification are trans-
mitted. No special equipment is required beyond an ordinary medium frequency
communication receiver, and very little skill or training is needed.

Consol is a British development of a German system known as sonne, which in
turn evolved from the nonrotating elektra. There are several consol installations
along the coasts of western and northern Europe. Two stations of an American
version, called consolan, are installed on the east and west coasts of the United States.
The Japanese also have a version.

1207. Radio ranges.—The airways of the United States and some other countries
are marked by a series of distinctive radiobeacons called ranges. Under suitable
conditions, these are useful in marine navigation.

Two different types of ranges are in use. The older low frequency four-course
range consists of two Adcock antennas (art. 1104) so oriented that their signal areas
occupy sectors, usually about 90° each. The edges of the sectors overlap to form nar-
row equisignal sectors or “beams” directed along the airways. One antenna transmits
the Morse code letter A (e ==), and the other the letter N (me). These signals are so
synchronized that when they are received with equal intensity, they interlock to form
a single monotone “on-course” signal. As the equisignal sector is left, one signal
predominates. As the angle from the center of the equisignal sector increases, the
predominating signal becomes more prominent and the monotone fades. The area
near each side of the equisignal sector is called a “twilight sector.”

Some equisignal sectors extend out to sea. Their locations and the identification
of the A and N sectors are shown on appropriate aeronautical charts. A marine
navigator equipped with such information may find the ranges useful for determining
bearings, or even for homing.

A newer type range eliminates the four-course limitations of the older ones by
transmitting a rotating pattern, using very high frequency signals. Two such
systems, tacan for military aircraft and omnirange (VOR) for others, together with
electronic equipment for determining distance by an interrogator-transponder (art.
1108), are located at each installation, called a vortac station. By means of the
special receiving and indicating equipment needed, one can determine either (1)
bearing and distance at any time by automatic dial and meter indications, or (2)
direction to turn to arrive at a selected “radial” (bearing). Because of its limited appli-
cation to marine navigation, the special equipment is not normally carried aboard ship.

318 DIRECTION AND DISTANCE BY ELECTRONICS

1208. Radar determines distance by measuring the time required for a radio
signal to travel from a transmitter to a “target” and return, either as a reflected š “echo”
(primary radar) or as a retransmitted signal from a transponder (art. 1108) triggered
by the original signal (secondary radar). The name is derived from radio detection and
ranging. Since radar uses a directional antenna, the direction of the target is also
determined, but with somewhat less accuracy than the distance.

In a radar set, signals are generated in a transmitter by a timing circuit so that
energy leaves the antenna in very short bursts or “pulses.” During transmission of a
pulse, the antenna is connected to the transmitter but not the receiver. As soon as
the pulse leaves, an electronic switch disconnects the antenna from the transmitter
and connects it to the receiver. Another pulse is not transmitted until after the pre-
ceding one has had time to travel to the most distant target within range, and return.
Since the interval between pulses is long compared with the length of a pulse, strong
signals can be provided with low average power.

From the receiver, the return signal goes to the indicator. This consists of a
cathode ray tube (art. 1019) and appropriate circuits. Many types of display have
been devised, a number of them to meet specialized requirements. For navigational
use, the earliest type of display was the A-scope. The principle of this scope is illus-
trated in figure 1208a. At A a pulse leaves the antenna of a ship, and a vertical
deflection appears at the start of the horizontal trace on the scope face. At B the pulse
has traveled some distance outward from the antenna. A short horizontal line appears
after the vertical deflection on the scope face. The length of this line is directly pro-
portional to the distance traveled by the pulse. At C the pulse encounters a target
with a reflecting surface. At D the original pulse has moved on beyond the target, but
part of its energy has been reflected back toward the transmitter. At E the echo has
arrived back at the transmitting. craft, causing a vertical deflection of the horizontal
trace. The height of this deflection is directly proportional to the strength of the
returning signal. At F the echo has proceeded on past the transmitting ship, and the
trace is completed.

This sequence is repeated a great many times, perhaps 1,000 per second, the rate
being called the pulse repetition rate (PRR) or pulse recurrence rate. The start of
each trace is synchronized with transmission of the signal so that each trace is a repeti-
tion of the previous one, if slight changes in relative positions of transmitting ship,
target, and antenna orientation are neglected. Therefore, the trace and all deflections
appear as a continuous line. The distance between leading edges of the vertical de-
flections, or “pips,” is directly proportional to range. A change of range alters the
position of the second pip. The orientation of the antenna is an indication of direction.
A pip appears only when the antenna is pointed toward the target.

The type of presentation now most commonly used for navigational radar is called
the plan position indicator (PPI). On this presentation the sweep starts at the center
of the tube face and moves outward along a radial line which rotates in synchronization
with the antenna. Instead of being deflected, the trace glows with greater intensity
(brightness) at the appropriate places. Because of the persistence of the tube face
coating, the glow continues after the trace rotates on past the target, resulting in a
maplike presentation on the scope. This presentation is shown in figure 1208b.

; On a PPI, the range of a target is proportional to the distance of its echo
signal from the center of the scope. This may be measured by a series of visible
concentric circles at established distances from the center, or by means of an adjust-
able ring. synchronized with a counter. Bearing is indicated by the direction of
an echo signal from the center of the scope. To facilitate measurement of direction,
a movable, radial, guide line or cursor is provided, and a compass rose is placed around

DIRECTION AND DISTANCE BY ELECTRONICS 319

FIGURE 1208a.—A-scope.

the outside of the scope. In the “heading-upward” presentation, relative bearings are
indicated, the top of the scope representing the direction of the ship's head. In the
“north-upward” presentation, gyro north is always at the top, regardless of the heading.
True bearings are indicated if there is no gyro error. On this type presentation a
radial line is customarily provided at the heading of the vessel.

Provision may be made for offsetting the center of the PPI presentation from the
center of the tube face, to permit large-scale observation of distant targets in one
direction. With “true motion” radar, the center of the tube face continues to represent
the same geographical position until reset. The actual motion of all moving objects,
including one's own vessel, appears on the scope, instead of the relative movement
usually shown.

Other modifications have been devised. In some installations a repeater dupli-

cates the presentation, making the information available at a distance from the radar.

320 DIRECTION AND DISTANCE BY ELECTRONICS

Figure 1208b.—Plan Position Indicator. 1. Ship's position. 2. Ship dead ahead. 3. Isone Misaki.
4. Futtsu Saki. 5. Fort No. 1. 6. Fort No. 2. 7. Small craft. 8. Ship. 9. Hort) Nowe.

10. Small craft. 11. Kannon Saki. 12. Ship. 13. Ship. See figure 2308 showing chart of
this area.

Since the receiver is disconnected during transmission of a signal, no echo can be
received during this period. As a result, there is a minimum range at which objects
can be detected. The shortest pulses are about 0.1 microsecond in duration, or approxi-
mately 98 feet long. Since the time measurement is of the round trip as the signal
travels to the target and the echo returns, the range is half the distance corresponding
to the measured time interval. Therefore, a minimum range of about 49 feet is theo-
retically possible with a pulse of 0.1 microsecond. However, the practical minimum
range is somewhat greater because of sea return of echoes from the water near the ship,
where the signals strike the surface of the sea almost vertically. A practical minimum
of 50 yards is considered excellent.

The maximum range is limited by the power, nature of the target, and by the
curvature of the earth, since radar operates in the higher frequencies that are essentially
line-of-sight. The radar horizon, at which rays from the transmitting antenna are
tangent to the surface of the earth, is at a distance about 15 percent greater than that

DIRECTION AND DISTANCE BY ELECTRONICS 921

of the visible horizon (tab. 8). Under conditions of abnormal refraction, both visible
. and radar horizons may be extended to greater distances.

1209. Scope interpretation.—With practice, one can acquire considerable skill in
interpreting the signals appearing on the radar scope face. Some of the factors to be
kept in mind in interpretation are the following: |

Resolution in range. In part A of figure 1209 a transmitted pulse has arrived at
the second of two targets of insufficient size or density to absorb or reflect all of the energy
of the pulse. While the pulse has traveled from the first to the second target, the echo
from the first has traveled an equal distance in the opposite direction. At B the trans-
mitted pulse has continued on beyond the second target, and the two echoes are returning
toward the transmitter. The distance between leading edges of the two echoes is
twice the distance between targets. The correct distance will be shown on the scope,
which is calibrated to show half the distance traveled out and back. At C the targets

TARGETS

Æ

TRANSMITTED PULSE

TARGETS
D ECHO G TRANSMITTED PULSE

ECHOES

TRANSMITTED PULSE

ECHOES TARGETS

TRANSMITTED PULSE

Figure 1209.— Resolution in range.

322 DIRECTION AND DISTANCE BY ELECTRONICS

are closer together and the pulse length has been increased. The two echoes merge,
and on the scope will appear as a single, large target. At D the pulse length has been
decreased, and the two echoes appear separated. The ability of a radar to separate
targets close together on the same bearing is called resolution in range. It is related
primarily to pulse length, the minimum distance between targets that can be distin-
guished as separate ones being half the pulse length. This (half the pulse length) is
the apparent depth or thickness of a target presenting a flat perpendicular surface to
the radar beam. Thus, several ships close together may appear as an island. Echoes
from a number of small boats, piles, breakers, or even large ships close to the shore may
blend with echoes from the shore, resulting in an incorrect indication of the position
and shape of the shore line.

Resolution in bearing is similar to that in range. A pulse proceeds outward along
a narrow sector. As the beam rotates, energy is returned during the entire time that a
target is “illuminated,” the same as with a searchlight. A vertical target such as a
mast is “seen” over the arc in which there is sufficient illumination to render it visible.
On a radar PPI a target appears widened by an amount equal to the beam width,
half the beam width being added to each side. Thus, the echoes from two or more
targets close together at the same range may merge to form a single, wider echo. The
ability to separate such targets is called resolution in bearing. In angular units it is
dependent primarily upon beam width, a narrower beam having a higher resolution.
In terms of distance between targets, range is also important, resolution increasing as
range decreases.

Height of antenna and target. If the radar horizon (art. 1208) is between the
transmitting vessel and the target, the lower part of the target will not be visible. A
large vessel may appear as a small craft, a shore line may appear at some distance
inland. Areas within radar shadows (art. 1009) may not be visible at all.

Reflecting quality of target. Echoes from several targets of the same size may be
quite different in appearance. A metal surface is a better reflector of radio waves
than a wooden surface. A surface perpendicular to the beam returns a stronger echo
than a nonperpendicular one. For this reason, a gently sloping beach may not be
visible. A vessel encountered broadside returns a stronger echo than one heading
toward or away from the radar vessel. In some instances, the strength of an echo
can be increased by means of a corner reflector. This is a device with several reflecting
surfaces so arranged that a radar signal from any direction is returned toward its
source. Corner reflectors are fitted to a number of buoys (labeled “Ra Ref” on the
chart), and are carried in some lifeboats. The strength of a returning echo can be
reduced by coating a surface with radar absorbent material.

Frequency. As the frequency is increased, reflections occur from smaller targets.
Thus, a ten-centimeter radar generally penetrates fog, rain, snow, etc., while a three-
centimeter radar receives returns from such obstacles, and can be used to track storms.
Radar frequencies are sometimes indicated by “band,” as follows:

Band Frequency (mc) Approx. wave length (cm)
P 225-390 100

L 390-1,550 30

S 1,550-5,200 10

x 5,200-11,000 3

K 11,000-36,000 1

Q 36,000-46,000 0.75

V 46,000—56,000 0.6

A C-band extending from 3,500 mc to 5,850 me is sometimes mentioned.

DIRECTION AND DISTANCE BY ELECTRONICS "5929

Scope interpretation is complicated somewhat by the presence of unwanted signals
from atmospheric noise, sea return, precipitation, etc. Collectively, this is called
clutter. Generally, it is strongest near the vessel and gradually decreases with in-
creased range, because of reduced sea return. Strong echoes can sometimes be detected
by reducing the volume or “gain” of the receiver (not the image intensity of the indi-
cator), so that weaker signals will not appear. Even when the amplitude of the clutter
is about the same as that of desired signals, the latter can sometimes be detected by
watching the scope during several rotations of the antenna. At each rotation the
signals from targets remain at about the same place, and of about the same magnitude,
while those from waves, noise, etc., fluctuate, appearing different on each revolution.
Floating ice or a small boat may not be detected at any range if the waves are high.
A rough surface returns a stronger echo than a smooth surface.

Sometimes a signal appears on a radar screen when there is no visible object at
the point indicated, and no apparent source of the signal. This is called a ghost. It
may be due to faulty operation of the radar set, or to an actual echo returned from a
discontinuity in the atmosphere. Sometimes such discontinuities reflect light, also,
producing images or apparent images similar to mirages and of seeming apparent
reality. A similar condition occasionally occurs in the sea. This phenomenon is
undoubtedly the basis of many reports of strange objects sighted visually or by radar.
Sometimes such apparent objects exhibit incredible speed or maneuverability.

1210. Radar navigation.—Radar provides a means of establishing position, or
keeping a vessel in safe water during periods of reduced visibility, or at considerable
distance from shore, when other methods may not be available. Since both range and
bearing can be obtained, a single identifiable object is needed. However, if a visual
bearing is available, it should be more reliable than one obtained by radar. Since
radar range is usually more accurate than radar bearing, a fix by two or more ranges
is generally preferable to one obtained by two bearings or by range and bearing. How-
ever, accurate range requires reliable identification of the part of the target returning
the echo. This is not always apparent when natural objects are used.

Radar beacons have been installed at some places. One type, called ramark (from
radar mark), transmits continuously in all directions. On the scope of a radar receiving
the signal a radial line appears at the bearing of the beacon. The beacon does not
have to be within the range to which the scope is adjusted. A limited number of this
type beacon has been installed for experimental use by ships.

Another type beacon, called racon from the words radar beacon, consists essen-
tially of a transponder (art. 1108) which returns a coded signal when triggered by a
signal from a radar transmitter. The code, consisting of a series of dots and dashes,
provides identification of the beacon. The range and bearing are indicated by the
position of the first character of the code on the PPI. This type beacon is used prin-
cipally by aviators. Information on these installations is given m various aeronautical
publications (art. 2802). Because the return signal is of a different frequency than
the outgoing signal, radar equipment must provide for the change in frequency if
racon signals are to be used. Echoes returning at the frequency of the outgoing signals
do not appear on the scope.

In addition to the usual methods of piloting, radar is adapted to several methods
of somewhat limited application. If a single prominent target is available in an oper-
ating area, a series of concentric circles and radial lines—a polar plot similar to that
of a maneuvering board (art. 1212)—can be drawn on the chart and suitably labeled.
If bearing and distance are measured frequently, an almost continuous fix can be
obtained by spotting in the positions by eye. If a polar plot is made on a piece of
transparent material to the same scale as the chart, the ranges and bearings of a number

324 DIRECTION AND DISTANCE BY ELECTRONICS

of points can be plotted in quick succession, and the transparent material fitted to the
chart by trial and error. The center of the plot is then the position of the radar.

Several models of chart comparison unit (CCU) have been devised. By means
of this device, an image of the chart is superimposed over the PPI, or an image of the
PPI is superimposed over the chart. Either method permits direct comparison of
radar image and chart, if the two are of the same scale. Although distortion of the
PPI presentation is not the same as that of the chart, an experienced person can usually
effect a reliable match, providing reasonably accurate determination of position. A
chart comparison unit designed to produce a virtual image of the chart on the face of
the scope is sometimes called a virtual PPI reflectoscope (VPR). ;

Early models of the chart comparison unit were used with white-on-black charts
designed especially for the purpose. Later models can be used with ordinary nautical
charts. Various other special chart presentations have been devised for radar, but the
present trend is toward modification of nautical charts to make relief and radar-con-
spicuous objects more prominent. This is accomplished primarily by shading and the
use of additional contours.

Useful information can sometimes be obtained from radar scope photographs
made at known positions on previous runs or by other vessels with comparable installa-
tions. In certain confined waters, notably along certain stretches of the Ohio River, a
series of such photographs made with a typical radar installation have been combined
to form a mosaic which presents a continuous maplike presentation. In some cases
this mosaic has been printed in fluorescent ink on the regular chart. When the chart is
illuminated by fluorescent light, the mosaic glows in a manner that resembles a PPI.

1211. Harbor radar.—At a number of ports, shore-based radar has been installed
to assist in the movement of traffic during periods of low visibility. Each installation
is tailored to fit its surroundings and requirements. A typical installation consists of a
large antenna installed at a prominent point in the harbor, and one or more scopes
manned by competent personnel with knowledge of local conditions. The installations
are not intended to control shipping in the vicinity, but are considered advisory only.
Upon their own request, vessels about to enter or leave port, or shift berth, are advised
of traffic conditions, and other matters of concern. During passage between harbor en-
trance and the berthing area or anchorage, they may be warned of possible danger.
Customarily, communication with the vessel is through the pilot, who comes aboard
equipped with a portable radio. Resolution of present radars is not sufficiently great
to permit docking a vessel by radar alone.

A secondary use of harbor radar is to detect drift of aids to navigation from their
assigned stations. It is also used to assist a pilot vessel locate an entering ship, or to
direct a vessel to a craft in distress or to any other desired point.

One of the principal problems associated with harbor radar is the identification
of the echo from a vessel with which radio communication has been established. At
least two systems for accomplishing this are under development.

1212. Radar as an anticollision device.—Radar has not materially reduced the
number of collisions, as might have been anticipated. This may be due to any of a
number of reasons, or probably to a combination of several. Among these are the
following: uncertainty as to whether the other vessel has radar, failure to use radar
information, lack cf confidence in radar, lack of appreciation of the limitations of
radar, failure to act promptly, failure to establish prompt communication with the
other vessel, uncertainty as to obligation under rules of the road, misinterpretation of
radar information, difficulty of adequately visualizing a situation presented on a radar
scope, and lack of knowledge of use to be made of radar information. Most of these
can be summed up as lack of adequate training. There is record of radar actually

DIRECTION AND DISTANCE BY ELECTRONICS 325

having been removed from vessels because it was considered a collision hazard. A
better remedy would undoubtedly have been to instruct ships’ personnel in proper
use of this valuable aid.

Neither the international nor inland rules of the road provide special procedure
for a radar-equipped vessel, which is therefore expected to obey the same rules appli-
cable to other vessels. This is particularly important in view of the fact that radar is
not infallible in detecting the presence of small vessels. In some cases the mere presence
of radar is somehow believed to offer a protection or provide an immunity which does
not in fact exist. If a vessel has radar, the equipment should be kept in good working
condition and used whenever visibility is reduced. Even in clear weather it can be a
valuable aid in evaluating a situation, although it is not a substitute for visual observa-
tion.

The principal value of radar as an anticollision device is its ability to give early
information on the locations and movements of other vessels. Two fundamental
problems are involved. The first is the determination of relative motion of two or more
vessels if they maintain courses and speeds. The second is the determination of the
action to take to produce a desired result. Both problems can be solved by a simple
plot. Either a navigational or relative movement plot will suffice.

In the navigational plot, positions of one’s own vessel are plotted at intervals of a
few minutes. From each position the bearing and distance of the other vessel are
plotted. From these positions the course and speed of the other vessel can be deter-
mined. The dead reckoning of both ships can be run ahead to determine where they
will be at any future time. By trial and error, the point of nearest approach and the
distance and bearing at this point can be determined. Similarly, the effect of changing
course or speed can also be determined.

A somewhat simpler and more direct solution can be made by means of a relative
movement plot. This is most easily performed on a polar plotting diagram such as a
radar plotting sheet (H.O. 4665 series) or maneuvering board, H.O. 2665-20 (large size)
or H.O. 2665-10 (small size, usually used). If such a plotting sheet is not available,
one can easily be constructed, or any compass rose can be used. On these forms,
position of one’s own ship remains at the center, as on the usual PPI. Positions of
the other ship are plotted from the position of one’s own vessel.

Example 1.—A ship underway obtains the following radar bearings and ranges of
another vessel at the times indicated:

Time Bearing Range

1510 030° 8,500 yds.
1512 029° 7,600 yds.
1514 026°5 6,700 yds.
1516 024° 5,800 yds.
1518 02325 5,000 yds.

Required.—(1) The nearest approach of the two vessels.

(2) The bearing of the other vessel at the point of nearest approach.

(3) Time of arrival at the point of nearest approach.

Solution (fig. 1212a).—Let the distance between consecutive circles represent
1,000 yards. i

(1) Plot each of the given positions from the center, and label each with the time.
If the course and speed of each vessel are constant, the points should plot in approxi-
mately a straight line. This is the relative movement line. At any moment the other
vessel is at some point on this line. The direction of this point is the bearing of the other
vessel at the moment the point is occupied, and the distance between this point and the

326 DIRECTION AND DISTANCE BY ELECTRONICS

q EM T TE
M UT A ee: sem E E E E j

SCALES ig^ s Š

MANEUVERING BOARD

d

th. alitia, Agel 1938 No 2665 1

FīGuRE 1212a.—Finding time, bearing, and range of nearest approach by relative plot.

center is the range. The direction of the relative movement line is the direction of
relative movement (DRM) of the other vessel with respect to one’s own vessel. The
DRM of one’s own ship with respect to the other vessel is the reciprocal of this line (as
are the bearings). The length of the relative movement line in one hour is the relative
speed or speed of relative movement (SRM). The DRM and SRM, representing
relative motion, should not be confused with the actual course and speed of the other
vessel. The nearest approach of the other vessel is on the relative movement line, at
lts nearest point to the center. The required distance is therefore the perpendicular
distance from the center (own ship) to this line (extended). The graduations indicate
this to be 1,500 yards.

(2) The direction of the perpendicular, 310°, is the bearing of the other vessel at
the point of nearest approach.

(3) The time at which the other vessel is at the foot of the perpendicular is the
time of arrival at the point of nearest approach. In this problem it can be determined
by using a pair of dividers and stepping off a succession of two-minute runs along

DIRECTION AND DISTANCE BY ELECTRONICS 827

the relative movement line. Another way is by means of the nomogram at the bottom
of the diagram. By dividers, the distance between the 1510 and 1518 positions is
measured, and also the distance between the 1518 position and the point of nearest
approach. These are marked on the center line of the nomogram, being careful to
distinguish between the “yards” and “miles” scales. A mark is placed at eight on the
top line of the nomogram to represent the interval between 1510 and 1518. A straight
line connecting the eight-minute mark on the top line with the corresponding distance
mark on the middle line, if extended, intersects the bottom line at a point indicating the
relative speed. A second line from this point, through the second distance mark on the
middle line, if extended, intersects the top line at 11”, the time needed for the other
vessel to cover the distance along the relative movement line from the 1518 position to the
point of nearest approach. Therefore, time of arrival at this point is 1518+11"=1529.

Answers.—(1) D 1,500 yds., (2) B 310°, (3) T 1529.

With the information given in example 1, and the course and speed of one’s own
vessel, a person can determine course and speed of the other vessel, a process called
tracking. A speed vector diagram (art. O18) is used:

Example 2.—Find the course and speed of the other vessel of example 1, if own ship
is on course 110%, speed 12 knots.

Solution (fig. 1212b).—Let the distance between consecutive circles represent two
knots.

Draw the speed vector of own ship (12 knots in direction 110?), starting at the
center. Label the outer end of this liner. Read the relative speed (SRM), 13.5 knots,
from the bottom line of the nomogram of figure 1212a. Relative speed might also be
determined by arithmetic. In eight minutes (1510-1518) the other vessel moves 1.8

S i EMT 60
miles (3,600 yards) relative to own ship. In 60 minutes it will travel 1.8Xg=13.5

miles. From 7, draw a line parallel to, and in the same direction as, the relative move-
ment line, and measure off a speed of 13.5 knots. Label the end of the vector m. The
line rm is the relative speed vector, its length representing the speed of relative move-
ment, and its direction representing the direction of relative movement. A line from
the center to m is the speed vector of the other vessel, its length representing the actual
speed, and its direction the course.

Answers. —C 170%, S 14.7 kn.

It is good practice to continue plotting relative positions of the other vessel until
it has passed. Any change in the direction of the relative movement line indicates a
change of course or speed. After enough positions have been plotted to establish the
new direction of the line, a new solution can be made. If the bearing becomes constant
and the distance is decreasing, the two vessels are on collision courses, and unless
remedial action is taken, a collision will take place. | |

It is good practice to start such a plot at the earliest practicable time, remembering
that if ships are approaching head on, the relative speed is equal to the sum of their in-
dividual speeds. If the situation is seen to be a dangerous one, action can be taken in
time to prevent a close situation. Many accidents are caused by waiting until the vessels
are so close that a change by the other vessel, which may not have radar, brings the
vessels together before there is time to detect the change and take action. Since the
rules of the road regarding passing or crossing are not applicable until the vessels are
in sight of each other, any action based upon radar information before the other vessel
is sighted is in harmony with the law. Unless the intentions of the other vessel are
known, it is good practice to prevent his close approach, if possible, by taking bold

action early. j !
Example 3.—The “own ship” of examples 1 and 2 is capable of a maximum speed

328 DIRECTION AND DISTANCE BY ELECTRONICS

E E — — M: pi.
SCALES | FAO et

pb
AS A | mp ORE A A

— SO

C209 9

SPEED 3
LL " P A AAA Al Relativa

MANEUVERING BOARD

(p: Werrington gei May, 1920. a M

Now Publication: 4t Ed. Apr, 1938 Ath. den, Api 1988

Figure 1212b.— Finding course and speed of other vessel, by relative plot.

of 16 knots. It is decided that at 1521 full speed will be used, and the course will be
changed to prevent the ships from approaching closer than 3,000 yards.

Required.—The new course. i

Solution (fig. 1212c).—Find the relative position of the other ship at 1521. "This
can be estimated from the previous plot, or determined accurately by connecting the
relative speed (13.5 knots) on the bottom line of the nomogram with three minutes on
the top line, and noting the point at which this line crosses the center line (1,350 yards),
or mathematically, taking % the relative distance covered in eight minutes. The rela-
tive distance (1,350 yards) is measured off along the relative movement line from the
1518 position. From this point draw a new relative movement line tangent to the
3,000-yard circle. From m on the speed vector diagram, draw a line parallel but in
the direction opposite to the new relative movement line. Label the intersection of this
line and the 16-knot speed circle 7^. A line from the center to this point is the speed
vector of own ship. Its direction is the required course.

Answer.—C 134°.

DIRECTION AND DISTANCE BY ELECTRONICS 329

The minimum speed at which the desired result can be obtained may be found by
drawing a perpendicular from the center to the relative speed vector zim. The direction
of this perpendicular is the course at minimum speed. For this problem the values
(not shown in the illustration) are 14.4 knots on course 160°. ' Since the relative speed
vector would then be very short (the ships would be on nearly parallel courses at nearly
the same speed), the distance between ships would change slowly. If the relative speed
is known, the time to cover any relative distance can be found by nomogram or
by arithmetic.

A number of variations of this problem may suggest themselves. With practice,
one can acquire the ability to make approximate solutions mentally. Such mental
solutions should be checked by plot. This is particularly important if the bearing is
changing slowly. It is good practice to have the plot kept by one person who can
observe the changing relationship as the vessels proceed. However, one should keep in
mind the fact that although a plot adds to the value of radar, it is not a magic solution
to all radar problems. It may not reflect small changes in course, and its indications
are not instantaneous.

EAN

er scales and read

MANEUVERING BOARD [tc SE
er pad of 50) a

Pesca 75 cents (i

Figure 1212c.— Finding course at given speed to produee desired result, by relative plot.

330 DIRECTION AND DISTANCE BY ELECTRONICS

1213. Shoran is a form of secondary radar (art. 1108) using two transponder
beacons located ashore and a single indicator aboard ship to measure the distance from
each beacon. By this means two distances are continually available, permitting rapid
determination of position. Special charts are not needed, but where they have been
provided, they show a number of concentric circles centered upon each beacon. Approxi-
mate positions can be plotted by inspection.

Shoran was developed during World War II to permit bombing through undercast.
It provided such high accuracy that after the war it was further developed for possible
use insurveying. Its use permitted measurement of distances over water or inaccessible
terrain, thus providing means for more accurate positioning of offshore islands and
other features inaccessible by previous methods.

The name shoran was derived from short range navigation. A higher precision
version used to meet the most exacting survey requirements is called hiran, from high
precision shoran. Because of the high frequency used (230-310 mc), shoran is limited
in range by the curvature of the earth. A lower frequency (1,900 ke) version permitting
use by ships at distances of several hundred miles from shore was developed by the
U. S. Coast and Geodetic Survey and called electronic position indicator (EPI). A
British system similar to shoran, but with transmitters at the fixed ground stations and
a transponder beacon at the mobile station, is known as oboe.

Since these systems provide simultaneous measurement of two distances, the
difference in the two measurements might be used to provide a hyperbolic system (ch.
XIII). However, for the use generally made of such equipment, the need for estab-
lishing hyperbolas would be a disadvantage.

1214. Pure-range Raydist measures distance electrically by phase comparison of
beat frequency signals (art. 1108) resulting from transmission of signals at the two
points between which the distance is to be measured. This method has had limited
use, primarily in survey operations.

Hyperbolic Raydist is discussed in article 1311.

Problems

1204. The DR position of a ship is lat. 44?08/2S, long. 62°56/9W. A radio bear-
ing is taken on Isla Leones Light Station, at lat. 45%03/037 S, long. 65?36/33" W.
The uncorrected reading is 03975 relative, the ship being on true heading 205° at the
moment the bearing is observed. The calibration table indicates a correction of (—)
2° should be applied.

Required.—The equivalent true rhumb line bearing.

Answer.—B 24325.

1212a. A ship on course 230°, speed 15 knots, obtains the following radar bearings
and ranges of another vessel at the times indicated:

Time Bearing Range

0820 2155 24.0 mi.
0824 21575 23.4 mi.
0828 21625 22.8 mi.
0832 217 22:9 mm
0836 218? HIY
0840 219° 21.2 mi.

Required.—( 1) The nearest approach of the two vessels.
(arde he bearing of the other vessel at the point of nearest approach.
(3) Direction of relative movement (DRM).

DIRECTION AND DISTANCE BY ELECTRONICS 331

(4) Speed of relative movement (SRM).

(5) Time of arrival at the point of nearest approach.

(6) Course and speed of the other vessel.

Answers.—(1) D 10.6 mi.; (2) B 278°; (3) DRM 009°; (4) SRM 9.7 kanas (m
1033; (6) C 270°, S 10 kn.

1212b. At 0848 the other vessel of problem 1212a changes course to 034% and
increases speed to 20 knots.

Required.—(1) The nearest approach of the two vessels if both maintain course
and speed.

(2) New relative speed.

(3) Time of arrival at point of nearest approach.

Answers.—(1) D 0 (collision), (2) SRM 34.6 kn., (3) T 0923.

1212c. At 0858 the “own ship” of problem 1212b changes course to the right,
coming to the course that will result in a nearest approach of five miles without changing
speed.

Required.—(1) The new course.

(2) New relative speed.

(3) Time and distance at which “own ship” will be dead ahead of the other vessel.

(4) Time of arrival at the point of nearest approach if both vessels maintain
course and speed.

(5) Bearing of the other vessel at nearest approach.

Answers.—(1)'C 278°. (2) SRM 297 kn.; (3) T 0905, D 10.9 mi; (4) ‘TY 0925;
(5) B 152°.

References

Hall, J. S. Radar Aids to Navigation. M. I. T. Radiation Laboratory Series. New
York, McGraw-Hill, 1947.

Penrose, H. E., and Boulding, R. S. H. Principles and Practice of Radar. New
York, Van Nostrand, 1950.

Reintjes, J. F., and Coate, G. T. Principles of Radar. 3rd ed. M. I. T. Radar
School. New York, McGraw-Hill, 1952.

Roberts, Arthur. Radar Beacons. M. I. T. Radiation Laboratory Series. New
York, McGraw-Hill, 1947. i

U.S. Department of the Navy. Radar System Fundamentals. NAVSHIPS 900,016
and 900,017. Washington, 1944.

U.S. Department of the Navy. Radarman 3 de 2. NAVPERS 10144. Washington,
1964.

U.S. Navy Hydrographic Office. Maneuvering Board Manual. H.O. Pub. No. 217.
Washington, U.S. Govt. Print. Off., 1963.

U.S. Navy Hydrographic Office. Radar Plotting Manual. H.O. Pub. No. 257. Wash-
ington, U.S. Govt. Print. Off., 1964.

U. S. Office of Scientific Research and Development. Electronic Navigation Systems.
National Defense Research Committee, Division 13. OSRD Report No. 6279.
Cambridge, Harvard University, 1945.

Wylie, F. J. The Use of Radar at Sea. Institute of Navigation (British). London,
Hollis and Carter, 1952.

SNLVIS ABONVIS „

'e89u19A00 W-NVUOT—'BZOET GUNDIJ

WVu5vIG 35VTHAOO V

O2ILIOMWY

ay!

"uouisod jo sau (Ajuo 4uBiu)
SADMÁNS JO SĻIUJI] [091431094] ET
"uonisod jo saul (4yBiu pup Ap)
SADMPUNOJB jo su [091431034]

GN3931

eon

KK

ør

m m D

332

CHAPTER XIII

HYPERBOLIC SYSTEMS

1301. Introduction.—The principles of hyperbolic systems are discussed in article
1109. The present chapter describes the distinctive features of some of the more
widely used systems.

1302. Loran is a hyperbolic system of navigation by which difference in distance
from two fixed points on shore is determined by measurement of the time interval
between reception of pulse-modulated (art. 1016), synchronized signals from trans-
mitters at the two points. The name loran is derived from long range navigation. Since
16 operates in the 1,750 to 1,950 ke frequency range, both ground waves and sky waves
can be used to provide coverage over an extensive area with relatively few stations.
Since ships do not transmit, they can use loran without breaking radio silence.

Usually, stations of a pair are located from 200 to 400 miles apart, although they
may be as close as 100 miles or as far as 700 miles. At one time several station pairs
separated by distances of 1,000 to 1,400 miles were operated. In this SS loran, sky
waves only were used. Generally, a number of stations are located so as to form a chain,
with all but the end stations in the group being “double pulsing." In most parts of the
coverage area (fig. 1302a), sig-

nals can be received from at ONE-HOP-E

least two pairs of stations, thus 1

making it possible to obtain a "Së vo or vāji

fix by loran alone. N A ARR ve i

` . | S S S M —— — — —— +4

The range at which sig- ONE-HOP-F TWO-HOP-F

nals are received varies mon FIGURE 1302b.—A typical train of loran signals from a single

siderably with kind of signal transmitted pulse.

(ground wave or sky wave),

route of the signal (over land or water), time of day, atmospheric noise level, geo-
graphie region, ionospheric conditions, and possible directional properties of the
receiving antenna.

As a general rule, ground-wave coverage during the day extends to about 700
miles in the Atlantic and 800 miles in the Pacific. At night the range is about two-
thirds this amount. During daylight hours, relatively few sky-wave signals are received,
but at night, signals arrive by so many different paths that a train of signals may be
received from a single transmitted pulse. Figure 1302b shows a typical scope appear-
ance of such a train near the limit of ground-wave coverage. All of the signals are
from a single transmitted pulse. One-hop-E signals are received to a maximum
distance of about 1,400 miles. Curvature of the earth prevents their reception at
greater distances regardless of power of the transmitter. Beyond this, strong signals
may be received by multihop-E waves or by one or more reflections from the F layer.
Because of relatively large uncertainties in the lengths of the paths of such signals,
and the increased uncertainty of identification, loran tables and charts do not provide
facilities for their use. The extending of lines to provide coverage for such signals is not
recommended. Reception of reliable signals on some occasions is no assurance that
those received at other times can be trusted. Typical variation in appearance of ground-
wave and sky-wave signals with time of day is shown in figure 1302c.

333

334 HYPERBOLIC SYSTEMS

The range at which a ground-wave signal can be received is much less if the path
is across land than if it is across water. For this reason loran stations are located so
that signal paths are as much as possible across water in the direction of greatest
importance, and it is desirable that the base line also be across water. The retarding
effect varies greatly with the type of land, and is somewhat less when the land is not
adjacent to the transmitter. The paths of sky waves are so high that signal strengths
are not noticeably affected by land un-
less it is within about 20 or 30 miles of
the transmitter or receiver.

When the atmospheric noise level is
high, signals which may otherwise be
usable are lost in the clutter.

The areas near the base line exten-
sions are excluded from the diagram of
figure 1302a because of the relatively
large error of position for a small error
in the time difference reading.

Transmitting antennas are vertical,
to avoid directional properties in the hori-
zontal plane. Vertical receiving antennas

1600 local time. 1700 local time. are desirable for the same reason.
Skywave becoming stronger. — stronger than ground wave. Pulse signals from each pair of sta-
tions are transmitted continually. Iden-
tification is by means of frequency and
pulse repetition rate (PRR), sometimes
called pulse recurrence rate. Frequency
is identified by channel number, as follows:

1300 local time.
Skywave visible but weak.

GROUND WAVE

SECOND

4 d 4
52800 local time. |, 1900 local time. A n Channel Frequency
unset. Gain reduce ¡ j
SN Left edge of skywave is fading. No. (ke) No. kc)
1 1950 3 1900

FIGURE 1302c.—Typical variation in appearance 5
of signals with local time. 2 1850

The same frequency can be used for signals from a number of different station
pairs, by varying the rate at which the signals are transmitted. Three basic pulse
repetition rates are available, as follows:

E Lee 20 pulses per second,
Low (Ljósa ul ae e 25 pulses per second,
Bað a a les er second.

The interval between the start of consecutive pulses is 50,000 us for the special
rate, 40,000 us for the low rate, and 30,000 us for the high rate. The special rate is
retained for future use.

A further breakdown of repetition rate can be accomplished by varying the basic
rate slightly. In practice, the difference between consecutive specific pulse repetition
rates is 100 us. The specific rates in use are identified by number, starting with 0
for the basic rate and increasing to 7 (eight rates), each higher number increasing
slightly the rate at which signals are transmitted, and decreasing by 100 us the interval
between signals.

Thus, a total of 24 rates is available (if the special basic rate is used) for each of
the four frequencies. The same rate may be used in areas so widely separated that

HYPERBOLIC SYSTEMS 335

interference is not likely to occur. Each rate is identified by three characters. The
first is a number identifying the frequency channel; the second a letter identifying
the basic pulse repetition rate, and the third a number identifying the specific pulse
repetition rate. Thus, the designation 1L7 indicates frequency channel 1, low basic
pulse repetition rate, and specific pulse repetition rate 7. Stated differently, pulses
are transmitted at intervals of 39,300 us, on a frequency of 1950 ke. The term rate,
implying the number of pulses per unit time, is now used for the full three-character
designation, and even for the station pair, their signals, and the resulting hyperbolic
lines of position and the tables and curves by which they are represented.

The system described in this article is sometimes called standard loran to dis-
tinguish it from a 100 ke or 180 ke experimental system called low frequency loran,
which might provide ground-wave coverage over very great ranges but at reduced
accuracy, and loran-C, an operational system of great range and high accuracy.

1303. The loran receiver-indicator.—The receiver used for loran signals is similar
to that used in ordinary radio communication, except that it has no speaker. Signals
are sent to an indicator consisting of a cathode ray tube (art. 1019) and the necessary
timing circuits and controls. The major portion of the space needed for the equip-
ment is occupied by the indicator.

On the face of the scope a visible line is produced by the spot of light formed at
the point of impact of the moving beam of electrons. This line is divided into two
parts, one above the other. The upper part is called the A trace, and the lower part
the B trace. When the controls are set for a given rate, the length of the combined
trace, in microseconds, is adjusted to the interval between beginning of pulses. "Thus,
if à reading is desired on rate 2H5, separate switches are set on 2, H, and 5 to control
the frequency, basic pulse repetition rate, and specific pulse repetition rate, respectively.
'The combined length of the two traces is then 29,500 ys.

When the controls are thus set for a given rate, the signals of that rate appear as
vertical deflections which remain stationary because a signal is received at the same
part of each trace. Signals of the same basic pulse repetition rate, but of a different
specific pulse repetition rate, appear to drift along the trace. Those of a lower rate
drift to the right and those of a higher rate drift to the left. The greater the difference
between the given rate and that of the signal, the faster the rate of drift.

The drift is due to the difference between the length of the combined trace and
the time interval between the start of consecutive signals. Suppose the indicator is
set for rate 2H3. The length of the combined A and B traces is 29,700 us. A rate 2H2
signal is received at intervals of 29,800 us. The spot of light forming the traces completes
a cycle in 29,700 us and moves an additional 100 us before the next 2H2 signal is
received. Each succeeding 2H2 signal appears 100 us to the right (motion is left-to-
right) of the previous one, and after 297 signals have been received (9 seconds), will
have moved the entire length of both traces and returned to its original position.
Signals of rate 2H5 will move to the left at twice the speed, completing the circuit in
4% seconds. On some scopes a faint line called a retrace (fig. 1304a) can be seen con-
necting the ends of the two traces. This indicates the path of the spot of light in mov-
ing from the end of one trace to the beginning of the next, during a period of about 70
These two periods of 70 us are part of the total length of the combined trace.
Signals of the same frequency but another basic pulse repetition rate can be seen,
but they appear as flickering signals called ghosts, which may drift faster than other
signals. Each succeeding signal appears at a point 10,000 us from the preceding one.
Thus, every third or fourth signal may appear at about the same place, but the rate at
any given place is so slow (approximately six or eight per second) that the deflection
does not appear continuous. Since the spot of light is not deflected in most of its pas-

us.

336 HYPERBOLIC SYSTEMS

CORRECT. RATE GHOST

FIGURE 1303.—A signal of the correct basic FIGURE 1304a.—The loran scope.
pulse repetition rate, and a ghost.

sages, the line appears continuous with the deflection superimposed on it. The appear-
ance of a signal of the correct rate and a ghost is shown in figure 1303.

Strong signals from a frequency channel different from that to which the receiver is
tuned may be received. This is called spillover. It can be detected by tuning to a
different frequency. The frequency at which the signal appears strongest is the
correct one.

1304. A loran reading.—Details of loran receiver-indicators differ, but the prin-
ciples of all are the same. Near the start of each trace of a typical indicator, a portion
of the visible line is raised to form a ped-
estal, as shown in figure 1304a. The ped-
estal of the A trace is fixed, but that of
the B trace can be moved to nearly any
location along the line.

When the entire cycle is shown, as in
figure 1304a, a signal of 40 us duration ap-
pears as a vertical line, as indicated. It
can be moved right or left by means of a
switch which temporarily shortens or
lengthens the trace by a small amount,
causing the signal to drift. After the

Fiaure 1304b.—Two loran signals properl c i e
marched’ DTN ` correct signals have been identified, they

are moved, if necessary, until the signal
on the A trace is to the left of that on the B trace, and mounted near the left edge of
the pedestal. The pedestal of the B trace is moved until the other signal is mounted

near its left edge. By a series of successive magnifications, the left portions of

the two pedestals are placed under each other and made to occupy the entire length of
the original trace. The two traces are then brought to the same horizontal line, and one
signal superimposed over the other, a process called matching. Figure 1304b is a
photograph of a loran scope with signals properly matched, at greatest magnification.
When the signals are matched, they occupy the same position with respect to the two
pedestals. The reading is the distance (time separation) between the two pedestals, indi-
cated by downward deflections of the traces, or by dial. At greatest amplification the
signals appear as in figure 1303 or figure 1304b. |

HYPERBOLIC SYSTEMS Bor

A loran reading is influenced by three delays introduced in the transmission of the
slave signal, as follows:

Half pulse repetition rate delay. A delay equal to half the interval between start
of consecutive pulses is introduced so that one signal can be placed on each trace at
approximately the same relative position. If this were the only delay, and a receiver
were at some point on the center line, one signal would be directly under the other.
Without the delay they would appear at the same place on the same trace. This delay
is introduced for convenience in making a reading, and is not included in the reading.

Base line delay. If the half pulse repetition rate delay were the only one, readings
would increase from zero along the center line to a maximum along each base line
extension. Since both master and slave signals look alike, there would be no way of
identifying them if the position of the receiver was sufficiently in doubt that it might
be on either side of the center line. The base line delay, equal to the length of time
needed for a signal to travel the length of the base line (6.18 us times the length of
the base line in nautical miles), causes the readings to increase from zero along the base
line extension beyond the slave to a value of twice the base line delay along the base
line extension beyond the master station. Because of this delay, the master signal can
never appear to the right of the slave signal if one signal is placed on each trace.

Coding delay. With a reading near zero one might find difficulty at small scale
in determining which signal was left and which was right. An additional delay of
500, 950, or 1,000 us is provided_to increase all readings by this amount. This increases
the distance between the master signal and the slave signal when one is on each trace.
This delay can be changed easily at the slave transmitter according to a prearranged
schedule, to provide some measure of security in time of war.

The reading at any point is equal to 6.18 times the difference in distance (in nautical
miles) of the receiver from the two stations (considered negative if nearer the slave),
plus the base line delay, plus the coding delay. However, it is not necessary for
the navigator to compute readings, because this is done electronically for the whole
coverage area of each rate, and the information given in tables and special charts
(art. 1307).

1305. Identification and use of various waves.—Travel times of ground waves
and various sky waves differ, resulting in reception of a wave train (fig. 1302b) from a
single transmitted signal. Since different readings are obtained with different com-
binations of signals, identification is important.

If a single wave is received, it 1s almost surely a ground wave. If a ground wave
is received as part of a train of waves, it is the first or left-hand wave of the group. The
position of the receiver relative to the transmitter is some guide. Within a few hundred
miles of the station, the first signal is nearly always a ground wave, unless there is in-
tervening land. Near the extreme limit of the coverage area, ground waves are not
received. Between these limits is a critical range in which the first signal may be either
a ground wave or sky wave. ‘This critical range varies with time of day, location, and
conditions, as discussed in article 1302. In general, it can be considered to be between
about 600 and 900 miles by day, and between about 500 and 700 miles by night.

The appearance of the waves can be helpful in their identification. A ground
wave is characteristically steady in shape and amplitude. Sky waves may at times
appear as steady as ground waves, but such steadiness seldom lasts for more than a
few minutes. Because of constant changes in the intensity (reflecting power) and
height of the ionosphere (arts. 1007, 1008), and changing phase relationships, sky waves
are subject to two characteristic fluctuations. ) | l

Changes in intensity, and changing phase relationships, cause changes in the
strength of the reflected signal arriving at the receiver. This is called fading. It may

338 HYPERBOLIC SYSTEMS

be a relatively small change in the amplitude of the signal, or it may be so severe that
the signal disappears altogether for a short time. The complete cycle of fading from
full strength to minimum and back to full strength may be completed in a period of
less than a minute, or it may extend over several minutes.

Changes in height of the ionosphere cause the signal to move right or left along
the trace. This motion is not apparent by itself, and equal changes in those parts
of the ionosphere reflecting signals from the two transmitters has little effect on the
reading. However, a change in intensity may result in shifting the reflecting surface
to a higher level. When there are two or more such surfaces a short distance apart,
splitting of the signal occurs, resulting in more than one crest of the same signal, close
together. As the various reflecting surfaces change in intensity and height, the dif-
ferent crests move up and down relative to each other, and change their spacing.

It is good practice to watch the signals for several minutes before making a reading,
to be sure of their identification and also to be sure that the leading edge of each is
visible, for it is this edge, however weak, that should be matched. In a loran area
the best practice is to make readings at regular intervals, at least once each hour.
The changing appearance with time of day (fig. 1302c) should be helpful in identifying
signals. Also, an inconsistency of one loran fix relative to such a series is an indication
of possible error of identification.

In general, sky waves are steadier at greater distances from the transmitter,
because reflection takes place over a larger area and local variations have less effect,
and also because changes in height have less effect upon the length of the path. There-
fore, the changes are less extreme. One-hop-E waves are usually steadier than multi-
hop-E waves, or those reflected from the F layer (fig. 1302b). Changes in these signals
are so great that intolerably large errors in readings may be introduced. For this
reason and the uncertainty in identification of these waves, it is generally considered
advisable to limit readings to ground waves and one-hop-E waves.

If a vessel is rolling heavily, all signals of a train may fade somewhat in synchronism
with the roll. A weak ground-wave signal may flicker due to random noise signals
which appear as continually-fluctuating grass on the trace. This momentary change
is not easily confused with the slower fading.

For most rates, ground waves should always be matched if available. If ground
waves are available from one station, but not from the other, the one-hop-E sky waves
of both stations should be matched. In general, multihop-E waves and F waves
should not be used. In some instances, where the base line is long, a correction table
is provided for matching a ground wave from one station with a sky wave from the
other. These corrections are given in the Loran Tables, H.O. Pub. No. 221, and in the
Catalog of Aeronautical Charts and Publications, H.O. Pub. No. 1-V.

1306. Accuracy.—The accuracy of a loran fix depends upon the accuracy of the
individual lines of position, and the angle at which the lines intersect (art. 906). The
accuracy of individual lines of position depends upon the following factors:

Synchronization of signals. Transmission of loran signals is continuously monitored.
Normally, the timing is correct to a fraction of one microsecond, but if the signals
get out of synchronization by as much as two microseconds (five microseconds for rate
114), either the master or slave signals, or both, are made to blink to warn the user
of the situation, so that readings on this rate can be avoided until the synchronization
is restored, usually in a matter of minutes. Blinking is the shifting of signals right and
left about 1,000 microseconds, at intervals of two seconds.

Position relative to transmitting stations. Accuracy is related to the spacing between
consecutive lines of position separated by a constant difference of reading, as every
mīčrosecond. Lines are most closely spaced, giving highest accuracy, along the base

HYPERBOLIC SYSTEMS 339

line between the stations, where an error of one microsecond in the reading produces
an error of 0.081 mile, or 492 feet. From this the lines of position fan out, as shown in
figure 1109. Near the base line extensions, an error of one microsecond in the reading
produces an error of several miles in position. Any ground-wave reading within 25
us of those of the base line extensions, or any sky-wave reading within 200 us of those
along these lines, should be considered of doubtful value.

Uncertainty in travel time of signal. The time needed for a signal to travel from
the transmitter to the receiver depends upon the speed and distance. The speed is so
nearly constant that the slight variations involved do not introduce a significant error.
The distance between two points, however, depends upon the path followed by the
wave. Ground waves follow the curvature of the earth with little variation, so that
any error introduced by variations in the path is negligible. This is not true, however,
of sky waves. Continual changes in the height and intensity of the ionosphere, as
well as tilting of it from the horizontal, produce changes in the length of the path of the
radio signal. The increased length of the sky-wave path over the ground-wave path
decreases with greater distance from the transmitter. Along the center line, where the
distance from the two transmitters is the same, the time difference is the same for sky
waves as for ground waves. At other places, signals from one station are delayed
more than those from the other. A sky-wave correction is provided in the loran tables
and on the loran charts to convert a sky-wave reading to the equivalent ground-wave
reading. At distances of 800 miles or more, carefully made sky-wave readings have
an average error of about two microseconds. The error increases as the stations are
approached, reaching an average value of about seven microseconds at a distance of
250 miles from one of the transmitters. This increased error is partly offset by closer
spacing of the lines of position. However, since individual errors can be more than
twice the average, the use of sky waves is not generally recommended within 250 miles
of either station, and corrections for these areas are not usually tabulated.

Skill in making a reading. The principal source of error in making a reading is in
identifying the signals. Patience and judgment are needed to avoid an error due to
use of the wrong wave or failure to detect the true leading edge. With a reasonable
signal-to-noise ratio, a careful operator should be able to match signals and read the
indicator with an error not to exceed one microsecond. With patience, even very
weak signals can be matched with an error of not more than a few microseconds.

Alignment of the indicator. Instructions for checking the “alignment” (adjustment)
of the indicator are included in the instruction manual provided with each loran receiver-
indicator. If the alignment is incorrect, errors may be introduced in the readings.

Incorrect location of transmitters. Computations are made for carefully determined
positions of transmitters. However, where isolated stations require independent position
determinations, the relative positions of the two stations may not be correct, however
carefully determined, because of deflection of the vertical (art. 1610). When errors
are established through usage, correction chartlets are provided in the loran tables
and on loran charts. If the position of one station is found to be in error, the correc-
tions are applicable in radial sectors around that station. If the positions of both
stations are incorrect, the pattern is more involved.

Errors in loran tables and charts. Errors due to imperfections in tables and charts
are negligible. |

Plotting errors. Plotting of loran lines of position requires the same care as plotting
of other navigational information if accurate results are to be obtained. For maximum
accuracy, a large scale should be used. |

1307. Loran lines of position.—Computation of the coordinates of points along
various loran lines of position is performed electronically, allowance being made for

340 HYPERBOLIC SYSTEMS

the spheroidal shape of the earth. The results are published in H.O. Pub. N 0. 221,
Loran Tables. Several rates may be given in each volume, although a change is being
made to publication of each rate in a separate pamphlet. From these computations,
loran charts are prepared showing the lines of position at suitable intervals. Aeronauti-
cal loran charts are available for the entire coverage area, but relatively few nautical
loran charts have been published. In areas where nautical loran charts are not
available, either the tables or aeronautical charts can be used and the information trans-
ferred to the nautical chart.

The loran tables for each rate consist of a small-scale chartlet showing the pattern
of the loran lines of position, and any corrections due to incorrect locations of the
stations, a sky-wave correction table for one-hop-E waves, and the principal table
giving coordinates of points on the lines of position. This table is entered with the
loran reading in microseconds, and the latitude or longitude. For a line running in a
generally north-south direction, the table is entered with the latitude, and the corre-
sponding longitude is taken from the table. For an east-west line, the table is entered
with longitude, and latitude is taken from the table. Two such points are thus deter-
mined and plotted, usually one on each side of the dead reckoning position. The
straight line connecting them is an approximation of a small part of the line of position.
Latitude and longitude are given at intervals of whole degrees, half degrees, or quarter
degrees, depending upon the degree of curvature of the line. A separate column is
given for each tabulated reading, at suitable intervals. An auxiliary tabulation
labeled A (delta) gives the change in longitude or latitude (to 0/01) for a one-micro-
second change in the reading. The main table should be entered with the nearest
reading. If interpolation is toward a smaller reading, the printed sign of A should be
reversed. Sample pages of a loran table are given in appendix BB.

Tabulated readings are for ground waves. Sky-wave readings are corrected to
the equivalent ground-wave readings before entering the tables. A ground-wave
reading is designated Te, and a sky-wave reading Ts. If a ground wave is matched
with a sky wave, the reading is labeled Tas if the ground wave is from the master sta-
tion, and Tsa if from the slave station. A line of position may appropriately be labeled
with the time above the line and the identification below the line. It is good practice
to give full identification, as 2H3 Te 2154 or 1L0 Ts 1893 (Te 1891).

Example 1—The 1900 DR position of a ship is lat. 42?48/3 N, long. 62°28/3 W.
About this time loran readings are obtained, as follows:

1859 1H4 Ts 6258
1900 1H2 T¿ 2229

Reguired.—The 1900 fix, using appendix BB.

Solution.—Enter the sky-wave correction table of 1H4 with the dead reckoning
position, and find the correction, (+)37, by double interpolation (art. P2). x lane
equivalent ground-wave reading is 6258--37—6295. Enter the 6300 column of the
1H4 table, with the following results:

Long. Tab. lat. A Corr. Lat.
622 W 43020 N (+) 56 (—) 2/8 42959'2 N
63° W 42%43'1 N (+)51 CR 42%40'5 N
Next, enter the 2220 column of the 1H2 table, with the following results:
Lat. Tab. long. A Conn Long.
42230" N 62”13'9 W (edis (—)1'6 622123 W
43°00’ N 62933'9 W (16 (—)1'4 62°32'5 W

Plot the two points of each line of position, and draw and label the lines. The
common intersection of the two lines is the required fix, as shown in figure 1307a.

HYPERBOLIC SYSTEMS 341

GN
1900 DR

A O I

`~

wW
o

|

FIGURE 1307a.—A loran fix by table and plotting sheet.

Answer.—1900 fix: L 42?51:0 N, 4 62?26:2 W.

It is good practice to watch the scope for a few minutes before making a reading
to be sure of correct identification of signals. If this is done for all rates before &
reading is made, and sky-wave readings are made first, the intervals between readings
can be kept to a minimum, and a skillful operator can often obtain two or three readings,
over such a short period of time that the run between them can be ignored. However,
where necessary, loran lines of position should be advanced or retired in the same
manner as other lines of position (art. 908). If all readings are made within an in-
terval of a few minutes, as customary, the position is considered a fix, rather than a
running fix, following the practice of celestial navigation (art. 1707) rather than that
of piloting (art. 909).

Figure 1307b is a reproduction, at half scale, of a small part of Hydrographic
Office loran chart VRL-201. This small scale was chosen for illustration because it
shows the pattern of loran lines in an area that is not congested by a large number of
rates. A larger scale is recommended for marine navigation.

The plotted lines are for ground-wave readings. The small numbers near the inter-
sections of printed meridians and parallels are one-hop-E sky-wave corrections at the
intersections. On older charts the rate to which each applies is indicated both
by color and by superscript. Italic type is used for high basic pulse repetition rate
sky-wave corrections, and roman type for the low rate. On newer charts the rate is
indicated in full, and both the rate indication and correction are printed in black
(as 2L7 + 09), as shown in figure 1307b.

Eye interpolation can be used to locate lines between those printed. Graphs
to facilitate such interpolation have been devised. They are available on a card
published by the U. S. Navy Hydrographic Office as H.O. Misc. 11,691, and on some
loran charts. When the correct position has been located, a short line is drawn paral-
lel to the printed lines. The common intersection of the various lines of position,

advanced or retired as necessary, is the fix.

342 HYPERBOLIC SYSTEMS

LOS 1HA

A WË 95555544

bat At
p^ A
=

chart VRL-201, reduced 50%.

dus

1307b.—Part of Hydrographic Office loran

UN x

FIGURE

HYPERBOLIC SYSTEMS 343

Example 2.—The 0600 DR position of a ship is lat. 39°06’ N, long. 126%41' W.
About this time loran readings are made in quick succession, as follows:

0559 2H5 Ty 3205
0600 2H2 Ta 4436
0601 2H3 Ta 3225.

Required.—The 0600 fix, using figure 1307b.

i Solution.—By interpolation, find the sky-wave correction for the 2H5 reading.
This is (+)10 us, making the equivalent ground-wave reading 3205+ 103215 us.

Locate the three readings by eye interpolation and draw short lines of position.
At their common intersection, read the latitude and longitude.

Answer.—0600 fix: L 38°57’ N, ^ 126°20’ Wi

Do not expect high accuracy at such small scale.

Where a number of rates are available, only the three or four most useful ones
may be shown on the chart. Thus, all or part of useful rates in an area may be
omitted. Full information on the reliable coverage areas of all rates is included in
the tables.

1308. Gee is a British hyperbolic navigation system in many respects resembling
loran (arts. 1302-1307). In both systems the difference of the distances from two
transmitters is determined by measurement of the time interval between reception
of synchronized pulse-modulated signals (art. 1016). Gee operates in the 20-85
me frequency range, and is therefore limited essentially to line-of-sight distances.
However, refraction and ducting (art. 1006) sometimes extend the range somewhat,
and sky waves are occasionally available. Because of this line-of-sight feature, the
system is used largely by aircraft. At a height of 30,000 feet the operational range
is considered to be about 400 miles.

Transmitting stations are arranged in groups of four, each group being considered
a chain. One of the four is a master station controlling synchronization of the group.
All stations of a chain operate on the same frequency. Pulses are two to ten micro-
seconds in length. The master transmits at a pulse repetition rate of 500 per second.
Two of the slaves transmit at a rate of 250 pulses per second, being synchronized
with alternate pulses from the master. The third slave transmits at the rate of i
per second, being synchronized with each third pulse from the master. Signals from
the third slave, and each alternate one from the master, consist of two pulses with a
very short interval between them, the two being considered a double pulse constituting
a single unit in the pulse repetition rate. Assuming a difference of 700 us between
reception of the master and synchronized slave signals, the sequence of transmitted
signals would be as shown in figure 1308a. The spacing of signals at the receiver would
depend upon its position relative to the transmitters.

On the scope of the indicator the trace is divided into two parts, as in loran, each
part being 2,000 us in length. When the single-pulse master signal is placed at the
left part of the upper trace, the other signals might appear as shown in figure 1308b.
The first part of the double-pulse master signal would be directly below the single-
pulse master signal. The second part of this double-pulse signal is called a ghost, and
is used only to identify that master signal used with the second slave. It therefore
serves as identification of the first two slaves, which are downward deflections on small
steps serving the same function as the pedestals of loran (art. 1304).

Since the first two slaves transmit at half the rate of the master, one appears on
each trace. Each can be matched with the master signal with which it is synchronized,
permitting two readings to be made with a single setting. Two magnifications are

344 HYPERBOLIC SYSTEMS

provided, one of the strobe (the pedestal-like step) and the other of the central portion
of the strobe. At greatest magnification, correctly matched signals appear as shown
in figure 1308c. The third slave appears alternately on the two traces, but at such
a rate that it seems continuous at both places. It is used only when a check is needed
on the position determined by the first two slaves, or when these do not provide a
reliable fix.

In the gee system, base lines are about 70 to 80 miles long, the appropriate length
for the coverage area. Gee is considered a medium-base-line system. Readings

MASTER
1st SLAVE
2nd SLAVE

3rd SLAVE

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000
p S Ed L OS rat | 1 L E. l 1
Time scale, microseconds

FIGURE 1308a.—Typical sequence of gee signals.

í
Third Slave 1
MASTER

-—-—MASTER CH

First Slave
peFirst Slave MASTER

host j
SÉ att $ | Second * Slave
/ Å í :

Second Slave

FIGURE 1308b.—Typical appearance FIGURE 1308c.—Gee signals correctly
of signals on a gee scope. matched 4

are based upon direct waves. Under good conditions readings can be made with an
error not exceeding 2/3 microsecond. As in other hyperbolie systems, maximum ane
curacy of position occurs along the base line, where a 2/3 Eh difference
represents a distance of 0.054 mile, or 328 feet.

The Germans at one time used gee under the title hyperbol.

1309. Decca Is a British hyperbolic navigation system using phase comparison
for determining difference of distances from the transmitters. Each chain consists of
spe E and three slaves. In the ideal installation the slaves are E anneal
bas, the circumference of a circle 70 to 80 miles in radius, with the master at the

Each stati i j j
ach station transmits a continuous wave at a different frequency, the four fre-

HYPERBOLIC SYSTEMS 345

quencies for a chain being in the ratio 5, 6, 8, and 9, and the entire group being in the
70-130 ke band. In a typical installation the master uses 85 ke and the slaves 70.833,
113.333, and 127.500 kc. For purposes of identification, these slaves are designated
purple, red, and green, respectively.

The receiving unit consists of four receivers, one for each frequency, and circuits
for comparing the phase of each slave signal with that of the master signal. If the signals
are in phase at the time of transmission, they will also be in phase along the center line
of each pair of transmitters. If a receiving unit were at the intersection of the center
line and the base line, zero phase difference would be measured. If the unit then
moved along the base line, the phase of signals from the station approached would
decrease, and that of signals from the other station would increase. At a distance
equal to half the wave length of the comparison frequency (the least common multiple
of the two transmission frequencies), the signals would again be in phase, one signal
being half a cycle less, and the other half a cycle more than at the center line. A line
through all points having this phase relationship would be a hyperbola (assuming a
plane surface). A series of such lines could be drawn, each representing a specific
phase relationship.

Along the base line, the distance the receiving unit would travel from one in-phase
condition to the next would be about 1157, 1446, and 1928 feet, respectively, for the
three slaves operating at the frequencies stated above. The distance between in-phase
hyperbolas becomes greater as the curves fan out from the base line. The area between
any two consecutive in-phase hyperbolas is called a lane. Within each lane all phase-
difference readings are available. The measurement is shown automatically on a dial
called a Decometer, one being provided for each slave. If there were no way of determin-
ing in which lane the receiving unit was located, the position would need to be known
to a high degree of accuracy to resolve the ambiguity. Lane identification is provided
by periodic transmission of signals producing a coarser pattern. At short intervals
each Decometer identifies the lane.

Each Decometer indicates hundredths of a lane width, and a series of Decca
charts having hyperbolas printed in colors agreeing with the identification colors of the
slaves permit determination of position by direct plot, as on loran charts (art. 1307).
Two slaves provide a fix, the third serving as a check and permitting fixing in areas un-
favorable to one of the slaves. To obtain a position, one has merely to read the
Decometers and locate the common intersection of the two or three lines indicated.
There is no manipulation of dials or matching of signals.

Since the reading is to a precision of 0.01 lane width, the theoretical accuracy is
about 12, 14, and 19 feet, respectively, along the base lines between the master and
each of the three slaves. The practical accuracy is considerably less, but still very
good, the average error along the center line being about as follows, according to The
Decca Navigator Company, Ltd.:

Nautical miles from Line of position errors in yards

master station Day Night
100 30 100
150 60 250
200 100 500
250 150 800

American tests indicate a somewhat greater error, with further increase with distance
from the center line. The greater error by night is due to mingling of sky waves and
ground waves. This factor reaches a maximum at a distance of about 350 miles.
Signals of reasonable strength have been received at distances as great as 1,000 miles,

346 HYPERBOLIC SYSTEMS

but the reliable day-and-night range is considered to be 240 miles. Even if good
signals are received at greater distances, good fixes are not available because of the
small angle of intersection of the lines of position, unless readings are taken from
different chains.

Decca coverage extends over much of western Europe and parts of eastern Canada,
the Persian Gulf, and the Bay of Bengal.

1310. Lorac is a hyperbolic system using phase comparison of beat frequencies
(art. 1108) to measure difference of distances from transmitters. Each chain consists
of a central station and two side stations. Some installations also have an additional
station called the reference station. These stations provide two families of curves by
which position can be determined.

The continuous-wave signals from the central station and one of the side stations
are received at the second side station and also at the vessel. At each receiver, the
two signals are combined to obtain a beat frequency signal in the audio frequency .
range (art. 1003). At the second side station, the beat frequency signal is used to mod-
ulate (art. 1016) the carrier wave of the transmitter at that station. This transmitter
then sends a phase wave signal to the vessel. This received phase wave signal is com-
pared with another phase wave signal produced at the vessel. The signal produced at
the vessel is obtained from signals received from the central station and the first side
station. The phase difference of these two phase wave signals varies with the position
of the vessel, and depends on the difference in distances from the central station and
the first side station. Thus, phase differences determine a family of hyperbolas. A
second family of hyperbolas is produced similarly but from signals originated from the
central station and the second side station.

As in Decca (art. 1309), the readings appear automatically and continuously on
dials. Charts showing the lines of position are needed. Because of the frequencies
used, in the 1,700 to 2,500 ke region, the lanes are very narrow, providing accuracies
of the order of three feet along the base lines. However, the system does not provide
a method of lane identification. It is intended primarily for use in surveying, where the
survey vessel starts from a known position. Changes in lane are indicated automatically.

The name Lorac is derived from long range accuracy. It is intended for use
for distances up to 100 to 150 miles Fy day and 75 to 100 miles by night. Accordingly,
the base lines are about 35 miles long. The intended distances are considered long
range for the surveying accuracy claimed.

1311. Hyperbolic Raydist is basically similar to Lorac (art. 1310), but differs in
several respects. Raydist places one of the transmitters at the mobile station (the
vessel), and uses frequency modulation (art. 1016) for relaying the audible signal.
Indication can be provided at either the mobile station or one of the fixed stations,
but a limited number of mobile stations can be accommodated simultaneously. The
frequency range is 1,600 to 2,500 ke, although Raydist can also be used in the 100-150
ke and 30-40 me regions. An accuracy of 25 feet has been attained at 50 miles. Under
favorable conditions readings can be obtained at distances as great as 250 miles. As
with Lorac, hyperbolic Raydist does not provide lane identification.

Pure-range Ravdist is discussed in article 1214.

1312. Consol (art. 1206) is a short-base-line hyperbolic system providing a rotating
pattern of dot-dash signals. Because of the short base line and the long ranges at which
the signals are available, the system is used as a directional one.

1313. Sofar is a hyperbolic system using sound transmissions in the ocean. The
speed of sound in sea water generally decreases with depth until a minimum is reached,

below which the speed increases (art. 3503). The existence of such a minimum-speed

HYPERBOLIC SYSTEMS 347

level permits transmission of sound over great distances, a range of more than 3,000
miles having been achieved. If a sound, as that of an explosion, is created in or near
the minimum-speed level, and microphones are located at the correct depth, a single
signal may be received at several widely spaced listening stations. The differences
in time of reception at these stations define hyperbolas. The origin of the sound can
be located by reference to a chart on which the hyperbolas have been printed. The
name sofar is derived from sound fixing and ranging.

Sofar was developed by the U. S. Navy, for possible use in search and rescue
operations. One set of four sofar listening stations has been installed in the California-
Hawaii area for experimental purposes. A small depth charge, dropped overboard by
the craft, explodes at the proper depth. The time of reception of the signal at the
four stations is automatically timed to an accuracy of about 0.1 second. Comparison
of the times at the various stations provides readings which can be translated into
position. by reference to a sofar chart. Location of the stations is such that position
can be determined within an elongated area about one and one-half miles wide and
four miles long. About 20 minutes are needed for the sound to travel 1,000 miles.
At this distance, a signal is heard over a period of about 12 seconds, gradually building
up intensity to a maximum, with a sharp cut-off announcing the arrival of the direct
signal, the instant of time measurement.

An intervening obstruction such as an island or seamount produces “shadows”
which interfere with reception of sofar signals. One reason for selection of the Cali-
fornia-Hawail area as the site for the first installation is its freedom from obstructions.

Rafos (““sofar” spelled backwards) is the reverse of sofar, sound signals being
produced at the shore stations and the differences in reception times being determined
at the vessel, using a microphone lowered to the correct depth.

1314. Omega is an experimental, very low frequency, hyperbolic navigation
system. The predicted fix accuracy of this system is 0.5 mile or better at a range of
5,000 miles. The basic system will have lanes approximately 15 miles wide over most
of the coverage area. Lane identification can be provided by the use of a second
frequency.

Problems

1307a. The 0630 DR position of a ship is lat. 42%52/2N, long. 62°28'5W. The
ship is on course 330°, speed 20 knots. About this time loran readings are obtained,
as follows: Å
0621 1H4 Ty 6254
0630 1H2 Tau 2193

Required.—The 0630 fix, using appendix BB. (Plot can be made directly on fig.
1307a.)

Answer.—0630 fix: L 42°50!3 N, ^ 62%32'0 W.

1307b. The 2000 DR position of a ship is lat. 35?26' N, long. 125?29' W. About
this time loran readings are made in quick succession, as follows:

1958 2H5 Ts 3115

2000 2H2 Te, 3356
2002 2H3 Te 3523

Required.—The 2000 fix, using figure 1307b.
Answer.—200u fix: L 35?29' N, ^ 128?25' W.

348 HYPERBOLIC SYSTEMS

References

Burmister, C. A. “Shoran in Hydrographic Surveying." International Hydrographic
Review. Vol. XXIV. Monaco, International Hydrographic Bureau, 1947.

Decca Navigator Company, Ltd. Decca Navigator System. London, 1948.

Hall, J. S. Radar Aids to Navigation. M. I. T. Radiation Laboratory Series. New
York, McGraw-Hill, 1947.

Pierce, J. A., McKenzie, A. A., and Woodward, R. H. Loran. M. I. T. Radiation
Laboratory Series. New York, McGraw-Hill, 1948.

Seismograph Service Corporation. Lorac. Tulsa, 1948.

Sonnenberg, G. J. Radar and Electronic Navigation. London, Newnes, 1951

U. S. Office of Scientific Research and Development. Electronic Navigation Systems.
National Defense Research Committee, Division 13. OSRD Report No. 6279.
Cambridge, Harvard University, 1945.

PART FOUR
CELESTIAL NAVIGATION

CHAPTER XIV. Navigational Astronomy
CHAPTER XV. Instruments for Celestial Navigation
CHAPTER XVI. Sextant Altitude Corrections
CHAPTER XVII. Lines of Position from Celestial Observations
CHAPTER XVIII. The Almanac

CHAPTER XIX. Time

CHAPTER XX. Sight Reduction
CHAPTER XXI. Comparison of Various Methods of Sight Reduction
CHaPTER XXII. Identification of Celestial Bodies

PART FOUR

CELESTIAL NAVIGATION

CHAPTER XIV
NAVIGATIONAL ASTRONOMY

Preliminary Considerations

1401. Introduction. —Astronomy is that science which deals with the size, con-
stitution, motions, relative positions, etc., of celestial bodies. Navigational astronomy
is that part of astronomy of direct use to a navigator, comprising principally celestial
coordinates, time, and the apparent motions of celestial bodies with respect to the
earth. Sometimes it is called nautical astronomy. |

1402. Apparent and absolute motions.—All celestial bodies of which man has
knowledge are in motion. Since the earth itself is one of these moving bodies, the
motion of other bodies, as seen by an observer on the earth, is apparent motion. If
the earth were stationary in space, any change in the position of another body, relative
to the earth, would be due only to the motion of that body. "This would be absolute
motion, or motion relative to a fixed point. But since it has been impossible to identify
a fixed point in space, all motion of which man is aware is apparent, made up of a
combination of the movement of the other body and the motions of the observer.
A person without suitable instruments is not aware of motion in the line of sight, and
therefore only motions across the line of sight are observed.

Since all motion is relative, one should be cognizant of the position of the ob-
server when motions are discussed. When one speaks of planets following their orbits
around the sun, he is placing the observer at some distant point in space, usually one
of the poles of the ecliptic (art. 1419). When he speaks of a body rising or setting,
the observer is on the earth. If he refers to a particular rising or setting, he must
locate the observer at a particular point on the earth, since the setting sun for one
observer may be the rising sun for another. At the same time it may be crossing the
meridian of a third observer.

1403. The celestial sphere.—As one looks at the sky on a dark night, he is not
aware of the differences in the distances to the various celestial bodies. They might
easily be imagined as being equally distant from the earth, all located on the inner
surface of a vast hollow sphere of infinite radius, with the earth at its center. This is
the celestial sphere (fig. 1403). For most purposes of navigation it can be considered
an actuality. Since the navigator is concerned primarily with apparent motion for an
observer on the earth, this geocentric universe of Ptolemy (art. 121) is a useful concept.
While the motions of various bodies relative to each other are important to the astrono-
mer who predicts future positions of celestial bodies, and perhaps to the navigational
scientist who designs navigation tables, the navigator speaks of bodies rising, crossing
the celestial meridian, and setting, as though these were absolute motions.

1404. Units of astronomical distance.—The distances between celestial bodies,
even those within a single family such as the solar system, are so great that
terrestrial units are unsatisfactory to express them. The units commonly used for
astronomical distances are:

Astronomical unit (AU), the mean distance between the earth and the sun,
approximately 92,900,000 statute miles. The astronomical unit is often used as a unit

of measurement of distance within the solar system. e
351

352 NAVIGATIONAL ASTRONOMY

Figure 1403.—The celestial sphere.

Light-year, the distance light travels in one year. Since the speed of light is
about 186,000 statute miles per second and there are about 31,600,000 seconds per
year, the length of one light-year is about 5,880,000,000,000 (5.88 10'*) statute miles,
or 63,300 astronomical units. The light-year is commonly used for expressing distances
to the stars and galaxies. Alpha Centauri and its neighbor Proxima, generally con-
sidered the nearest stars, are 4.3 light-years away. Relatively few stars are less than
100 light-years away, and the most distant galaxies thus far observed are 1.6 billion
light-years away. However, most navigational stars are relatively close. Light
travels from the sun to the earth in about 8% min utes, and from the moon to the earth
in about 1% seconds.

Parsec, the distance at which the heliocentric parallax (difference in apparent
position as viewed from the earth and the sun) is 1". At this distance a star would
appear to change its position 2” among the distant stars, if observed from points 180°
apart on the earth’s orbit. The name is derived from the first letters of the words

parallax and second. One parsec is equal to about 3.26 light-years Hence, even the

NAVIGATIONAL ASTRONOMY 353

nearest star is more than one parsec away. This unit is used to express distances to
stars and galaxies.

The difficulty of illustrating astronomical distances and sizes is indicated by the
fact that if the earth were represented by a circle one inch in diameter, the moon would
be a circle one-fourth inch in diameter at a distance of five feet, the sun would be a circle
nine feet in diameter at a distance of nearly a fifth of a mile, and Pluto would be a circle
half an inch in diameter at a distance of about seven miles. The nearest star would be
one-fifth the actual distance to the moon.

1405. Magnitude.—The relative brightness of celestial bodies is indicated by a
scale of stellar magnitudes. In the Almagest (art. 121) Ptolemy divided the stars into
six groups according to brightness, the 20 brightest being classified as of the first mag-
nitude, and the dimmest being of the sixth magnitude. In modern times, when it
became desirable to define more precisely the limits of magnitude, a first magnitude
star was.considered 100 times brighter than one of the sixth magnitude, the approximate
value of Ptolemy’s ratio. Since the fifth root (art. O9) of 100 is 2.512, this number
is considered the magnitude ratio. A first magnitude star is 2.512 times as bright as a
second magnitude star, which is 2.512 times as bright as a third magnitude star, etc. A
second magnitude star is 2.512 < 2.512 =6.310 times as bright as a fourth magnitude star.
A first magnitude star is 2.512%=100*=100,000,000 times as bright as a star of the
twenty-first magnitude, the dimmest that can be seen through the 200-inch telescope.

Brightness is normally tabulated to the nearest 0.1 magnitude, about the smallest
change that can be detected by the unaided eye of a trained observer. In the American
Ephemeris and Nautical Almanac it is given to the nearest 0.01 magnitude, for precise
astronomical purposes. All stars of magnitude 1.50 or brighter are popularly called
“first magnitude" stars. Those between 1.51 and 2.50 are called “second magnitude"
stars, those between 2.51 and 3.50 are called “third magnitude" stars, etc. Sirius, the
brightest star, has a magnitude of (—) 1.6. The only other star with a negative
magnitude is Canopus, (—) 0.9. At greatest brilliance Venus has a magnitude of
about (—) 4.4. Mars, Jupiter, and Saturn are sometimes of negative magnitude.
The full moon has a magnitude of about (—) 12.6, but varies somewhat. The mag-
nitude of the sun is about (—) 26.7.

The Universe

1406. The solar system.—The sun, the most conspicuous celestial object in the
sky, is the central body of the solar system. ` Associated with it are at least nine
principal planets, of which the earth is one; a number of satellites accompanying some
of the planets; thousands of minor planets or asteroids; multitudes of comets; and vast
numbers of meteors.

1407. Motions of bodies of the solar system.—Astronomers distinguish between
the two principal motions of celestial bodies, as follows: rotation is a spinning motion
about an axis within the body, while revolution is the motion of a body in its elliptical
orbit around another body, called its primary. For the satellites, the primary is a
planet. For the planets and other bodies of the solar system, the primary is the sun.
The entire solar system is held together by the gravitational force of the sun. The
whole system revolves around the center of its galaxy (art. 1415) as a unit, and the
galaxy is probably iu motion relative to its neighboring galaxies. The motion of
bodies of the solar system relative to surrounding stars is called space motion. |

Rotation and revolution may be further classified as synodic or sidereal. During
one synodic rotation the body makes one complete turn relative to the sun. On the
earth it is called an apparent solar day. During one sidereal rotation the body makes

354 NAVIGATIONAL ASTRONOMY

one complete turn relative to the stars. Because of motion of the body in its orbit, a
sidereal rotation is either longer or shorter, by a small amount, than a synodic rotation.
If both rotation and revolution are in the same direction (in the solar system they are
both east for most bodies, that is, counterclockwise as seen from above the north pole)
the sidereal rotation is shorter. During a synodic revolution a celestial body makes one
trip around the sun, as viewed from the earth. Hence, the earth cannot have a synodic
revolution. During a sidereal revolution, a celestial body makes one trip around its
orbit with respect to the stars; to an observer on the celestial body, the sun would
appear to make one trip around the celestial sphere, with respect to the stars. On the
earth this is one year.

All of the planets are believed to be in rotation, although this point is in doubt in
the case of Venus and, to a lesser exteat, Mercury. The periods of rotation of these
bodies have not been established because of the absence of visible surface markings of
sufficient constancy to permit measurement. The period of Mercury has been estab-
lished tentatively as 88 days. The rotation of all planets is from west to east, with
the possible exception of Uranus (ü'rà-nüs) (art. 1411).

FIGURE 1407a.—Relative size of planetary orbits.

All of the planets revolve around the sun in nearly circular orbits. The flattening
or eccentricity of the earth’s orbit is only 0.017 (zero would be a circle). Some of the
minor planets have orbits more eccentric than that of any principal planet (note the
orbit of Hidalgo in fig. 1407a). The orbits of comets are highly eccentric. The orbits
of all known planets except Pluto are in nearly the same plane, that of the ecliptic
(art. 1419). The orbit of Pluto is inclined more than 17° to the ecliptic

The laws governing the motions of planets in their orbits were discovered by
Johannes Kepler, and are now known as Kepler’s laws:

1. The orbits of the planets are ellipses, with the sun at a common focus.

2. The straight line joining the sun and a planet (the radius vector) sweeps over
equal areas in equal intervals of time.

3. The squares of the sidereal periods of any two planets are proportional to the cubes
of their mean distances from the sun.

In 1687 Isaac Newton stated three “laws of motion," which he believed were
applicable to the planets. Newton's laws of motion are:

1. Every body continues in a state of rest or of uniform motion in a straight line
unless acted upon by an external force. :

NAVIGATIONAL ASTRONOMY 355

2. When a body is acted upon by an external force, its acceleration is directly pro-
portional to that force, and inversely proportional to the mass of the body, and acceleration
takes place in the direction in which the force acts.

3. To every action there is an equal and opposite reaction.

From Kepler’s laws and his own, Newton fashioned a single universal law of gravita-
tion, which he believed applied to all bodies, although it was based upon observation
within the solar system only:

Every particle of matter attracts every other particle with a force that varies directly
as the product of their masses and inversely as the square of the distance between them.

According to these laws the planets remain in their orbits because of a balance
of forces between the gravitational attraction of the sun and the tendency of the planet
to continue in motion along a straight line. As a planet approaches closer to the sun,
its gravitational attraction increases, but by Kepler’s second law the speed increases,
resulting in stronger centrifugal force. These laws (Newton’s laws of motion) have
been modified very slightly by Albert Einstein’s theory of relativity.

P, (April)
East Ee
Q |
O
PERIHELION
R r * ey ¿E (January)
EN R LINE OF APSIDES Bed SUN] — E )
y» de A \ r
APHELION C) " S

(July)

East SE
)

(October

9.

Figure 1407b.—Orbits of the earth and moon.

‘Both the sun and each body revolve about their common center of mass. Because
of the preponderance of the mass of the sun over that of the individual planets, the
common center of the sun and each planet except Jupiter lies within the sun. The
common center of the combined mass of the solar system moves in and out of the sun.

The various laws governing the orbits of planets apply equally well to the orbit

r with respect to its primary.
ķi SC GE rends that SE nearest the sun is called the perihelion. ; That
point farthest from the sun is called the aphelion (á-fe'le-ón). The line joining perihelion
and aphelion is called the line of apsides (āp'si:dēz). In the orbit of the moon,
that point nearest the earth is called the perigee, and that point farthest from the earth
is called the apogee. Figure 1407b shows the orbit of the earth (with exaggerated
eccentricity), and the orbit of the moon around the earth.

356 NAVIGATIONAL ASTRONOMY

1408. The sun is the dominant member of the solar system because its mass is
nearly a thousand times that of all other bodies of the solar system combined. It
supplies heat and light to the entire system. |

The diameter of the sun is about 866,000 miles. At the distance of the earth, varying
between 91,300,000 and 94,500,000 miles, the visible diameter is about 32’, : At the
closest approach early in January the sun appears largest, being 32:6 in diameter.
Six months later the apparent diameter is 31'5, the minimum.

Of the various physical features of the sun, one of particular interest is the appear-
ance from time to time of sun spots on the surface (fig. 1408). These spots are appar-
ently areas of cooler gas which have risen to the surface and appear dark in contrast
: to the hotter gases around them. In size
they vary from perhaps 50,000 miles in
diameter to the smallest spots that can be
detected (a few hundred miles in diameter),
and perhaps smaller. They generally ap-
pearin groups. At the start of each cycle
of about 11 years the spots appear at a
maximum distance of about 40? on each
side of the solar equator. Succeeding
spots of the cycle appear progressively
closer to the solar equator, until a mini-
mum solar latitude of 5? may be reached.
The maximum number of sun spots occurs
about midway in the cycle, when the spots
are about 16? from the solar equator.
The present cycle began in 1954, and
should reach maximum activity late in
1959, with à new cycle beginning about
1965. Large sun spots can be seen with-
out a telescope if the eyes are protected,
as by the shade glasses of a sextant. Sun
spots have magnetic properties. For one
cycle all spots north of the solar equator
are of positive polarity, and all those to
the south are of negative polarity. Dur-

Courtesy of Mt. Wilson and Palomar Observatories. ing the next cycle, which may begin before

Figure 1408.—Whole solar disk and an enlarge- the last spots of the old cycle have disap-

ment of the great spot group of April 7, 1947. peared, the polarity isteversed? (aie spots

are related to magnetic storms which adversely affect radio, including radio aids

to navigation, on the earth. At such times the auroras (art. 2526) are particu-
larly brilliant and widespread.

The sun rotates on its axis, the period of rotation varying from about 25 days at
the solar equator to 34 days at the poles, but this fact has little or no navigational
significance beyond its effect upon the changing positions of sun spots relative to the
earth. The sun is moving approximately toward Vega at about 12 miles per second,
or about two-thirds as fast as the earth moves in its orbit around the sun. The path
of the sun toward Vega is called the sun’s way. This is in addition to the motion of
the sun around the center of its galaxy (art. 1415).

1409. Planets.—The principal bodies having nearly circular orbits around the
sun are called planets, from a Greek word meaning "wandering." They were so named
because they were observed to change position or “wander” among the “fixed stars"

NAVIGATIONAL ASTRONOMY 357

which remained in about the same positions relative to each other. Because the sun
and moon had a similar wandering motion, the ancients considered them planets, also.

Nine principal planets are known. In order of increasing distance from the sun,
these are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.
Of these, only four are commonly used for celestial navigation. These are Venus,
Mars, Jupiter, and Saturn, sometimes called the navigational planets. The two planets
with orbits smaller than that of the earth are called inferior planets, and those with or-
bits larger than that of the earth are called superior planets. The four planets nearest
the sun are sometimes called the inner planets, and the others the outer planets.
Jupiter, Saturn, Uranus, and Neptune are so much larger than the others that they
are sometimes classed as major planets. Neptune and Pluto are not visible to the
unaided eye, and Uranus is barely so, being of the sixth magnitude.

The orbits of the many thousand tiny minor planets lie chiefly between the orbits
of Mars and Jupiter.

Six of the planets are known to have satellites, a total of 31 having been discovered.
Mercury, Venus, and Pluto have no known satellites.

Various items of general interest regarding the planets are given in appendix F.

1410. The earth as a planet.—In common with other planets, the earth rotates on
its axis and revolves in its orbit around the sun. These actual motions (discussed in
articles 1416 and 1417) are the principal source of the apparent motions of other celes-
tial bodies. Also, the rotation of the earth results in a deflection of water and air
currents to the right in the northern hemisphere and to the left in the southern hemi-
sphere. Because of the earth’s rotation, the high tides on the open sea lag behind the
meridian transit of the moon.

For most navigational purposes, the earth can be considered a sphere, but, like the
other planets, the earth is approximately an oblate spheroid, or ellipsoid of revolution,
being flattened at the poles and bulged at the equator. Therefore, the polar diameter
is less than the equatorial diameter, and the meridians are slightly elliptical, rather
than circular. The dimensions of the earth are recomputed from time to time, as
additional and more precise measurements become available. Since the earth is not
exactly an ellipsoid, results differ slightly when equally precise and extensive measure-
ments are made on different parts of the surface. Hence, different “spheroids” are
used for mapping various parts of the earth. That used for charts of North America
was computed by the English geodesist A. R. Clarke in 1866. However, since Clarke
did not clearly define his units, the U. S. Coast and Geodetic Survey in 1880 considered
it desirable to adopt standard values which probably added about 170 feet to the
diameter computed by Clarke. In 1880, also, Clarke himself made a new estimate of
the size and shape of the earth but this has not been adopted by the United States.
Although the Clarke spheroid of 1866 is still used for charting North America, the
International Spheroid, based upon work done by Hayford in 1909-10, is considered
a slightly better approximation of the size and shape of the earth. According to these
calculations, the dimensions of the earth are:

Equatorial diameter (2a) =7,926.694 statute miles=6,888.110 nautical miles

Polar diameter (26) =7,900.004 statute miles=6,864.918 nautical miles
Mean diameter =7,917.797 statute miles=6,880.379 nautical miles
2(a—b) = 26.690 statute miles= 23.192 nautical miles
a—b 2(a—b) 2600 Za LOZA
Oblateness— 7 —- 24 —7,926.694'' 6,888.110 297

The mean diameter is the average of the polar diameter and two p. diameters
: : : 2 (2a +
perpendicular to each other (the three dimensions of the solid), or ee

358 NAVIGATIONAL ASTRONOMY

Because of unequal distribution of mass near the surface of the earth, the direction
of gravity is tilted slightly at various places. The amount of tilt is called deflection
of the vertical (art. 1610). If the surface of the spheroid is altered so as to be everywhere
perpendicular to the direction of gravity, the earth is considered a geoid.

The average density (ratio of mass of the earth to mass of an equal volume of water)
is 5.517. This is greater than that of any other planet, as far as is known (the density
of Pluto has not been determined). The total mass is about 6,600,000,000,000,000,000,000
(6.6 10%) short tons. Virtually all statements regarding the interior of the earth are
matters of conjecture, but it is believed that the density increases from about three at
the surface to about ten at the center, where the temperature is believed to be close to
5,0009 F. The earth is generally considered to be composed of a solid shell several
hundred miles thick surrounding a molten interior, but there is some evidence to sup-
port the belief that it is solid throughout.

Since gravity acts approximately toward the center of the planet, the direction `
“up” varies with the observer, being nearly perpendicular to the spheroid at all places.
In general, gravity increases with latitude, because both the distance from the center of
the earth and the centrifugal force decrease.

One of the conditions considered essential to life on any celestial body is the exist-
ence of an atmosphere. Whether or not a body has an atmosphere depends at least
partly upon its velocity of escape, or the speed the molecules of the gas making up the
atmosphere must attain to overcome the force of gravity. The velocity of escape of
the earth is about 6.94 statute miles per second, at the surface, and decreases slowly
with distance from the earth. Since the molecules of the earth’s atmosphere rarely
exceed this value for a sufficiently long time to escape, the earth has lost relatively
little of its atmosphere. The velocity of escape is approximated by a space ship leaving
the earth.

The total mass of air surrounding the earth is 5,800,000,000,000,000 (5.8 1015)
short tons. This is less than a millionth part of the mass of the entire earth. The
average pressure exerted by this envelope of air is 14.696 pounds per square inch. The
pressure decreases rapidly with altitude. About half of the atmosphere is within 18,000
feet (about 3.5 miles) of the surface. Breathing begins to be labored at 10,000 feet.
Twilight extends to about 50 miles. Meteors generally appear at about 50 miles.
Auroral phenomena may be as low as 40 miles, and may extend as high as above 500
miles (fig. 1410).

The lower portion of the atmosphere, the troposphere, is composed of the following
elements, in addition to dust and water vapor:

Element Percent

Nitrogen 78.08

Oxygen 20.95

Argon 0.93

Carbon 0.03

Neon 0.0018

Helium 0.000524

Krypton 0.0001

Hydrogen 0.00005

Xenon 0.000008

Ozone 0.000007 (increasing with altitude)
Radon 0.000000000000000006 (decreasing with altitude)

To the precision given, the first four elements total 99.9 percent.

>
Z
=
Z
©
D
E
Y
4
H
<
Z
©
H
<
[45]
kel
>
z

ALTITUDE IN MILES

span
que2nju2oN `

Orgia

434V1 3. ` i
SLHOII NN3HInOS
Snvauisnv vaounv

'SIHOM NUJHLION
| snvadog VIOYNV

U3AY1 «dx

(856 1) 4310W
IW OG PC -sei[eios

343HdSONOI

/

(
W e d 3sn vdONOI

N

(Z-A Wou payounb7)
g jpsodioD YM 460000000"

343HdSOS3W
UOOW YHM
ļDĻUOJ JPPPY
ISNVIOSIW

SHEI Get |

|

360 NAVIGATIONAL ASTRONOMY

The atmosphere is considered to be composed of several distinctive layers, as
follows (fig. 1410):

Height

Layer Kilometers 4 Statute miles Upper limit
Troposphere 0-11 0-6.8 Tropopause
Stratosphere 11-32 6.8-19.9 Stratopause
Chemosphere 32-80 19.9-45.7 Chemopause
Ionosphere 80-400 45.7-248.5 Ionopause
Mesosphere 400-1000 248.5-621.4 Mesopause
Exosphere Above 1000 Above 621.4

In addition to providing life-sustaining oxygen, the atmosphere makes the earth a
more habitable place by holding the moisture that produces rain, preventing an ex-
cessive change of temperature of several hundred degrees between day and night,
shielding the surface from an overdose of cosmic rays, providing a medium to permit
sound to occur, and providing the sky and cloud coloring that adds beauty to man’s
surroundings. If there were no atmosphere, stars would shine with a steady light
day and night, the sky would be black, complete darkness would prevail in shadows,
and there would be no twilight. It is the atmosphere that produces the refraction
which causes celestial bodies to appear elevated in the sky (art. 1613).

1411. Other planets and the minor planets.—Mercury in some ways resembles the
moon more than it does other planets. Its diameter is only about 50 percent larger than
that of the moon and about the same as those of Jupiter’s two largest satellites. Like
the moon it has little or no atmosphere, and is believed to keep the same side turned
toward its primary. Mercury’s mass is only four percent that of the earth, and its
orbit is so small that the planet is never seen more than about 28° from the sun. It
is for this reason that Mercury is not commonly used for navigation. Near greatest
elongation (art. 1422) it appears near the western horizon after sunset or the eastern
horizon before sunrise. At these times it resembles a first magnitude star, and is
sometimes reported as a new or strange object in the sky. As seen from the earth,
Mereury goes through all the phases of the moon, and occasionally transits (crosses)
the face of the sun, appearing as a tiny, dark, inconspicuous dot on the surface. Mer-
cury has no known satellite. |

Venus, like Mercury, has no known satellite, goes through the various phases of
the moon, and may transit the sun. In size of orbit, sidereal period of revolution,
diameter, volume, mass, density, and surface gravity it resembles the earth more than
any other planet. Its orbit is more nearly circular than that of any other planet
(eccentricity 0.007). At maximum brilliance, about five weeks before and after inferior `
conjunction (art. 1422), it has a magnitude of about (—)4.4 and is brighter than
any other object in the sky except the sun and moon. At these times it can be seen
during the day, and is sometimes observed for a celestial line of position. The surface
of the planet has not been observed because it is covered by a layer of dense clouds or
gases. Its period of rotation is believed to be of the order of four or five weeks.

Mars (fig. 1411) has a diameter only a little more than half that of the earth, and a
mass of 11 percent as much, although its density is nearly 72 percent that of the earth.
It has a thin atmosphere, but few clouds. Its day is only slightly longer than that
on the earth, but its year is nearly twice as long. Being a superior planet (art. 1409),
it is seen only in the full or gibbous phase (art. 1423). When nearest the earth, its
apparent diameter is about eight times that at conjunction (art. 1422). Mars has
two satellites. Phobos is about ten miles in diameter and has an orbit only about 50
percent greater than the diameter of Mars. To an observer on Mars it would appear
about a third as large as the moon does to an observer on the earth, and would appear

NAVIGATIONAL ASTRONOMY 361

to rise in the west and set in the east, going through three-fourths of its cycle of phases
while above the horizon. It would do this twice each day, since its sidereal period of
revolution is only about half the period of rotation of Mars. No other natural satellite
is known to revolve faster than its primary rotates. Deimos is only about five miles in
diameter, and at greatest brilliance would appear as a very bright star. About two
days would elapse between rising and setting, during which it would go through the
various phases twice.

Jupiter (fig. 1411), largest of the known planets, has more than twice the mass of all
other known planets combined. Its density is low and its rotation fast (9"50™), resulting
in a pronounced equatorial bulge. It is believed to have a dense, solid core, sur-
rounded by lighter material, and a deep atmosphere of ammonia, methane, helium,

JUPITER

Courtesy of Mt. Wilson and Palomar Observatories.

Ficure 1411.— Mars, Jupiter, Saturn, and Pluto. First three photographed with 100-inch
telescope, Pluto with 200-inch telescope.

and hydrogen. Two of Jupiter's twelve known satellites are about the same size as
Mercury, and may have atmospheres. 'The four outermost satellites revolve from
east to west, opposite to the general direction of revolution within the solar system.
Saturn (fig. 1411) is the only planet having a density less than that of water, yet it
has a mass of nearly one-third that of Jupiter, and nearly three times that of all other
known planets combined. Its composition is believed to be similar to that of
Jupiter. It is more oblate than any other known planet. Perhaps the most inter-
esting feature of this planet is its rings, composed of a great number of small solid
particles spread out in three thin, flat rings more than 170,000 miles in diameter. The
particles nearest the planet revolve more rapidly than those farther out, the innermost
ones completing a revolution in less time than the planet completes a rotation. During
half the 29.5-year sidereal period of revolution of the planet one side of the rings 1s

362 NAVIGATIONAL ASTRONOMY

visible to observers on the earth, and during the second half of the period the opposite
side is visible. Saturn has nine known satellites, the outermost one of which revolves
from east to west. Ë , ;

Uranus is barely visible to the unaided eye, being of the sixth magnitude. It is
a comparatively large planet, and probably is similar in composition to Jupiter and
Saturn. The inclination of the equator of Uranus to the plane of the ecliptic is 98°, or
82° if the revolution is considered from east to west. Its five known satellites, all
small, revolve in the equatorial plane, in the same direction as that of rotation of the
planet. Á

Neptune is slightly smaller than Uranus, but has greater mass, and a longer period
of rotation. Relatively little is known of this remote planet of the eighth magnitude.
However, it is known to have two satellites, the larger (probably bigger than the
moon) revolving from east to west.

Pluto (fig. 1411) was identified in 1930. It is of the 15th magnitude, and cannot .
be seen in small telescopes. In all but the 200-inch telescope it appears as a point of light.
Its diameter is less than half that of the earth. Its orbit is the most eccentric and has
the greatest inclination to the ecliptic of any of the known planets. At perihelion it
is closer to the sun than Neptune, and there is some evidence to support the view that
it was at one time a satellite of the larger planet.

Minor planets. About 1,500 of these tiny planets have been discovered, but it is
estimated that there may be as many as 40,000 bright enough to be seen by the largest
telescopes, when they are nearest the earth. The largest, Ceres, has a diameter of
about 480 miles. All but a few are less than 100 miles in diameter. Since there is
no known lower limit, there may be no distinction between minor planets and meteors.
The combined mass of all minor planets probably does not exceed 0.1 percent that of the
earth. The orbits, of various degrees of eccentricity and inclination to the ecliptic,
lie mostly between those of Mars and Jupiter. However, at perihelion some of the
minor planets are inside the earth’s orbit. The orbit of Hidalgo is shown in figure 1407a.

1412. The moon is the only satellite of direct navigational interest, although the
satellites of Jupiter were at one time used to determine Greenwich mean time, so that
longitude could be found (art. 126). The rotation and revolution of the moon are
both west to east, and both are of the same duration, 2707"43"115 with respect to
the stars (the sidereal month) and 2912"44"02s8 with respect to the sun (the
synodical month). Because there is no difference in the periods of rotation and revolu-
tion, the same side of the moon is always turned toward the earth. However, about 59
percent of the moon's surface has been seen, due to libration. Libration in latitude
occurs because the axis of rotation is tilted about 6?5 with respect to the axis of revolu-
ton. Libration in longitude occurs because the speed of revolution varies in accordance
with Kepler's second law (art. 1407), while the rotational speed is essentially constant.
Diurnal libration occurs because of the changing position of the observer relative to
the moon, due to rotation of the earth. Physical libration is a small pendulum-like
rotational oscillation of the moon with respect to its radius vector.

At perigee the moon is about 221,000 statute miles from the earth's center, and
at apogee it is about 253,000 miles distant. The average distance is about 238,862
miles. Because of the relative nearness of the moon, its geocentric parallax (difference
in position relative to the background of stars, as observed from the surface and center
of the earth) is comparatively large. It is a maximum when the moon is on the
horizon, when it is called horizontal parallax. The equatorial horizontal parallax for
an observer at the equator, where the maximum radius of the earth is involved, is
tabulated in the Nautical Almanac and the American Ephemeris and Nautical Almanac,
and used in sextant altitude corrections given in the nautical and air almanacs. The

NAVIGATIONAL ASTRONOMY 363

parallax varies from a maximum at the horizon to zero at the zenith. The parallax at
any altitude is sometimes called parallax in altitude. The apparent diameter of the
moon is approximately the same as that of the sun, but varies through wider limits.
Because the moon is so near, the radius of the earth is an appreciable percentage of the
distance between earth and moon, and the apparent diameter of the moon increases a
measurable amount as its altitude increases (decreasing the distance from the observer).
This apparent increase is called augmentation (fig.
1412). A similar effect for the sun is very small.

As with the planets and sun, the moon and
earth both revolve around their common center of
mass, which is about 2,900 miles from the center of
the earth. It is this center of mass that describes
the orbit of the earth (and moon) around the sun.

Because of its relative nearness and size, the
moon is the principal source of the gravitational
attraction that causes tides, although the sun has
an appreciable effect, also. The action of these
bodies in causing tides is described in article 3103.
Because of the frictional action of tides, the rotation
of the earth is slowing, the length of the day in-
creasing about 08001 per century.

On the moon, the day is equal in length to the
synodical month (about 29% days). The earth would
remain almost stationary in the sky for an observer
on the 41 percent of the moon’s surface always visible
from the earth, would rise and set at about the
same point on the horizon for one on the 18 percent
which is sometimes visible, and would never appear
for one on the 41 percent not seen from the earth.

Because of the relatively low velocity of escape
(art. 1410) on the moon, 1.49 miles per second, this
satellite has lost virtually all of its atmosphere, if it
ever had one. Even water vapor is nonexistent, in-
dicating an absence of water on the moon. Since
there is practically no atmosphere, there is no sound,
no twilight, and the temperature change between
day and night is sudden and large, changing from
perhaps (+) 200? F or more by day to about (—) 250°
F by night. The sky is black and stars would be
visible in broad daylight. Without water or air the
moon has no clouds, no rain, no wind, no life. The Figure 1412.—Augmentation.
numerous conspicuous “craters” are probably the
results of meteor falls. There is no atmosphere to slow the meteors, and no erosion
to erase the marks they leave. The “seas” are relatively flat plains. Some of the
mountains are high, the maximum height on the visible side being nearly 30,000 feet.
Gravity on the surface of the moon is about one-sixth that on the surface of the earth.
The mass of the moon is about % that of the earth. The diameter of the moon 1s
2,160 miles. The size of the moon relative to the earth is greater than that of any
other satellite relative to its planet.

1413. Comets and meteors.—Comets are swarms of relatively small, widely
separated, solid bodies held together by mutual attraction. Around this nucleus, a

364 NAVIGATIONAL ASTRONOMY

Halley’s Comet
in 1910

May 15

May 23 June 3 June © June 9 June 11

Courtesy of Mt. Wilson and Palomar Observatories.
FIGURE 1413.—Halley’s Comet; fourteen views, made between April 26 and June 11, 1910.

more spectacular, gaseous head or coma and tail may form as the comet approaches
the sun. The tail is directed away from the sun, so that it follows the head while the
comet is approaching the sun, and precedes the head while the comet is receding. The
total mass of a comet is very small, and the tail is so thin that stars can easily be seen
through it. In 1910 the earth passed through the tail of Halley’s comet (fig. 1413)
without noticeable effect.

Comets are erratic and inconsistent. Some travel east to west and some west to
east, in highly eccentric orbits inclined at any angle to the ecliptic. "The shortest
period of revolution is about 3.3 years. Some periods are so long that astronomers
speculate as to whether some comets may not come in from outside the solar system
for a single trip around the sun, and then leave the solar system, never to return. In
such a case the orbit would be approximately a parabola (art. 034).

Without their tails, which exist only when near the sun, comets are not spectacular.
Because of the small size of their nuclei, which shine by reflected light from the sun,
comets are visible for only a small part of their period of revolution, and this is the
part of most rapid motion, in accordance with Kepler’s second law (art. 1407). An
average of about five comets is observed each year, and about two-thirds of these are
identified as previously observed comets. Very few comets are ever visible without
a telescope. The spectacular Halley’s comet reached aphelion in 1948 and started
back toward the sun. It is expected to reach perihelion about February, 1986.

NAVIGATIONAL ASTRONOMY 365

Because of the great distances of the aphelion of some comets, a few astronomers
have speculated that additional planets may exist beyond Pluto. This curiosity is
heightened by the attempt of some astronomers to identify a family of comets with
orbits of nearly equal size, similar to those associated with Jupiter, Saturn, Uranus, and
Neptune. Massive planets may influence the orbits of comets, particularly at great
distances from the sun.

Meteors, popularly called shooting stars, are tiny, solid bodies too small to be
seen until heated to incandescence by air friction while passing through the earth’s
atmosphere. A particularly bright meteor is called a fireball. One that explodes is
called a bolide. A meteor that is not consumed during its fall through the atmosphere,
but lands as a solid particle, is called a meteorite. These are composed principally of
iron, with some nickel, and smaller quantities of other material.

Vast numbers of meteors exist. It has been estimated that an average of about
1,000,000 bright enough to be seen enter the earth’s atmosphere each hour, and many
times this number undoubtedly enter, but are too small to attract attention. A faint
glow sometimes observed extending upward approximately along the ecliptic before
sunrise and after sunset has been attributed to the reflection of sunlight from quantities
of such material. This glow is called zodiacal light. A faint glow at that point of the
ecliptic 180° from the sun is called the gegenschein or counterglow. Comets may be
an assemblage of a large number of meteors traveling together, and minor planets (art.
1411) may be larger meteors. Meteor showers occur at certain times of the year when
the earth is believed to be passing through meteor swarms, the scattered remains of
comets that have broken up. At these times the number of meteors observed is many
times the usual number.

Since such large amounts of this material are in existence, much of it in an orbit
near the ecliptic, and since the orbits of most minor planets lie between those of Mars
and Jupiter, where.astronomers compute the orbit of another planet should be located,
it is possible that another planet may have existed there at one time and been disrupted,
perhaps by an atomic explosion of hydrogen or other material. The estimated total
mass of all meteors, comets, and minor planets would make a small planet, but if the
material which has fallen on other planets and satellites, and perhaps some or all of the
satellites themselves, are added, a sizeable planet might be accounted for.

1414. Stars are distant suns, in many ways resembling the body which provides
the earth with most of its light and heat. Even the nearest star is too distant to be
seen as more than a point of light in the largest telescope. If planets, satellites, comets,
etc., accompany those distant suns, as they do the one nearby, they have not been
detected. However, comparatively dark companions of planetary size are known to
accompany some stars. Nonluminous stars may exist, since most of the radio stars
(points from which radio energy emanates) are not marked by a body visible to observers
on the earth. The distance of the stars is so great that none is known to have a helio-
centric parallax (difference in apparent position as observed from the earth and the sun)
of as much as 1”.

Stars differ in size from gaseous giants having diameters greater than that of the
orbit of the earth, to dense dwarfs which may be no larger than the major planets.
Although the size and density cover wide ranges, the mass does not differ greatly.
Relatively few stars have more than five times or less than one-fifth the mass of the
sun, which is also about average in size, density, and temperature. The color pone
with the temperature. A very hot star, having a surface temperature of perhaps 20,000
K (Celsius absolute) or more, is bluish-white; while a cooler star, having a temperature
of perhaps 2,000° K, is faintly reddish. In Orion, blue Rigel and red Betelgeuse,
located on opposite sides of the belt, constitute a noticeable contrast.

366 NAVIGATIONAL ASTRONOMY

Under ideal viewing conditions, the dimmest star that can be seen with the unaided
eye is of the sixth magnitude. In the entire sky there are about 6,000 stars of this
magnitude or brighter. Half of these are below the horizon at any time. Because of
the greater absorption of light near the horizon, where the path of a ray travels for a
greater distance through the atmosphere, not more than perhaps 2,500 stars are visible
to the unaided eye at any time. The 200-inch telescope on Palomar Mountain permits
stars as dim as the twenty-first magnitude to be seen. It has been estimated that
there are about 1,000,000,000 of this magnitude or brighter. A long-term photographic
exposure with the 200-inch telescope permits observation of about twice this number.
There is no indication that this is more than a tiny fraction of the total number. How-
ever, the average navigator seldom uses more than perhaps 20 or 30 of the brighter
stars. Stars which exhibit a noticeable change of magnitude are called variable stars.
A star which suddenly becomes several magnitudes brighter and then gradually fades
is called a nova. A particularly bright one is called a supernova. k

Two stars which appear to be very close together are called a double star. If
more than two stars are included in the group, it is called a multiple star; and if a
large number appear in approximately spherical shape, it is called a globular cluster.
A group of stars moving through space together, but not exhibiting the intimate
relationship of a globular cluster, is called an open cluster. The Pleiades and some
stars. of the big dipper (with certain other stars) are examples of open clusters. A
group of stars which appear close together, regardless of actual distances, is popularly
called a constellation, particularly if the group forms a striking configuration. Among
astronomers a constellation is now considered a region of the sky having precise bound-
aries so arranged that all of the sky is covered, without overlap. The ancient Greeks
recognized 48 constellations covering only certain groups of stars. Modern astron-
omers recognize 88 constellations. The constellation names and meanings are given in
appendix I.

A cloudy patch of matter in the heavens is called a nebula (plural nebulae). If it
is within the galaxy of which the sun is a part, it is called a galactic nebula; if outside,
it is called an extragalactic nebula.

Stars rotate on their axes, and revolve around the center of their galaxy, in addition
to influencing and being influenced by surrounding stars. Motion of a star through
space, like that of any celestial body, is called space motion. That component in the
line of sight is called radial motion; while that component across the line of sight,
causing a star to change its apparent position relative to the background of more
distant stars, is called proper motion.

1415. Galaxies.—A great number of the nebulae have been identified as extra-
galactic, and as telescopes became more powerful, it was discovered that these small
cloudy patches are groups of stars, in many ways resembling the group of stars of which
the sun is a part. Each such vast assemblage of stars constitutes an island universe as
widely separated from others, comparatively, as individual stars in one group. Such
2 group is called a galaxy. It was not until well within the twentieth century that the
sun was recognized as a part of such a galaxy, the Milky Way. In a galaxy the stars
tend to congregate in groups called star clouds arranged in long spiral arms. The spiral
nature is believed due to revolution of the stars about the center of the galaxy, the inner
stars revolving more rapidly than the outer ones (fig. 1415). At the position of the
pus abont mod hirds of the way out from the center, and nearly midway between

top” and bottom, ’ the period of revolution is about 200,000,000 years at the present
speed of about 175 miles per second. This is nearly ten times the speed of the earth in
its orbit. An average estimate of the size of a galaxy is that it is about 100,000 light

NAVIGATIONAL ASTRONOMY 367

years in diameter, 15,000 light
years thick at the center, and
5,000 light years thick near the
outer edge, and that it contains
perhaps 100,000,000,000 stars.
This is about 100 times the
number of stars that can be seen
through the 200-inch telescope.
Within the radius of 1,600,000,-
000 light years that man is able
to penetrate there are perhaps
100,000,000 galaxies, although
only a small fraction of this num-
ber has been actually observed.
The galaxies which have
been discovered are observed
to congregate in groups, some-
what similar to stars in a
galaxy. Whether the part seen
is but a small portion of a
larger an o vast to be seen FIGURE 1415.—Spiral nebula Messier 51, in Canes Venetici.
with present instruments has Satellite nebula is NGC 5195.
not been established. Develop-
ment work is being done to attempt to adapt the electron microscope for use with
the telescope. By this means man hopes to see much more of what surrounds him
in space, and perhaps to answer some of the questions which confront him.

Courtesy of Mt. Wilson and Palomar Observatories.

Apparent Motion

1416. Apparent motion due to rotation of the earth is much greater than any other
observed motion of celestial bodies. It is this motion that causes celestial bodies to
appear to rise somewhere along the eastern half of the horizon, climb to maximum
altitude as they cross the meridian, and set along the western horizon, at about the
same point relative to due west as the rising point was to due east. This apparent motion
along the daily path, or diurnal circle, of the body is approximately parallel to the plane
of the equator. It would be exactly so if rotation of the earth were the only motion,
and the axis of rotation of the earth were stationary in space (arts. 1417 and 1419).

The apparent effect due to rotation of the earth varies with the latitude of the ob-
server. At the equator, where the equatorial plane is vertical (since the axis of rotation
of the earth is parallel to the plane of the horizon), bodies appear to rise and set verti-
cally. Every celestial body is above the horizon approximately half the time. The
celestial sphere as seen by an observer at the equator is called the right sphere, shown in
figure 1416a. Several unique relationships of the right sphere are discussed in article 1432.

For an observer at one of the poles, bodies having constant declination neither
rise nor set (neglecting precession of the equinoxes and changes in refraction), but circle
the sky, always at the same altitude, making one complete trip around the horizon
each day. At the north pole the motion is left to right, and at the south pole it is
right to left. Approximately half the stars are always above the horizon and the other
half never are. This is modified somewhat by actual conditions, a description of which
is given in chapter XXV. The parallel sphere at the poles is illustrated in figure
1416b.

368 NAVIGATIONAL ASTRONOMY
Zenith
North Pole
Declination 60% N

Zenith

Declination 22-5. N

Equator

5 N

South Celestial Eguator Horizon

Pole

North Horizon

Pole

Declination 60% N
Declination 60°S

Declination 23

Celestial

Declination 60° S

Nadir Nadir

5 South Pole
FIGURE 1416a.—The right sphere.

FiGurRE 1416b.—The parallel sphere.

Between these two extremes, the apparent motion is a combination of the two.
On this oblique sphere, illustrated in figure 1416c, circumpolar celestial bodies remain
above the horizon during the entire 24 hours, circling the elevated celestial pole (art.
1426) each day. The stars of the big dipper and Cassiopeia are circumpolar for many
observers in the United States. An approximately equal part of the celestial sphere
remains below the horizon during the entire day. The southern cross is not visible
to most observers in the United States. Other bodies rise obliquely along the eastern
horizon, climb to maximum altitude at the celestial meridian, and set along the western
horizon. The length of time above the horizon, and the altitude at meridian transit,
vary with both the latitude of the observer and the declination of the body. Several
useful relationships of the oblique sphere are indicated in article 1432. The relative
portions of the celestial sphere that remain either above or below the horizon varies
with the latitude, from none at the equator to 100 percent at the poles. At the polar
circles (art. 1419) of the earth and beyond, even the sun becomes circumpolar. This
is the land of the midnight sun, where the sun does not set during part of the summer,
and does not rise during part of the winter.

This increased obliquity at higher latitudes explains why days and nights are
always about the same length in the tropics, and the change of length of the day be-
comes greater as the latitude increases. It also explains why twilight lasts longer in
higher latitudes. Twilight is that period of incomplete darkness following sunset and
preceding sunrise. Evening twilight starts at sunset, and morning twilight ends at
sunrise. The darker limit of twilight occurs when the center of the sun is stated
number of degrees below the celestial horizon. Three kinds of twilight are defined,
depending upon the darker limit. These are:

Twilight Lighter limit Darker limit At darker limit
civil 0° —6° Horizon clear and bright stars visible
nautical 0° 12% Horizon vague
astronomical 0° Ss Full night

The conditions at the darker limit are relative and vary
atmospheric conditions.

In figure 1416d the twilight band is shown,
kinds indicated.

considerably under different

| with the darker limits of the various
The nearly vertical celestial equator line is for an observer at latitude

NAVIGATIONAL ASTRONOMY 369

Zenith
S2 S
E E N
/ d x
À Ex. i
Pi
/ S A
14 S A \
/ j ye

/ ð À
j Ah \
| e \

Horizon

sag] Civil
me Nautical
Astronomical

Nadir Nadir
FIGURE 1416c.—The oblique sphere at Freure 1416d.— The various twilights at lat.
lat. 40? N. 20? N and lat. 60? N.

20°N. The nearly horizontal celestial equator line is for an observer at latitude 60? N.
The broken line in each case is the diurnal circle of the sun when its declination is
15°N. The relative duration of any kind of twilight at the two latitudes is indicated
by that portion of the diurnal circle between the horizon and the darker limit, although it
is not directly proportional to the relative length of line shown, since the projection is
orthographic (art. 319). The duration of twilight at the higher latitude is longer,
proportionally, than shown. Note that complete darkness does not occur at latitude
60? N when the declination of the sun is 15? N.

1417. Apparent motion due to revolution of the earth.—If it were possible to
stop the rotation of the earth so that the celestial sphere would appear stationary,
the effects of the revolution of the earth would become more noticeable. In one
year the sun would appear to make one complete trip around the earth, from west to
east. Hence, it would seem to move eastward a little less than 1? per day. This
motion can be observed by watching the changing position of the sun among the stars.
But since both sun and stars generally are not visible at the same time, a better way
is to observe the constellations at the same time each night. On any night a star
rises nearly four minutes earlier than on the previous night. "Thus, the celestial sphere
appears to shift westward nearly 1? each night, so that different constellations are
associated with different seasons of the year.

Apparent motions of planets and the moon are due to à combination of their
motions and those of the earth. If the rotation of the earth were stopped, the combined
apparent motion due to the revolutions of the earth and other bodies would be similar
to that occurring if both rotation and revolution of the earth were stopped, as discussed
in article 1418, but with different timing. Stars would appear nearly stationary in
the sky, but would undergo a small annual cycle of change due to aberration. The
motion of the earth in its orbit is sufficiently fast to cause the light from stars to
appear to shift slightly in the direction of the earth's motion. This is similar to
the illusion one has when walking in rain that is falling vertically, but appearing
to come from ahead due to his own motion. The apparent direction of the light
ray from the star is the vector difference (art. O18) of the motion of light and the
motion of the earth, similar to that of apparent wind on a moving vessel (art. 3709).
This effect is most apparent for a body perpendicular to the line of travel of the earth

370 NAVIGATIONAL ASTRONOMY

in its orbit, for which it reaches a maximum value of 20" 5. The effect of aberration
can be noted by comparing the coordinates (declination and sidereal hour angle)
of various stars throughout the year. A change is observed in some bodies as the
year progresses, but at the end of the year the values have returned almost to what
they were at the beginning. That they do not return exactly is due to proper motion
(art. 1418), precession of the equinoxes (art. 1419), and nutation, which is an irregular-
ity in the motion of the earth due to the disturbing effect of other celestial bodies,
principally the moon. Eulerian motion is a slight wobbling of the earth about its axis
of rotation, often called polar motion, and sometimes wandering of the poles. This
motion, which does not exceed 40 feet from the mean position, produces slight variation
of latitude and longitude of places on the earth.

By the calendar, one year is of 365 days duration for common years and 366 days
for leap years. A leap year is any year divisible by four, unless it is a century year,
which must be divisible by 400 to be a leap year. Thus, 1900 was not a leap year, but
2000 will be. "This calendar, now in general use, is called the Gregorian calendar.
Astronomically, the year is not divisible into a whole number of days, and the present
system will introduce an error of three days in about 10,000 years. The length of the
year with respect to the vernal equinox (art. 1419) is about 365 days, 5 hours, 48
minutes, 46 seconds. This is the tropical, astronomical, equinoctial, natural, or solar
year. Since the vernal equinox is in motion on the celestial sphere (art. 1419), this
does not quite agree with the sidereal year of about 365 days, 6 hours, 9 minutes, 10
seconds, with respect to the stars. The period of revolution from perihelion to perihelion,
about 365 days, 6 hours, 13 minutes, 53 seconds, is called the anomalistic year. "These
values vary slightly from year to year, and progressively over the years, as shown in
appendix D.

1418. Apparent motion due to movement of other celestial bodies.—Even if it
were possible to stop both the rotation and revolution of the earth, celestial bodies
would not appear stationary on the celestial sphere. The moon would make one
revolution about the earth each sidereal month (art. 1412), rising in the west and
setting in the east. The inferior planets would appear to move eastward and westward
relative to the sun, as explained in article 1422, staying within the zodiac. Superior
planets would appear to make one revolution around the earth, from west to east, each
sidereal period (app. F).

Since the sun (and the earth with it) and all other stars, as far as is known, are in
motion relative to each other, slow apparent motions would result in slight changes of
the positions of the stars relative to each other. This space motion (art. 1414) is, in
fact, observed by telescope. That component of such motion across the line of sight,
called proper motion, produces a change in the apparent position of the star. The
maximum which has been observed is that of “Barnard's Star," which is moving at the
rate of 1073 per year. This is a tenth-magnitude star, and hence not visible to the
unaided eye. Of the 57 stars listed on the daily pages of the almanacs, Rigil Ken-
taurus has the greatest proper motion, about 3"7. Arcturus, with 273, has the greatest
proper motion of the navigational stars in the northern hemisphere. In a few thousand
years proper motion will be sufficient to materially alter some familiar configurations
of stars, notably the big dipper.

1419. The ecliptic is the path the sun appears to take among the stars due to the
annual revolution of the earth in its orbit. It is considered a great circle of the celestial
sphere, inclined at an angle of about 23°27’ to the celestial equator, but undergoing a
continuous slight change. This angle is called the obliquity of the ecliptic. This
inclination is due to the fact that the axis of rotation of the earth is not perpendicular
to its orbit. It is this inclination which causes the sun to appear to move north and

NAVIGATIONAL ASTRONOMY 371

south during the year, giving the earth its seasons, and changing lengths of periods of
daylight. This seasonal variation is one of the factors making the earth a desirable
place on which to live.

Refer to figure 1407b. The earth is at perihelion early in January and at aphelion
six months later. On or about June 21, about ten or eleven days before reaching
aphelion, the northern part of the eartb's axis is tilted toward the sun. The north polar
regions are having continuous sunlight; the northern hemisphere is having its summer
with long, warm days and short nights; the southern hemisphere is having winter with
short days and long, cold nights; and the south polar region is in continuous darkness.
This is the summer solstice. Three months later, about September 23, the earth has
moved a quarter of the way around the sun, but its axis of rotation still points in
about the same direction in space. The sun shines equally on both hemispheres, and
days and nights are the same length over the entire world. The sun is setting at the
north pole, and rising at the south pole. The northern hemisphere is having its
autumn, and the southern hemisphere its spring. This is the autumnal equinox. In
another three months, on or about December 22, the southern hemisphere is tilted
toward the sun and conditions are the reverse of those six months earlier, the northern
hemisphere having its winter, and the southern hemisphere its summer. This is the
winter solstice. Three months later, when both hemispheres again receive equal
amounts of sunshine, the northern hemisphere is having spring and the southern hemi-
sphere autumn, the reverse of conditions six months before. This is the vernal equinox.

The word “equinox,” meaning “equal nights,” is applied because it occurs at the
time when days and nights are of approximately equal length all over the earth. The
word “solstice,” meaning “sun stands still,” is applied because the sun stops its apparent

Summer
Solstice

QD (June)

Winter Solstice

[Í
(March)

b

Ficure 1419a.— Apparent motion of the sun in the ecliptic.

312 NAVIGATIONAL ASTRONOMY

northward or southward motion and momentarily “stands still” before it starts in the
opposite direction. This action, somewhat analogous to the “stand” of the tide (art.
3104), refers to the motion in a north-south direction only, and not to the daily apparent
revolution around the earth. Note that it does not occur when the earth is at peri-
helion and aphelion (fig. 1407b). Refer to figure 1419a. At the time of the vernal
equinox, the sun is directly over the equator, crossing from the southern hemisphere to
the northern hemisphere. It rises due east and sets due west, remaining above the
horizon about 12 hours. It is not exactly 12 hours because of refraction, semidiameter,
and the height of the eye of the observer. These cause it to be above the horizon a little
longer than below the horizon. Following the vernal equinox, the northerly declina-
tion increases, and the sun climbs higher
in the sky each day (at the latitudes of
the United States), until the summer
solstice, when a declination of about 23°27’
north of the celestial equator is reached.
The sun then gradually retreats southward
until it is again over the equator at the
autumnal equinox, at about 23°27’ south
of the celestial equator at the winter
solstice, and back over the celestial equa-
tor again at the next vernal equinox.

The sun is nearest the earth during
the northern hemisphere winter. Hence,
it is not the distance that is responsible
for the difference in temperature during
the different seasons. The reason is to be
found in the altitude of the sun in the sky
- SEA i and the length of time it remains above
5 == S > the horizon. During the summer the rays

F ==> are more nearly vertical, and hence more
concentrated, as shown in figure 1419b.
Faure 1419b.—Sunlight in summer and winter. Since the sun is above the horizon more

A UE rini s m a same than half the time, heat is being added by
absorption during a longer period than it
is being lost by radiation. This explains the lag of the seasons. Following the longest
day, the earth continues to receive more heat than it dissipates, but at a decreasing
proportion. Gradually the proportion decreases until a balance is reached, after which
the earth cools, losing more heat than it gains. This is analogous to the day, when the
highest temperatures normally occur several hours after the sun reaches maximum
altitude at meridian transit, and for the same reason. A similar lag occurs at other
seasons of the year. Astronomically, the seasons begin at the equinoxes and solstices.
Meteorologically, they differ from place to place.
By Kepler’s second law, the earth travels faster when nearest the sun, as shown
in figure 1419c. Hence, the northern hemisphere (astronomical) winter is shorter than
its summer, the difference being about seven days.
Everywhere between the parallels of about 23°27’N and about 23227/8 the sun
is directly overhead at some time during the year. Except at the extremes, this occurs
twice, once as the Sun appears to move northward, and the second time as it moves
southward. This is the torrid zone. The northern limit is the tropic of Cancer, and

December 22

NAVIGATIONAL ASTRONOMY 373

the southern limit the tropic of Capricorn. These names come from the constellations
which the sun entered at the solstices when the names were first applied, more than
2,000 years ago. ‘Today, the sun is in the next constellation toward the west, because
of precession of the equinoxes, described below. The parallels about 23°27’ from the
poles, marking the approximate limits of the cireumpolar sun, are called polar circles,
the one in the northern hemisphere being the arctic circle and the one in the southern
hemisphere the antarctic circle. The areas inside the polar circles are the north and
south frigid zones. The regions between the frigid zones and the torrid zones are
the north and south temperate zones.

The expression “vernal equinox,” and associated expressions, are applied both to
the times and points of occurrence of the various phenomena. Navigationally, the vernal
equinox is sometimes called the first point of Aries, because, when the name was given,
the sun entered the constellation Aries, the
ram (T), at this time. This point is of
interest to navigators because it is the
origin of measurement of sidereal hour
angle (art. 1426). The expressions March
equinox, June solstice, September equinox,
and December solstice are occasionally
applied as appropriate, because the more
common names are associated with the
seasons in the northern hemisphere, and
are six months out of step for the southern
hemisphere.

The axis of the earth is undergoing a
precessional motion similar to that of a top
spinning with its axis tilted. In about d l
25,800 years the axis completes cyclosnd Fort. Kepler second law. Ringe the
returns to the position from which it start- greater than at aphelion.
ed. Since the celestial equator is 90° from
the celestial poles, it too is moving. The result is a slow westward movement of the
equinoxes and solstices, which has already carried them about 30%, or one constel-
lation, along the ecliptic from the positions they occupied when named more than 2,000
years ago. Since sidereal hour angle (art. 1426) is measured from the vernal equinox,
and declination (art. 1426) from the celestial equator, the coordinates of celestial
bodies would be changing even if the bodies themselves were stationary. This westward
motion of the equinoxes along the ecliptic is called precession of the equinoxes (fig.
14192). The total amount, called general precession, is about 50727 per year (in 1958).
It may be considered divided into two components, precession in right ascension (about
46"10 per year) measured along the celestial equator, and precession in declination
(about 20705 per year) measured perpendicular to the celestial equator. The annual
change in the coordinates of any given star, due to precession alone, depends upon its
position on the celestial sphere, since these coordinates are measured relative to the polar
axis while the precessional motion is relative to the ecliptic axis (art. 1429).

Due to precession of the equinoxes, the celestial poles are describing circles in the
sky. The north celestial pole is moving closer to Polaris, which it will pass ata distance
of approximately 28’ about the year 2102. F ollowing this, the polar distance will
increase, and eventually other stars, in their turn, will beome the pole star. Similarly,
the south celestial pole will some day be marked by stars of the false southern cross.

374 NAVIGATIONAL ASTRONOMY

1420. The zodiac is a circular band of the sky extending 8° on each side of the
ecliptic. The navigational planets and the moon are within these limits. The zodiac :
is divided into 12 sections of 30° each, each section being given the name and symbol
(“sign”) of the constellation within it. These are shown in figure 1420. The complete
list of signs and names is given in appendix A.

The sun remains in each part for approximately one month. When the names were
assigned, more than 2,000 years ago, the sun entered Aries (T) at the vernal equinox,
Cancer (93) at the summer solstice, Libra (=) at the autumnal equinox, and Capricornus
(13) at the winter solstice. Even though this is no longer true because of precession
of the equinoxes, The American Ephemeris and Nautical Almanac still lists the sun as
entering these constellations at the times of the equinoxes and solstices, for this has

Figure 1420.— The zodiac.

come to be their principal astronomical significance. The pseudo science of astrology
assigns additional significance, not recognized by scientists, to the positions of the sun and
planets among the signs of the zodiac.

1421. Time.—Traditionally, astronomy has furnished the basis for measurement
of time, a subject of primary importance to the navigator. The year is associated
with the revolution of the earth in its orbit. The day is one rotation of the earth
about its axis.

The duration of one rotation of the earth depends upon the external reference point
used. One rotation relative to the sun is called a solar day. However, rotation relative
to the apparent sun (the actual sun that appears in the sky) does dot provide time of
uniform rate, because of variations in the rate of revolution and rotation of the earth
The error due to lack of uniform rate of revolution is removed by using a fictitious mean
sun. Thus, mean solar time is nearly equal to the average apparent solar time. Because

NAVIGATIONAL ASTRONOMY 310

the accumulated difference between these times, called equation of time, is continually
changing, the period of daylight is shifting slightly, in addition to its increase or decrease
in length due to changing declination. Apparent and mean suns seldom cross the
celestial meridian at the same time. The earliest sunset (in latitudes of the United
States) occurs about two weeks before the winter solstice, and the latest sunrise about
two weeks after winter solstice. A similar apparent discrepancy occurs at the summer
solstice.

With an increase in precision of the instruments used for measuring the rotation
of the earth, it became apparent that the speed of rotation is not constant, increasing
slightly during the northern hemisphere spring, and decreasing during the opposite
season. Other changes, more erratic, are also noted. These are in addition to the
slowing due to tidal action (art. 1412), and are not fully explained. These changes
have led the International Bureau of Weights and Measures to adopt the year
as the basic unit for time, rather than the day, so that daily irregularities can be reduced
or eliminated. Time based upon uniform division of the year is called ephemeris time.
The atomic clock developed by the U. S. Bureau of Standards provides time which in
some respects is superior to that based upon the daily rotation of the earth, but is
inferior to that based upon the annual revolution of the earth around the sun. This
device is based upon the motion of the atoms of ammonia molecules.

If the vernal equinox is used as the reference, a sidereal day is obtained, and from
it, sidereal time. This indicates the approximate positions of the stars, and for this
reason is the basis of star charts (art. 2204) and star finders (art. 2210). Because of
the revolution of the earth around the sun, a sidereal day is about 3756! shorter than a
solar day, and there is one more sidereal than solar days in a year. One mean solar day
equals 1.00273791 mean sidereal days. Because of precession of the equinoxes, one
rotation of the earth with respect to the stars is not quite the same as one rotation with
respect to the vernal equinox. One mean solar day averages 1.0027378118868 rota-
tions of the earth with respect to the stars.

In tide analysis, the moon is sometimes used as the reference, producing a lunar
day averaging 24^50" (mean solar units) in length, and lunar time.

Since each kind of day is divided arbitarily into 24 hours, each hour having 60
minutes of 60 seconds, the length of each of these units differs somewhat in the various
kinds of time.

Time is also classified according to the terrestrial meridian used as a reference.
Local time results if one's own meridian is used, zone time if a nearby reference meridian
is used over a spread of longitudes, and Greenwich or universal time if the Greenwich
meridian is used.

'The subject of time is discussed in more detail in chapter XIX.

1422. Planetary configurations.—Since the orbit of an inferior planet lies within
that of the earth, the planet and sun are nearly in line twice each synodic period of
revolution of the inferior planet. When the sun is between the earth and the other
planet, that planet is at superior conjunction. When the planet is between the earth
and sun, it is at inferior conjunction. If the orbit of the planet had no inclination to
the ecliptic, the planet would cross or transit the face of the sun at inferior conjunction
and be eclipsed or occulted by the sun at superior conjunction. Occasionally this
does occur.

Refer to figure 1422, showing orbits of the earth, Venus (an inferior planet), and
Mars (a superior planet). As shown, the relative sizes of the orbits are correct, and the
relative sizes of the planets are correct, but the planets are too large for their orbits and
the sun, and the sun is too large for the orbits of the planets. The earth is considered
stationary in its orbit. The positions of Venus are shown at superior and inferior

376 NAVIGATIONAL ASTRONOMY

conjunctions. In moving eastward from one to the other, Venus appears to move to
the left of the sun. As observed from the earth, the angle between lines to the sun and
a planet, particularly an inferior planet, is called the planet’s elongation, which may be
designated east or west to indicate the apparent position of the planet relative to the
sun. As Venus continues along its orbit, its elongation increases slowly until the planet
arrives at the point where a straight line from the earth is tangent to its orbit, when the
elongation becomes maximum. Here it is called greatest elongation east. As Venus
continues along its orbit, its elongation decreases rapidly, becoming zero at inferior
conjunction. Through the second half of its synodic period its elongation increases
rapidly to greatest elongation west, and then decreases slowly to zero at the next

Conjunction
e
Orb;
x Ár
«o | 95.
|
Now
Superior mr
N
st ae? k
S E |
ES
AS 3

Greatest g AG
d | reatest
SE Oy iso Conjunction, Elongation

= West
AE
East ` Pee | katas or West
Sech, RA Ø we

Earth
|

Opposition
Figure 1422.— Planetary configurations.

superior conjunction. The greatest elongation of Venus is about 46°, but varies be-
cause its orbit and that of the earth are elliptical, and the phenomenon occurs at dif-
ferent points on the orbits.

The orbit of the planet Mercury lies inside that of Venus, and hence the greatest
elongation IS not as great, being about 28°. It is because the apparent position of
Mercury is never far from the sun that this planet is not considered navigationally
important. Since lts synodic period of revolution is only 115.9 days, it is at con-
junction a little oftener than once every two months. By dapes Venus Á at

conjunction a little oftener than once ever | | j
| every ten months, having a
revolution of 583.9 days. s aparab ana

NAVIGATIONAL ASTRONOMY 377

As shown in figure 1422, an inferior planet goes through all phases of the moon
p 1229); being full” at superior conjunction, “new” at inferior conjunction, and at
quarter when it reaches greatest elongation. A telescope is needed to see the phases.
For a superior planet the situation is different. Refer again to figure 1422. When
the sun is between the earth and the planet, that planet (Mars in the illustration)
is at conjunction Lo js The adjective "superior" is not needed because a superior planet,
when on the opposite side is away from the sun, or at opposition ( 2) and can never be
at inferior conjunction. When its elongation is 90°, a superior planet is at east or west
quadrature (D), depending upon its apparent position relative to the sun. Since a
superior planet has a longer period of revolution than the earth, it appears to move
westward around the sun, being at conjunction, east quadrature, opposition, west quad-
rature, and back to conjunction. It is at “full” phase at conjunction and opposition,
and gibbous between.

Unless a planet is in the ecliptic, it is not directly in line with the earth and sun
at conjunction and opposition. "These points are defined as those at which either the
sidereal hour angles (art. 1426) or the celestial longitudes (art. 1429) are the same (in
the case of conjunction) or 180? apart (at opposition).

The apparent positions of the planets in relation to other members of the solar
system, particularly the relationships shown in figure 1422, are called planetary con-
figurations. The motions of planets with respect to the sun would be true, generally,
with respect to the stars, also, if the earth were stationary in its orbit, as shown. How-
ever, because of the earth's motion around the sun, the sun appears to move eastward
among the stars. This is usually the direction of apparent motion of the planets, too,
and is called direct motion. When a planet is near opposition or inferior conjunction,
its apparent westerly motion relative to the sun is greater than the apparent easterly
motion of the sun relative to the stars, and the planet appears to move in a westerly
direction relative to the stars. This is called retrograde motion.

The brightest planet in the western sky following sunset is popularly called the
evening star, and the brightest planet in the eastern sky preceding sunrise is popularly
called the morning star.

1423. Phases of the moon.—Relative to the sun, the moon makes one complete
trip around the celestial sphere each synodical month (about 29) days). As it does so,
it goes through a cycle of aspects or phases to an observer on the earth, because the
moon, like the planets, shines chiefly by reflected light from the sun. The orbit of the
moon is inclined about 5? to the ecliptic, and undergoes a precessional motion called
regression of the nodes. It is similar to precession of the equinoxes of the earth (art.
1419), and is chiefly responsible for nutation (art. 1417). However, the cycle is com-
pleted in a little more than 18 years, as compared with about 25,800 years for the earth.

Because of the small inclination of its orbit, the moon is never far from the ecliptic.
At conjunction, when the moon passes nearly between the earth and sun, its illuminated
portion is away from the earth (toward the sun), as shown in figure 1423. (In this illus-
tration, the outer figures show various positions of the moon relative to the earth and
sunlight. The inner circle of moons shows the appearance from the earth.) It is then
a new moon, and may be barely visible because of earthshine, which is sunlight reflected
from the illuminated side of the earth. To an observer on the moon, the “full earth”
would be visible at this time, three and one-half times as great in diameter and nearly 40
times as bright as the full moon appears to an observer on the earth. „Since it is at
conjunction, the new moon rises, transits the celestial meridian, and sets at approximately
the same time as the sun.

A day later the moon has moved about 12?2 eastward of the sun and a thin crescent
appears on the side toward the sun, with the horns or cusps pointing away from the sun.

378 NAVIGATIONAL ASTRONOMY

uu Crescent :

FIGURE 1423.—Phases of the moon. The inner figures of the moon represent its appearance from the earth.

The moon is low in the western sky after sunset. Because of glow from this illuminated
portion, and the fact that the side of the earth toward the moon is not quite “full,”
that part of the moon illuminated by earthshine is not quite as bright. Each day the
moon moves approximately 1272 east, relative to the sun. As it does so, the crescent
grows fatter, and the earthshine less conspicuous.

When the moon reaches quadrature, about a week after new moon, it Is at first
quarter. That half of the moon toward the sun is illuminated. The moon is now about
90° or six hours behind the sun. It rises about noon, is on the celestial meridian about
6 PM, and sets about midnight.

As the moon continues eastward on successive days, the line separating the il-
luminated and dark portions, called the terminator, moves on across the moon. The
moon is now in the gibbous phase, which continues until the moon is at opposition,
or full moon. It now rises about the time of sunset, reaches the celestial meridian
about midnight, and sets about the time of sunrise.

On succeeding days the moon again becomes gibbous, and at quadrature it is at
last quarter, rising about midnight, crossing the celestial meridian about 6 Am, and
setting about noon. During the remainder of its cycle the moon again goes through
the crescent phase and returns to new moon to start another cycle.

During the first half of the cycle, the moon is waxing, and during the second half
it is waning. The elapsed time since new moon, usually expressed as days and tenths

NAVIGATIONAL ASTRONOMY 379

of a day is called age of the moon. Since the moon appears to move eastward relative
to the sun, crossing the meridian later each day, one day each synodical month is without
a moonrise, and another is without a moonset.

The times of moonrise and moonset indicated above are approximate only. When
the difference between the declination of the sun and moon is considerable, the times
given may be in error by as much as several hours, particularly in high latitudes.
The times of crossing the celestial meridian vary through smaller limits.

At full moon, the sun and moon are on opposite sides of the ecliptic. Therefore,
in the winter the full moon rises early, crosses the celestial meridian high in the sky,
and sets late; as the sun does in the summer. In the summer the full moon rises in
the southeastern part of the sky (northern hemisphere), remains relatively low in the
sky, and sets along the southwestern horizon after a short time above the horizon.

At the time of the autumnal equinox, that part of the ecliptic opposite the sun
is most nearly parallel to the horizon. Since the eastward motion of the moon is
approximately along the ecliptic, the delay in the time of rising of the full moon from
night to night is less than at other times of the year. The full moon nearest the autum-
nal equinox is called the harvest moon. The full moon occurring about a month later
is called the hunter’s moon.

1424. Eclipses.—Because of the inclination of the moon's orbit with respect to
the ecliptic, the sun, earth, and moon are usually not so nearly in line at conjunction
and opposition of the moon that either the earth or moon passes through the shadow
of the other. However, when this does occur, an eclipse takes place. Since the sun
and moon are of nearly the same apparent size to an observer on the earth, an eclipse
is a much more spectacular occurrence than the transit of an inferior planet across
the face of the sun, or the occultation of a star or planet by the sun or moon (art.
1422).

When conditions are suitable, the moon passes between the sun and earth, as
shown in figure 1424a. If the moon’s apparent diameter is larger than that of the sun,
the moon being near perigee, its shadow reaches the earth as a nearly round dot only
a few miles in diameter. The dot moves rapidly across the earth, from west to east,
as the moon continues in its orbit. Within the dot, the sun is completely hidden
from view, and a total eclipse of the sun occurs. For a considerable distance around
the shadow, part of the surface of the sun is obscured, and a partial eclipse occurs. In
the line of travel of the shadow a partial eclipse occurs as the round disk of the moon
appears to move slowly across the surface of the sun, hiding an ever-increasing part of
it, until the total eclipse occurs. Because of the uneven edge of the mountainous
moon, the light is not cut off evenly, but several last illuminated portions appear through
the valleys or passes between the mountain peaks. These are called Baily’s Beads.

oret Moon

cmm : ,
— nr Eclipse Q _

C MEA

Figure 1424a.—Eclipses of the sun and moon.

380 NAVIGATIONAL ASTRONOMY

Courtesy of Mt. Wilson and Palomar Observatories.

FIGURE 1424b.—Solar prominence, 140,000 miles high, photographed in light of calcium.
July 9, 1917. Small white disk shows relative size of earth.

A total eclipse is a spectacular phenomenon. As the last light from the sun is cut off,
the solar corona, or envelope of thin, illuminated gas around the sun, becomes visible.
Wisps of more dense gas may appear as solar prominences (fig. 1424b). The only
light reaching the observer is that diffused by the atmosphere surrounding the shadow.
As the moon appears to continue on across the face of the sun, the sun finally emerges
from the other side, first as Baily's Beads, and then as an ever widening crescent
until no part of its surface is obscured by the moon.

The duration of a total eclipse depends upon how nearly the moon crosses the
center of the sun, the location of the shadow on the earth, the relative orbital speeds
of the moon and earth, and (principally) the relative apparent diameters of the sun
and moon. The maximum length that can occur is a little more than seven minutes.

If the apparent diameter of the moon is less than that of the sun, its shadow does
not quite reach the earth. Over a small area of the earth directly in line with the
moon and sun, the moon appears as a black disk almost covering the surface of the sun,
but with a thin ring of the sun around its edge. This is an annular eclipse, and occurs
a little oftener than a total eclipse.

If the shadow of the moon passes close to the earth, but not directly in line with
it, a partial eclipse may occur without a total or annular eclipse.

An eclipse of the moon occurs when the moon passes through the shadow of the
earth, as shown in figure 1424a. Since the diameter of the earth is about three and
one-half times that of the moon, the earth's shadow at the distance of the moon is much
larger than that of the moon. A total eclipse of the moon can last nearly one and
three-quarters hours, and some part of the moon may be in the earth's shadow for
almost four hours. During a total solar eclipse no part of the sun is visible because a

NAVIGATIONAL ASTRONOMY 381

body (the moon) intervenes in the line of sight. During a lunar eclipse some light
does reach the moon because of diffraction by the atmosphere of the earth, and hence
the eclipsed full moon is visible as a faint reddish disk. A lunar eclipse is visible over the
entire hemisphere of the earth facing the moon. Anyone who can see the moon can
see the eclipse.

During any one year there may be as many as five eclipses of the sun, and always
there are at least two. There may be as many as three eclipses of the moon, or none.
The total number of eclipses during a single year does not exceed seven, and can be as
few as two. There are more solar than lunar eclipses, but the latter are more numerous
at any one place because of the restricted areas over which solar eclipses are visible.

The two points of intersection of the moon’s orbit and the ecliptic are called nodes,
and the line connecting them, the line of nodes. Eclipses occur when the sun, earth,
and moon are nearly on this line, twice each eclipse year of 346.6 days. This is less than
a calendar year because of regression of the nodes (art. 1423). In a little more than
18 years the line of nodes returns to approximately the same position with respect to
the sun, earth, and moon. During an almost equal period, called the saros, a cycle
of eclipses occurs. During the following saros the cycle is repeated with only minor
differences.

Eclipses have considerable value in establishing additional facts about the sun
and moon, and in determining distances between two widely separated points on the
earth, at which accurate timing of the eclipse is made.

Coordinates

1425. Latitude and longitude are coordinates used for locating positions on the
earth. Several types, differing slightly from each other, are defined. Three of these
are discussed here.

Astronomical latitude is the angle (ABQ, fig. 1425) between a line in the direction
of gravity (AB) and the plane of the equator (QQ’). Astronomical longitude is the
angle between the plane of the celestial me-
ridian and the plane of the prime meridian. Worth Po/e

These coordinates are customarily found by A

means of celestial observations. If the earth

were perfectly homogeneous and level, these

positions would be consistent and satisfac-

tory. However, because of deflection of the Q’ Q

vertical (art. 1610) due to uneven distribu-

tion of the mass of the earth, lines of equal

astronomical latitude and longitude are not

circles, although the irregularities are small.

In the United States the prime-vertical com- South Pole

ponent (affecting longitude) may be a little Figure 1425.— Three kinds of latitude at

more than 18”, and the meridional com- point A.

ponent (affecting latitude) as much as 25044
Geodetic latitude is the angle (40Q, fig. 1425) between a normal to the spheroid

(AC) and the plane of the equator (QQ. Geodetic longitude is the angle between the

plane defined by the normal to the spheroid and the axis of the earth, and the plane of

the prime meridian. These values are obtained when astronomical latitude and longi-

tude are corrected for deflection of the vertical. These coordinates are the ones used

for charting, and are frequently referred to as geographic latitude and geographic longi-

382 NAVIGATIONAL ASTRONOMY

tude, although these expressions are sometimes used to refer to astronomical latitude
and longitude.

Geocentric latitude is the angle (ADQ, fig. 1425) between a line to the center of
the earth (AD) and the plane of the equator (QQ’). This differs from geodetic latitude
because the earth is a spheroid, rather than a sphere, and the meridians are ellipses.
Since the parallels of latitude are considered to be circles, geodetic longitude is geocentric,
and a separate expression is not used. The difference between geocentric and geodetic
latitudes is a maximum of about 11/6 at latitude 45°.

Because of the oblate shape of the earth, the length of a degree of geodetic latitude
is not everywhere the same, increasing from about 59.7 nautical miles at the equator
to about 60.3 nautical miles at the poles, as shown by table 6. The value of 60 nautical
miles customarily used everywhere by the navigator is correct at about latitude 45°.

1426. Celestial equator sys-
tem.—Positions on the celestial `
Celestial Pol sphere are located by any of
several sets of coordinates anal-
ogous to latitude and longi-
tude on the earth. The most
directly related system is based
upon the celestial equator (some-
times called equinoctial). This
is the great circle formed on the
celestial sphere by extension of
the plane of the equator of the
earth (fig. 1426a). Declination
(d) is measured northward or
southward from the celestial
l equator, similar to latitude on
Celestial Equator the earth. Like latitude, it is
labeled N or S (sometimes (+)
instead of N and (—) instead
of S) to indicate the direction
of measurement, and has a
maximum value of 90° at the

Figure 1426a.—Declination and sidereal hour angle. north and south celestial poles,
which are directly over corre-
sponding poles of the earth. The celestial pole above the horizon is called the elevated
pole, and that below the horizon the depressed pole. The angular distance from a
celestial pole, usually the elevated pole, is called polar distance (p). Polar distance is
90° minus declination if the body is between the celestial equator and the pole; other-
wise it is 90° plus declination. A circle of the celestial sphere, parallel to the plane
of the celestial equator, is called a parallel of declination. This would be the diurnal
circle (art. 1416) of a body having constant declination.
A great circle through the celestial poles and the zenith (art. 1428) of an observer
is his celestial meridian (fig. 1426b). That half which includes his zenith, and ends
at the celestial poles, is called the upper branch. The other half is the lower branch.
A reference to a celestial meridian is generally understood to mean the upper branch
unless the lower branch is specified. The celestial meridian remains stationary over
a meridian on the earth, and does not participate in the daily apparent rotation of the
celestial sphere. A similar great circle of the celestial sphere, but related to a point
on that sphere, or to a celestial body, is called an hour circle or circle of declination

Declination
MÆ

i Sidereal Hour Angle D

NAVIGATIONAL ASTRONOMY 383

(fig. 14262). The hour circle through the point vertically above an observer coincides
with his celestial meridian.

The hour circle through the vernal equinox (art. 1419) is used as a reference
somewhat analogous to the prime meridian on the earth. It is the origin from which
sidereal hour angle (SHA) is measured, westward through 360°. Thus, sidereal hour
angle is similar to longitude on the earth, except that longitude is measured either
eastward or westward through 180%. If the vernal equinox and all celestial bodies
were fixed points, both declination and sidereal hour angle of celestial bodies would
remain the same, but these coordinates change as a body alters its position on the
celestial sphere, and also as precession of the equinoxes (art. 1419) takes place, resulting
in movement of the vernal equinox and celestial equator. Sidereal hour angle is used
primarily by navigators. Astronomers usually measure eastward in time units, through
24 hours. This quantity is called right ascension (RA). Thus, converted to the same
units, SHA+ RA —360?— 24^,

Measurement is often made from a celestial meridianrather than from the hour circle of
the first point of Aries. "This is another form of hour angle (HA) which, like sidereal
hour angle, is measured westward through
360? (fig.1426b). Itis usually designated
Greenwich hour angle (GHA) or local hour
angle (LHA) depending upon whether the
Greenwich or local celestial meridian is
used as the reference. If measurement
is made from the local celestial meridian,
either eastward or westward through 180°,
similar to measurement of longitude on
the earth, the quantity is called meridian
angle (t). This is the angle between the
plane of the celestial meridian of the ob-
server and the plane of the hour circle of
the body. Because of the apparent daily
rotation of the celestial sphere, hour angle
continually increases, but meridian angle
increases from 0° at the celestial meridian
to 180° W, which is also 180° E, and then Figure 1426b.—Local hour angle and meridian
decreases to 0? again. The rate of change | angle.
for the mean sun (art. 1421) is 15? per
hour. The rate of all other bodies except the moon is within 3” of this value. The
average rate of the moon is about 1475.

As the celestial sphere rotates, each body crosses each branch of the celestial
meridian approximately once a day. This crossing is called meridian transit (some-
times called culmination). It may be called upper transit to indicate crossing of the
upper branch of the celestial meridian, and lower transit to indicate crossing of the
lower branch. À

1427. Time diagram.—To an observer outside the celestial sphere (if this were
possible), at such a distance that his view would be orthographic, the outer limit of
the sphere would appear as a great circle. If he were over one of the celestial poles,
the circle would be the celestial equator. Parallels of declination would appear as circles
concentric with, but usually smaller than, the celestial equator. Hour circles would ap-
pear as radials. If the observer were over the south celestial pole and rotating with the
earth, the celestial sphere would appear to rotate in a counterclockwise direction. The
difference in hour angle of any two bodies would be indicated by the angle between

384 NAVIGATIONAL ASTRONOMY

their hour circles. The hour
angles themselves would be in-
dicated by the angles, at the
pole, between a celestial meridi-
an and the hour circles. On a
reduced scale, and without bene-
fit of actual circles showing in
the sky, such a view is available
to a northern-hemisphere ob-
server who looks at the north
celestial pole (approximately at
Polaris) and observes stars of
high northerly declination, such
as those of the big dipper and .
Cassiopeia, circle the sky.

A diagram based upon this
concept, called a time diagram
or diagram on the plane of the
celestial equator, can be useful
in visualizing the relationships

FiavRE 1427a.—Time diagram. of the various “longitude” terms

of article 1426. Refer to figure

1427a. The circle represents the celestial equator. The parallels of declination are
not of concern, and are omitted. By convention, the diagram is oriented so that
the upper branch of the local celestial meridian is at the top, labeled M. The
lower branch is shown as a broken line, labeled m. The observer in this case is at
longitude 27? W. "Therefore, the Greenwich meridian is 27° east, as shown. It is
labeled G and g to indicate the upper and lower branches, respectively. The vernal
equinox is 30° west of the meridian, as shown,
and labeled Y. The moon is 70° west of the M
celestial meridian, and the sun is 75° east of
the celestial meridian. Various quantities are
shown and labeled. To one who knows these x
relationships, a time diagram is often useful
in visualizing conditions of a given situation, 8
particularly when some quantities are to be p
found from others.

Example.—An observer is at longitude G
104° WY GHA ie 195%. 'The'ŠHA ofre star
19220091

Required —(1) LHA, (2) t, (9) CHAT:
Solution.—Draw the diagram, as shown in

figure 1427b. From the diagram determine the m

required relationships: (1) LHA=GHA Y +

Freu 27b.—Soluti i
S (2) t=360—LHA. (3) LHA? = IGURE me by time
GHA Y—4.

Answers.—(1) LHA 297°, (2) t 63? E, (3) LHA 912:

1428. Horizon system.—The celestial equator system of coordinates is not con-
venient for locating celestial bodies relative to an observer. For this purpose the
horizon system is preferable. In this system, the horizon is the primary great circle
analogous to the equator (fig. 1428a). The zenith (Z) is that point directly overhead

NAVIGATIONAL ASTRONOMY 385

dE

[Sino
A ts "REI MEN;
EN DNA | Á 18 ep
A SS alle hay

Figure 1428a.—The horizon system of coordinates.

The nadir (Na) is 180° from the zenith. The
A circle parallel to the plane of the horizon
Angular

(opposite to the direction of gravity).
zenith and nadir are the poles of the system.
is a parallel of altitude (sometimes called an altitude circle or almucantar).

distance above the horizon is altitude (h); angular distance from the zenith is zenith
distance (z). Great circles through the zenith and nadir, and therefore perpendicular
to the horizon, are vertical circles. The vertical circle through the east and west
points of the horizon is the prime vertical circle, or, as usually stated, the prime vertical
(PV). The vertical circle through the north and south points of the horizon is the
principal vertical circle. It is also the celestial meridian (art. 1426).

The angular difference between north and any other horizontal direction (the
bearing) is called azimuth (Zn) when referred to a celestial body. Azimuth, like
bearing, is measured clockwise around the horizon from 000° at north through 360°.
It is usually expressed in three figures. Sometimes it is convenient to express direction
in terms of azimuth angle (Z) which is usually measured from the direction of the
elevated pole (north or south to agree with the latitude), through 180°, but occasionally
from the nearer north or south point, through 90°. Azimuth angle is labeled to avoid

386 NAVIGATIONAL ASTRONOMY

ambiguity. It is given a prefix, N or S, to indicate the origin of measurement, and a
suffix, E or W, to indicate the direction of measurement. By means of these labels
azimuth angle can be converted to azimuth. Thus, N37°W means that the given
direction is found by starting at north and measuring 37° in a westerly direction, or
360°—37°=323°. Similarly S164” W is 164° west of south, or 180°+164°=344°. In
converting from azimuth to azimuth angle, one must know the name (N or S) of the
latitude if the 180° system is used. Thus, Zn 068° is equal to N 68? E in north latitude,
and S112%E in south latitude. If the 90° system is used, it could be N 68? E only,
since this system is without ambiguity except at east and west. In either the 90° or
180° system the suffix agrees with meridian angle, for if a body is east by meridian
angle, it is also east by azimuth angle. If LHA is less than 180°, the body is west of
the meridian, and hence has an azimuth of more than 180°. Thus, both LHA and Zn

cannot be either less or greater than 180°. 20 AMOR
At rising or setting, a body is not on the prime vertical unless its declination is.
zero. The arc of the horizon between the prime vertical and the body is its amplitude
(A). This is given the prefix E (east) if
the body is rising and W (west) if setting.
It is given the suffix N if the body rises or
sets north of the prime vertical (which it
does if it has northerly declination) and S
if it rises or sets south of the prime vertical
(having southerly declination). Intercon-
version of amplitude and azimuth is similar
to that of azimuth angle and azimuth.
Thus, if A=E 1598, the body is 15? south
of east, or 90°+15°=105°. For any given
body, the numerical value of amplitude
would be the same at rising and setting if
the declination did not change. Ampli-
tudes to a declination range of 24° aregiven
in table 27. A correction to convert the ob-
served value when the body is on the ap-
Nadir parent horizon to the corresponding value
Figure 1428b.—The horizons. it would have if the body were on the celes-

tial horizon (tab. 27) is given in table 28.

The horizon system of coordinates is based upon the celestial horizon (sometimes
called rational horizon). This is a great circle (of the celestial sphere) midway between
the zenith and nadir. Its plane passes through the center of the earth, and is per-
pendicular to the zenith-nadir line (fig. 1428b). At the infinite distance of the celestial
sphere this is considered identical with the sensible horizon, one having a plane parallel
to that of the celestial horizon, but through the eye of the observer. At heights of eye
used in marine navigation, the sensible horizon may be considered identical with geoidal
horizon, the plane of which is parallel to that of the sensible horizon, but through the
point on the geoid (the sea-level surface of the earth) vertically below the observer.
Only the sun and moon are near enough to the earth that the difference of altitude
measured from the celestial and sensible horizons has practical significance to the
navigator. None of these horizons is marked by a line visible to an observer. In
practice, the marine navigator usually measures altitude from the visible horizon and
converts his readings to the corresponding value from the sensible horizon by means
of dip (art. 1606). The visible horizon is the line where earth and sky appear to meet.
Over land it is a somewhat irregular line, but at sea this line appears as a circle. It is

Zenith

Sensible

Horizon
e

Geoidal Horizon
Refraction dE LE
Celestial ELS

PS
Ss Horizon
~ orizo!

SS `

` `

`
` S

Ë "S
Visible Horizon *

^ L^ Visible Horizon /
a 7

4

S CH z
Geometrical Horizon Geometrical Horizon

`

NAVIGATIONAL ASTRONOMY

387

approximately a small circle of the celestial sphere differing from the sensible horizon
because of height of the observer's eye above the surface, and atmospheric refraction.
The geometrical horizon is below the visible horizon by the amount of terrestrial
refraction. A straight line from the eye of the observer tangent to the earth leads to
the geometrical horizon. Occasionally the expression geometrical horizon is used as
the equivalent of celestial horizon.

Altitude measured from the celestial horizon is the complement of zenith distance.
Celestial bodies below the celestial horizon have negative altitude, or a zenith distance
of more than 90°. In this case, z—90?— (— h) =90°-+h, when h is measured downward
or negatively from the celestial horizon. Because of dip a body may have slight nega-
tive altitude and still be above the visible horizon.

1429. Ecliptic system.— The ecliptic system is based upon the ecliptic as the primary
great circle, analogous to the equator. The points 90? from the ecliptic are the north
and south ecliptic poles. The series of great circles through these poles, analogous to
meridians, are circles of latitude. The circles parallel to the plane of the ecliptic, anal-
ogous to parallels on the earth, are parallels of latitude or circles of longitude. An-
gular distance north or south of the ecliptic, analogous to latitude, is celestial latitude.
Celestial longitude is measured eastward along the ecliptic through 360°, starting at
the vernal equinox. This system of coordinates is of interest chiefly to astronomers.

1430. Galactic system.—Another system of interest primarily to astronomers is
based upon a great circle called the galactic equator, considered to be in the plane of the
galaxy. The north and south galactic poles are 90? from the galactic equator. Galactic
latitude is measured north and south from the galactic equator. Galactic longitude is
measured eastward from a point on the galactic equator at about SHA 84°24’, declina-
tion 28?55' S in 1950.

1431. Summary of coordinate systems.— The four systems of celestial coordinates
are analogous to each other and to the terrestrial system, although each has distinctions
such as differences in directions, units, and limits of measurement. The following
table indicates the analogous term or terms under each system. For differences, see
the description of each system, given earlier in the chapter, or appendix E.

ridians

Earth Celestial Equator Horizon Ecliptic Galactic
equator celestial equator horizon ecliptic galactic equator
poles celestial poles zenith, nadir ecliptic poles galactic poles
meridians hour circles, celestial me- | vertical circles circles of latitude

prime meridian

hour circle T, Greenwich
celestial meridian, local
celestial meridian

principal vertical circle,
prime vertical circle

circle of latitude through
«n.

great circle through
galactic poles and
intersection of galac-
tic equator at about
SHA 84°24’, declina-
tion 28°55’ S (1950)

parallels of declination

parallels of altitude

parallels of latitude

amplitude

parallels

| latitude declination altitude celestial latitude galactic latitude
colatitude polar distance zenith distance celestial colatitude galactic colatitude
longitude SHA, RA, GHA, LHA, t | azimuth, azimuth angle, | celestial longitude galactic longitude

1432. Diagram on the plane of the celestial meridian.—From a point outside the
celestial sphere (if this were possible) and over the celestial equator, at such a distance
that the view would be orthographic, the great circle appearing as the outer limit would
be a celestial meridian. Other celestial meridians would appear as ellipses. The
celestial equator would appear as a diameter 90° from the poles, and parallels of declina-

388 NAVIGATIONAL ASTRONOMY

tion as straight lines parallel to the equator. The view would be similar to the ortho-
graphic view of the earth, as shown in figure 319b. h :

A number of useful relationships can be demonstrated by drawing a diagram on
the plane of the celestial meridian showing this orthographic view. , Arcs of circles can
be substituted for the ellipses without destroying the basic relationships. dus to
figure 1432a. In the lower diagram the circle represents the celestial meridian, QQ the
celestial equator, Pn and Ps the north and south celestial poles, respectively. if a star
has a declination of 30? N, an angle of 30? can be measured from the celestial equator, as

E

F; Meridian

Lower Branch

Parallel of
Altitude

Celestial

FIGURE 1432a.— Measurement of celestial FicunRE 1432b.— Measurement of horizon System
equator system of coordinates. of coordinates.

shown. It could be measured either to the right or left, and would have been toward
the south pole if the declination had been south. "The parallel of declination is a line
through this point and parallel to the celestial equator. The star is somewhere on this
line (actually a circle viewed on edge).

To locate the hour circle, draw the upper diagram so that Pn is directly above
Pn of the lower figure (in line with the polar axis Pn Ps), and the circle is of the same di-
ameter as that of the lower figure. This is the plan view, looking down on the celestial
sphere from the top. The circle is the celestial equator. Since the view is from above

NAVIGATIONAL ASTRONOMY 389

the north celestial pole, west is clockwise. The diameter QQ’ is the celestial meridian
shown as a circle in the lower diagram. If the right half is considered the upper branch,
local hour angle is measured clockwise from this line to the hour circle, as shown. In
this case the LHA is 80°. The intersection of the hour circle and celestial equator,
point A, can be projected down to the lower diagram (point A’) by a straight line parallel
to the polar axis. The elliptical hour circle can be represented approximately by an
arc of a circle through A’, Pn, Ps. The center of this circle is somewhere along the
celestial equator line QQ’, extended if necessary. It is usually found by trial and error.
The intersection of the hour circle and parallel of declination locates the star.

Since the upper diagram serves only to locate point A’ in the lower diagram, the
two can be combined. That is, the LHA arc can be drawn in the lower diagram, as
shown, and point A projected upward to A’. In practice, the upper diagram is not
drawn, being shown here for illustrative purposes only.

In this example the star is on that half of the sphere toward the observer, or the
western part. If LHA had been greater than 180°, the body would have been on the
eastern or “back” side.

From the east or west point over the celestial horizon, the orthographic view of the
horizon system of coordinates would be similar to that of the celestial equator system
from a point over the celestial equator (fig. 1432a), since the celestial meridian is also
the principal vertical circle. The horizon would appear as a diameter, parallels of
altitude as straight lines parallel to the horizon, the zenith and nadir as poles 90° from
the horizon, and vertical circles as ellipses through the zenith and nadir, except for the
principal vertical circle, which would appear as a circle, and the prime vertical, which
would appear as a diameter perpendicular to the horizon.

A celestial body can be located by altitude and azimuth in a manner similar to
that used with the celestial equator system. If the altitude is 25°, this angle is meas-
ured from the horizon toward the zenith and the parallel of altitude is drawn as a
straight line parallel to the horizon, as shown at Ah’ in the lower diagram of figure 1432b.
The plan view from above the zenith is shown in the upper diagram. If north is taken
at the left, as shown, azimuths are measured clockwise from this point. In the figure
the azimuth is 290? and the azimuth angle is N 70? W. "The vertical circle is located
by measuring either are. Point A thus located can be projected vertically downward to
A’ on the horizon of the lower diagram, and the vertical circle represented approximately
by the arc of a circle through 4” and the zenith and nadir. The center of this circle
is on NS, extended if necessary. The body is at the intersection of the parallel of
altitude and the vertical circle. Since the upper diagram serves only to locate A’ on
the lower diagram, the two can be combined, point A located on the lower diagram and
projected upward to A', as shown. Since the body of the example has an azimuth
greater than 180?, it is on the western or “front” side of the diagram.

Since the celestial meridian appears the same in both the celestial equator and
horizon systems, the two diagrams can be combined and, if properly oriented, a body
can be located by one set of coordinates, and the coordinates of the other system
can be determined by measurement.

Refer to figure 1432c, in which the black lines represent the celestial equator
system, and the red lines the horizon system. By convention, the zenith 1s shown at
the top and the north point of the horizon at the left. The west point on the horizon
is at the center, and the east point directly behind it. In the figure the latitude is
379N. "Therefore, the zenith is 37? north of the celestial equator. Since the zenith
is established at the top of the diagram, the equator can be found by measuring an
arc of 37? toward the south, along the celestial meridian. If the declination is 30% N and
the LHA is 80°, the body can be located as shown by the black lines, and described above.

390 NAVIGATIONAL ASTRONOMY

The altitude and azimuth can be determined by the reverse process to that de-
scribed above. Draw a line hh’ through the body and parallel to the horizon, NS.
The altitude, 25°, is found by measurement, as shown. Draw the arc of a circle
through the body and the zenith and nadir. From 4”, the intersection of this are
with the horizon, draw a vertical line intersecting the circle at A. The azimuth,
N 70° W, is found by measurement, as shown. The prefix N is applied to agree with the
latitude. The body is left (north) of ZNa, the prime vertical circle. The suffix W
applies because the LHA, 80°, shows that the body is west of the meridian.

If altitude and azimuth are given, the body is located by means of the red lines.
The parallel of declination is then drawn parallel to QQ’, the celestial equator, and the
declination determined by measurement. Point L’ is located by drawing the arc of a
circle through Pn, the star, and Ps. From L’ a line is drawn perpendicular to QQ’,
locating L. The meridian angle is then found by measurement. The declination is
known to be north because the
body is between the celestial
equator and the north ceiestial
pole. The meridian angle is
west to agree with the azi-
muth, and hence LHA is nu-
merically the same.

Since QQ’ and PnPs are
perpendicular, and ZNa and
NS are also perpendicular, are
NPn is equal to arc ZQ. That
is, the altitude of the elevated
pole is equal to the declination
of the zenith, which is equal to
the latitude. This relationship
is the basis of the method of
determining latitude by an ob-
servation of Polaris (art. 2105).

The diagram on the plane
of the celestial meridian is use-
ful in approximating a number
Figure 1432c.—Diagram on the plane of the celestial meridan. of relationships. Consider fig-

ure 1432d. The latitude of
the observer (VPn or ZQ) is 45°N. The declination of the sun (Q4) is 20? N.
Neglecting the change in declination for one day, note the following: At sunrise,
position 1, the sun is on the horizon (NS), at the “back” of the diagram. Its altitude,
h, is 0?. Its azimuth angle, Z, is the arc NA, N 63? E. This is prefixed N to agree
with the latitude and suffixed E to agree with the meridian angle of the sun at sunrise.
Hence, Zn—0"+63 °==063°. The amplitude, A, is the arc ZA, E27? N. The meridian
angle, t, is the are QL, 110? E. The suffix E is applied because the sun is east of the
meridian at rising. The LHA is 360°—110°=250°.

As the sun moves upward along its parallel of declination, its altitude increases.
It reaches position 2 at about 0600, when t—909 E. At position 3 it is on the prime verti-
cal, ZNa. Its azimuth angle, Z, is N 90° E, and Zn—090%. The altitude is Nh’ or SA QT S

Moving on up its parallel of declination, it arrives at position 4 on the celestial
meridian about noon—when t and LHA are both 0°, by definition. On the celestial
meridian a body's azimuth is 000° or 180°. In this case it is 180° because the body
is south of the zenith. The maximum altitude occurs at meridian transit, in this case

NAVIGATIONAL ASTRONOMY 391

the are S4, 65°. The zenith distance, z, is the arc Z4, 25°. A body is not in the zenith
at meridian transit unless its declination is numerically, and by name, the same as the
latitude. 4

k Continuing on, the sun moves downward along the “front” or western side of the
diagram. At position 3 it is again on the prime vertical. The altitude is the same as
when previously on the prime vertical, and the azimuth angle is numerically the same,
but now measured toward the west. The azimuth is 270°. The sun reaches position
2 six hours after meridian transit, and sets at position 1, when the azimuth angle is
numerically the same as at sunrise, but westerly, and Zn=360°—63°=297°. The
amplitude is W 27? N.

After sunset the sun continues on downward along its parallel of declination until
it reaches position 5, on the lower branch of the celestial meridian, about midnight.
Its negative altitude, arc N5, is now greatest, 25%, and its azimuth is 000?. At this
point it. starts back up along the “back” of the diagram, arriving at position 1 at the
next sunrise, to start another cycle.

Half the cycle is from the cross-
ing of the 90? hour circle (the PnPs
line, position 2) to the upper branch
of the celestial meridian (position
4) and back to the PnPs line (posi-
tion 2). When the declination and
latitude have the same name (both
north or both south), more than
half the parallel of declination (posi-
tion 1 to 4 to 1) is above the horizon,
and the body is above the horizon
more than half the time, crossing
the 90? hour circle above the hori-
zon. It rises and sets on the same
side of the prime vertical as the
elevated pole. If the declination is
of the same name but numerically
smaller than the latitude, the body
crosses the prime vertical above
the horizon. If the declination and FIGURE 1432d.—A diagram on the plane of the celestial
latitude have the same name and meridian for lat. 45° N.
are numerically equal, the body
is in the zenith at upper transit. If the declination is of the same name but numer-
ically greater than the latitude, the body crosses the upper branch of the celestial
meridian between the zenith and elevated pole, and does not cross the prime vertical.
If the declination is of the same name as the latitude and complementary to it (d+L=
90°), the body is on the horizon at lower transit, and does not set. If the declination
is of the same name as the latitude and numerically greater than the colatitude, the
body is above the horizon during its entire daily cycle, and has maximum and minimum
altitudes, as shown by the black dotted line in figure 1432d.

If the declination is 0° at any latitude, the body is above the horizon half the time,
following the celestial equator QQ’, and rising and setting on the prime vertical. If the
declination is of contrary name (one north and the other south), the body is above the
horizon less than half the time, and crosses the 90° hour circle below the horizon. It
rises and sets on the opposite side of the prime vertical from the elevated pole. If the
declination is of contrary name and numerically smaller than the latitude, the body

392 NAVIGATIONAL ASTRONOMY

crosses the prime vertical below the horizon. This is the situation with the sun in
winter, when days are short. If the declination is of contrary name and numerically
equal to the latitude, the body is in the nadir at lower transit. If the declination is of
contrary name and complementary to the latitude, the body is on the horizon at upper
transit. If the declination is of contrary name and numerically greater than the
colatitude, the body does not rise.

All of these relationships, and those that follow, can be derived by means of a
diagram on the plane of the celestial meridian. They are modified slightly by atmos-
pheric refraction, height of eye, semidiameter, parallax, changes in declination, and
apparent speed of the body along its diurnal circle.

It is customary to keep the same orientation in south latitude, as shown in figure
1432e. In this illustration the latitude is 45°S, and the declination of the body is
15°N. Since Ps is the elevated pole, it is shown above the southern horizon, with
both SPs and ZQ equal to the
latitude, 45°. The body rises at
position 1, on the opposite side
of the prime vertical from the
elevated pole; moves upward
along its parallel of declination
to position 2, on the upper
branch of the celestial meridian,
bearing north; and then down-
ward along the “front” of the
diagram to position 1, where
it sets; remaining above the ho-
rizon for less than half the time
because declination and latitude
are of contrary name. The
azimuth at rising is arc NA, the
amplitude ZA, and the azimuth
angle SA. The altitude circle
at meridian transit is shown
at hh’.

A diagram on the plane of
FIGURE 1432e.—A diagram on the plane of the celestial the celestial meridian can be

meridian for lat. 45° S. used to demonstrate the effect

of a change in latitude. As the

latitude increases, the celestial equator becomes more nearly parallel to the horizon.
The colatitude becomes smaller, increasing the number of circumpolar bodies and
those which neither rise nor set, and also increasing the difference in the length of
the days between summer and winter. At the poles (fig. 1416b), celestial bodies
circle the sky, parallel to the horizon. At the equator (fig. 1416a) the 90° hour
circle coincides with the horizon. Bodies rise and set vertically; and are above the
horizon half the time. At rising and setting the amplitude is equal to the declination.
At meridian transit the altitude is equal to the codeclination. As the latitude
changes name, the same-contrary name relationship with declination reverses. This
accounts for the fact that one hemisphere has winter while the other is having summer.
| The error arising from showing the hour circles and vertical circles as arcs of
circles instead of ellipses increases with increased declination or altitude. More
accurate results can be obtained by measurement of azimuth on the parallel of alti-
tude instead of the horizon, and of hour angle on the parallel of declination instead

NAVIGATIONAL ASTRONOMY 393

of the celestial equator. Refer to figure 1432f. The vertical circle shown is for
a body having an azimuth angle of S 60? W. The arc of a circle is shown in black,
and the ellipse in red. The black arc is obtained by measurement around the horizon,
locating A” by means of 4, as previously described. The intersection of this are with
the altitude circle at 60° places the body at M. If a semicircle is drawn with the altitude
circle as a diameter, and the azimuth angle measured around this, to B, a perpendicular
to the hour circle locates the body at M”, on the ellipse. By this method the altitude
circle, rather than the horizon, is, in effect, rotated through 90° for the measurement.
This refinement is seldom used because actual values are usually found mathematically,
the diagram on the plane of the meridian being used primarily to indicate relationships.
With experience, one may mentally visualize the diagram on the plane of the
celestial meridian without making an actual drawing. Devices with two sets of
spherical coordinates, on either
the orthographic (art. 319) or
stereographic (art. 318) projec-
tion, pivoted at the center, have
been produced commercially to
provide a mechanical diagram
on the plane of the celestial me-
ridian. However, since the dia-
gram's principal use is to illus-
trate certain relationships, such
a device is not a necessary part
of the navigator's equipment.
1433. The navigational tri-
angle.—A triangle formed by
arcs of great circles of a sphere
is called a spherical triangle.
A spherical triangle on the
celestial sphere is called a ce-
lestial triangle. The spherical
triangle of particular signifi-
cance to navigators is called
the navigational triangle. It
is formed by arcs of a celestial
meridian, an hour circle, and
a vertical circle. Its vertices pygure 1432f—Locating a point on an ellipse of a diagram
are the elevated pole, the zenith, on the plane of the celestial meridian.
and a point on the celestial
sphere (usually a celestial body). The terrestrial counterpart is also called a naviga-
tional triangle, being formed by arcs of two meridians and the great circle connecting
two places on the earth, one on each meridian. The vertices are the two places and a
pole. In great-circle sailing these places are the point of departure and the destina-
tion. In celestial navigation they are the assumed position (AP) of the observer and
the geographical position (GP) of the body (the place having the body in its zenith).
The GP of the sun is sometimes called the subsolar point, that of the moon the
sublunar point, that of a satellite (either natural or artificial) the subsatellite point,
and that of a star its substellar or subastral point. When used to solve a celestial obser-
vation, either the celestial or terrestrial triangle may be called the astronomical triangle.
The navigational triangle is shown in figure 1433a on a diagram on the plane of
the celestial meridian, labeled as in article 1432, but with the hour circle and vertical

394 NAVIGATIONAL ASTRONOMY

FIGURE 1433a.—The navigational triangle.

circle properly shown as ellipses.
The earth is at the center, O.
The star is at M, dd’ is its par-
allel of declination, and hh” its
altitude circle.

In the figure, arc QZ of the
celestial meridian is the latitude
of the observer, and PnZ, one
side of the triangle, is the co-
latitude. Arc AM of the ver-
tical circle is the altitude of the
body, and side ZM of the tri-
angle is the zenith distance, or
coaltitude. Arc LM of the hour
circle is the declination of the
body, and side PnM of the tri-
angle is the polar distance, or
codeclination.

The angle at the elevated
pole, ZPnM, having the hour
circle and the celestial meridian
as sides, is the meridian angle, t.

The angle at the zenith, PnZM, having the vertical circle and that are of the celestial
meridian which includes the elevated pole as sides, is the azimuth angle. The angle
at the celestial body, ZMPn, having the hour circle and the vertical circle as sides, is

FIGURE 1433b.—The navigational triangle in perspective.

APO

NAVIGATIONAL ASTRONOMY 395

the parallactic angle (X) (sometimes called the position angle), which is not generally
used by the navigator.

A number of problems involving the navigational triangle are encountered by the
navigator, either directly or indirectly. Of these, the most common are:

1. Given latitude, declination, and meridian angle, to find altitude and azimuth
angle. This is used in the reduction of a celestial observation, to establish a line of
position (ch. XX).

2. Given latitude, altitude, and azimuth angle, to find declination and meridian
angle. This is used to identify an unknown celestial body (ch. XXII).

3. Given meridian angle, declination, and altitude, to find azimuth angle. This
may be used to find azimuth when the altitude is known (ch. XX).

4. Given the latitude of two places on the earth and the difference of longitude
between them, to find the initial great-circle course and the great-circle distance (ch.
VIII). This involves the same parts of the triangle as in 1, above, but in the terrestrial
triangle, and hence defined differently.

Both celestial and terrestrial navigational triangles are shown in perspective in
figure 1433b.

Problems

1427. Given.—An observer is at longitude 77°E. The sun is 60° east of the
meridian. GHA f is 37°.

Required.—(1) LHA of the sun.

(2) GHA of the sun.

(3) SHA of the sun.

(4) Approximate time at the local meridian.

Answers.—(1) LHA 300°, (2) GHA 223°, (3) SHA 186°, (4) T 0800.

1428a. Required —Convert Z to Zn in the following:

(1) N174°E (4) S39°E
(2) S1°E (5) N106°W
(3) S90°W (6) N90°W

Answers —(1) Zn 174°, (2) Zn 179°, (3) Zn 270°, (4) Zn 141°, (5) Zn 254°, (6) Zn
2105:
1428b. Required.—Convert Zn to Z in the following, using the 180? system:

Zn Lat. Zn Lat.
Gy aes N (4) 333° S
(2) 163° S (5) 206° N
(3) 007° N (6) 206° S

Answers. —(1) Z N146°W, (2) Z S17%E, (3) Z N7?E, (4) Z S153°W, (5) Z
N 154? W, (6) Z S26-W. | | ‘
1428c. Required.—Convert Zn to Z in the following, using the 90° system:
(1) 051° (3) 251°
(D) 517 (E) FL
Answers —(1) Z N51%E, (2) Z S29?E, (3) Z S71°W, (4) Z N90? W.
1428d. Given.—The following amplitudes:
A Lat. A Lat.
(a) W24°N N (c) E5578 N
(b E18%N 5 (d) W4°S S

396 NAVIGATIONAL ASTRONOMY

Required.—(1) Zn, (2) Z (180° system), (3) Z (90° system).

Answers.—(1) (a) Zn 294°, (b) Zn 072°, (c) Zn 145°, (d) Zn 266°; (2) (a) ZN 66° W,
(b) Z S108? E, (c) Z N145%E, (d) Z S86°W; (3) (a) Z N66?W, (b) Z N72? E,
(c) Z S35? E, (d) Z S86? W.

1428e. Given.—The following azimuth angles at rising and setting:

(1) N80°E (3) S110? E
(2 N95°W (4) S90? W

Required.—Amplitude.
Answers. —(1) A E109 N, (2) A W5°S, (3) A E20°N, (4) A 0°.

Solve the following problems by diagrams on the plane of the celestial meridian:

1432a. Given.—L 32? N, t 71° W, d 27? N.
Required.—Altitude and azimuth.
Answers.—h 28°, Zn 288°.

1432b. Given. —L 1795, t 64? E, d 2895.
Required.—Altitude and azimuth.
Answers.—h 28°, Zn 115°.

1432c. Given.—L 59°N, h 27°, Zn 052°.
Required.—Declination and meridian angle.
Answers.—d 41? N, t 111? E.

1432d. Given.—L 31? N, declination of sun 18°S.

Required.—(1) Azimuth at sunrise, (2) maximum altitude, (3) altitude when the
azimuth is 234?, (4) azimuth angle when the altitude in the afternoon is 10?, (5)
amplitude at sunset.

Answers.—(1) Zn 111°, (2) h 41°, (3) h 18°, (4) Z N118°W, (5) A W21°S.

1432e. Given.—The declination of the star Dubhe is approximately 622 N. When
observed at lower transit, its altitude is 43°.

Reguired.—(1) Latitude of the observer, (2) azimuth at upper transit.

Answers.—(1) L 71? N, (2) Zn 180°.

1432f. Required.—For an observer at latitude 39? N, find for the sun at summer and
winter solstices, respectively: (1) LHA at sunrise, (2) LHA when on the prime vertical
during the morning, (3) maximum altitude, (4) LHA at sunset, (5) length of daylight
if the sun moves 15? per hour.

Answers.—
Summer Winter
(1) LHA 248° 292°
(2) LHA 304° 236° (below horizon)
(Slá 14? 28?
(4) LHA LU» 68?
y=) 14°56" 904"

1432g. Given.—L 83? N, sun’s declination 4°S.

Iteguired.—(1) LHA at sunrise, (2) maximum altitude, (3) LHA at sunset, (4)
length of daylight (sun moving 15% per hour).

Answers.—(1) LHA 305°, (2) max h 3°, (3) LHA 55°, (4) T 720".

NAVIGATIONAL ASTRONOMY 397

References

ELEMENTARY

Alter, D., and Cleminshaw, C. H. Pictorial Astronomy. New York, Crowell, 1952.

Baker, R. H. An Introduction to Astronomy. 6th ed. Princeton, Van Nostrand, 1961.

Hood, P. Observing the Heavens. New York, Oxford, 1951.

Mayall, R. N. and Mayall, M.W. A Beginner’s Guide to the Skies. New York, Putnam,
1960.

Struve, O., Lynds, B., and Pillans,H. Elementary Astronomy. New York, Oxford, 1959.

Wright, H. Palomar. New York, Macmillan, 1952.

ADVANCED

Baker, R. H. Astronomy. 7thed. Princeton, Van Nostrand, 1959.

Brouwer, D., and Clemence, G. M. Methods of Celestial Mechanics. New York, Aca-
demic, 1961.

Jones, Sir Harold Spencer. General Astronomy. 3d ed. New York, Longmans, 1951.

Krogdahl, W.S. The Astronomical Universe. New York, Macmillan, 1952.

Rudaux, L., and De Vaucouleurs, G. Larousse Encyclopedia of Astronomy. New York,
Prometheus, 1959.

Russell, H. N., Dugan, R. S., and Stewart, J. Q. Astronomy. Vol. I, The Solar System.
Rev. ed. 1945. Vol. II, Astrophysics and Stellar Astronomy. Boston, Ginn, 1938.

CHAPTER XV
INSTRUMENTS FOR CELESTIAL NAVIGATION

1501. The marine sextant is a hand-held instrument for measuring the angle
between the lines of sight to two points by bringing into coincidence at the eye of the
observer the direct ray from one point, and a double-reflected ray from the other, the
measured angle being twice the angle between the reflecting surfaces. Its principal
use is to measure the altitudes of celestial bodies above the visible sea horizon. Some-
times it is turned on its side and used for measuring the difference in bearing of two
terrestrial objects. Because of its great value for determining position at sea, the
sextant has been a symbol of navigation for more than 200 years. The quality of his
instrument, the care he gives it, and the skill with which he makes observations are to
the navigator matters of professional pride.

The name “sextant” is from the Latin seztans, “the sixth part." The arc of early
marine sextants is approximately the sixth part of a circle, but because of the optical
principle involved (art. 1502), the instrument measures angles of 120°. Most modern
instruments measure something more than this.

1502. Prineiple of operation.—When a ray of light is reflected from a plane surface,
the angle of reflection is equal to the angle of incidence (fig. 1502a). When the reflecting

\
N
PER RR M
FIGURE 1502a.—Angle of reflection equals angle Figure 1502b.—Optical principle of
of incidence. the marine sextant.

surface is rotated toward or away from the incident ray, each angle is changed by the
amount of rotation, so that the total angle between the incident and reflected rays 1s
altered by twice the change in the reflecting surface. With the sextant, the ray of
light is reflected by two mirrors; one movable and the other fixed. The angle between
the first and last directions is twice the angle between the mirrors.

In figure 1502b, AB is a ray of light from a celestial body. The index mirror of
the sextant is at B, the horizon glass at C, and the eye of the observer at D. Con-
struction lines EF and CF are perpendicular to the index mirror and horizon glass,

respectively, and lines BG and CG are parallel to these mirrors. Therefore, angles
398

INSTRUMENTS FOR CELESTIAL NAVIGATION 399

BFC and BGC are equal because their sides are mutually perpendicular (art. O27).
Angle BGC is the inclination of the two reflecting surfaces. The ray of light AB is
reflected at mirror B, proceeds to mirror C, where it is again reflected, and then continues
on to the eye of the observer at D. Since the angle of reflection is equal to the angle
of incidence,

ABE= EBC, and ABC=2EBC

BCF= FCD, and BCD=2BCF.
Since an exterior angle of a triangle equals the sum of the two nonadjacent interior
angles (art. O28),

ABC=BDC+BCD, and EBC— BFC-- BOF.
Transposing,

BDC=ABC—BCD, and BFC— EBC— BCF.
Substituting 2EBC for ABC, and 2BCF for BCD in the first of these equations,
BDC=2EBC—2BCF, or BDC=2(EBC-BCF).
Since
BFC=EBC— BCF, and BFC=BGC,

therefore

BDC=2BFC=2BGC.

That is, BDC, the angle between the first and last directions of the ray of light, is
equal to 2BGC, twice the angle of inclination of the reflecting surfaces. Angle BDC
is the altitude of the celestial body.

1503. Micrometer drum sextant.—A modern marine sextant, called a micrometer
drum sextant, is shown in figure 1503a. In most marine sextants, the frame. A, is

Figtre 1503a.—U. S. Navy standard micrometer drum sextant.

400 INSTRUMENTS FOR CELESTIAL NAVIGATION

made of brass or aluminum. There are several variations of the design of the frame,
nearly all conforming generally to that shown. The limb, B, is cub on its outer edge
with teeth, each representing one degree of altitude. The altitude graduations, C;
along the limb, are called the are. Some sextants have an arc marked in a strip of
brass, silver, or platinum inlaid in the limb.

The index arm, D, is a movable bar of the same material as the frame. It is
pivoted about the center of curvature of the limb. The tangent screw, E, is mounted
perpendicularly on the end of the index arm, where it engages the teeth of the limb.
Because the index arm can be moved through the length of the arc by rotating the
tangent screw, this is sometimes called an “endless tangent screw," in contrast with the
limited-range device on older instruments. The release, F, is a spring-actuated clamp
which keeps the tangent screw engaged with the teeth of the limb. By applying
pressure on the legs of the release, one can disengage the tangent screw. The index
arm can then be moved rapidly along the limb. Mounted on the end of the tangent
screw is a micrometer drum, G, which is graduated in minutes of altitude. One com-
plete turn of the drum moves the index arm one degree of altitude along the arc.
Adjacent to the micrometer drum and fixed on the index arm is a vernier, 7, which aids
in reading fractions of a minute. The vernier shown is graduated into ten parts,
permitting readings to six seconds. Other sextants (generally of European manu-
facture) have verniers graduated into only six parts, permitting readings to ten seconds.
The most expensive sextant in common use has no vernier, and readings more precise
than one minute can only be estimated.

The index mirror, 7, is à piece of silvered plate glass mounted on the index arm,
perpendicular to the plane of the instrument, with the center of the reflecting surface
directly over the pivot of the index arm. The horizon glass, J, is a piece of plate glass
silvered on its half nearer the frame. It is mounted on the frame, perpendicular to
the plane of the sextant. The index mirror and horizon glass are mounted so that
their surfaces are parallel when the micrometer drum is set at 0?, if the instrument is
in perfect adjustment. Shade glasses, K, of varying or variable darkness, are mounted
on the frame of the sextant in front of the index mirror and horizon glass. They can
be moved into the line of sight at will, to reduce the intensity of light reaching the eye
of the observer. Older sextants have two sets of shade glasses, as shown in figure
1504. Many modern sextants are fitted with a single Polaroid filter of variable dark-
ness in place of each set of shade glasses, as shown in figure 1503a.

The telescope, L, screws into an adjustable collar in line with the horizon glass,
and should then be parallel to the plane of the instrument. Most modern sextants
are provided with only one telescope, but some are equipped with two or more. When
only one telescope is provided, it is of the “erect image type," either such as shown or one
with a wider “object glass" (far end of telescope), which generally is shorter in length
and gives a greater field of view. The second telescope, if provided, is of the “inverting
type." The inverting telescope, having one lens less than the erect type, absorbs less
light, but at the expense of producing an inverted image. A small colored glass cap
is usually provided, to be placed over the “eyepiece” (near end of telescope) to reduce
the glare. With this in place, shade glasses are generally not needed. A “peep sight”
may be provided. It is a clear tube which serves to direct the line of sight of the
observer when no telescope is used.

The telescope shown in figure 1503a is fitted with a "spiral focusing mechanism.”
Other sextants substitute a “draw” for this mechanism. The draw is fitted inside the
telescope tube without threads and is slid in or out as necessary to focus the instrument.

INSTRUMENTS FOR CELESTIAL NAVIGATION 401

The spiral focusing mechanism is easily adjusted each time the sextant is used, but on
the draw type, the navigator should mark the draw to indicate the correct extension
for his eyes.

„The handle, M, of most sextants is made of wood or plastic. Sextants are
designed to be held in the right hand. Some are equipped with a small light on the
index arm to assist in reading altitudes. The batteries for this light are fitted inside
a recess in the sextant handle.

Figure 1503b shows a sextant with a silver arc inserted in the limb, a micrometer
drum graduated oppositely to the one in figure 1503a, a vernier graduated into six
parts, a shorter telescope with a
wider object glass than that in
figure 1503a, a telescope draw
substituted for a spiral focusing
mechanism, and a light fitted
on the index arm.

1504. Vernier sextant.—
Nearly all marine sextants of
recent manufacture are of the
type described in article 1503.
At least two older-type sextants
are still in use. These differ
from the micrometer drum sex-
tant principally in the manner
in which the final reading is
made. They are called vernier
sextants.

The clamp screw vernier
sextant is the older of the two.
In place of the modern “release,”
a clamp screw is fitted on the
underside of the index arm. To
move the index arm, one loosens
the clamp screw, releasing the FIGURE 1503b.—A micrometer drum sextant used in the
arm. When the arm is placed merchant marine.
at the approximate altitude of
the body being observed, the clamp screw is tightened. Fixed to the clamp screw and
engaged with the index arm is a long tangent screw. When this screw is turned, the
index arm moves slowly, permitting accurate setting. Movement of the index arm (by
the tangent screw) is limited to the length of the screw (several degrees of arc). Before an
altitude is measured, this screw should be set to the approximate mid-point of its range.
The final reading is made on a vernier set in the index arm below the arc. A small
microscope or magnifying glass fitted to the index arm is used in making the final read-
ing. Figure 1504 shows a clamp screw vernier sextant.

The endless tangent screw vernier sextant is identical with the micrometer drum
sextant, except that it has no drum, and the fine reading is made by a vernier along the
arc, as with the clamp screw vernier sextant. The release is the same as on the microm-
eter drum sextant and teeth are cut into the underside of the limb which engage with
the endless tangent screw. The vernier itself is explained in article 1506.

402 INSTRUMENTS FOR CELESTIAL NAVIGATION

f
ë
z
å

No. 1565

FIGURE 1504.—A clamp serew vernier sextant.

1505. Use of the sextant.—When the sun is observed, the sextant is held vertically
in the right hand, and the line of sight is directed at the point on the horizon directly
below the body. Suitable shade glasses are moved into the line of sight, and the index
arm is moved outward from near the 0° point until the reflected image of the sun
appears in the horizon glass, near the direct view of the horizon. The sextant is then
tilted slightly to the right and left to check its perpendicularity. As the sextant is
tilted, the image of the sun appears to move in an arc, and the observer may have to
change slightly the direction in which he is facing, to prevent the image from moving
out of the horizon glass. When the sun appears at the bottom of its apparent arc
resulting from this swinging the arc, or rocking the sextant, the sextant is vertical,
and in the correct position for making the observation. If the sextant is tilted, too
great an angle will be measured. When the sextant is vertical, and the observer is
facing directly toward the sun, its reflected image appears at the center of the horizon
glass, half on the silvered part, and half on the clear part. The index arm is then moved
slowly until the sun appears to be resting exactly on the horizon, which is tangent to
the lower limb. Occasionally, the sun image is brought below the horizon, and the
upper limb observed. It is good practice to make several observations, moving the limb
away from the horizon, alternately above and below 1t, between readings. Practice
is needed to determine the appearance at tangency, which occurs at only one point, to
avoid the common error of beginners of bringing the image down too far (too little for an
upper-limb observation). Some navigators get more accurate observations by letting
the body contact the horizon by its own apparent motion, bringing it slightly below
the horizon if rising, and above if setting. At the instant the horizon is tangent to
the disk, the time is noted. The sextant altitude is the uncorrected reading of the sex-
tant. Figure 1505a illustrates the major steps in making an observation of the sun.

INSTRUMENTS FOR CELESTIAL NAVIGATION 403

FIGURE 1505a.—Left, view through telescope with index arm set near zero. Center, "swinging the
arc” after the sun has been brought close to the horizon. Right, sun at the instant of tangency.

At the left, the index arm has been moved a short distance from 0°. In the center, it
has been clamped with the sun in the approximate position for a reading, and the
sextant is being rocked. At the right, the sun is in the correct position for a reading.

When the moon is observed, the procedure is the same as for the sun, except that
shade glasses are usually not required. The upper limb of the moon is observed more
often than that of the sun, because of the phases of the moon. When the terminator
(art. 1423) is nearly vertical, care should be exercised in selecting the limb that is
illuminated, if an inaccurate reading is to be avoided. Sights of the moon are best
made during daylight hours, or during that part of twilight in which the moon is least
luminous. During the night, false horizons nearly always appear below the moon, due
to illumination of the water by moonlight.

When a star or planet is observed, three methods of making the initial approxima-
tion of the altitude are in common use. In the most common, the index arm and
micrometer drum are set on zero and the line of sight is directed at the body to be ob-
served. Then, while keeping the reflected image of the body in the mirrored half of
the horizon glass, the index arm is slowly swung out and the frame of the sextant 1s
rotated down. The reflected image of the body is kept in the mirror until the horizon
appears in the clear part of the horizon glass.

When there is little contrast
between brightness of the sky
and the body, this procedure is
difficult, for if the body is “Tost”
while it is being brought down,
it may not be recovered without
starting again at the beginning
of the procedure. An alter-
native method sometimes used
consists of holding the sextant
upside down in the left hand,
directing the line of sight at the
body, and slowly moving the
index arm out until the horizon
appears in the horizon glass.
Thisisillustrated in figure 1505b.
After contact is made, the sex-
tant is inverted and the sight
taken in the usual manner. Ficure 1505b.—Method of bringing horizon “up” to body.

HORIZON

404 INSTRUMENTS FOR CELESTIAL NAVIGATION

A third method consists of determining in advance the approximate altitude and
azimuth of the body by a star finder such as H.O. 2102-D (art. 2210). The sextant is
set at the indicated altitude, and the observer faces in the direction indicated by the
azimuth. After a short search, during which the index arm is moved backward and
forward a few degrees, and the azimuth in which the observer faces is changed a little
to each side, the image of the body should appear in the horizon glass. The best
method to use for any observation is that which produces the desired result with the
least effort. It is largely a matter of personal preference.

Measurement of the altitude of a star or planet differs from that of the sun or
moon in that the center of a star or planet, rather than a limb, is brought into coin-
cidence with the horizon. Figure 1505c shows the reflected image of a star as it should
appear at the time of observation. Because of this difference, and the limited time
usually available for observation during twilight, the method of letting a star or
planet intersect the horizon by its own motion is little used. As with the sun and moon,
however, the navigator should not forget to swing
the arc to establish perpendicularity of the sextant.

Occasionally, fog, haze, or other ships may
obscure the horizon directly below a body which the
navigator wishes to observe. If the arc of the sextant
is sufficiently long, a back sight might be obtained,
using the opposite point of the horizon as the refer-
ence. The observer faces away from the body and
observes the supplement of the altitude. If the sun
or moon is observed in this manner, what appears in
the horizon glass to be the lower limb is in fact the
upper limb. In the case of the sun, it is usually

preferable to observe what appears to be the upper

Figure 1505¢.— Correct position pi limb. The arc that appears when rocking the sex-

e nip uana tant for a back sight is inverted; that is, the highest
point indicates the position of perpendicularity.

If more than one telescope is furnished with the sextant, the erecting telescope is
used to observe thesun. Generally, the inverting telescope will produce the best results
when observing the stars, although some navigators prefer not to use any telescope,
thus obtaining a wider field of view. "The collar into which the sextant telescope fits
may be adjusted in or out in relation to the frame. When moved in, more of the
mirrored half of the horizon glass is visible to the navigator, and a star or planet is
more easily observed when the sky is relatively bright. Near the darker limit of
twilight, the telescope can be moved out, giving a broader view of the clear half of the
glass, and making the less distinct horizon more easily discernible. If both eyes
are kept open until the last moments of an observation, eye strain will be lessened.
But in making the final measurement, the nonsighting eye should be closed to permit
full ocular concentration. Practice will permit observations to be made quickly,
reducing inaccuracy due to eye fatigue. If several observations are made in succession,
with a short rest between them, the best results should be obtained. With experience,
the observer should be able to “call his shots,” identifying the better ones.

When an altitude is being measured, it is desirable to have an assistant note the
time, so that simultaneous values of time and altitude will be available. He should be
given a warning "stand-by" when the measurement is nearly completed, and a “mark”
at the moment a reading is made. He should be instructed to read the three hands in
order of their rapidity of motion; the second hand first, then the minute hand, and

INSTRUMENTS FOR CELESTIAL NAVIGATION 405

finally the hour hand. If it is sufficiently dark that a light is needed to make the read-
ing, the assistant should read both the time, and then the altitude, behind the observer
and facing away from him, to avoid impairment of the observer’s eye adaption to sky
and horizon lighting conditions.

If an assistant is not available to time the observations, the observer holds the
watch in the palm of his left hand, leaving his fingers free to manipulate the tangent
screw of the sextant. After making the observation, he quickly shifts his view to the
watch, and notes the positions of the second, minute, and hour hands, respectively.
The delay between completing the altitude observation and noting the time should
not be more than one or two seconds. The average time should be determined by
having someone measure it for several observations, or by counting the half seconds
(learning to count with the half-second beats of a chronometer). This interval can
then be subtracted from the observed time of each sight.

1506. Reading the sextant.—The reading of a micrometer drum sextant is made
in three steps. The degrees are read by noting the position of the arrow on the index
arm in relation to the arc. The minutes are read by noting the position of the zero
on the vernier with relation to the graduations on the micrometer drum. The fraction
of a minute is read by noting which mark on the vernier most nearly coincides with
one of the graduations on the micrometer drum. This is similar to reading the time
by means of the hour, minute, and second hands of a watch. In both, the relation-
ship of one part of the reading to the others should be kept in mind. Thus, if the
hour hand of a watch were about on '4,” one would know that the time was about
four o’clock. But if the minute hand were on “58,” one would know that the time
was 0358 (or 1558), not 0458 (or 1658). Similarly, if the arc indicated a reading of

Fictre 1506a.— Micrometer drum sextant set at 2974215.

406 INSTRUMENTS FOR CELESTIAL NAVIGATION

80

UM S
$

FIGURE 1506b.—Vernier sextant set at 2942/30".

about 40°, and 58’ on the micrometer drum were opposite zero on the vernier, one
would know that the reading was 39°58’, not 40°58’. Similarly, any doubt as to the
correct minute can be removed by noting the fraction of a minute from the position of
the vernier. In figure 1506a the reading is 29425. The arrow on the index mark
is between 29° and 30°, the zero on the vernier is between 42’ and 43’, and the “0/5”
graduation on the vernier coincides with one of the graduations on the micrometer
drum.

The principle of reading a vernier type sextant is the same, but the reading is
made in two steps. Figure 1506b shows a typical altitude setting on this type sex-
tant. Each degree on the arc of this sextant is graduated into three parts, permitting
an initial reading by the reference mark on the index arm to the nearest full 20 minutes
of arc. In this illustration the reference mark lies between 29°40’ and 30°00’, in-
dicating a reading between these values. The reading for the fraction of 20’ is made
by means of the vernier, which is engraved on the index arm and has the small refer-
ence mark as its zero graduation. On this vernier, 40 graduations coincide with 39
graduations on the arc. Each graduation on the vernier is equivalent to % of one
graduation (20') on the arc, or 0/5 (307). In the illustration, the vernier graduation
representing 2% minutes (2/30") most nearly coincides with one of the graduations
on the arc. Therefore, the reading is 29%42'30”, or 29°42'5, as before. When a ver-
nier of this type is used, any doubt as to which mark on the vernier coincides with a
graduation on the arc can usually be resolved by noting the position of the vernier
mark on each side of the one that seems to be in coincidence.

Negative readings (as in determining index correction, art. 1603), are made in
the same manner as positive readings, the various parts being added algebraically

(art. O6). Thus, if the three parts of a micrometer drum reading are (—)1°, 56’,
and 0:3, the total reading is (—)1°+56’4 0:3=(—)3'7.

INSTRUMENTS FOR CELESTIAL NAVIGATION 407

1507. Developing observational skill.—A well-constructed marine sextant is
capable of measuring angles with an instrument error not exceeding 0/1. Lines of
position from altitudes of this accuracy would not be in error by more than about 200
yards. However, there are various sources of error, other than instrumental, in alti-
tudes measured by sextant. One of the principal sources is the observer himself.
There is probably no single part of his work that the navigator regards with the same
degree of professional pride as his ability to make good celestial observations. Probably
none of his other tasks requires the same degree of skill.

The first fix a student navigator obtains by his observation of celestial bodies is
likely to be disappointing. Most navigators require a great amount of practice to
develop the skill needed to make good observations. But practice alone is not sufficient,
for if a mistake is repeated many times, it will be difficult to eradicate. Early in his
career a navigator would do well to establish good observational technique—and con-
tinue to develop it during the remainder of his days as navigator. Many good pointers
can be obtained from experienced navigators, but it should be remembered that each
develops his own technique, and a practice that proves highly successful for one ob-
server may not help another. Also, an experienced navigator is not necessarily
a good observer, although he may consider himself such. Navigators have a natural
tendency to judge the accuracy of their observations by the size of the figure formed
when the lines of position are plotted. Although this is some indication, it is an
imperfect one, because it does not indicate the errors of individual observations, and
may not reflect constant errors. Also, it is a compound of a number of errors, some
of which are not subject to control by the navigator.

When a student first begins to use the sextant, he can eliminate gross errors of
principle in its use, and gain some ability in making observations, by accepting the
coaching of an experienced navigator. By watching the novice make observations,
the experienced navigator can observe a tendency to hold the instrument incorrectly,
swing the arc improperly, or make other mistakes. When a celestial body is near the
celestial meridian, the experienced navigator might make an observation and quickly
transfer the sextant to the inexperienced one, who can see how the sight should appear.
The two might make simultaneous observations and compare results. At first it is
well to select bodies of low altitude, if they are available.

This procedure is helpful in detecting gross mistakes, but since the observations of
the experienced navigator are not without error, this method is not suitable for final
polishing of technique. For this purpose, observations should be compared with a
more exact standard. Lines of position from celestial observations can be compared
with good positions obtained by electronics or by piloting, if near a shore. Although
this is good practice and provides a means of checking one’s skill from time to time,
it does not provide the large number of comparisons in a short time needed if technique
is to be perfected.

This can sometimes be accomplished when a vessel is at anchor, or at a pier, if a
stretch of open horizon is available. In advance, the altitude of a celestial body which
will be over the open horizon at a time favorable for observation is computed at intervals
of perhaps eight minutes (change in hour angle of 2°). If the body will be near the
meridian, a smaller interval should be used. The altitude is determined for the posi-
tion of the vessel, and all sextant altitude corrections (ch. XVI) are applied with re-
versed sign. These altitudes are then plotted versus time on cross-section paper, to a
large scale, and a curve drawn through the points. At the selected time, a large num-
ber of observations are made at short intervals, allowing only enough time between
observations for resting the eyes and arms. These observations are then plotted on
the cross-section paper and compared with the curve.

408 INSTRUMENTS FOR CELESTIAL NAVIGATION

An analysis of the results should be instructive. Erratic results indicate poor
observational conditions or the need for practice and more care in making observa-
tions. If the measured altitudes are consistently too great, the sextant may not be
rocked properly, the condition of tangency of the lower limb of the sun or moon may
not be judged accurately, a false horizon in the water may have been used, subnormal
refraction (dip) might be present, the eye might be higher above water than estimated,
time might be in error, the index correction may have been determined incorrectly, the
sextant might be out of adjustment, an error may have been made in the computation,
the horizontal (vertical) may be tilted slightly by nearby mountains, etc. If the
measured altitudes are consistently too low, the condition of tangency of the upper limb
of the sun or moon may not be judged accurately, a low cloud may have been used as
the horizon, abnormal refraction (dip) might be present, height of eye might be lower
than estimated, time might be in error, the index error may have been determined
incorrectly, the sextant might be out of adjustment, an error may have been made in
the computation, the waves or swell at the horizon might be higher than at the ship, the
horizontal (vertical) may be tilted slightly, a planet or bright star may have been
placed “tangent” to the horizon rather than centered on the horizon, etc.

A single test of this type, while instructive, may not be conclusive. Several tests
should be made with different celestial bodies, at various altitudes, under various con-
ditions of weather and sea, and at different places. Generally, it is possible and desir-
able to correct any errors being made in the technique of observation, but occasionally a
personal error (sometimes called personal equation) will persist. This might be differ-
ent for the sun and moon than for planets and stars, and might vary with degree of
fatigue of the observer, and other factors. For this reason, a personal error should be
applied with caution. However, if a relatively constant personal error persists, and
experience indicates that observations are improved by applying a correction to remove
its effect, better results might be obtained by this procedure than by attempting to
eliminate it from one’s observations.

When lines of position of great reliability are desired, even an experienced navigator
can usually improve his results by averaging to reduce random error (art. 2904). A
number of observations, preferably not less than ten, are made in quick succession.
These can then be plotted versus time, on cross-section paper, and a curve faired through
the points. Unless the body is near the celestial meridian, this curve should be very
nearly a straight line. Any point on the curve can be used as the observation, using
the time and altitude indicated by the point. It is best to use a point near the middle
of the line, to avoid possible errors in its slope.

The slope can be determined by means of H.O. Pub. No. 214, using At, which is
the change of altitude relative to change in meridian angle (time). Meridian angle

changes at the rate of 1’ in 45. Therefore, the change in altitude, in minutes of arc
,

per second of time, is equal to At (expressed as minutes of arc) divided by 48, or SCH

Thus, if Atis 0.66, the altitude changes 5—0! 165 per second, or 15" X0'66—=9:9 per

minute of time, increasing if the body is rising, and decreasing If it is setting. This
rate may be altered by motion of the ship, the amount being the distance traveled in
one minute, multiplied by the natural cosine of the relative azimuth of the body. Thus,
if the speed is 15 knots, the ship moves 0.25 mile per minute. If the body is 30? on the
bow, the altitude changes 0.25X0.86603=0'2 per minute due to motion of the ship, in
addition to its own apparent motion due to rotation of the earth. If the body is for-
ward of the beam, the effect of the ship’s motion is to increase the altitude; if abaft the
beam, to decrease it. The total effect is the algebraic sum of the separate effects due to

INSTRUMENTS FOR CELESTIAL NAVIGATION 409

rotation of the earth and motion of the vessel, since rate at the vessel is desired.
Rapid change of At indicates a curved rate line. If a large number of observations is
made, the slope of the line should be apparent from the plotted points.

A somewhat simpler variation is generally available if observations are made at
equal intervals, unless the body is near the meridian. It is based upon the assumption
that the change in altitude should be equal for equal intervals of time. A number of
observations might be made by having an assistant give a warning “stand-by” and
then a “mark” at equal intervals of time, as every ten or 20 seconds. Perhaps a better
procedure is to make the observations at equal altitude increments. After the first
observation, the altitude is changed by a set amount according to its rate of change,
as 5’. The setting is increased if the body is rising, and decreased if it is setting. The
body is then permitted to cross the horizon by its own motion, and at the instant of
doing so, the time is noted. If time intervals are constant, the mid time and the average
altitude are used as the observation. If altitude increments are constant, the average
time and mid altitude are used. An uneven number of observations simplifies the finding
of the mid value, but with ten observations the finding of the average value is easier.

If only a small number of observations is available, as three, it is usually prefer-
able to solve all observations and plot the resulting lines of position, adjusting them to
a common time. The average position of the line might be used, but it is generally better
practice to use the middle line (or a line midway between the two middle ones if there
are an even number).

In this discussion of averaging, it has been assumed that all observations are
considered of nearly equal value. Any observation considered unreliable, either in
the judgment of the observer or as a result of a plot, should be rejected in finding an
average.

1508. Care of the sextant.—The modern marine sextant is a well-built, precision
instrument capable of rendering many years of reliable service, with minimum at-
tention. However, its usefulness can easily be impaired by careless handling or
neglect. If it is ever dropped, it may never again provide reliable information. If
this occurs, the instrument should be taken to an expert for careful testing and
inspection.

When not in use, a sextant should invariably be kept in its case and properly stowed.
The sextant case should be a well-constructed hardwood box fitted on its exterior with
a lock, a handle, and two hooks, preferably the type having safety catches. The
interior of the case should be fitted with blocks in which the handle or legs, or both, are
placed when the sextant is stowed. Some sextant cases are fitted with catches which
clamp over the handle when the sextant is stowed, and some are fitted with felt-lined
blocks on the inside of the cover, to clamp down on the extreme ends of the arc when
the case is closed. The case should be so constructed that it can be closed with the shade
glasses and index arm in nearly any normal position, and preferably with the telescope
in place. The last is particularly valuable to the navigator on an overcast day when
only one opportunity to observe the sun may present itself, and the sight may have to
be taken quickly. i

The case itself should be securely stowed in a convenient place away from excessive
heat, dampness, and vibration. A shelf with built-up sides into which the case fits
snugly is a good stowage place. The practice of leaving the sextant in its case on a
chart room settee is a bad one, and the instrument should never be left unattended on
the chart table.

To remove the sextant from its case, grasp the frame firmly with the left hand,
making sure that no pressure is applied to the index arm, and lift the instrument from
the box. Then take the sextant in the right hand, by its handle, leaving the left hand

410 INSTRUMENTS FOR CELESTIAL NAVIGATION

free to make any adjustments necessary before taking a sight. The instrument should
never be held by its limb, index arm, or telescope.

Next to careless handling, the greatest enemy of the sextant is moisture. The
mirrors, especially, and the arc should be wiped dry after each use. A new sheet
of plain lens paper is best to use for this purpose, and linen second best. Over a
period of time, however, linen collects dust, which may contain abrasives that will
scratch the surface of the mirrors. For this reason, linen, if it is used, should be kept
in a small bag to protect it from dust in the air. Chamois leather and silk are par-
ticularly likely to collect abrasive dusts from the air and they should not be used to
clean the mirrors or telescope lenses. Should the mirrors become particularly dirty,
they can be cleaned with a small amount of alcohol, applied with a clean piece of lens
paper. The arc can be cleaned, when necessary, with ammonia, but never with a
polishing compound. In cleaning or drying the mirrors and arc, care should be taken
that excessive pressure is not applied to any part of the instrument.

A small bag of silica gel kept in the sextant case will help in keeping the air in
the case free from moisture, and will help to preserve the mirrors. Occasionally, the
silica gel should be heated in an oven to remove the adsorbed moisture.

The tangent screw and the teeth on the side of the limb should be kept clean and
lightly oiled, using the oil provided with the sextant. It is good practice to set oc-
casionally the index arm of an endless tangent screw at one extremity of the limb and
then to rotate the tangent screw over the length of the arc. This will clean the
teeth and spread the oil through them. At any time that the sextant is to be stowed for
a long period, the arc should be protected with a thin coat of petroleum jelly.

If the mirrors need resilvering, they are best taken to an instrument shop where a
professional job can be done. However, on rare occasions it may be necessary to re-
silver the mirrors of a sextant at sea. In anticipation of this possibility, the navigator
should obtain the necessary materials in advance, as makeshift substitutes cannot be
relied upon to do the job adequately. The required materials are xylene (available in
most pharmacies), dilute nitric acid (optional), alcohol, cotton, tin foil about 0.005 inch
thick, a small amount of mercury, a clean blotter, and some tissue paper. Do not sub-
stitute aluminum foil commonly used in packaging candy and cigarettes.

First, remove the protective coating with alcohol (or better, acetone) from the
back of the mirror to be resilvered, and clean the glass with xylene or acid. If the old
silvering is difficult to remove, soak it in water. Place the blotter on a flat surface and
turn up and seal the edges to form a tray. This will serve to contain the mercury if the
vessel should roll during the operation. Using cotton, clean and smooth out both sides
of a piece of tin foil slightly larger than the glass to be silvered, first with alcohol and
then with xylene (do not use acid). Make certain that no lint adheres to the foil, and
place it on the blotter. Clean the mercury by squeezing it through cheese cloth, and
apply a drop to the foil. Carefully spread it over the surface with a finger, making sure
that none of the mercury gets under the foil. Add a few more drops of mercury until
the entire surface of the foil is covered and tacky. The mercury combines with some of
the tin to form an amalgam. Place the chemically cleaned glass on a piece of clean
tissue paper with the side to be silvered face down. Then place the glass and the paper
on the amalgam. Apply slight pressure to the glass and withdraw the tissue paper.
Following this, grasp the edge of the tin foil and lift it and the mirror from the blotter.
Invert the glass and the tin foil and place in an inclined position, silvered side up. Any
mercury remaining on the blotter is no longer pure and should be disposed of. Five or
six hours later any loose foil may be scraped from the sides of the mirror, and the
following day a coat of commercial varnish or lacquer should be applied to the silvered

INSTRUMENTS FOR CELESTIAL NAVIGATION 411

surface. Should the mirrored half of the horizon glass require silvering, the clear half
may be protected by a strip of cellulose or adhesive tape.

1509. Sextant adjustments.—' There are at least seven sources of error in the
marine sextant, three nonadjustable by the navigator, and four adjustable.

The nonadjustable errors are: “prismatic error,” "graduation error," and "centering
error."

The prismatic error is present if the two faces of the shade glasses and mirrors are
not parallel. Error due to lack of parallelism in the shade glasses may be called shade
error. Shade error in the shade glasses near the index mirror can be determined
by comparison of an angle measured when a shade glass is in the line of sight with the
same angle measured when the glass is not in the line of sight. In this manner, the
error for each shade glass can be determined and recorded. If shade glasses are used in
combination, their combined error should be determined separately. If additional
shading is needed for the observations, use the colored telescope eyepiece cover. This
does not introduce an error because direct and reflected rays are traveling together
when they reach it, and are therefore affected equally by any lack of parallelism of its
two sides.

Lack of parallelism of the two faces of the index mirror can be detected by care-
fully measuring a series of angles; then removing the index mirror, inverting it, and
replacing it; and then measuring the same angles again. Half the difference is the
prismatic error. After the index mirror has been inverted, it should be checked
carefully for perpendicularity to the frame of the sextant, as explained below.

Lack of parallelism of the two faces of the horizon glass will appear as part of the
index error, and so need not have separate attention. The same is true of prismatic
error in the shade glasses located near the horizon glass, but unless index error is deter-
mined with the shade glasses in place, the measured index error will not be the correct
value for the combined error.

Graduation errors occur in the arc, micrometer drum, and vernier of a sextant
which is improperly cut or incorrectly calibrated. Normally, the navigator cannot
determine whether the arc of a sextant is improperly cut, but the principle of the vernier
makes it possible to determine the existence of graduation errors in the micrometer
drum or vernier and is a useful guide in detecting a poorly made instrument. The
first and last markings on any vernier should align perfectly with one less graduation
on the adjacent micrometer drum. In figure 1503a, the vernier is graduated in ten
units. When the zero point is aligned with any graduation on the micrometer drum,
the “ten” graduation should be in perfect alignment with a micrometer graduation
nine units greater than the one in line with zero on the vernier. In figure 1503b, the
vernier is graduated in six units and should align perfectly with any two graduations
five units apart on the micrometer.

Centering error results if the index arm is not pivoted at the exact center of
curvature of the arc. It can be determined by measuring known angles, after the
adjustable errors have been removed. Horizontal angles can be used by determining
the accurate value by careful measurement with a theodolite (art. 4004). Several
readings by both theodolite and sextant should minimize errors. An alternative
method is to measure angles between the lines of sight to stars, comparing the measured
angles with computed values. To minimize refraction errors, one should select stars
at about the same altitude, and avoid stars near the horizon.

The same shade glasses, if any, used for determining or eliminating index error
should be used for measuring centering error. The errors determined in this manner
include any error due to faulty graduation, and prismatic error of the index mirror,

412 INSTRUMENTS FOR CELESTIAL NAVIGATION

unless corrections are applied for these errors. However, since all vary with the angle
measured, they need not be separated. Usually, it is preferable to make a single
correction table for all three errors, called instrument error. Customarily, such a table
is determined by the manufacturer and attached to the inside cover of the sextant
case. The sign of the error is reversed, so that the values given are for instrument
correction (I). !

The adjustable errors in the sextant are those related to perpendicularity of (1)
the frame and the index mirror, and (2) the frame and the horizon glass, and parallelism
of (3) the index mirror and horizon glass to each other at zero setting, and of (4) the
telescope to the frame. Each of these errors, if it exists, can be removed from. the
sextant by careful adjustment. In making these adjustments, never tighten one adjust-
ing screw without first loosening the other screw which bears on the same surface. The
adjustments should be made in the order indicated.

The first adjustment is for perpendicularity of the index mirror to the frame of
the sextant. To test for perpendicularity, place the index arm at about 35? on the arc,

MIRROR LEANING FORWARD

FIGURE 1509a.— Testing the perpendieularity of the index mirror. Here the mirror is not
perpendicular.

and hold the sextant on its side, with the index mirror “up” and toward the eye. Ob-
serve the direct and reflected views of the sextant arc, as illustrated in figure 1509a.
If the two views do not appear to be joined in a straight line, the index mirror is not
perpendicular. If the reflected image is above the direct view, the mirror is inclined
forward. If the reflected image is below the direct view, the mirror is inclined back-
ward. An alternative and sometimes more satisfactory method of determining per-
pendicularity involves the use of two small vanes, or similar objects, of exactly the
same height. Figure 1509b illustrates this method. Again the index arm is set at
about 35°. The vanes are placed upright on the extremities of the limb, in such a
way that the observer can, by placing his eye near the index mirror, see the direct
view of one vane and the reflected image of the other. The tops of the objects are
then observed for alignment. The use of vanes permits observation in the plane of
adjustment, rather than at an angle. Adjustment is made by means of two screws
at the back of the index mirror.

The second adjustment is for perpendicularity of the horizon glass to the frame
of the sextant. An error resulting from the horizon glass not being perpendicular is

INSTRUMENTS FOR CELESTIAL NAVIGATION 413

==
SO
NS INDEX MIRROR PERPENDICULAR
nu 129
f '
ct al! E
Da MAD. TO FRAME A D
1 sÅ. í Thos 1,
va 1 i
` Vi Ji Lu 1
uo Se i fas
Ju H d ` ,
dees M 5 X '
D slk ap
` E '
Via ACEN ES E
as the 1 a k FELLUR LUND) A ES 1
Æ Erte ` es! H Ai Os Ee GZ ES
DH t P R Y, A MAGES H (kd al Mill yy
rat 1 ASIN NUN AS ndi eee [TTD UL Le ETT
re Tene i 1 LE An IES ried (CNS T: gun ty d Ü
a nm LUE TUE) H
YN if ew Mo E 1 1 1 (I Da BORA m ELEME vi LI ` 1
ES sn ARA 4 ' 4 1 1 +- ANN SAN V at A ies aie
kunn hund tipora SON PRO Ege eH
Hem ut (n 1 ! DE, (Ee ek IMITA
AA pog Ke H 1 l pig, ad kaas V (ene pda nes m]
(oí or D d A pp EUR E
na th D V Leen ae? " 4 BH IA
D ne. i ' DO ADT KU IA Ae per]
An oe D H 3-34.54 TE I Y v. et ee: Ø
hm wy 1 mim ET de SADA Tf M A
Ch VM, 1 Ne, He AEZ
dch VA SSK d A A Lt: Leg
ih Ty NA í 1 um
Ü í SEG CHEN y
A EI d H EA ni
HE KI i!
1 4!

c

Figure 1509b.—Alternative method of testing the perpendicularity of the index mirror. Here the
mirror is perpendicular.

called side error. To test for perpendicularity, set the index arm at zero and direct
the line of sight at a star. Then rotate the tangent screw back and forth so that the
reflected image passes alternately above and below the direct view. If, in changing
from one position to the other, the reflected image passes directly over the star as seen
without reflection, no side error exists, but if it passes to one side, the horizon glass is
not perpendicular to the frame of the sextant. Figure 1509c illustrates observations
without side error (left) and with side error (right). Whether the sextant reads zero
when the true and reflected images are in coincidence is immaterial in this test. An
alternative method is to observe a vertical line, such as one edge of the mast of another
vessel (or the sextant can be held on its side and the horizon used). If the direct and
reflected portions do not form a
continuous line, the horizon glass
is not perpendicular to the frame
of thesextant. A third method
is to hold the sextant vertical,
as in observing the altitude of a
celestial body, and bring the re-
flected image of the horizon into
coincidence with the direct view,
so that it appears as a contin-

uous line across the horizon glass.

1 H Figure 1509c.—Testing the perpendicularity of the horizon
Bhengtiltethe pent right i glass. Left, side error does not exist. Right, side error
left. If the horizon still appears does exist.

continuous, the horizon glass is

perpendicular to the frame, but if the reflected portion appears above or below that
part seen direct, the glass is not perpendicular. Adjustment is made by means of two
screws near the base of the horizon glass.

The third adjustment is to make the index mirror and horizon glass parallel when
the index arm is set exactly at zero. The error which results when the two are not
parallel is the principal cause of index error, the total error remaining after the four
adjustments have been made. Index error should be determined each time the sextant
is used and need not be removed if its value is known accurately. To make the test
for parallelism of the mirrors, set the instrument at zero, and direct the line of sight
at the horizon or a star. Side error having been eliminated, the direct view and
reflected image of the horizon appear as a continuous line, or the star as à single point,

414 INSTRUMENTS FOR CELESTIAL NAVIGATION

if the two mirrors are parallel. If the mirrors are not parallel, the horizon appears
broken at the edge of the mirrored part of the horizon glass, one part being higher than
the other. The reflected image of a star appears above or below the star seen without
reflection. If the star appears as a single point, move the tangent screw a small
amount to be sure both direct view and reflected image are in the range of vision.
The sun can be used by noting the reading when the reflected image is tangent to the
sun as seen direct, first above it and then below. These should be numerically equal
but of opposite sign (one positive and the other negative). To avoid variations in
refraction, do not use low altitudes; or turn the sextant on its side and use the two sides
of the sun. Adjustment is made by two screws near the base of the horizon glass. If
the error is not to be removed, turn the tangent screw until direct view and reflected
image of the horizon or a star are in coincidence. The reading of the sextant is the
index error. It is positive if the reading is “on the arc” (positive angle), and negative
if “off the arc” (negative angle). In the case of the sun it is half the numerical difference
(algebraic sum) of the readings, positive or negative to agree with the larger reading.
Index correction (IC) is numerically the same as index error, but of opposite sign.
Since both the second and third adjustments involve the position of the horizon glass,
it is good practice to recheck for side error after index error has been eliminated. Index
error should always be checked after adjustment for side error.

The fourth adjustment is to make the telescope parallel to the frame of the sex-
tant. If the line of sight through the telescope is not parallel to the plane of the
instrument, an error of collimation will result, and altitudes will be measured as greater
than their actual values. To check for parallelism of the telescope, insert it in its
collar, and observe two stars 90° or more apart, bringing the reflected image of one
into coincidence with the direct view of the other, near either the right or left edge
of the field of view (the upper or lower edge if the sextant is horizontal). Then tilt
the sextant so that the stars appear near the opposite edge. If they remain in coin-
cidence, the telescope is parallel to the frame, but if they separate, it is not. An
alternative method is to place the telescope in its collar and then lay the sextant on
a flat table. Sight along the frame of the sextant and have an assistant place a mark
on the opposite bulkhead, in line with the frame. Place another mark above the first
at a distance equal to the distance from the center of the telescope to the frame. This
second line should be in the center of the field of view of the telescope if the telescope
is parallel to the frame. Adjustment for nonparallelism is made to the collar, by means
of the two screws provided for this purpose.

Determination of any of the errors should be based upon a series of observations,
rather than a single one. This is particularly true in the case of index error, which
should be determined by approaching coincidence from opposite directions (up and
down) on alternate readings. If adjustments are made carefully, and the sextant is
given proper handling, it should remain in adjustment over a long period of time.
Unless the navigator has reason to question the accuracy of the adjustments, they
need not be checked at intervals of less than several months, except in the case of
index error, which has the greatest effect on accuracy of readings, and should be checked
each time the sextant is used. If the horizon is used for determining index error, this
check should be made before evening twilight observations, and after morning twilight
observations, while the horizon is sharp and distinct. If a star is used, the index
error should be determined after evening observations and before morning sights are
taken. During the day, it should be checked both before and after observations.

Frequent manipulation of the adjusting screws should be avoided, as it may cause
excessive wear. Except in the case of index error, slight lack of adjustment has little

INSTRUMENTS FOR CELESTIAL NAVIGATION 415

effect on the results, and should be ignored. If adjustments are needed at frequent
intervals, the sextant is not receiving proper care, or has worn parts which should be
replaced at a navigation instrument shop. If index error is not constant, it should
not be removed, but index correction should be determined before or after every obser-
vation and applied to the readings, until the sextant can be repaired. A small variable
error might well be accepted, but should be watched to see that it does not become
unduly large.

1510. Selection of a sextant.—For satisfactory results a sextant should be selected
carefully. For accurate work the radius of the arc should be about 7% inches or more.
The instrument should be light, but strongly built. The various moving parts should
fit snugly, but move freely without binding or gritting. If the index arm is either too
loose or too tight at either end of the arc, the pivot may not be perpendicular to the
frame of the sextant. The telescope should be easy to insert or remove from its holder,
and to focus.

The use to be made of a sextant should be considered in its selection. For ordinary
use in measuring altitudes of celestial bodies, an arc of 90° or slightly more is sufficient.
A longer arc is desirable if back sights are to be made, or if horizontal angles are to be
measured. If use of the sextant is to be limited to horizontal angles, less accuracy
is required. The arc can be of smaller radius, and small nonadjustable errors aie
unimportant.

If practicable, a sextant should be examined by an expert, and tested for non-
adjustable errors before acceptance.

1511. Octants, quintants, and quadrants.—Originally, the term “sextant” was
applied to the navigator's double-reflecting, altitude-measuring instrument only if
its arc was 60° in length—a sixth of a circle—permitting measurement of angles from 0°
to 120%. In modern usage the term is applied to all navigational altitude-measuring
instruments, regardless of angular range or principles of operation, although some are
octants (angular range 90°), some quintants (144°), some quadrants (180°), and many
have an intermediate range.

1512. The artificial horizon.—Measurement of altitude requires a horizontal
reference. In the case of the marine sextant this is commonly provided by the visible
sea horizon. If this is not clearly visible, reliable altitudes cannot be measured unless
a different horizontal reference is available. Such a reference is commonly called an
artificial horizon. If it is attached to, or part of, the sextant, altitudes can be meas-
ured at sea, on land, or in the air, whenever celestial bodies are available for observa-
tions. On land, where the visible horizon is not a reliable indication of the horizontal,
an external artificial horizon can be devised.

Any horizontal reflecting surface will serve the purpose. A pan of mercury,
heavy oil, molasses, or other viscous liquid sheltered from the wind is perhaps simplest.
A piece of plate glass fitting snugly across the top of the container is usually the best
shelter. If there is any reasonable doubt as to the parallelism of the two sides of the
glass, two readings should be made with the glass turned 180° in azimuth between
readings, and the average value taken. The pan and liquid should be clean, as foreign
material on the surface of the liquid is likely to distort the image and introduce an
error in the reading. jme e

To use an external artificial horizon, the observer stands or sits in such a position
that the celestial body to be observed is reflected in the liquid, and is also visible by
direct view. By means of the sextant, the double-reflected image is brought into co-
incidence with the image appearing in the liquid. In the case of the sun or moon the
bottom of the double-reflected image is brought into coincidence with the top of the

416 INSTRUMENTS FOR CELESTIAL NAVIGATION

image in the liquid, if a lower-limb observation is desired. For an upper-limb ob-
servation, the opposite sides are brought into coincidence. If one image is made to
cover the other, the observation is of the center of the body.

When the observation has been made, apply the index correction and any other
instrumental correction, as well as any correction for personal error. Then take half
the remaining angle and apply all other corrections except dip (height of eye) cor-
rection, since this is not applicable. If the center of the sun or moon 1s observed, omit,
also, the correction for semidiameter. Chapter XVI explains the various corrections
h and their applications.

A commercial artificial horizon con-
sisting of a metal tray, mercury, cover of
two sloping glass sides held in a metal
frame, metal bottle to hold the mercury
when not in use, and a funnel for pouring, `
was at one time a familiar part of a navi-
gator’s equipment, but the modern naviga-
tor might experience difficulty in locating
such a device.

1513. Artificial-horizon sextants.—
Shortly after the marine sextant was in-
vented (art. 124), an attempt was made
to extend its use to periods of darkness.
This was done by providing a spirit level
attachment. The observer brought the
double-reflected image of the celestial body
being observed into coincidence with the
bubble of the spirit level. Such devices
have been made available from time to
time, and are still being manufactured.
However, they have never come into gen-
eral use, and are of questionable value.

Charles A. Lindbergh’s historic solo
flight across the North Atlantic in 1927
demonstrated the practicability of long
over-water flights. The development of
a suitable instrument for observing alti-
tudes of celestial bodies during darkness

Figure 1513a.— Modern periscopic sextant. and when the horizon was obscured by

clouds or haze became a virtual require-

ment. Various forms of artificial horizon have been used, including a bubble, gyroscope,

and pendulum. Of these, the bubble has been most widely used. Figure 1513a illus-

trates a modern periscopic sextant permitting observation with only a small tube

protruding through the top of the airplane. Figure 1513b shows the optical principle
of a different type aircraft sextant.

With an artificial horizon of the bubble or pendulum type, considerable skill is
needed to make an observation. The image of the horizontal reference (a circle or
horizontal line) and the celestial body both appear in the field of view, and both may
seem unsteady. An observation is made by matching the two near the center of the field
of view. The appearance at coincidence depends upon the instrument. Some bubbles
appear dark and are placed on a level with the body. Others have a clear center and are
placed over the body. One pendulum type has a horizontal line that is customarily

INSTRUMENTS FOR CELESTIAL NAVIGATION 417

placed directly across the body, although a limb observation can be made if desired.
Bubbles can be regulated in size, and the instructions provided with the instrument
should be followed. In general, the bubble diameter should be about one-sixth to
one-fourth the size of the field of view. This is about three to four times the size of the
sun or full moon as seen through the eyepiece. A very small bubble should be avoided
because it tends to lag sextant movements so much that it is unreliable as a horizontal
reference.

A considerable amount of practice is needed to develop skill in making reliable
observations with an artificial-horizon sextant, even on land or other steady platform.
At sea or in the air the motions of the craft LAÐ increase the difficulty of observation.
In addition to compounding the difficulty of making coincidence, the craft motion
introduces a sometimes large and rapidly varying acceleration error. That is, motions
of the craft produce an acceleration on the
pendulum or the liquid of the bubble cham-
ber, causing false indication of the hori-
zontal. In smooth air the accelerations
tend to follow a cycle of about one to two
minutes in length. They are largely elimi-

nated by use of an averaging device. In INDEX PRISM
making an observation, the observer at- Sinn
tempts to maintain coincidence continu- EYEPIECE EYEPIECE es GLASS
ously over a period, usually two minutes. LENS PRISM ES -ASTIGMATIZER

POLARIZING

The average altitude, generally indicated
on a dial or drum, is used with the mid time Sal
of observation. Thus, perhaps 60 indi- »

vidual observations, or a continuously

integrated altitude, are available to smooth

out errors of individual observations.

On land or other steady platform a
skillful observer using a two-minute aver- REFLECTOR
aging bubble or pendulum sextant can pus PRISM
measure altitudes to an accuracy of per-
haps 2” (two miles). This, of course, refers
to the accuracy of ri n only, and Fīaune 1513b.—Optical principle of a typical
does not include additional errors such as bubble sextant.
abnormal refraction, deflection of the verti-
cal, computational and plotting errors, etc. In steady flight through smooth air the
error of a two-minute observation is increased to perhaps five to ten miles. Atsea, con-
ditions are different. In a glassy sea with virtually no roll or pitch, results should
approach those on land. However, with even a slight, gentle roll the accelerations to
which a vessel is subjected are quite complex, as indicated by the difficulty one not
accustomed to the sea has in getting his “sea legs" during the early part of a voyage.
If the vessel is yawing, a large Coriolis error (art. 1611) may be introduced. Under
these conditions observational errors of 10-15 miles are not unreasonable. With a
moderate sea, errors of 30 miles or more are common. In a heavy sea, any useful
observations are virtually impossible to obtain. Single altitude observations in a
moderate sea can be in error by a matter of degrees.

Because of the difficulty of observing, and the large acceleration errors encountered
aboard a vessel, bubble and pendulum type sextants have very limited use at sea. A
submarine on war patrol, surfacing only during darkness, may have use for such an
instrument. A large number of observations on a reasonably calm night can produce

418 INSTRUMENTS FOR CELESTIAL NAVIGATION

results of some value. However, even under these conditions some navigators report
better results with a marine sextant and dark-adapted eyes. In pack ice a ship
generally provides a reasonably steady platform. When the horizon is obscured
by ice or haze, polar navigators can sometimes obtain better results with an artificial-
horizon sextant than with a marine sextant. Some artificial-horizon sextants have
provision for making observations with the natural horizon as a reference, but since
this is a secondary usage, results are not generally as satisfactory as by marine sextant.
Because of their more complicated optical systems, and the need for providing a hori-
zontal reference, artificial-horizon sextants are generally much more costly to manu-
facture than marine sextants. Designed for use in the air, they serve a useful purpose
there, but for ordinary use aboard ship they have little to recommend them.

Altitudes observed by artificial-horizon sextant are subject to the same errors as
those observed by marine sextant, except that dip (height of eye) correction does not
apply. Also, when the center of the sun or moon is observed, no correction for semi-
diameter should be made. Chapter XVI explains the various sextant altitude correc-
tions and their applications.

Adjustment of an artificial-horizon sextant should not be attempted by other than
an instrument man qualified to handle the particular type instrument involved. An
exception is the adjustment of the size of the bubble. Also, with some instruments
an easily movable index permits elimination or reduction of index error. This error
can best be determined in an instrument shop equipped with a collimator. If one
is not available, the error can be determined by comparing the average of a number
of observations made at a known point on land with the computed values. A precom-
puted curve of altitude versus time is useful for this purpose. Altitude ‘corrections
equal to the errors but with reversed sign should be applied to computed altitudes.
With normal usage, the index error should not change. In most artificial-horizon
sextants there is no index error.

The care and operation of various types of instruments vary considerably. The
instruction booklet provided with each instrument should serve as the guide. Informa-
tion on certain artificial-horizon sextants, and a general guide to artificial-horizon sextant
observation, is given in H.O. Pub. No. 216, Air Navigation, and other texts.

1514. The marine chronometer is a timepiece having a nearly constant rate.
It is used aboard ship to provide accurate time, primarily for timing celestial observa-
tions for lines of position, and secondarily for setting the ship’s other timepieces. It
differs from a watch principally in that it contains a variable lever device to maintain
even pressure on the mainspring, and a special balance designed to compensate for
temperature variations. A ship in which celestial navigation is used carries one or
more chonometers.

A chronometer is set approximately to Greenwich mean time (GMT) and is not
reset until the instrument is overhauled and cleaned, usually at three-year intervals.
Resetting might disturb the rate. Instead, the difference between GMT and chro-
nometer time (C) is carefully determined, and applied as a correction to all chronometer
readings. This difference, called chronometer error (CE), is “fast” (F) if chronometer
time is later than GMT, and “slow” (S) if earlier. The amount by which chronometer
error changes in one day is called chronometer rate, or sometimes daily rate, con-
sidered “gaining” or “losing” as the chronometer is running faster or slower than the
correct rate. An erratic rate indicates a defective instrument, or need for overhaul.

The methods of determining and applying chronometer error and chronometer rate
are explained in chapter XIX.

INSTRUMENTS FOR CELESTIAL NAVIGATION 419

A chronometer is mounted in gimbals in a box, which should be carefully stowed
to protect the instrument from damage due to heavy rolling and pitching, vibration,
temperature variations, and electrical and magnetic influences. Usually this is done
by fitting the box snugly into a heavily padded case suitably located in the chart room
of merchant ships, and below decks, near the center of motion, in U. S. Navy ships.

The principal maintenance requirement aboard ship is regular winding at about
the same time each day. Aboard United States naval vessels this is customarily done
at about 1130 each morning, and reported to the commanding officer at 1200. Aboard
merchant ships it is usually wound at about 0800. Although a chronometer is designed
to run for more than two days, daily winding helps insure a uniform rate, and constitutes
a daily routine that decreases the possibility of letting the instrument run down. On
the face of each chronometer is a small dial that indicates the number of hours before
the chronometer will be run down. To wind the chronometer, gently turn the instru-
ment on its side, and slide back the guard covering the keyhole. Insert the key and
carefully wind in a counterclockwise direction. Seven half-turns should suffice. If a
chronometer should run down, wait until GMT is nearly the same as the time indicated
before winding. If the chronometer does not start after winding, move the case back
and forth gently. Check the error and rate carefully.

At maximum intervals of about three years, a chronometer should be sent to a good
chronometer repair shop for cleaning and overhaul. When transported by hand,
a chronometer should be clamped in its gimbals and stowed in the large case provided.
When shipped, it should be allowed to run down, and the balance secured by a cork
before the chronometer is stored in the large case.

Detailed instructions for the care and handling of chronometers are available to
U. S. Navy ships in the Bureau of Ships Manual and current directives.

1515. Watches.—In the interest of accuracy, a chronometer is not disturbed more
than necessary. Celestial observations are timed and ship’s clocks set by means of a
comparing watch. This is a high-grade pocket watch which is set by comparison with
a chronometer, and then carried to the place where accurate time is needed. For
celestial navigation, a comparing watch should have a large sweep-second hand which
can be set. A comparing watch used for timing celestial observations should preferably
be set to Greenwich mean time, to avoid the necessity of applying a correction for
each observation.

If the second hand cannot be set, the watch should be set to the nearest whole
minute, being sure that the second hand is in synchronism with the minute hand, and
the watch error (WE) determined. If a watch is to be used for other purposes than
timing of celestial observations, it might preferably be set to zone time. A comparing
watch should be set, or watch error determined, immediately before or after celestial
observations are made, to avoid the necessity for determining and applying a correction
for watch rate, and to eliminate a possible error due to an inaccurate or variable rate.
If a watch set to GMT is used for timing celestial observations, care should be taken to
avoid a possible error of 12 hours or 24 hours. The mental application of zone descrip-
tion to ship’s time indicates the approximate GMT and the Greenwich date. The
subject of time is discussed more fully in chapter XIX. A stop watch may also be
used for celestial observations.

Watches rated to sidereal time (art. 1913) can be purchased, but these have limited
use aboard ship.

1516. Other instruments.—The sextant, chronometer, and comparing watch (or
stop watch) are the principal instruments of celestial navigation. The azimuth circle

420 INSTRUMENTS FOR CELESTIAL NAVIGATION

for observing azimuths of celestial bodies is discussed in article 629. Plotting equipment
is the same as that for dead reckoning (arts. 602-606). A flashlight might be needed
for reading the sextant and the comparing watch. A pocket notebook is desirable
for recording predicted positions of celestial bodies if a star finder is used, and for
recording the observations. A workbook is desirable for solving celestial observations,
so that a permanent record is available. Work forms are desirable, but should form
part of the work book, and not be kept separately. These might be provided by rubber
stamp, or by printing. In the latter case a looseleaf work book may be desirable to
permit arrangement of the various papers in chronological order.

CHAPTER XVI
SEXTANT ALTITUDE CORRECTIONS

1601. Need for correction.—Altitudes of celestial bodies, obtained aboard ship for
the purpose of establishing lines of position, are normally measured by a hand-held
sextant, described in chapter XV. The uncorrected reading of a sextant after such an
operation is called sextant altitude (hs). If the sextant is in proper adjustment, certain
sources of error are eliminated, as explained in article 1509. There remains, however,
a number of sources of error over which the observer has little or no control. For each
of these he applies a correction. When all of these sextant altitude corrections have
been applied, the value obtained is the altitude of the center of the celestial body above
the celestial horizon, for an observer at the center of the earth. This value, called
observed altitude (Ho), is compared with the computed altitude (Hc) to find the altitude
difference (a) used in establishing a line of position, as explained in chapter XVII.

Articles 1602-1620 describe the various corrections. For highly accurate results,
all of these are needed to the greatest accuracy obtainable. The needs of ordinary
practical navigation, however, make no such exacting requirements, and in the course
of his usual day’s work at sea, the navigator has relatively few corrections to apply,
from conveniently-arranged tables readily accessible to him. The detailed information
in articles 1602—1620 is given to (1) provide the basis for a better understanding of the
problem, (2) furnish the information needed for evaluation of results, and (3) provide
a source of reference material beyond that given in the usual navigation text.

1602. Instrument correction (I) is the combined correction for nonadjustable
errors (prismatic error, graduation error, and centering error) of the sextant, as ex-
plained in article 1509. Usually, this correction is determined by the manufacturer,
and recorded on a card attached to the inside of the top of the sextant box. It varies
with the angle, may be either positive or negative, and is applied to all angles measured
by that instrument. For a well-made instrument, the maximum value is so small that
this correction can be ignored for all except the most accurate work. Normally, instru-
ment error of artificial-horizon sextants is so small, considering the precision to which
angles can be measured by such instruments, that no correction is provided.

1603. Index correction (IC), due to lack of parallelism of the horizon glass and
index mirror at zero reading, is discussed in article 1509. Until the adjustment is
disturbed, the index correction remains constant for all angles, and is applicable to all
angles measured by the instrument. It may be either positive or negative. Normally,
artificial-horizon sextants do not have index corrections. Some navigators prefer to
adjust their marine sextants so as to eliminate index correction. This is good practice
if one remembers to check the value each time the sextant is used. Other navigators
prefer to retain an index correction to serve as a reminder to check the values. Since
dip (art. 1606) at any given height of eye is also a constant for all altitudes, the need
for applying both IC and dip can be eliminated by adjusting the sextant so that IC is
numerically equal to dip, but of opposite sign. Such a practice should not be used
unless the observer has some positive system of reminding himself that the value should
be checked each time the instrument is used, and changed if the height of eye changes.
It is of little value if observations are not generally made from the same height of eye.
If personal correction (art. 1604) is constant, it can also be combined with the index

421

422 SEXTANT ALTITUDE CORRECTIONS

correction. However, it is generally preferable to keep each of these corrections
separate, to avoid possible error.

1604. Personal correction (PC) is numerically the same as personal error (art.
1507), but of opposite sign, either positive or negative. If experience indicates the
need for such a correction, it should be made to altitudes of the bodies to which it
applies. However, the observer should be sensitive to changes in its value. Unless
the observer has sufficient evidence to be sure of the existence and relative constancy
of a personal error, no correction should be applied. The possibility of combining
this correction with dip is explained in article 1603.

1605. Tilt correction (N).—The altitude of a celestial body is the vertical angle
above the horizon. The angular distance from the body to any point on the horizon
other than that vertically below the body is greater than the altitude. Therefore, if
the frame of a marine sextant is not held vertical during observation, the angle measured
is too great, and a negative tilt correction is needed. Tables of this correction have
been prepared, but they are generally not applicable because tilt error can be eliminated
by rocking the sextant (art. 1505). If this is not done accurately, an error may remain,
but the observer is not aware of it, and therefore does not know the size of the angle
of tilt. A “ball recording” artificial-horizon sextant used to some extent during World
War II measured the tilt angle, and a tilt correction table was provided with the sextant.
Bubble sextants are kept vertical by centering the bubble. With an artificial horizon,
there is no tilt error because the celestial body is aligned with its own image.

Tilt correction increases with greater angle of tilt. For the same angle it also
increases with greater altitude of the body. There is difference of opinion as to whether
the value continues to increase after an altitude of 45%, or whether it then begins to
decrease. This question resolves itself into one of whether the axis of tilt is horizontal
or in the line of sight to “he body. Evidence seems to favor the line of sight axis, with
the error being maximum at altitude 45%. The correction, if there is one, applies
equally to all celestial bodies. In rough weather, when observation may be difficult,
this error can be minimized by observing bodies that are not high in the sky.

1606. Dip (D) of the horizon is the angle by which the visible horizon (art. 1428)
differs from the horizontal at the eye of the observer (the sensible horizon, art. 1428).
Thus, it applies only when the visible horizon is used as a reference, and not when an
artificial horizon, either internal or external to the sextant, is used. It applies to all
celestial bodies. If the eye of the observer were at the surface of the earth, visible
and sensible horizons would coincide, and there would be no dip. This is never the
situation aboard ship, however, and at any height above the surface, the visible horizon
is normally below the sensible horizon, as shown in figure 1428b. N ormally, then, an
altitude measured from the visible horizon is too great, and the correction is negative.
It increases with greater height of the observer’s eye. Because of this, it is sometimes
called height of eye correction.

If there were no atmospheric refraction, dip would be the angle between the
horizontal at the eye of the observer, and a straight line from this point tangent to
the surface of the earth. In figure 1606a, the eye of the observer is at A, at some
point above the surface of the earth. The line AB is the horizontal through A, and AC
is the tangent through this point. Angle BAC is the dip at A, neglecting refraction.
Since OA is perpendicular to AB, and OD is perpendicular to AC (art. 030), angle
AOD is equal to angle BAC (art. 027). If r is the radius of the earth, and h is the
height of the observer’s eye above the surface, the cosine of angle AOD is uy

+h

The line of sight to the horizon, however, passes through the lowest layers of
the earth's atmosphere, where the density of the atmosphere normally decreases as

SEXTANT ALTITUDE CORRECTIONS 423

B A

DAT

FIGURE 1606a.—Dip without

A FIGURE 1606b.—Dip with refraction.

height above the surface increases. Consequently, the ray of light from the horizon
to the observer's eye is bent by refraction. The result of this terrestrial refraction
is to increase the distance to the horizon, which is at D” (fig. 1606b) instead of at D.
This actual distance, under normal conditions, is given in table 8. Although the
horizon is farther away than it would be if there were no refraction, it appears higher,
for the eye of the observer does not detect the curvature of the line of sight. Therefore,
the horizon appears to be at C’ instead of at C. The dip shown in the tables is BAO’.
The effect of refraction, C” AC, is shown exaggerated for purposes of illustration.

The amount by which refraction alters dip varies with changing atmospheric
conditions. Even the average value has not been established with certainty, and several
methods of computing dip have been proposed. The values given in the critical
table on the inside front cover of the Nautical Almanac were computed by the equation

D=0.97Vh,

where D is the dip, in minutes of arc; and h is the height of eye of the observer, in feet.
Part of this table is repeated on the page facing the inside back cover. The Air
Almanac table was computed independently by a different method, to a precision of
whole minutes. The minor discrepancies thus introduced are not important in practical
navigation.

The values given in the table are satisfactory for practical navigation under
most conditions. An investigation by the Carnegie Institution of Washington showed
that of 5,000 measurements of dip at sea, no value differed from the tabulated value
by more than 2/5, except for one difference of 10/6. Extreme values of more than 30’
have been reported, and even values of several degrees have been encountered in polar
regions. Greatest variations from tabulated values can be expected in calm weather,
with large differences between sea and air temperatures, particularly if mirage effects
are present. Irregularities in the shape of the rising or setting sun may indicate
abnormal conditions. Large variations may also be present shortly after passage of a
squall line, when errors of as much as 15' have been reported. When a temperature
inversion is known to exist, the tabulated dip may be too small, numerically. The
effect of sea-air temperature difference is discussed in greater detail in article 1607.

In the determination of height of eye, position on the ship should be considered,
and also the condition of loading and trim. If an observation is made from a position
differing from the usual place, the altered height of eye should not be overlooked.
Momentary changes due to rolling and pitching can be neutralized, to a large extent,
by making observations from a point on the center line of the vessel, at the axis of
pitch. The possibility of combining dip and index corrections is discussed in article 1603.

Instruments and marine sextant attachments for measurement of dip have been
devised, but are not generally available to the navigator. However, the sextant can

424 SEXTANT ALTITUDE CORRECTIONS

be used without special attachment if it has an arc of sufficient length. The method
is to measure the “altitude” of the opposite horizon; that is, the angle (through the
zenith) between the lines of sight to the horizon on reciprocal bearings. This is equal
to 180° plus the sum of the dip in the two directions. If these can be considered
equal, and under stable conditions the difference is probably not great, dip is equal to
half the difference between 180 and the measured angle (corrected as necessary).
However, direct measurement of an angle greater than 180° cannot be made with an
ordinary sextant because the reflecting surfaces of the sextant mirrors would have an
angle of more than 90° with respect to each other, and a ray of light could not be reflected
from the index mirror to the surface of the horizon glass. Satisfactory results can
sometimes be obtained by observing the altitude of a body first by facing toward
it, in the usual manner, and then by facing 180° from it (a back sight, art. 1633).
In the case of the sun or moon, the same limb should be observed in both directions.
(It will appear as the opposite limb.) Instrument correction, index correction, and
personal correction, as applicable, are applied, and the two altitudes added. The
difference between this value and 180% is the sum of the dip in the two directions,
if allowance is made for the change of altitude between observations. Unless the
body is near the celestial meridian, this is best done by taking a direct sight, a back-
sight, and another direct sight, with equal time intervals between observations. The
average of the two direct sights is used.

Since variations from normal dip may be one of the principal sources of error in
celestial observations, a method of determing dip at sea can be of considerable value.
If such a method is not available, the observer should be alert to conditions affecting
terrestrial refraction. Any observation taken within half an hour after passage of
a squall line should be regarded as unreliable. If dip cannot be measured, the effects
of abnormal conditions can be minimized by observing three bodies differing in azimuth
by about 120° (or four bodies by 90°, five bodies by 72°, etc.). If the error is constant
in all directions, its effect is to increase (or possibly to decrease) the size of the closed
figure formed by the lines of position without altering the position of its center. Hence,
the size of the figure is not necessarily an indication of the accuracy of the fix.

Recent evidence accumulated by the Office of Naval Research indicates that dip
may fluctuate somewhat erratically over a range of at least several tenths of a minute,
in addition to the slower changes associated with abnormal conditions. This may be
caused by irregularities in the atmosphere, producing variations in the refraction.
This effect cannot be removed either by measurement of dip or by observations of
bodies equally spaced in azimuth, because the dip is likely to change between observa-
tions. Over a period of several minutes the variation from the mean value can probably
be considered a random error (art. 2904) and therefore might be reduced by making
a large number of observations of a single body, and plotting the results on cross-
section paper in the manner explained in article 1507.

If land, another ship, or other obstruction is between the observer and his horizon,
an altitude can be measured by using the water line of the obstruction as a horizontal
reference, if its distance from the observer is known. In this case the dip is greater
than that given in the almanacs. Table 22 gives the values to be used.

Further discussion of refraction is given in article 1613. When abnormal astro-
nomical refraction occurs, abnormalities in terrestrial refraction can be expected.

1607 . Sea-air temperature difference correction (S).—Under normal atmospheric
conditions, the temperature and pressure both decrease at standard rates with increase
in height above the surface. Accordingly, the density of the atmosphere also decreases
at a standard rate, which is uniform over the height encountered aboard ship. The
effect of refraction upon dip, as given in the tables, is based upon this standard rate.

SEXTANT ALTITUDE CORRECTIONS 425

Usually, the difference between standard and actual conditions is not great enough to
introduce important errors in the assumption that standard conditions exist.

However, when there is a difference between sea and air temperatures at the
surface, the air in contact with the sea is warmed or cooled by the sea water, upsetting
the normal rate of decrease near the surface. The effect is greater as the temperature
difference increases. It may extend only a few inches above the surface, or for hundreds
of feet. Under extreme conditions, if the air is very much colder than the water, the
surface may steam. The frost smoke rising from the water may obscure the horizon,
and under the most severe conditions it may rise to such heights as to interfere with
visibility. Celestial bodies can be seen, but altitudes cannot be measured with a
marine sextant because of lack of a horizon.

Under less extreme conditions, the dip is altered, but observations may seem
normal. If the water is warmer than the air, the horizon is depressed and dip is
increased. Under these conditions the measured altitudes are too great. Therefore,
as a correction to the altitude, the sea-air temperature difference correction is negative
when the water is warmer than the air. When the air is warmer, the reverse is true,
and the altitude correction is positive.

Various attempts have been made to establish a simple relationship between the
sea-air temperature difference and the correction, but the results reported by different
investigators differ considerably. This is due, in part, to difference of opinion as to
the height and depth at which measurements should be made, difficulties in obtaining
accurate readings near the surface, variations of temperature differences at the ship
and along the line of sight to the horizon, and influence of the vessel on temperatures
in its immediate vicinity. Wind, too, has a considerable effect. On a calm day, the
lower portion of the atmosphere tends to form in layers, without mixing. If there is
a strong, gusty wind, turbulence in the air minimizes the effect due to temperature
difference. Actually, sea temperature serves only to indicate temperature at the
surface, but temperature gradient in the water may be large, as in the air. Therefore,
the ideal would seem to be the measurement of air temperature at the surface, and at
some greater height, since it is the abnormal lapse rate (decrease of air temperature
with height) that produces the change in normal terrestrial refraction.

Suggested factors based upon difference between temperature of the sea and air
vary from about 0/11 per degree Fahrenheit (0:20 per degree Celsius) to 0:21 per
degree Fahrenheit (0/37 per degree Celsius). The average of these is about 0:16 per
degree Fahrenheit (0/28 per degree Celsius). Thus, the correction is about one-sixth
of a minute per degree Fahrenheit, or one minute for each six degrees. The methods
of measuring sea and air temperature are discussed in article 3712.

This correction applies to all bodies when the sea horizon is used. However, it
should be used with caution, and only under conditions which indicate that better
results will be obtained if it is used. Under normal conditions, it is not used. If
abnormal conditions are suspected, observations are avoided or considered of question-
able reliability; or the precautions indicated in article 1606 are used. If allowance for
abnormal conditions is made by using an altered value of dip, as one obtained by
measurement, the sea-air temperature difference correction is not used. That is, if
allowance is made for abnormal dip, either the tabulated value of dip is altered or the
sea-air temperature correction is applied, but not both.

1608. Wave height correction (W).—Corrections for dip are based upon the as-
sumption of a calm sea. Waves disturb this condition, causing the surface to be
alternately raised and lowered. At the horizon, the troughs of waves are usually not
visible. Through binoculars, irregularities in the line forming the horizon can some-
times be seen, but observations are made from the tops or nearly the tops of the waves.

426 SEXTANT ALTITUDE CORRECTIONS

Tf it is assumed that the vessel is not raised and lowered by the waves, the line of
sight to the horizon is raised by waves. Refer to figure 1608. The wavy line repre-
sents the surface of the sea, with the size of the waves exaggerated. The equivalent
still water level is shown by the broken line. The line AB is the curved tangent to
the still water level, representing the line of sight if there were no waves. The line
AC represents the actual line of sight to the top of a wave. If the slight curvature

E . CB
of AB and AC is neglected, the tangent of the wave height correction (CAB) is AB

F1IGURE 1608.— Effect of wave height on line of sight to horizon.

In this case, CB is approximately one-half the wave height, and AB is the distance to
the horizon, bothin feet. Thatis, ABis the value from table 8 multiplied by 6076.11549

. if nautical miles are used, or 5,280 if statute miles are used. The increased height
of the sea decreases this distance slightly, but the decrease is too small to be a considera-
tion except at low heights of eye or with very high waves. For waves two feet high, the
correction is 0:2 for a height of eye of seven feet. For waves six feet high, the correction
is 0:3 for a height of eye of 30 feet. For waves 20 feet high, the correction is 1/3 for
height of eye of 15 feet, 0/9 for 30 feet, and 0/7 for 50 feet. For waves 40 feet high,
the correction is 2/0 at 30 feet, and 1/1 at 80 feet.

This correction is always positive, and applies to all celestial bodies, but only if
the sea horizon is used as a reference. Normally, it is not applied because of the
difficulty of determining (1) wave height at the horizon, and (2) height of eye above
the equivalent calm level of the sea. Better practice is usually to estimate height of
eye above the wave tops, allowing for motions of the vessel, and make no correction.

1609. Sea tilt correction (H).—The height of the sea at any place is affected by the
density of the sea water, its temperature, and atmospheric pressure. Because of differ-
ences in these values, the height varies from place to place. This results in tilting of
the surface of the sea, which is “downhill” from the ridge of high water to that of low
water. The maximum tilt due to these causes is probably a little more than 1"5. The
wave caused by the tides also tilts the sea surface. However, on the open sea, tides
are seldom more than about two and one-half feet high, and the distance from crest
to trough is about 5,400 miles, or one-quarter of the great-circle distance around the
earth. Under these conditions, the maximum tilting of the sea surface due to tides is
about 07025. "This may be increased somewhat by storm waves (art. 3311) or tsunamis
(art. 3310). In confined waters, particularly in a funnel-shaped area where tides
enter from the wide end and progress up à narrowing estuary, the error may be very
much greater, possibly reaching a value of half a minute. The expression tide cor-
rection may be used instead of “sea tilt correction."

The correction is positive in the direction of high water and negative in the direction
oflow water. Between these directions it is equal approximately to the value in these
directions multiplied by the cosine of the angle between the wave axis (the line per-
pendicular to the wave front) and the azimuth of the body. It applies equally to all
bodies when the visible horizon is used as the reference. In practice it is not applied.

SEXTANT ALTITUDE CORRECTIONS 427

1610. Deflection of the vertical (V).—Usually, the direction of gravity is assumed
to be normal (vertical) to the spheroidal surface of the earth. This assumption is not
quite correct. Irregularities in density and height of the material making up the
surface crust of the earth result in slight alterations of the direction of gravity. This
deflection of the vertical is most apparent near high mountains bordering a deep sea
(fig. 1610) where an extreme value of more than 1/1 might be encountered. An
experienced geodesist can predict the value with an average error of perhaps 50 percent

Figure 1610.—Deflection of the vertical. AB is normal to spheroid. AC is normal to
geoid. Angle BAC is deflection of the vertical.

of the true value. On land, deflection of the vertical can be measured by carefully
determining a highly accurate position by celestial observation, called an astronomical
position (composed of astronomical latitude and astronomical longitude), and com-
paring this position with one determined by measurement (either by triangulation or
trilateration) from a “known” position. Deflection of the vertical is always a relative
value depending upon the position considered “known.” A position expected to be
relatively free from deflection is usually used as the starting point for a system of
measurements, and is known as a datum. The North American Datum of 1927, used
for surveying most of North America, is a station known as Meades Ranch, Kansas.

It has not been possible to measure deflection of the vertical by means of a single
observation at sea, due largely to lack of a stable platform and the inability to extend
triangulation or trilateration to ships at sea, with the required accuracy. However,
this correction is of interest only when establishing a position relative to a fixed point
on land, as when a shore-based electronic aid is used. For normal purposes of celestial
navigation, it is not significant, for it is usually quite small. Moreover, it changes
gradually from the position of the vessel to the destination, so that as land is approached,
deflection of the vertical tends to approach the value on shore.

The shape of the earth, if surface irregularities (mountains, etc.) are neglected, is
considered a spheroid if deflection of the vertical is neglected, and a geoid if that
deflection is considered. The surface of the geoid is everywhere perpendicular to the
direction of gravity. In general, the geoidal surface is higher than the spheroidal
surface ashore, and lower at sea, as shown in figure 1610.

Normally, values of deflection of the vertical are not available to the navigator,
and are not needed by him. In precise work, however, such values for a particular area
might be furnished. The correction is negative in the direction toward which the
zenith is deflected, and positive in the opposite direction. In any other direction it is
equal approximately to the maximum deflection times the cosine of the angle between
the given direction and the direction of maximum deflection, taking the sign of the
nearest maximum deflection. It is applicable to all celestial bodies, whether the
natural sea horizon or an artificial horizon is used.

428 SEXTANT ALTITUDE CORRECTIONS

1611. Coriolis correction (Z).—When a body is in motion over the surface of the
earth, its motion in space is a combination of its motion relative to the earth, and the
motion of the earth. Because of the rotation of the earth, principally, the path is a
curved one. As a result, there is an apparent force causing deflection to the right in
the northern hemisphere and to the left in the southern hemisphere. Because of this
Coriolis force, ocean currents set in motion by wind flow in a direction to the right
(northern hemisphere) of the direction in which the wind blows. Wind, too, is de-
flected. Instead of blowing directly from an area of high pressure to one of low pres-
sure, and soon neutralizing the pressure difference, it moves toward one side. The
result is the characteristic circulation around highs and lows.

The liquid of the bubble chamber of a bubble sextant, and a pendulum, are similarly
affected, causing them to give a false indication of the vertical (or horizontal). The
same is true of an artificial horizon. The equation for the deflection is

Z=2'62 S sin L+0'146 S? sin C tan L—5:25 SC’,

where Z is the Coriolis correction, S the speed over the surface of the earth in units of
hundreds of knots, L the latitude, C the true course angle, and C’ the rate of change of
true course angle in degrees per minute. The first term, 2'62 S sin L, corrects for motion
along a great circle; the second term, 07146 S? sin C tan L, is an additional correction
for the difference between motion along a rhumb line, and equivalent motion along a
great circle; and the third term, 5/25 SC’, is an additional correction for departures
from the course, being negative (as shown) if the departure is right in the northern
hemisphere or left in the southern hemisphere. Coriolis corrections (first term only)
are given on the inside back cover of the Air Almanac.

Coriolis correction may be either positive or negative, and varies with speed and
latitude. It applies to all bodies equally, and therefore can be applied to the altitude,
the assumed position, or even as an adjustment to the plotted line of position or fix.
If the AP or fix is adjusted, it is moved perpendicular to the course line, to the right in
the northern hemisphere and to the left in the southern hemisphere, unless the third
term is of such magnitude and sign as to make the entire correction negative, when it
is applied in the opposite direction. If the correction is applied to the altitude, the
value obtained by formula is multiplied by the sine of the relative azimuth. In the north-
ern hemisphere, the resulting altitude correction is positive if the celestial body is on
the starboard side, and negative if on the port side. In the southern hemisphere these
signs are reversed. These signs assume that the value obtained by the formula is posi-
tive. If it is negative, all signs are reversed.

At ship speeds, the Coriolis correction is not large, unless the vessel is yawing con-
siderably. For a ship steaming at 20 knots on a steady course of 090° at latitude 40°,
the maximum Coriolis correction is 0/3 for a celestial body which is abeam. Accelera-
tion error due to rolling and pitching of the vessel is usually much greater than this,
and is the principal reason why bubble or pendulum sextants are not often used
aboard ship, as indicated in article 1513.

There is no Coriolis correction when the visible horizon is the horizontal reference.

1612. Acceleration correction (C).—If an artificial horizon-sextant with a bubble
or pendulum is used, the liquid of the bubble chamber or the pendulum is affected
by all accelerations of the instrument. The same is true of the free surface of the
liquid of an artificial horizon. With high accelerations such as those due to rolling
and pitching of a vessel, or changes of course or speed, the error can be very large.
It is for this reason that such instruments are not customarily used aboard ship. Under
normal conditions at sea the navigator does not have the information needed to compute
the correction. The error is minimized by making observations at the center of roll

SEXTANT ALTITUDE CORRECTIONS 429

and piteh of the ship, or averaging the values taken at both ends of a roll or piteh.
Observations should not be made during a turn or when the speed is being changed.
Even with these precautions the error is usually unacceptably large except with an
almost flat, calm sea. The effect on the level of the sea surface due to accelerations
of the earth in its rotation or revolution is considered negligible.

The correction may be either positive or negative, and applies equally to all
bodies observed with a bubble or pendulum sextant.

1613. Refraction (R).—Light, or other radiant energy, is assumed to travel in
a straight line at uniform speed, if the medium in which it is traveling has uniform

N

FIGURE 1613a.—No refraction oc- FIGURE 1613b.—A ray entering a
curs when light enters denser denser medium at an oblique
medium normal to the surface. angle is bent toward the normal.

properties. But if light enters a medium of different properties, particularly if the
density is different, the speed of light changes somewhat. Light from a single point
source travels outward in all directions, in an expanding sphere. At great distances,
a small part of the surface of this sphere can be considered flat, and light continuing to
emanate from the source can be considered similar to a series of waves, in some re-
spects resembling the ocean waves encountered at sea. If these light “waves” enter
a more dense medium, as when they pass from air into water, the speed decreases.
If the light is traveling in a direction perpendicular to the surface separating the two
media (in this case vertically downward), all parts of each wave front enter the new
medium at the same time, and so all parts change speed together, as shown in figure
1613a. But if the light enters the more dense medium at an oblique angle, as shown
in figure 1613b, the change in speed occurs progressively along the wave front as the
different parts enter the more dense medium. This results in a change in the di-
rection of travel, asshown. This change in direction of motion is called refraction. [flight
enters a more dense medium, it is refracted toward the normal (NN’), as in figure 1613b.
If it enters a less dense medium, it is refracted away from the normal, as light traveling
in the opposite direction to that shown in figure 1613b.

The amount of the change in direction is directly proportional to the angle between
the direction of travel and the normal (angle ABN in figure 1613b). The ratio of this
angle to the similar angle after refraction takes place (angle CBN’ in figure 1613b)
is constant, so that as one increases, the other increases at the same rate. Hence,
the difference between them (the change in direction) also increases at the same rate.
Therefore, if the incident ray (AB) is nearly parallel to the surface at which refraction
takes place, relatively large amounts of refraction occur.

The amount of refraction is also directly proportional to the relative speed of travel
in the two media. Various substances are compared by means of a number called the

430 SEXTANT ALTITUDE CORRECTIONS

index of refraction (u), which depends primarily upon the density of the — x
In figure 1613b, angle ABN is called the angle of incidence (6) and angle CBN
the angle of refraction (6). These are related by Snell’s law, which states that the
sines of the angle of incidence and angle of refraction are inversely proportional to the
indices of refraction of the substances in which they occur. Thus, if ui is the index of
refraction of the substance in which ¢ occurs, and us is the index of refraction of the
substance in which 0 occurs

sin ó vs

sin 6 my

If the index of refraction changes suddenly, as along the surface separating water
and air (as shown in fig. 1613b), the change in direction is equally sudden. However,
if a ray of light travels through a medium of gradually changing index of refraction,
its path is curved, undergoing increased refraction as the index of refraction continues
to change. This is the situation in the earth's atmosphere, which generally decreases in
density with increased height. The gradual change of direction occurring there is
called atmospheric refraction. The bending of a ray of light traveling from a point
on or near the surface of the earth, to the eye of the observer, is called terrestrial
refraction. This affects dip of the horizon, as discussed in article 1606. A ray of
light entering the atmosphere from outside, as from a star, undergoes a similar bending
called astronomical refraction.

The effect of astronomical refraction is to make a celestial body appear higher
in the sky than it otherwise would, as shown in figure 1613c. If a body is in the zenith,
its light is not refracted, except for a very slight amount when the various layers of
the atmosphere are not exactly horizontal. As the zenith distance increases, the re-
fraction becomes greater. At an altitude of 20? it is about 2:6; at 10?, 5:3; at 5?,
9:9; and at the horizon, 34:5. A table of refraction is given on the inside front cover
and facing page of the Nautical Almanac, in the columns headed “Stars and Planets."
As height above the surface of the earth increases, light from an outside source travels

through less of the atmosphere,
x Apparent Position and refraction decreases. At
L shipboard heights the difference

dré is negligible, but at aircraft

54 Actual Position heights the change is a consid-
⁄ eration. Therefore, the table
given on the inside back cover

of the Air Almanac is a double-
entry table.

The values given in the
tables are for average condi-
tions. This is called mean

FIGURE 1613c.—Astronomical refraction. refraction. A considerable
amount of research has been con-

ducted to determine the mean values, the conditions under which values differ from
the mean, and the amount of such differences. A number of different mean refraction
tables have been produced. Values in the various tables differ slightly because of dif-
ferent assumptions, different methods of observation, and different observed results
under apparently similar conditions. This last source of difference is due primarily to
the fact that conditions could be determined at the position of the observer, but not
at various points along the line traveled by the ray of light in passing through the
atmosphere. Nevertheless, the various tables agree very well down to a minimum
altitude of 2%. Below this, the refraction is erratic, and differences between values

SEXTANT ALTITUDE CORRECTIONS 431

in the various tables are not as important as differences between mean and instan-
taneous values. The values given in the almanac tables are in excellent agreement with
those actually measured.

Because of their variability, refraction and dip (also affected by refraction) are
the principal uncertainties in the accuracy of celestial observations of a careful observer.
As a result of this uncertainty, navigators formerly avoided all observations below some
arbitrary altitude, usually 15%. While this is still good practice if higher bodies are
available, the growing knowledge of atmospheric refraction has increased the confi-
dence with which navigators can use low-altitude sights. There is little reason for lack
of confidence in sights as low as 5°. Below this, other available corrections should be
applied (art. 1632). If altitudes below 2° are used, larger probable errors should be
anticipated, even with the use of additional corrections. Generally, the error in tabu-
lated refraction should not exceed two or three minutes, even at the horizon. However,
a knowledge of conditions affecting refraction is helpful in determining the confidence
to be placed in such observations. Since refraction elevates both the celestial body and
the visible horizon, the error due to abnormal refraction is minimized if the visible
horizon is used as a reference.

The atmosphere contains many irregularities which are erratic in their influence
upon refraction. Normally, the navigator has not the information needed to correct
for such conditions, but only to recognize their existence. As indicated in article 1606,
observations made within half an hour after passage of a squall might be considerably
in error. The passage of any front might have a similar effect. A temperature inver-
sion (art. 3815) may upset normal refraction. Abnormal values may be expected when
there is a large difference between the temperature of the sea and air. With an absence
of wind, the air tends to form in layers. When this condition becomes extreme, mirage
effects occur. Sometimes the rising or setting sun or moon appears distorted. Multiple
horizons may appear, and other ships or islands may seem to float a short distance
above the water. Under any such conditions large errors in refraction might be encountered.

Conditions causing abnormal refraction can be expected to occur with considerable
frequency in the vicinity of the Grand Banks, along the west coast of Africa from
Mogador to Cap Blanc and from the Congo to the Cape of Good Hope, in the Red Sea
and the Persian Gulf, and over ice-free water in polar regions. Abnormal refraction
may be encountered when offshore winds blow from high, snow-covered mountains to
nearby tropical seas, as along the west coast of South America; where cold water from
large rivers such as the Mississippi flows into warm sea water; when a strong current
flows past a bay or coast, causing colder water to be drawn to the surface, as in the Bay
of Rio de Janeiro and Santos, and along the Atlantic coast of Africa between Cape
Palmas and Cape Three Points during the time of the southwest monsoon; and along
the east coast of Africa in the vicinity of Capo Guardafui during the summer. In the
temperate zones abnormal refraction is most common during the spring and summer.

Of the more systematic errors which affect refraction, two can be evaluated, and
corrections applied. These are for air temperature (art. 1614) and atmospheric pres-
sure (art. 1615). However, these corrections are based upon assumed standard gradients
(changes) with height. Temperature gradients are known to vary with type of weather,
time of day, season, etc., as well as in a more irregular manner. The various layers of
the atmosphere are assumed to be horizontal to the surface, but this is not always the
situation. When they tilt, refraction changes. No correction for this cause is available.

Humidity has a relatively slight effect on refraction. In completely dry air,
astronomical refraction at the horizon (sometimes called horizontal refraction) 1s
perhaps 0/1 greater than the tabulated value. In very moist air, sometimes encountered

in the tropics, the maximum refraction might possibly decrease by as much as 0/2.

432 SEXTANT ALTITUDE CORRECTIONS

Wind speed is believed to have some effect upon refraction and dip. Apparently,
refraction increases as wind speed becomes greater, the amount of change increasing
in direct proportion to the square of the wind speed. At 20 knots the change is believed
to be about 0/1 at the horizon, and 0115 at altitude 2%. At 30 knots these values are

imately doubled. Å
por ges a slight effect upon refraction because of the decrease in the radius
of the earth and the increase of gravity as latitude increases. Both radius and gravity
affect density of the atmosphere, and hence refraction. Because of this, mean horizontal
refraction is decreased about 0/2 to 0/3 at the equator, and increased about an equal
amount at the poles. For nermal altitudes the change is negligible. I. |

Azimuth may have an effect at some locations. The reason for this is not entirely
clear, but is believed to be due to a somewhat permanent tilt of certain atmospheric
layers. A series of observations at a location in Germany indicated a difference of as
much as 0/5 between northerly and southerly observations of 0° altitude. At altitude 2°
the difference was only 3”. The navigator normally does not have information required
to apply such a correction, nor is it of navigational significance at normal altitudes.
However, differences should be anticipated when the appearance of the horizon varies
with azimuth, or large sea temperature differences exist within a few miles, as near the
edge of the Gulf Stream. The same might be true near land, particularly in the tropics.

Dispersion of light of various colors results in light from blue stars being refracted
more than light from red stars. At the horizon the maximum correction would be
about 2” for blue stars, and 8” for red stars. At 5° the amount would be less than one-
third these values.

Errors in the tables due to incorrect assumptions are probably too small to be of
practical interest to the navigator. If increased knowledge indicates errors exist in
the tables, corrected values will undoubtedly be provided.

Since refraction causes celestial bodies to appear elevated in the sky, they are
above the horizon longer than they otherwise would be. The mean diameter of the
sun and moon are each about 32’, and horizontal refraction is 34/5. Therefore, the
entire sun or moon is actually below the visible horizon when the lower limb appears
tangent to the horizon. The effect of dip is to further increase the time above the
horizon. Near the horizon the sun and moon appear flattened because of the rapid
change of refraction with altitude, the lower limb being raised by refraction to a greater
extent than the upper limb.

As a correction to sextant altitudes, refraction is negative because it causes the
measured altitude to be too great. It decreases with increased altitude, and applies to
all celestial bodies, regardless of sextant or horizon used.

1614. Air temperature correction (T).—The Nautical Almanac refraction table is
based upon an air temperature of 50°F (10°C) at the surface of the earth. At other
temperatures the refraction differs somewhat, becoming greater at lower temperatures,
and less at higher temperatures. Table 23 provides the correction to be applied to
the altitude to correct for this condition. If preferred, this correction can be applied
with reversed sign to the refraction from the almanac, and a single refraction applied to
the altitude. A combined correction for nonstandard air temperature and nonstandard
atmospheric pressure (art. 1615) is given on page A4 of the Nautical Almanac. The
correction for air temperature varies with the temperature of the air and the altitude
of the celestial body, and applies to all celestial bodies, regardless of the method of
observation. However, except for extreme temperatures or low altitudes, this correc-
tion is not usually applied unless results of unusual accuracy are desired.

1615. Atmospheric pressure correction (B).—The Nautical Almanac refraction
table is based upon an atmospheric pressure of 29.83 inches of mercury (1010 millibars)

SEXTANT ALTITUDE CORRECTIONS 433

at sea level. At other pressures the refraction differs, becoming greater as pressure in-
creases, and smaller as it decreases. Table 24 provides the correction to be applied to
the altitude for this condition. A combined correction for nonstandard air tempera-
ture (art. 1614) and nonstandard atmospheric pressure is given on page A4 of the
Nautical Almanac. If the correction is to be applied to the refraction, reverse the
sign. This correction varies with atmospheric pressure and altitude of the celestial
body, and is applicable to all celestial bodies, regardless of the method of observation.
However, except for extreme pressures or low altitudes, this correction is not usually
applied unless results of unusual accuracy are desired.

1616. Irradiation correction (J).—When a bright surface is adjacent to a darker
one, an optical illusion takes place and the bright area appears to be larger than
is actually the case. This is called irradiation. Thus, when the sky is considerably
brighter than the water, the horizon appears slightly depressed. The apparent diameter
of the sun is increased slightly by irradiation, and the bright stars appear to have a
measurable diameter. Opinions differ on the need for a sextant altitude correction for
irradiation. It is probable that during twilight there is insufficient contrast between
sky and water to warrant the use of a correction. During the day a slight apparent
depression of the horizon may occur. Altitudes of the lower limb of the sun should
not be altered because the irradiation effect of sun and horizon are in the same direction
and cancel out, approximately. The effect on the upper limb, however, is opposite to
that on the horizon. The table of upper limb corrections of the sun given on the
inside front cover and facing page of the Nautical Almanac includes an irradiation cor-
rection of (—)1:2, half for the apparent lowering of the horizon, and half for the
apparent raising of the upper limb. No irradiation correction is given for bodies other
than the sun. "Thus, in terms of available corrections, irradiation is negative, is essen-
tially constant, and applies only to the upper limb of the sun when the visible horizon
is used as the reference. If an artificial horizon is used, it applies to either limb.

1617. Semidiameter (SD) of a celestial body 1s half the angle, at the observer's
eye, subtended by the visible disk of the body. "The position of the lower or upper
limb of the sun or moon with respect to the visible horizon can be judged with greater
precision than that of the center of the body. For this reason it is customary, when
using a marine sextant and the visible horizon, to observe one of the limbs of these two
bodies, and apply a correction for semidiameter. Normally, the lower limb is used if
it is visible. In the case of a gibbous or crescent moon, however, only the upper limb
may be available.

The semidiameter of the sun varies from a little less than 15'8 early in July, when
the earth is at its greatest distance from the sun, to nearly 16:3 early in January, when
the earth is nearest the sun. In the Nautical Almanac the semidiameter of the sun at
GMT 12" on the middle day of each page opening of the daily page section is given to
the nearest 0/1 at the bottom of the sun's GHA column. "The altitude correction tables
of the sun, given on the inside front cover and facing page, are divided into two parts,
to be used during different periods of the year. The mean semidiameter of each period
is included in the tables of both upper and lower limb corrections. The semidiameter
each day is listed to the nearest 0701 in the American Ephemeris and Nautical Almanac.
In the Air Almanac the semidiameter to the nearest whole minute (always 16’) is given
near the lower right-hand corner of each odd-numbered daily page.

The moon undergoes a similar change in semidiameter as its distance from the
earth varies. However, because of the greater eccentricity of the moon's orbit than
that of earth, the variation in semidiameter is also greater, varying between about
14/7 and 16/8. The variation is more rapid, partly because of the greater spread of
values, but principally because the moon completes its revolution in approximately

434 SEXTANT ALTITUDE CORRECTIONS

one month, while the earth makes one revolution per year. In the Nautical Almanac,
semidiameter of the moon at 12" each day is given to the nearest 0/1 at the bottom of
the moon data columns. The correction for semidiameter of the moon is included in
the corrections given on the inside back cover and facing page. In the Air Almanac,
semidiameter is given to the nearest whole minute, being shown on the daily pages,
immediately below the value for the sun. The semidiameter at intervals of half a day
is given to the nearest 0701 in the American Ephemeris and Nautical Almanac.

The navigational planets have small semidiameters. For Venus it varies between
about 5” and 32”; for Mars, 2"7 to 126; for Jupiter, 16" to 25"; and for Saturn, 7”
to 10”. The value for any date is given in the American Ephemeris and Nautical
Almanac, but not in the Nautical Almanac or Air Almanac because the apparent centers
of these bodies are customarily observed.

Stars have no measurable semidiameter.

The computed altitude of a body refers to the center of that body, since the coordi-
nates listed in the almanacs are for the center. If the lower limb is observed, the sextant
altitude is less than the altitude of the center of the body, and hence the correction is
positive. If the upper limb is observed, the correction is negative. The correction
does not apply when the center of the body is observed, which is usually the case when
an artificial-horizon sextant is used. With a marine sextant and either the natural or
an artificial horizon, semidiameter is customarily applied to observations of the sun
and moon, but not other celestial bodies.

1618. Phase correction (F).—Because of phase (art. 1423), the actual centers of
planets and the moon may differ somewhat from the apparent centers. Average cor-
rections for this difference are included in the additional corrections for Venus and
Mars given on the inside front cover of the Nautical Almanac. They should be applied
only when these bodies are observed during twilight. At other times the magnitude
and even the sign of the correction might differ from those tabulated, because of a
different relationship between the body and the horizon. The phase correction for
navigational planets other than Venus and Mars is too small to be significant.

A phase correction may apply to observations of the moon if the apparent center
of the body is observed, as with an artificial-horizon sextant. However, no provision
is made for a correction in this case; the need for it can be avoided by observing one of
the limbs of the body.

Phase correction does not apply to observations of the sun or stars.

1619. Augmentation (A).—As indicated in article 1617, semidiameter changes
with distance of the celestial body from the observer, becoming greater as the distance
decreases. The semidiameter given in the ephemeris and used in the almanacs is
for a fictitious observer at the center of the earth. If the celestial body is on the actual
observer’s horizon, its distance is approximately the same as from the center of the
earth; but if the body is in the zenith, its distance is less by about the radius of the
earth (fig. 1412). Therefore, the semidiameter increases as the altitude becomes
greater. This increase is called augmentation. For the moon, the augmentation
from horizon to zenith is about 0/3 at the mean distance of the moon. At perigee
it is about 2” greater, and at apogee about 2” less. Augmentation of the sun from
horizon to zenith is about 1/24 of one second of arc. For planets it is correspondingly
small, varying with the positions of the planets and the earth in their orbits. At any
altitude the augmentation is equal to the sine of the altitude times the value at the zenith.

Augmentation increases the size of the semidiameter correction, whether positive
or negative. It is included in the moon correction tables on the inside back cover and
facing page of the Nautical Almanac. It is not included in the correction tables of
other bodies or in the Air Almanac tables.

SEXTANT ALTITUDE CORRECTIONS 435

1620. Parallax (P) is the difference in apparent position of a point as viewed
from two different places. Tf a finger is held upright at arm's length and the right
and left eyes closed alternately, the finger appears to move right and left a short dis-
tance. Similarly, if one of the nearer stars were observed from the earth and from
the sun, it would appear to change slightly with respect to the background of more
distant stars. This is called heliocentric parallax or stellar parallax. The nearest
star has a parallax of less than 17. Even if the value were greater, no correction to
sextant altitudes would be needed, for the
difference would be reflected in the tabulated Z
position of the body.

However, positions of celestial bodies
are given relative to the center of the earth,
while observations are made from its sur-
face. The difference in apparent position
from these two points is called geocentric (

\

[
|
|
|
|
|
|
|

parallax. If a body is in the zenith, at Z
in figure 1620, there is virtually no parallax,
for the line from the body to the center of
the earth passes approximately through the
observer at A. Suppose, however, the moon
is at M. From A it appears to be along the
line AM, while at the center of the earth it Figure 1620.—Geocentric parallax.
would appear to be along OM. The altitude

at A would be the angle SAM, and that at O the angle COM. Angle COM is equal
to angle SBM (art. 027), which is exterior to the triangle ABM, and hence equal to
the sum of angles SAM and AMO (art. 028).

Since

ZCOM= ZSBM= ZSAM-+ LAMO,
then

ZAMO= ZCOM— ZSAM.

That is, the angle at the body between lines to the observer and the center of the
earth is equal to the difference in altitude at the two places. Angle AMO is the geo-
centric parallax. Since it varies with altitude, it is sometimes called parallax in alti-
tude (P in A). The maximum value for a visible body occurs when that body is on
the horizon, at S. At this position the value is called horizontal parallax (HP).

The sine of horizontal parallax is equal to a where r is the radius of the earth,
and D the distance of the body from the center of the earth. Thus, the sine of the
horizontal parallax is directly proportional to the radius of the earth, and inversely
proportional to the distance of the body. Since the earth is an oblate spheroid, and
not a sphere, the parallax varies slightly over different parts of the earth. The value
at the equator, called equatorial horizontal parallax, is greatest, and the value at the
poles, called polar horizontal parallax, is least. The difference is not enough to be of
practical navigational significance. The parallax in altitude is equal almost exactly to
the horizontal parallax times the cosine of the altitude (h). That is,

P in A=HP cos h.

The moon, being nearest the earth, has the greatest parallax of any celestial body
used for navigation. The equatorial horizontal parallax at mean distance is 57'02'70.
As the distance of the moon varies, so does the parallax, becoming greater as the moon

436 SEXTANT ALTITUDE CORRECTIONS

approaches closer to the earth, and less as it recedes, horizontal parallax varying several
minutes each side of the value at mean distance. For the sun, mean equatorial hori-
zontal parallax, called solar parallax, is 8780. Differences in position on the earth, and
distance from the sun, have small effect, the maximum variation due to the latter being
about 0/15. Horizontal parallax of the planets varies considerably because of the large
differences in their distances from the earth. For Venus the value varies between 5”
and 32”; for Mars, 3” and 24”; for Jupiter, 1” and 2”; and for Saturn, 078 and 1^0.
The geocentric parallax of stars is too small to be measured, even by the most precise
telescopes, since the value for the nearest star is only 0700003.

Daily values of horizontal parallax for the sun, moon, and planets are given in the
American Ephemeris and Nautical Almanac, to a precision of 0701. In the Nautical
Almanac, mean values for the sun are included in the two sun correction tables given on
the inside front cover and facing page. Horizontal parallax of the moon is tabulated at
intervals of one hour on the daily pages. "This value is used to enter the lower part of
the moon correction tables on the inside back cover and facing page. "The additional
corrections for Venus and Mars given on the inside front cover are partly for parallax.
No correction is given for parallax of Jupiter and Saturn. The Air Almanac, giving
values only to the nearest whole minute of arc, includes parallax corrections only
for the moon. These values are given in the “Moon's P in A" column on the right-hand
daily page.

Because of geocentric parallax, a body appears too low in the sky. Therefore,
the correction is always positive. It applies regardless of the method of observation.

1621. Summary of corrections.— The essential information regarding the ap-
plication of the various corrections may be tabulated as shown below. In the “Bodies”
column, the symbols are: ©, sun; C, moon; P, planets; Y, stars. In the “Sextants””
column, M refers to a marine sextant with visible horizon, A refers to a marine sextant
with artificial horizon, and B refers to an artificial-horizon sextant. "The tabulation
assumes that completely accurate results are desired and that corrections are to be made
in the usual manner, where they are available. Some of the entries need qualification,
which may be found in the preceding articles.

Correction Symbol Sign Increases with Bodies Sextants Source
Instrument I + changing altitude O, C,P, Y M,A,B sextant box
Index IC ae constant ©, C, P, Y M, A, B measurement
Personal PC + constant ©, C, P, Y M,A,B measurement
Tilt N — greater tilt angle ONCE M computation
Dip D — higher height of eye (8). (8. ke Ww almanacs
Sea-air temp. diff. S + greater temp. diff. ORG dro M computation
Wave height W + higher waves OG, EV computation
Sea tilt H + greater tilt of surface OMG eM computation
Deflection of vert. V + position, azimuth O, C, P, Y M, A, B geodesist
Coriolis Z ae higher lat., greater speed O, C, P, Y A,B Air Almanac
Acceleration C + greater acceleration ONCAE RAE computation
Refraction R — lower altitude ©, C, Br M,A,B almanacs
Air temp. Ir + greater diff. from 50? ©, C, P, « M,A,B almanacs,

i table 28
Atmospherie B + greater diff. from 29.88 O, C, P, % M, A, B Nautical
pressure inches of mercury Almanac,

n table 24
Irradiation J — constant O M,A Nautical

T Almanac
Semidiameter SD + lesser dist. from earth o, C M, A almanacs
Phase F + phase P M,A,B Nautical

Almanac
Augmentation A + higher altitude C M,A Nautical
e Almanac
Parallax IP + lower altitude ©), (C12 M, A,B almanacs

SEXTANT ALTITUDE CORRECTIONS 437

These corrections can be considered to fall into five groups:

1. Corrections for inaccuracies in reading. Instrument correction, index correc-
tion*, personal correction, and tilt correction.

2. Corrections for inaccuracies in reference level. Dip*, sea-air temperature differ-
ence, wave height, sea tilt, deflection of the vertical, Coriolis, acceleration.

3. Corrections for bending of ray of light from body. Refraction*, air temperature,
atmospheric pressure.

4. Adjustment to equivalent reading at center of body. Irradiation, semidiameter*,
phase, augmentation.

5. Adjustment to equivalent reading at center of earth. Parallax*.

In the ordinary practice of seamen, extreme accuracy is not required, and only
the principal correction of each group is applied (except that irradiation is applied for
the upper limb of the sun, and augmentation for the moon). These principal correc-
tions are indicated by asterisks. For low altitudes, additional corrections are applied,
as indicated in article 1632.

1622. Order of applying corrections.—For purposes of ordinary navigation, sex-
tant altitudes can be applied in any order desired, using sextant altitude for the enter-
ing argument whenever altitude is required. This practice is not strictly accurate,
but for altitudes usually observed, the error thus introduced is too small to be of
practical significance. When extreme accuracy is desired, however, or at low altitudes,
where small changes in altitude result in significant changes in correction, the order
of applying corrections is important. Corrections from the first two groups of article
1621 are applied to sextant altitude (hs) to obtain rectified altitude (hr), called “ap-
parent altitude” by astronomers, which is then used as an entering argument for obtain-
ing corrections of the third group. For strictest accuracy, all corrections of the first
three groups and, in addition, irradiation and semidiameter, should be applied before
augmentation, and all other corrections before parallax.

1623. Marine sextant corrections.—As shown in the tabulation of article 1621,
all corrections except Coriolis and acceleration apply to marine sextant observations
when the visible horizon is used. Of the five corrections ordinarily used, index cor-
rection can be eliminated by sextant adjustment (art. 1509), or it can be combined
with dip in such manner as to eliminate both (art. 1603). Of the remaining three
corrections, only refraction and parallax apply to planets; and only refraction applies
to stars.

1624. Artificial-horizon corrections.—When an artificial horizon is used, index
correction (and any others of the first group of article 1621) is first applied. The
result is then divided by two. Other corrections are then applied to the result, as
applicable, in the same manner as for observations using the visible horizon. The
sun and full moon are normally observed by bringing the lower limb of one image
tangent to the upper limb of the other image. The lower limb is observed if the
image seen in the horizon mirror is above the image seen in the artificial horizon, unless
an inverting telescope is used, when the opposite relationship holds. With a gibbous
or crescent moon, judgment may be needed to establish the positions of the limbs.
In some cases better results may be obtained by superimposing one image over the
other, as with a planet or star. When this is done, the center of the body has been
observed, and no correction is applied for semidiameter (or irradiation, phase, or aug-
mentation). If the lower limb of the sun is observed, an irradiation correction of (5)
1/2 may be applicable, if experience so indicates. There is no correction for dip (or
sea-air temperature or wave height) when an artificial horizon is used. l

1625. Artificial-horizon sextant corrections are the same as those for observations
made by the use of the visible horizon, with two notable exceptions. First, there is

438 SEXTANT ALTITUDE CORRECTIONS

no correction for dip (or sea-air temperature difference or wave height), none for semi-
diameter (or irradiation, phase, or augmentation), and usually none for index correc-
tion (or instrument correction). Second, because of the lower accuracy normally obtain-
able by artificial-horizon sextant, corrections are normally made only to the nearest
whole minute of arc. As a result of these differences, refraction is the only correction
normally applied, except in the case of the moon, where parallax is also applied.
Many air navigators, principal users of artificial-horizon sextants, avoid altitudes
below 20° and accept the error introduced by refraction, so that no correction is needed.
As flight altitudes increase, the error thus introduced becomes correspondingly smaller.
However, at modern aircraft speeds, Coriolis correction is of increased importance.

1626. Corrections by American Nautical Almanac.—In the Nautical Almanac,
certain corrections or parts of corrections are combined. Index correction, of course,
is not included because this depends upon adjustment of the sextant. The various
correction tables are as follows:

“Sun,” on the inside front cover and facing page, gives mean refraction, mean
semidiameter for each of two periods during the year, and mean solar parallax. lrradia-
tion is also included in the upper limb corrections, given in separate columns from lower
limb corrections. "The table on the inside front cover, and repeated on the loose book-
mark, is of the critical type, with altitude as the entering value. Thus, a tabulated
correction applies to any value of altitude between that given half a line above it and
that half a line below it. If an exact tabulated altitude is used to enter the table, the
correction half a line above it should be used. In ordinary navigation, index correction,
dip, and the correction from this table are needed for correcting marine sextant observa-
tions of the sun. For low altitudes or extremes of temperature or atmospheric pressure,
a correction from the table on almanac page A4 (or tables 23 and 24 of this volume)
should be applied.

“Stars and planets," on the inside front cover and repeated on the loose bookmark,
gives mean refraction only, for the main tabulation. This is a critical type table, with
altitude as the entering argument. The correction is always negative. In ordinary
navigation, index correction, dip, and the correction from this table are the only ones
needed for stars and the planets Jupiter and Saturn. For Venus and Mars, an additional
correction for parallax and phase is given to the right of the main tabulation. The
entering altitudes are limited to those occurring during twilight. If observations are
made at other times, this additional correction should not be applied even though the
altitude may fall within the tabulated range.

“Dip,” on the inside front cover and repeated on the loose bookmark, is for dip of
the horizon. An abbreviated dip table is also given on the page facing the inside back
cover. The tables are of the critical type, and the entering argument is the height of
the observer's eye, in feet, above the surface of the sea. The correction, always nega-
tive, applies to all observations made with the visible sea horizon as a reference.

“Additional Correction Tables” for nonstandard conditions, given on almanac page
A4, provides an additional correction for nonstandard temperature and atmospheric
pressure. The sign of each correction is indicated. Equivalent information is given,
with increased range of entering values, in tables 23 and 24 of this volume.

i “Altitude Correction Tables—Moon,” on the inside back cover and facing page,
gives mean refraction, semidiameter, augmentation, and parallax. The entering
argument is altitude for the upper portion of the table, and altitude and horizontal
parallax for the lower portion. The combined correction is always positive, but 30’ is
to be subtracted from the altitude of the upper limb. In ordinary navigation, index

correction, dip, and the correction from this table are needed in correcting marine
sextant observations of the moon.

SEXTANT ALTITUDE CORRECTIONS 439

The various separate corrections available from the Nautical Almanac can be found
as follows:

Dip. Dip table on inside front cover and repeated on loose bookmark, and on the
page facing the inside back cover.

Refraction. Mean refraction from “Stars and Planets” table on inside front cover
and repeated on loose bookmark, and on the facing page.

Irradiation. A value of (—) 1/2 is included in the tables of corrections for the upper
limb of the sun, given on the inside front cover and repeated on the loose bookmark,
and on the facing page, to allow (—) 0/6 for the upper limb and (—) 0/6 for the horizon.

Semidiameter. For the sun, the semidiameter for the middle day of each page
opening of this daily page section is given at the bottom of the sun GHA column.
For the moon, semidiameter for each day is given at the bottom of the moon data
columns. The values given are for GMT 1200 on the dates indicated.

Parallax. For the sun, parallax in altitude can be considered 0/1 for altitudes 0° to
70°07’, and 0:0 for higher altitudes, with negligible error. This is based upon the mean
value of 8780. For the moon, horizontal parallax each hour is tabulated on the daily
pages. Parallax in altitude is this value multiplied by the cosine of the altitude.

If artificial-horizon sextant altitudes of the sun or moon are corrected by Nautical
Almanac, the upper and lower limb corrections can be found and the average computed.

1627. Corrections by Air Almanac.—In the Air Almanac, various corrections
are given separately in critical type tables, to the nearest whole minute (nearest two or
five minutes of refraction for low altitudes), as follows:

Dip. Outside back cover.

Refraction. Inside back cover. Aboard ship use the values for zero height. A
special table for H.O. Pub. No. 218 is given on the page facing the inside back cover.
A dome refraction table for use in aircraft is given on the same page.

Coriolis. Inside back cover, below the refraction table.

Air temperature. Inside back cover. This is shown, not as a separate correction,
but as an adjustment to mean refraction. Instructions for use of the table are given
on the inside back cover of the Aur Almanac.

Semidiameter. For the sun and moon, on the right-hand daily page, below the
moon’s P in A. Values given are for GMT 1200. The value given for the sun is
always 16’.

Parallax. For the moon, in the P in A table on the right-hand daily page. Hori-
zontal parallax is the value for 0° altitude. Values given are for GMT 1200.

1628. Correcting altitudes of the sun.—In the normal practice of navigation,
sun observations obtained by marine sextant with the visible horizon as reference are
corrected as shown in the following examples:

Example 1.—On June 2, 1958, the lower limb of the sun is observed with a marine
sextant having an IC of (—) 2/0, from a height of eye of 38 feet. The hs is 519284.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—

(1) + D — (2) au pe.
EAN IC 2

D 6/0 D 6'

O 15/2 R i

sum 15/2 8/0 Duo” « .

hs 51°28/4 corr. GDK

Ho ^ 51935'6 hs 51°28’

Ho 51°35’

440 SEXTANT ALTITUDE CORRECTIONS

Example 2.—On June 2, 1958, the upper limb of the sun is observed with a marine
sextant having an IC of (+) 1/0, from a height of eye of 45 feet. The hs is 32?47:9.
Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—

(1) Sagina (2) EEG:

IC 1:0 IG 1*
D 6:5 D T
© 18/5 R 24
sum 1/0 25/0 SD 16’
corr. (—) 24/0 sum IAS
hs 32°47/9 corr. (22:
Ho ' :32?23!9 hs 32948'
Ho 32°24’

A convenient work form is helpful in the solution. Once the form is prepared, the
corrections can be entered in any order desired. The symbols © and O are used for
the corrections from the sun table on the inside front cover of the Nautical Almanac.
If additional corrections are used, they are included in the same manner as those shown.
Observations by artificial horizon and by artificial-horizon sextant, and low-altitude
observations and back sights, are discussed elsewhere in this chapter.

1629. Correcting altitudes of the moon.—Moon observations by marine sextant with
the visible horizon as reference are normally corrected as shown in the following examples:

Example 1.—At about GMT 1100 on June 2, 1958, the lower limb of the moon is
observed with a marine sextant having an IC of (+) 3/2, from a height of eye of 32
feet. The hs is 18°04/6.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—
(1) "EN CONES (2) TONO
IG 73:2 1631
D 515 D 6’
C 62:5 R 9
Line O SD 16’
sum 72:4 5:5 P56?
corr. (4-)1?06'9 sum 75' 9’
hs 18°04/6 corr. (+)1°06’
Ho 19%11/5 hs 18°05’
Ho 19°11’

Example 2.—At about GMT 0900 on June 2, 1958, the upper limb of the moon is

observed with a marine sextant having an IC of (—)1'6, from a height of eye of 70
feet. The hs is 66°47/3.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—

(1) cc (2) AO ey
IC 1/6 IC 21
D 8/1 D EN
(273570 R —
U38 SD 16’

add'1 30/0 R23
sum 36/8 39/7 sum 23’ 26'
corr. (—) 2/9 corr. (—)8/
hs 66°47/3 hs 66°47’

Ho 66%44/4 Ho 66°44’

SEXTANT ALTITUDE CORRECTIONS 441

The typical work forms shown are useful in problems of this type. The symbol C
is used for the correction from the upper part of the moon correction table on the inside
back cover, and facing page, of the Nautical Almanac. The symbols L and U are used
for the corrections from the lower part of this table. Observations by artificial horizon,
and by artificial-horizon sextant, and low-altitude observations and back sights, are
discussed elsewhere in this chapter, as are additional corrections for use when unusual
accuracy is desired.

1630. Correcting altitudes of planets.—When Venus and Mars are observed by
marine sextant using the visible horizon as reference, sextant altitudes are normally
corrected as shown in the following example:

Example.—On May 19, 1958, Venus is observed with a marine sextant having no
IC, from a height of eye of 28 feet. The hs is 44°21/3.

Regutred.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—

(1) io dz (2) LN

Ic; — -— Tess E

D oti D 54

*-P 1/0 R 14

add’l 0/2 sume yh alent!

sum 0/2 6:1 COIT. (Os

corr. (—) 519 hs 44°21’

hse 4492143 bo Ziy

Ho 44%15/4

For Jupiter and Saturn, no additional correction is given. Correction of observa-
tions of these bodies is the same as corrections of star observations (art. 1631). Work
forms are useful. The symbol %-P is used for the correction taken from the “Star-
Planet” table on the inside front cover of the Nautical Almanac. If additional cor-
rections are to be used, for results of unusual accuracy or low altitudes, they are
included in the form in the same manner as those shown. Observations by artificial
horizon and by artificial-horizon sextant, and low-altitude observations and back sights
are discussed elsewhere in this chapter.

1631. Correcting altitudes of stars.—Star observations by marine sextant, using
the visible horizon as reference, are normally corrected as shown in the following
example:

Example.—Miaplacidus is observed with a marine sextant having an IC of (+)1:0,
from a height of eye of 50 feet. The hs is 275410.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Solution.—

(1) Md Be (2) uii ds

IC 1/0 1671:
D 6:9 D T
KR pis R 2^
sum 1:0 Sl sum 1’ 9’
corr. (Mi COIT. (—)8'
hs 27540 hs AN
Ho 27%46'3 Ho 27%46'

Work forms for such problems are helpful. Additional corrections, used when
unusual accuracy is desired, are included in the same manner as those shown. Obser-
vations by artificial horizon and by artificial-horizon sextant, and low-altitude observa-
tions and back sights, are discussed elsewhere in this chapter.

449 SEXTANT ALTITUDE CORRECTIONS

1632. Low altitudes are normally avoided because of large and variable refraction.
But sometimes these are the only observations available. This is particularly true in
polar regions, where the sun may be the only celestial body available, and may not
reach an altitude of more than a few degrees over a considerable period. In lower
latitudes the sun may appear briefly just before sunset or just after sunrise. Low-
altitude observations can supply useful information if additional corrections are applied.
Reliable lines of position can generally be obtained from low-altitude observations,
but when conditions are abnormal, the errors introduced are generally larger than for
higher altitudes, and the precautions of article 1613 should be particularly observed.

In correcting low-altitude observations, which for normal conditions can be defined
as those less than 5°, first apply corrections from the first two groups of article 1621 to
obtain rectified altitude (hr), called “apparent altitude" in the almanac. Normally,
this includes only index correction and dip. Then apply the remaining corrections,
using rectified altitude when an altitude is needed for entering correction tables. The `
corrections normally applied are mean refraction, air temperature, atmospheric pres-
sure, semidiameter (as applicable), and parallax (for the sun and moon).

In practice, sextant altitudes are corrected in the usual manner, except that addi-
tional corrections are applied, and the process is divided into two parts. The use of
rectified altitude for finding parallax introduces an error but this is too small (less
than 0/1) for practical consideration. If the Nautical Almanac is used, corrections for
altitudes between the horizon and 10° are given in a noncritical type table on almanac
page A3. The correction for a negative altitude can be obtained by extrapolation
without introducing a significant error for values obtained at ship heights of eye.
A combined temperature-atmospheric pressure correction can be obtained from the
table on almanac page A4. This table is intended for use without interpolation be-
tween columns. Separate corrections can be obtained from tables 23 and 24 of the
present volume, which provide interpolated values for greater accuracy. They also
provide greater range of temperature and atmospheric pressure.

To correct a low altitude of the sun, then, apply index correction and dip to sextant
altitude to find rectified altitude. Using this altitude as an entering value, find the
following corrections and apply them to rectified altitude:

sun correction (C or ©), from page A3 of the Nautical Almanac;

combined temperature-atmospheric pressure correction (TB), from page A4 of
the Nautical Almanac (separate corrections for temperature (T) and atmos-
pheric pressure (B) from tables 23 and 24, respectively, can be used 4n place of
the combined correction).

If the Air Almanac is used, the mean refraction and air temperature corrections
can be combined by using the factor on the inside back cover. A semidiameter cor-
rection of 16' is added if the lower limb is observed, and subtracted if the upper limb
is observed. Since corrections are to whole minutes only, parallax is not used for the
sun. In summary, apply index correction and dip to sextant altitude to find rectified
altitude. Using this altitude as an entering value, where needed, apply the following
corrections to rectified altitude:

refraction (adjusted for air temperature) (R), from inside back cover of Air
Almanac;

atmospheric pressure (B), from table 24;

semidiameter (SD), 16’ (add if lower limb, and subtract if upper limb).

Example 1.—On June 2, 1958, the lower limb of the sun is observed with a marine

sextant having an IC of (+) 178 from a height of eye of 45 feet. The hs is 1?24'4, air
temperature 88? F, and atmospheric pressure 29.78 inches.

SEXTANT ALTITUDE CORRECTIONS 443

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Solution:
(1) EU asc (2) DE EON (3) ied VON ee
IC 1/8 IG 148 ICP2/
D 6/5 D 6/5 D Ki
sum 1/8 6/5 sum 1/8 6/5 sum 2’ "i
corr. (—) 417 corr (=) 417 COIT. (—)5'
hs 1274.04. hs 122474 hs 12247
hr 191025 be pel?10/7 hr 19104
© 6/0 © 6/0 R 18’
TB i225 TIS B —
sum 2:5 6/0 B — SD 16'
corr. (—) 3/5 sum 1/5 6/0 sum 16’ 18’
hr ESO Corr (—)4:5 COIT. (—)2'
Ho V 1672 hr 191917 hr 1°19’
Ho 19152. Ho TEE

The larger intervals given in the Air Almanac refraction table may introduce
additional error. In this example, the temperature is changed to Celsius (centigrade),
giving a value of 31?. "The factor at a height of 0 feet corresponding to this temperature
is 0.9. With this and the rectified altitude, the combined refraction and air tempera-
ture correction is found to be as shown. Approximately the same result would have
been obtained by correcting for mean refraction (without the factor) and temperature
(from table 23) separately.

If the moment at which either limb is tangent to the horizon is noted, an ob-
servation of 0? altitude has been made without a sextant.

Example 2.—On June 2, 1958, the sun is observed at sunset as the upper limb
drops below the horizon, from a height of eye of 38 feet. The air temperature is
(—)10?F, and atmospheric pressure 30.06 inches. Double extrapolation would
be needed to solve this problem by the Nautical Almanac. A better solution is provided
by means of tables 23 and 24.

Required.—Ho using (1) tables 23 and 24, and (2) Air Almanac.

Solution.—

(1) + ð - (2) tid ON E
IC — = Ker zT

D 6/0 DNE

sum — 6/0 sum AE, 0-

COIT. (—)6:0 corr. (—) 6’

hs 0°00/0 eee 0.

hr (—)0°06/0 hr (—)0%06'

6 52/6 R 42

Ë 4/8 B SCH

B 0/3 AAA

sume S m sum WAR

corr. AE corr. (OS.

hr (—)0°06/0 vidi VA

Ho (—) 1°03/7 izjust 104.

Corrections are applied algebraically. Therefore, for negative altitudes a negative
correction is numerically added, and a positive correction is numerically subtracted.

444 SEXTANT ALTITUDE CORRECTIONS

To correct low altitudes of the moon, apply index correction and dip to sextant
altitude to find rectified altitude. Using this altitude as an entering value, find the
following corrections and apply them to rectified altitudes:

moon correction (C), from inside back cover, and facing page, of Nautical Almanac;

lower or upper limb correction (L or U), from inside back cover, and facing page,
of Nautical Almanac;

additional correction (add’l, (—) 30’, for upper limb observation only);

combined temperature-atmospheric pressure correction (TB), from page A4
of the Nautical Almanac (separate corrections for temperature (T) and atmos-
pheric pressure (B) from tables 23 and 24, respectively, can be used in place of
the combined correction).

If the Air Almanac is used, correct the rectified altitude by applying the following
corrections:

refraction (adjusted for air temperature) (R), from inside back cover of Aur

Almanac;

atmospheric pressure (B), from table 24;

semidiameter, from right-hand daily page;

parallax, from right-hand daily page.

Example 8—At GMT 17^14727* on June 2, 1958, the upper limb of the moon is
observed with a marine sextant having no IC, from a height of eye of 33 feet. The
hs is 2°35'4, air temperature 63°F, and atmospheric pressure 29.81 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Solution.—

(1) apr © = (2) LP = (3) d. CV
IC — — IC — — IC — —
D 516 D 516 D 6’
sum — 5:6 sum — 5:6 sum — 6’
corr. (—) 5'6 corr (—) 5:6 corr. (—) 6’
hs 2°35/4 hs 229001 hs 22357
hr 2929/8 hr 299979 hr 2°29’
Capea (59 T R 16’

U 45 U 4:5 B —
add” 30/0 add” 30/0 SD 16’

TB 0/4 I OEZ P 59’
sum 57/0 30/0 B — sum 59’ 324
corr. (+) 27/0 sum 57/0 30/0 corr. (+) 27°
hr 2298 corr. (+) 27'0 hr 2°29.
Ho 2956/8 hr 22298 Ho 2°56’

Ho 2°56/8

A lower limb solution would be the same, except that an L correction would have
been used from the Nautical Almanac and there would be no “add'1” correction, and
in the Air Almanac solution the sign of the semidiameter correction would be reversed.
The moon correction table on the inside back cover, and facing page, of the Nautical
Almanac extends to a minimum altitude of 0°. The corrections for negative altitudes
can be found by extrapolation.

To correct low altitudes of the planets Venus and Mars, apply index correction
and dip to sextant altitude to find rectified altitude. Using this altitude as an entering
value, find the following corrections and apply them to rectified altitude:

SEXTANT ALTITUDE CORRECTIONS 445

star-planet correction Ce Pi, from page A3 of the Nautical Almanac:

additional correction (add’l), from page A2 of the Nautical Almanac; i

combined temperature-atmospheric pressure correction (TB), from page A4 of
the Nautical Almanac (separate corrections for temperature (T) and atmos-
pheric pressure (B) from tables 23 and 24, respectively, can be used in place of
the combined correction).

If the Air Almanac is used, correct the rectified altitude by applying the following
corrections: N

refraction (adjusted for air temperature) (R), from inside back cover of Air
Almanac;

atmospheric pressure (B), from table 24.

Example 4.—On September 28, 1958, Mars is observed with a marine sextant
having an IC of (4-) 3:5, from a height of eye of 17 feet. The hs is 4%02/6, air tem-
perature 2°F, and atmospheric pressure 29.67 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Solution.—

(1) + M — (2) + M — (3) + M —

10485 102355 IC 4’
D 40 D 4:0 D 4'
sum 3/5 EM sum 3/5 40 sum 4’ 44
COIT. (—)0:5 corr. (—)0:5 corr —
hs 4?02:6 hs 490216 hs 4°03’
hr 4°02/1 hr 490271 hr 4°03’
x-P TT x-P (Bag R 14’

add’l 0/3 add’l 0/3 B —
TB T is quo sum — 14’
sum 0/3 = 13/2 B 0/1 corr (—)14’
corr. (—)12:9 sum 0/4 12/9 hr 4°03’
hr 4%02*1 corr (—)12'5 Ho 3°49’

Ho 374972 hr 4°02'1

Ho ` 3%49/6

The solution for Jupiter and Saturn, and for stars, is identical with that of example
4, except that the additional correction (phase and parallax) is omitted.

1633. Back sights.—An altitude measured by facing away from the celestial body
being observed is called a back sight. It may be used when an obstruction, such as
another vessel, obscures the horizon under the body; when that horizon is indistinct;
or when observations are made in both directions, either to determine dip or to avoid
error due to suspected abnormal dip. Such an observation is possible only when the
arc of the sextant is sufficiently long to permit measurement of the angle, which is
the supplement of the altitude. For such an observation of the sun or moon, the
lower limb is observed when the image is brought below the horizon, appearing as &
normal upper limb observation, and vice versa. To correct such an altitude, subtract
it from 180? and reverse the sign of corrections of the first two groups of article 1621
(normally only index correction and dip).

Example.—On June 2, 1958, a back sight is taken of the lower limb of the sun,
with a marine sextant having an IC of (—) 2/0, from a height of eye of 24 feet. The
measured sextant altitude is 118?41:4.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

446 SEXTANT ALTITUDE CORRECTIONS

Solution.—

(1) + 9 — (2) IMG tus

IQ» TOR
© 1514 R 1/

sum 22/2 BER SD 16'
corr. (+) 2212 sum 23’ M
180?—hs 61°18/6 corr. (+) 22’
Ho 61°40/8 180°—hs 61°19’
Ho 61°41’

1634. Correcting horizontal angles.—When a marine sextant is used to measure
the horizontal angle between two objects, the result is not usually desired to a precision
that makes correction necessary, unless the sextant has an unusually large index error.
However, if precise results are desired, corrections of the first group only of article
1621 are applied. If a personal error exists, it is not likely to be the same as for
altitudes. For measuring angles between two objects differing widely in altitude, as
between two stars, it is not likely that results will be required to such precision that
additional correction for the third, fourth, and fifth groups of article 1621 will be
needed. If they are, the method of application can be determined from the principles
of spherical trigonometry (app. O). In this case, the altitudes of both bodies will also
be needed. Corrections for the second group of article 1621 are not applicable.

Problems

1624. At about GMT 0800 on June 2, 1958, the following bodies are observed
with marine sextants having an IC of (+)2/2, using an artificial horizon: sun (lower
limb) hs 134?33:9, moon (upper limb) hs 77°23/4, Venus hs 98%04/6, Schedar hs 43°24/4.

Reguired—Ho of each observation using (1) Nautical Almanac, and (2) Air
Almanac.

Answers.—(1) Sun Ho 67?33:6, moon Ho 39%11/7, Venus Ho 49°02/6, Schedar
Ho 21?40:9; (2) sun Ho 67°34’, moon Ho 39°12’, Venus Ho 49°03’, Schedar Ho 21°41’.

1625. At about GMT 0300 on June 2, 1958, the following bodies are observed with
bubble sextants having no IC: sun hs 23°51’, moon hs 52°20’, Jupiter hs 63°18’,
Eltanin hs 24°45’.

Required.—Ho of each observation using (1) Nautical Almanac, and (2) Air
Almanac.

Answers.—(1) and (2) Sun Ho 23°49’, moon Ho 52°56’, Jupiter Ho 63°18’, Eltanin
THo7249197.

1628a. On June 2, 1958, the lower limb of the sun is observed with a marine
sextant having an IC of (+)1/8, from a height of eye of 34 feet. The hs is 41%34/8.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 41%45/8; (2) Ho 41°46’.

1628b. On June 2, 1958, the upper limb of the sun is observed with a marine
sextant having no IC, from a height of eye of 30 feet. The hs is 15°21/7.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 14°56/0; (2) Ho 14°57’.

1628c. On June 2, 1958, the lower limb of the sun is observed with a marine
sextant having an IC of (—)1'3, from a height of eye of 43 feet. Another ship is
between the observer and the horizon, at a distance of 1.4 miles from the observer.
The water line of this ship is used as the horizontal reference. The hs is 259182.

SEXTANT ALTITUDE CORRECTIONS 447

Required.—Ho using table 22 and (1) Nautical Almanac, and (2) Air Almanac.
Answers.—(1) Ho 25°13/0; (2) Ho 25°13’,
| 1629a. At about GMT 2100 on June 2, 1958, the lower limb of the moon is observed

with a marine sextant having an IC of (—) 2/5, from a height of eye of 55 feet. The
hs is 47°35/5.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 48%20/5; (2) Ho 48°22’.

1629b. At about GMT 2300 on June 2, 1958, the upper limb of the moon is observed
with a marine sextant having an IC of (+)4/0, from a height of eye of 12 feet. The
hs is 22°58/3.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 23%34:7; (2) Ho 23°35’.

1630a. On June 18, 1958, Mars is observed with a marine sextant having an IC of
(+) 2:2, from a height of eye of 60 feet. The hs is 34%11/7.

HRequired.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 34?05'1; (2) Ho 34°05’.

1630b. Jupiter is observed with a marine sextant having an IC of (—)1/0, from a
height of eye of 27 feet. The hs is 11°23/9.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 11?13:2; (2) Ho 11913”:

1631. Alpheratz is observed with a marine sextant having no IC, from a height of
eye of 42 feet. The hs is 38?20'3.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 38?12:8; (2) Ho 38°13’.

1632a. On June 2, 1958, the lower limb of the sun is observed with a marine
sextant having an IC of (—) 2/3, from a height of eye of 24 feet. The hs is 290416, air
temperature 65°F, and atmospheric pressure 30.81 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho 1°55/1; (2) Ho 1?55'1; (3) Ho 1°56’.

1632b. On July 2, 1958, the sun is observed as the upper limb drops below the
horizon at sunset, from a height of eye of 19 feet. The air temperature is 16? F, and
atmospheric pressure 29.90 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho (—)1°01/4; (2) Ho (—)0?59:2; (3) Ho (—)0°58’.

1632c. At GMT 6%03”29* on June 2, 1958, the upper limb of the moon is observed
with a marine sextant having an IC of (+)2'6, from a height of eye of 35 feet. The
hs is 1?12/6, air temperature (—) 23°F, and atmospheric pressure 29.04 inches.

Required.—Ho using (1) tables 23 and 24, and (2) Air Almanac.

Answers.—(1) Ho 1?26:1; (2) Ho 1°24’.

1632d. At GMT 12544701? on June 2, 1958, the lower limb of the moon is observed
with a marine sextant having an IC of (+)3/2, from a height of eye of 22 feet. The
hs is 0924/4, air temperature 40°F, and atmospheric pressure 29.94 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho 1°07/4; (2) Ho 1?07:6; (3) Ho 1°04’.

1632e. On January 19, 1958, Venus is observed with a marine sextant having an
IC of (—)0/5, from a height of eye of 31 feet. The hs is 392918, air temperature ls
and atmospheric pressure 30.15 inches.

448 SEXTANT ALTITUDE CORRECTIONS

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho 3°11!3; (2) Ho 3°11/1; (3) Ho 3°11’.

1632f. Saturn is observed with a marine sextant having an IC of (—)2:3, from a
height of eye of 37 feet. The hs is 4%39/2, air temperature 76° F, and atmospheric
pressure 28.89 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho 4?21:4; (2) Ho 4°21/1; (3) Ho 4°21’.

1632g. Gienah is observed with a marine sextant having no IC, from a height of
eye of 44 feet. The hs is 2°46/1, air temperature 35°F, and atmospheric pressure
29.92 inches.

Required.—Ho using (1) Nautical Almanac, (2) tables 23 and 24, and (3) Air
Almanac.

Answers.—(1) Ho 2°23'4; (2) Ho 292316; (3) Ho 2°21’.

1633. On June 2, 1958, a back sight is taken of the lower limb of the sun, with a
marine sextant having an IC of (+) 177, from a height of eye of 49 feet. The measured
sextant altitude is 1419049.

Required.—Ho using (1) Nautical Almanac, and (2) Air Almanac.

Answers.—(1) Ho 39?15:0; (2) Ho 39°15’.

1634. The horizontal angle between two objects is measured with a marine sextant
having an IC of (2-) 4:0. The measured angle is 85%14/6.

Required.—Corrected angle.

Answer.—Corrected angle 85°18'6.

CHAPTER XVII
LINES OF POSITION FROM CELESTIAL OBSERVATIONS

1701. Circles of equal altitude.—For every point on the earth there is a zenith
(art. 1428) vertically overhead on the celestial sphere (art. 1403). Likewise, every
point on the celestial sphere is vertically over some terrestrial point, called its geo-
graphical position (GP). However, since the earth rotates on its axis, causing ap-
parent rotation of the celestial sphere, the GP of any point on the celestial sphere is
continually moving to the westward, at the rate of about 15° per hour. If a celestial
body is changing its apparent position on the celestial sphere, this motion is added
to that caused by rotation, so that the rates of motion of the GP’s of various bodies
differ slightly. Further, this motion may not be exactly westward, having a small
northerly or southerly component as the body changes declination, due either to its
own proper motion or precession of the equinoxes (art. 1419), or a combination of the
two.

At any moment the declination of a celestial body is equal to the latitude of its
GP. The Greenwich hour angle (GHA) of the body, if not greater than 180°, is
equal to the longitude (west) of the GP. If the GHA is greater than 180°, its ex-
plement (art. 027) is equal to the longitude (east). Thus, if it is established that a
body of known coordinates is in the zenith of an observer, the position of the observer
is known. However, for the celestial bodies used in navigation, this condition rarely
occurs for any individual observer, and is difficult to determine when it does occur.

More commonly, the altitude (art. 1428) is measured, and from this the zenith
distance (art. 1428) can be determined. This value defines a circle on the earth, as
shown in figure 1701a. Thus, if the observer is one mile from the GP, in any direction,
he is 1’ from it, and his zenith is 1’ from the celestial body. Anywhere on a circle of one
mile (1^) radius, with the GP as the center, the zenith distance is 1'. Similarly, if
the zenith distance is 10°, the observer may be anywhere on a circle (assuming a
spherical earth) of radius 1060600 miles, with the GP as the center. If the zenith
distance is 30°, the radius is 1,800 miles; if 60°, the radius is 3,600 miles; and if 90°
(body on the celestial horizon), the radius is 5,400 miles. This is a great circle dividing
the earth into two hemispheres. Anywhere within that hemisphere having the GP
as its center the celestial body is above the celestial horizon. Anywhere within the
opposite hemisphere the body is below the celestial horizon.

These circles of equal altitude are circles of position, or circular lines of position.
Two such circles for different celestial bodies, or for the same body at different times,
may intersect at two points, as shown in figure 1701b. If these circles have radii
equal to the zenith distances at the observer, the position of the observer is established
at one of the two intersections. Normally, these intersections are separated by such
great distances that no question arises as to which represents the position of the ob-
server. However, uncertainty can be removed if additional altitude circles can be
established by observation of other celestial bodies. It would be a rare coincidence
for a third such circle to pass through both intersections of the first two. The third
observation also serves as a check on the accuracy of the first two. The ambiguity
might also be resolved by noting the azimuth of either or both of the bodies, for the
azimuth should be in the same direction as the radius of the circle of position, measured

at the intersection.
449

450 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

1702. Utilizing circles of equal altitude.—For most altitudes conveniently ob-
served, the plotting of circles of equal altitude involves certain difficulties. Because
of the long radii of such circles, a chart of very small scale would be needed, and vir-
tually any chart distortion would introduce some error, unless an azimuthal projection
(ch. III) centered upon the GP were used, an impractical procedure with a moving
GP for each body. The appearance of two circles of equal altitude plotted on a
Mercator chart is shown in figure 1702.

It has been suggested that the second difficulty, that of distortion, might be over-
come by plotting directly on a sphere, using equipment designed for this purpose.
While theoretically sound, this procedure does not overcome the first difficulty, that
of scale, and has not proved practical. A variation of this has been the use of movable
arcs, by which a small-scale model of one or more navigational triangles (art. 1433) is
mechanically produced. The coordinates are carefully measured by means of sliding
indices controlled by verniers or micrometers. Another variation has been a graphical
solution based upon the drawing of a diagram according to any of various principles.
Although a number of mechanical and graphical solutions have been devised, and some
have proved practical (ch. XXI), none has been generally accepted as superior to the
commonly used tabular methods of solution.

— Ec é

ZI VJ < E dE i

ad:

Figure 1701a.— Circles of equal altitude. Figure 1701b.—Intersections of two circles of
equal altitude.

However, as the altitude of a body increases, reducing the zenith distance, both
distortion and scale difficulties decrease. Also, on a Mercator chart, they decrease
as the GP approaches the equator. The observation of a celestial body near the zenith
is difficult, but in the case of the sun no alternative may be available near noon in the
tropics. Such a situation does provide an easy solution and may permit obtaining of
à fix from two observations of the same body, with only a few minutes between ob-
servations. This solution is discussed further in article 2011.

1703. The line of position.—For zenith distances too great to plot conveniently
a line of position can be laid down in another manner. |!

The altitude of a celestial body may be measured. After appropriate corrections
are applied, this is called observed altitude (Ho). For the instant of observation. the
altitude and azimuth at some convenient assumed position (AP) near the actual Bos
tion of the observer are determined by calculation or equivalent process. The differ-
ence between this computed altitude (Hc) and Ho is the altitude difference (a), some-

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 451

GP /

FIGURE 1702.—Circles of equal altitude on a Mercator chart.

times called altitude intercept. Since a is the difference in altitude at the assumed
and actual positions, it is also the difference in zenith distance, and therefore the
difference in radii of the circles of equal altitude at the two places. The position having
the greater altitude is on the circle of smaller radius, and hence is closer to the GP of
the body. In figure 1703a the AP is shown on the inner circle. Hence, Hc is greater
than Ho.

The line of position can be plotted by using part of the information within the
broken circle of figure 1703a, as shown in figure 1703b. First, the AP is plotted. The
circle of equal altitude through this position is not needed, and is not plotted. From
the AP the azimuth line is measured toward or away from the GP as appropriate, and
the altitude difference is measured along this line. At the point thus located, a line is
drawn perpendicular to the azimuth line. For several miles on each side of the azimuth
line, this perpendicular can be considered part of the circle of position through the
observer, as shown in figure 1703a. This perpendicular is the line of position. It is
labeled with the time of observation above the line, and the name of the celestial body
below the line, as shown in figure 1703b.

For neatness of plot the azimuth line should not be extended beyond the line of
position or the AP, unless it is extended a short distance in the direction of the body,
and the symbol of the body observed is shown to indicate whether a “toward” or

452 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

“away” observation. This
method is used in the examples
of H.O. Pub. No. 214. Some
navigators omit the azimuth
line, showing only the AP and
line of position, and using a
straightedge as a guide for the
dividers in measuring the alti-
tude difference. This is good
practice, for it reduces the num-
ber of lines on the plotting
sheet, and therefore minimizes

| | the possibility of making an
si / error. However, until one gains
; j^

confidence in plotting lines of

^ia position, it is desirable to show

5 A the azimuth line.
Uy fa AP For plotting a line of posi-
Up E LAA” | tion from a celestial observation,
DIFFERENCE / then, only the assumed posi-
A tion, altitude difference (with

Figure 1703a.—The basis for the line of position from an indication of which altitude
a celestial observation. is greater), and azimuth are

needed.

The assumed position is chosen somewhat arbitrarily. It may be the dead reck-
oning position, an estimated position, or any arbitrarily chosen position nearby. Most
commonly, however, the assumed latitude (aL) is taken as the nearest whole degree
of latitude to the DR or EP; and the assumed longitude (aX) is selected so that the
local hour angle is a whole degree. The location of the line of position is independent
of the location of the AP (within reasonable limits), assuming only that the altitude
difference is measured from the AP used for determining He. That is, each AP has
its own altitude difference, depending upon its distance from the line of position.

The altitude difference, the numerical difference between Hc and Ho, is customarily
expressed in nautical miles (minutes of arc), and labeled T or A to indicate whether
the line of position is toward or away from the GP, as measured from the AP:

He “8795116 He 0195773
Ho 37%43/9 Ho 6221217
a TA a 15.4 T
The azimuth is customarily determined by com- AP
putation or table at the time of determining He.
This method of plotting a line of position from a AS

celestial observation was suggested by Marcq St.-Hilaire

(art. 2108), and generally bears his name. It is used

almost universally by modern navigators. The method

is based upon knowledge of one point on the line, and

the direction of the line. Another method of utilizing

the same principle is to assume the latitude and com- Ka

pute the longitude at which the line of position crosses SO

that parallel (the time sight method, art. 2106), or

vice versa. When this method is used, the azimuth ` Fong 1703b.—A line of position

Is customarily found separately, from a table or graph. CABE EO ERE dT Ep

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 453

A third method is to compute two points on the line of position and draw a straight
line through them. This line is a chord, rather than a tangent, of the circle of position,
but in most cases the difference is negligible. This third method was that originally
proposed by Captain Thomas H. Sumner (art. 131), and for this reason the resulting
line of position is sometimes called a Sumner line, although the expression may be
applied to any line of position resulting from celestial observation.

When celestial navigation is used, plotting is generally done on plotting sheets (art.
323) published by the U. S. Navy Hydrographic Office. These are less expensive than
charts, and the absence of detail eliminates a possible source of confusion and error.

1704. Using lines of position from celestial observations.—Like any other line of
position, one resulting from a celestial observation does not pinpoint the position of
the craft, but may provide all the information needed to insure safety of the vessel.
The selection of a celestial body and the time of observation to provide the desired
information is based upon the fact that the line of position is perpendicular to the
azimuth line. If the celestial body is on or near the celestial meridian, the line of
position is a latitude line, indicating the latitude at the time of observation, some-
times called the observed latitude. Similarly, a body on or near the prime vertical pro-
vides a longitude line, indicating the observed longitude. One ahead or astern provides
a speed line, since the line of position is perpendicular to the course, and hence is an
indication of the speed made good since the last speed line or fix. Similarly, a body
on the beam provides a course line which indicates to what extent the course is being
made good. If the azimuth line is perpendicular to a coast line, shoal, or other hazard,
the line of position indicates the distance of the vessel from the danger. Passage
parallel to such a danger, or between two of them, might be made safely by means of
a series of observations of a body on the beam during passage, without fixing the
position of the vessel. This problem might be simplified by precomputing the sextant
altitude at intervals during passage, and plotting this versus time on cross-section
paper, so that sextant altitudes can be compared immediately with the values taken
from the curve to determine any deviation from the desired track. In a perpendicular
approach to a coast, the point at which landfall will be made can be predicted with
considerable accuracy if a body having an azimuth parallel to the beach is observed.

During twilight, with clear skies, the selection of a celestial body to provide
desired information is simply a matter of choosing the body with azimuth nearest that
desired, remembering that bodies having azimuths differing by 180° should provide the
same line of position. Observation of bodies in opposite directions provides a check,
and a better one than two observations of the same body, or observations of two bodies
having nearly the same azimuth, for any constant error in the observations, such as
might be caused by abnormal dip, can be eliminated by observing bodies on opposite
azimuths and using a line midway between the two plotted lines of position.

When a limited number of bodies is available for a considerable period, as during
daylight, the best time to make an observation to obtain a line of position in a desired
direction can be determined by means of an azimuth table or diagram, or an inspection
table such as H.O. Pub. No. 214. The azimuth is located, and the corresponding
meridian angle is recorded. The meridian angle can then be converted to GHA, and
the time at which this GHA occurs can be determined from the almanac (art. 2104).

Lines of position can be used for determining an estimated position (art. 1705), or
they can be advanced or retired (art. 1706) to obtain a fix (art. 1707) or running fix
(art. 1708). If a single body is available for observation, increased accuracy can
usually be obtained by making three or more observations, adjusting all lines to a
common time (art. 1706), and using either the middle line, or the average position of all

lines.

454 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

1705. Estimated position.—As indicated in chapter VIII, a dead reckoning (DR)
position is determined by advancing a known position for courses and distances. In
the absence of additional information, the DR position is the best estimate of the posi-
tion of the vessel. However, the expression estimated position (EP) is generally applied
to one determined by using additional but inconclusive information. If the effects
of wind and current can be estimated, and these effects have not been considered in
establishing the DR position, they can be applied separately to establish an EP. As
each additional item of information is received, an improved estimate might be made.

A single line of position can
be useful in establishing an esti-

EP after observation of sun y 1630 EP mated position. If an accurate
line is obtained, the actual posi-
tion is somewhere on this line.
In the absence of better infor-
mation, a perpendicular from
the previous DR position or EP
to the line of position establishes
the new EP, as shown in figure
17052. The foot of the perpen-
dicular from the AP has no sig-

nificance in this regard, since it
FIGURE 1705a.—Estimated positions before and after ob- js used only to locate the line of
servation of the sun for a line of position, allowing for SS
current. position.

The establishment of a good
EP is dependent upon accurate interpretation of all information available. Generally,
such ability can be acquired only by experience. If, in the judgment of the nav-
igator or captain, the course has been made good, but the speed has been uncertain,
the best estimate of the position might be at the intersection of the course line and
the line of position, as shown in figure 1705b. If the speed since the last fix is considered
accurate, but the course is considered uncertain, the EP might be at the intersection
of the line of position and an arc centered on the previous fix and of radius equal to
distance traveled, as shown in figure 1705c.

1210 FIX

0700 FIX _0700 FIX

~ distance

1100 EP

1100 EP

FīGURE 1705b.—An estimated position when the FiaurE 1705c.—An estimated position when the
course and a line of position are considered speed and a line of position are considered
accurate. accurate.

0700 FIX

1100 EP

FIGURE 1705d.—An estimated position when a
line of position is considered of first accuracy,

speed of second accuracy, and course of third
accuracy.

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 455

| More often, neither course nor speed is known to be entirely accurate, but if one
is considered more accurate than the other, the EP may be located accordingly. Even
the line of position might properly be considered of questionable accuracy, and some
estimate of its reliability established. Figure 1705d shows an EP that might be
established by considering the line of position of greatest but incomplete accuracy,
the speed of secondary accuracy, and the course as least accurate.

The expression most probable position (MPP) is sometimes used as the equivalent
of estimated position. However, the former is of somewhat broader application, since
it may apply equally well to establishment of the fix when more than two lines of
position are available.

Further discussion of navigational accuracy is included in chapter XXIX.

1706. Advancing and retiring lines of position.—For a stationary observer, lines
of position resulting from observations made at different times are equally applicable
without adjustment. However, for a moving observer, as one aboard a vessel underway
at sea, any line of position (except a course line) applies only to the position at the time
of observation. If lines resulting from observations made at different times are to be
utilized for determining position, they should be adjusted for the motion of the observer
between observations.

A line of position resulting from observation of a celestial body can be advanced
or retired in the same manner as other lines of position (ch. IX), by selecting any
point associated with the line of position and running it forward or backward by dead
reckoning, or by estimate. For most accurate results, the best estimate of course and
speed made good (over the bottom) between the time of observation and the time to
which the line is to be adjusted should be used. Any error in determining these values is
reflected in the adjusted line of position. However, error in speed does not affect the
accuracy of an adjusted course line, nor does error in course introduce an appreciable
error in the accuracy of an adjusted speed line. The time label of an adjusted line of
position includes both the time of observation and the time to which the line is adjusted.

As in the case of a line of position resulting from observation of the bearing of an
identifiable, charted object (art. 904), the number of lines on the chart can be kept
to a minimum, reducing the possibility of confusion, by adjusting the point from which
the line is drawn. In the case of celestial navigation, this is the assumed position.
This method applies equally well to all observations, and avoids some possible dif-
ficulty which might arise in advancing a line of position nearly parallel to the course
line. When the AP is advanced or retired, the initial line of position need not be
drawn unless it serves some useful purpose.

1707. The fix.—The common intersection of two or more lines of position con-
stitutes a fix, regardless of the source of the position lines, provided only that the lines
are based upon simultaneous observations. Celestial observations are seldom simul-
taneous because all sights of a group are customarily taken by a single observer, usually
the navigator. If observations are made a few minutes apart (a round of sights), as
during a twilight period, all lines are adjusted to a common time, and the position
is considered a fix, rather than a running fix. Many navigators advance earlier lines
to the time of the last observation, and consider the fix applicable at this time, as
shown in figure 1707a. An alternative procedure, which is gaining in acceptance, is
to advance earlier sights and retire later ones to an intermediate time, cither the time
of the mid observation or a convenient time during the period of observation, such
as a whole, half, or quarter hour. This results in a more accurate and convenient time
of the fix. In figure 1707b the lines of figure 1707a are adjusted to a common time at
a whole hour. With any procedure, the time of the fix is the common time to which
the lines of position are adjusted.

456 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

(4j 0605 FIX

AR AR, AP,

Fiaure 1707a.—A fix obtained by advancing earlier lines of position to the time of the last
observation.

In figures 1707a and 1707b the assumed positions are typical of those which might
be used with a modern method of sight reduction such as H.O. Pub. No. 214 (ch. XX).
Any position in the vicinity might be used. If the dead reckoning (or estimated)
position at the time of each observation is used as the assumed position for that sight,
all sights are plotted from the DR position (or EP) at the time for which the fix is
desired. If the same AP is used for all sights, the advanced or retired AP’s are along a
straight line extending in the direction of the course line, the AP corresponding to the
earliest observation being farthest advanced along this line, and others progressing
along it in a direction opposite to that of the course. If there is any change of course
or speed between observations, this should be considered in advancing or retiring a line
of position, as it would in running forward the dead reckoning. Under normal condi-
tions, lines of position adjusted for a short interval to obtain a fix are moved by dead
reckoning, without separate allowance for current.

Two lines of position provide a fix, but when additional celestial bodies are available,
it is good practice to observe them. Additional lines serve as a check on the accuracy of
the first two, and should decrease the error of the fix. However, the increased accuracy

FIGURE 1707b.—A fix obtained by adjusting the lines of position of figure 1707a to a
convenient time during the period of observation.

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 457

of a fix resulting from a number of lines of position, over that resulting from only
two, is not great under normal conditions, and the principal reason for the additional
observations is the increased confidence the navigator has in the reliability of his fix.

In selecting bodies for observation, one should generally consider azimuth pri-
marily, and such factors as brightness, altitude, ete., secondarily. Individual cir-
cumstances, however, may dictate departures from this procedure. During twilight,
when skies are clear and the entire horizon is good, one generally has ample choice of
bodies to observe. It is good practice to make several more observations than the
minimum considered acceptable, so that additional lines of position will be available,
if needed, to resolve possible ambiguities or confirm doubtful results.

Sights need not be solved in the order taken. During evening twilight the brightest
bodies should be observed first, as soon as they can be “brought down” successfully
to the horizon. During morning twilight the reverse is true, the dimmer stars being
observed while they are still visible. However, with advance planning, one can include
in the list of bodies to be observed those which should provide the best fix.

If all observations were precisely correct, in every detail, the resulting lines of
position would meet at a point. However, this is rarely the case. Three observations
generally result in lines of position forming a triangle. If this triangle is not more than
two or three miles on a side under good conditions, and five to ten miles under unfavorable
conditions, there is normally no reason to suppose that a mistake has been made. Even
a point fix, however, is not necessarily accurate. An uncorrected error in time, for
instance, would move the entire fix eastward if early and westward if late, at the rate of
1’ of longitude for each 4° of error in time.

With two or four observations, the ideal is to have them crossing at angles of
90°. With three observations, the ideal is angles of 60°. With three observations it
is good practice to observe bodies differing in azimuth by 120°, as nearly as possible.
This provides lines of position crossing at angles of 60°, and, in addition, any constant
error in altitude is eliminated, serving only to increase or decrease the size of the tri-
angle, but not affecting the position of its center. If the azimuths differ by 60°, a large
constant error in altitude would result in a fix outside the triangle, asshown in figure 1707c.

FIX

i siti S i Ë i i ll lines
1707c.—4A fix from three lines of position, assuming a constant error in altitude. If all li
OR Pe aay (in this case) from the bodies observed, they would meet in a point which might
be either inside (left) or outside (right) the triangle.

458 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

With lines of position crossing at 60%, the assumed constant error for a fix outside
the triangle is three times that for a fix inside the triangle. With four bodies,
azimuths differing by 90° produce a box fix, with constant error eliminated by using
the mid point as the fix. With more than four observations, the selection of the fix
becomes more complex, and general rules are probably undesirable. The evaluation of
each observation and the exercise of judgment become of greater importance. What-
ever the number of observations, common practice, backed by logic, is to take the
center of the figure formed unless there is reason for deviating from this procedure.
By “center” is meant the point representing the least total error of all lines considered
reliable. With three lines of position, the center is considered that point, within the
triangle, which is equidistant from the three sides. It may be found by bisecting the
angles, but more commonly it is located by eye. If a fix outside the triangle is to be
used, and eye interpolation is not considered sufficiently reliable, the point can be
found by bisecting two external angles and the internal angle at the third intersection.
If a constant error is assumed, the most probable position of the fix can always be
found, whether within or outside the triangle, by bisecting the angle formed by azimuth
lines originating at each intersection.

The matter of navigational errors as applied to this problem is further discussed
in chapter XXIX.

1708. A running fix (R fix), in celestial navigation, is a position obtained by
observations separated by a considerable time interval, usually several hours. The
usual occasion for a running fix is the availability of a single celestial body for observa-
tion, generally the sun. The delay between observations is usually to permit the
azimuth to change sufficiently to provide a good angle of cut between lines of position.
Thus, the sun may be observed about 0900, and again about noon.

Generally, a longer wait results in a more nearly perpendicular intersection of
the two lines of position, but it may also increase the error of the advanced line. The
earlier line is advanced for the course and distance made good. The ability with
which these can be predicted determines the accuracy of the running fix, assuming
accurate observation, sight reduction, and plotting. For this reason it is impractical
to set a specific time limit upon the advancement of a line of position. This should be
determined by the conditions of each situation, in the best judgment of the navigator.
Experience is valuable in acquiring such judgment.

When an observation of a single body is made, with the intent of later advancing
it to obtain a running fix with a second observation, the line of position should be
plotted for the time of observation, regardless of the method used for advancing it,
for the single line usually provides some useful information, as indicated in article
1704.

Allowance for current, when advancing a line of position, can be made by solving
a vector diagram, as indicated in article 807, to determine the course and speed made
good. An alternative method is to advance the AP or line without allowance for
current, and then to advance it a second time in the direction of set of the current,
for a distance equal to the drift multiplied by the number of hours between the time
of observation and the time to which the line is advanced. This method is illustrated
in figure 1708a. The distance AB is equal to the distance between the 0800 and 1152
DR positions. The direction BC is the estimated set of the current, and the length BC
is the distance through which the current is assumed to act.

A third method provides accurate results even when a reliable estimate of the
current is not available, provided (1) a good fix was obtained several hours before the
time of observation, and (2) the average current between the time of the previous fix
and the time of observation can be assumed to continue until the time to which the

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 459

O
ģ
O

SUN

0800

FIGURE 1708a.—Advancing a line of position with allowance for current,
without determining course and speed made good.

line is to be advanced. This method is illustrated in figure 1708b. The 0510 fix
is shown at the left, and the DR positions at 0830 and 1215, the ship being on course
074°, speed 12 knots. The sun is observed at 0830 and again at 1215, and it is desired
to advance the earlier line to obtain a running fix at 1215. The lines of position at
0830 and 1215 are plotted. To advance the 0830 line of position, the distance AB
is assumed to increase uniformly with time interval from 0510. The interval to 0830

h m
is 3220", and that to 1215 is 7°05". Therefore, A'B'=ABX Gong = ABX2.1. The

advanced line of position is drawn through B’, parallel to the original line through B.
The running fix is at the intersection of the 1215 line and the advanced 0830 line.
The set of the average current between 0510 and 0830 is the direction from A’
to the 1215 running fix, and the drift is equal to this distance divided by 7°05”. The
direction of a straight line (not shown) from the 0510 fix to the 1215 running fix is

0510
FIX

Ficure 1708b.—Advancing a line of position without previous knowledge of the current.

460 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

the course made good between 0510 and 0830, and the length of this line divided by
the time (7505?) is the speed made good to 0830. x

The points B and B’ need not be at the intersection of the lines of position and
the course line. Any point on the line of position can be used, and the line A’B’
drawn parallel to AB. Changes of course and speed do not affect the accuracy of the
solution as long as A’B’ is parallel to AB.

Several other variations are possible. A convenient one is to measure the dis-
tance from the earlier fix to point B, and divide this by the time to determine an *'as-
sumed” speed (based upon the assumption that point B represents the position of the
vessel at the time of observation), and then to use this speed to advance the line of
position. This variation should not be used without adjustment if a change of course
or speed is involved between the earlier fix and the time to which the line is to be
advanced.

This method should be used with caution. Any error in either the earlier fix -
or the first line of position is increased in proportion to the elapsed time. Thus, in
figure 1708b, if AB is in error by one mile, A'B' is in error by 2.1 miles. It should
not be used when there is reason to suspect à change in current between fixes.

1709. Celestial navigation and dead reckoning.—As indicated in chapter VIII,
dead reckoning consists of advancing a known position for courses and speeds. Some
difference in technique arises from a difference of opinion among navigators on the
definition of (1) “known position" and (2) courses and speeds.

Regarding the first, no position determined by celestial navigation as commonly
practiced at sea is known with perfect accuracy. An average error of two miles is
realistic. Because of the varying conditions encountered, it is difficult to establish
limits of a “known” position. In general, however, a reasonably reliable fix or running
fix is considered sufficiently accurate to justify a new start in the dead reckoning. An
estimated position or & fix or running fix of doubtful accuracy is considered an indi-
cation, but an inconclusive one, of the error in the dead reckoning. Therefore, it is
considered good practice to avoid starting a new dead reckoning track from such a
position unless there is à compelling reason for doing so. After long experience and
the development of sound judgment, a navigator might acquire great skill in establish-
ing & most probable position of sufficient reliability to justify more frequent breaks
in the continuity of the dead reckoning, but even under these conditions any reasonable
element of doubt should be given great respect.

What has been said regarding “known position" applies, also, in large measure to
course and speed. The course steered and the speed at which a ship is being driven
forward by its engines can be determined with relatively little error. Allowance for
wind and current is a matter largely of judgment based upon experience. If the dead
reckoning is to be meaningful, considerable caution should be exercised in allowing for
wind and current when determining the course and speed to use for plotting. In the
absence of information of a high degree of reliability, it is considered prudent to deter-
mine dead reckoning without allowing for estimated effects of wind and current.

In the absence of better information, then, it is considered good practice to start
a new dead reckoning track only from a reliable fix or running fix, and to use courses
and speeds without allowance for wind and current. This does not mean, however,
that the navigator should not continually be aware of the possibility of error in his
position as determined by dead reckoning, nor should he fail to make an estimate of
the size and direction of the error. In this ability, and that of accurately interpreting
all navigational information received, lies the test of a good navigator. This is largely
the art of navigation, as distinguished from the somewhat mechanical process of making

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 461

observations and computing and plotting the results, and also from the science of
devising the aids that are used in modern navigation.

When it is desired to determine “average current,” this expression being used to mean
the resultant of all dead reckoning errors, the dead reckoning should be run forward
from a fix (not a running fix) to the time of the next fix (or running fix if the method
of art. 1708 is used). A dead reckoning position determined in any other way is not
usable, unless it is adjusted to provide a “no-current” position. A straight line con-
necting such a dead reckoning position and the fix at the same time indicates the
current. "The direction of the line from the DR position to the fix is the set of the cur-
rent, and the length of this line divided by the number of hours since the last fix is the
drift, as in piloting.

Problems

A plotting sheet such as H.O. 3000-9Z (or 3000—5), covering latitudes 27° to 30?
north and south is needed for most of the problems of this chapter. If this is not avail-
able, one can be constructed by means of table 5, as explained in article 307; or small
area plotting sheets can be constructed as explained in article 324.

1703a. In each of the following, determine the altitude difference, a, and label it
T or A, as appropriate:

Hc Ho
(1) 18°21'4 189259
(2) 53.0227 522305
(3) (—)0°05:2 (—)0°12!7
(4) (—)0?11*1 0°01/1

Answers (1) a 4.5T, (2) a 27.2A, (3) a 7.5 À, (4) a 12.2 T.
1703b. The 0930 DR position of a ship is lat. 29°20/4N, long. 130?25:2W. At
this time the navigator observes the sun, and computes Hc and Zn for the 0930 DR
position, as follows: Hc 45%42/9, Ho 45?50:2, Zn 15773. As & check, he also solves
the same sight for an assumed position of lat. 29%00:0 N, long. 130?30:0 W, with the
following results: Hc 46?00:0, Zn 15770.
Required.—Plot the two lines of position, and account for the result.
Answer.—The two lines of position plot as approximately the same line, which is
not dependent upon the assumed position, but only upon the observed altitude and
the time of observation.
1705a. The 0500 fix of a ship is lat. 27°10/0N, long. 142%55:5W. The ship is on
course 068°, speed 9 knots. At 0800 the navigator observes the sun, with the following
results:
a 6.6T au 27°0070N
Zn 105%0 an 142°39'1 W

The current since the morning fix is estimated to set 130°, at a drift of 1.4 knots.

Required —(1) The 0800 DR position.

(2) The 0800 EP if there were no observation, and no current was anticipated.

(3) The 0800 EP using the current, if there were no observation.

(4) The 0800 EP using the line of position, but not the current.

(5) The 0800 EP using all available information.

Answers.—(1) 0800 DR: L 27?20:0 N, A 142927/2W ; (2) 0800 EP without current
and line of position: L 27?20:0 N, A 142927'2 W; (3) 0800 EP with current but no line
of position: L 272174 N, X 142?23:5 W; (4) 0800 EP with line of position but no current:
L 27°19/5N, à 142°25/3 W; (5) 0800 EP with current and line of position: L 27?18:7 N,

2314292558 We

462 LINES OF POSITION FROM CELESTIAL OBSERVATIONS

1705b. The 0530 fix of a ship is lat. 2855/8 N, long. 161?51:7 E. The ship is on
course 060°, speed 10 knots. At 0830 the navigator observes the sun, with the follow-
ing results:
a 6.7A aL 29%0010N
Zn 110?0 an 162?28:9E

Required.—(1) 'The 0830 EP if the course is believed to have been made good, and
the line of position is considered accurate.

(2) The 0830 EP if the speed is believed to be correct, and the line of position is
considered accurate.

(3) The 0830 EP if the course and speed are considered of equal reliability, and
the line of position is considered accurate.

(4) The 0830 EP if the course is of questionable accuracy, but considered more
reliable than the speed, and the line of position is considered accurate.

(5) The 0830 EP if the speed is of questionable accuracy, but considered more
reliable than the course, and the line of position is considered accurate.

(6) The 0830 EP if the course is believed to have been made good, and the error
contributed by the uncertainty of the line of position is believed to be twice that
contributed by the uncertainty of the speed.

Answers.—(1) 0830 EP: L 29%13/5N, A 162%26/3E; (2) 0830 EP: L 29%06/5N,
^ 162%23/6E; (3) 0830 EP: L 29%09/8N, x 162%25/0E; (4) 0830 EP: any place between
(1) and (3); (5) 0830 EP: any place between (2) and (3); (6) 0830 EP: L 29%11:4N,
^ 162%22/8 E.

1707a. At 1740 the navigator and two assistants observe simultaneously three
stars, with the following results:

Fomalhaut Deneb Aldebaran
Hee, 28 10-5 34759'6 3995218
Ho 28?05:3 35°05/6 39%46/8
Zn 210°0 30827 08993
aL 28900:0N 2800/0N 2800/0N
ON ol WV, 42°29'0 W 42525 21

Required.—The 1740 fix.

Answer.—1740 fix: L 28%06:6 N, ^ 42°30/5 W.

1707b. The 1800 DR position of a ship is lat. 27°02/2N, long. 170°17/0W. The
ship is on course 045°, speed 14 knots. During evening twilight the navigator observes
three stars, with the following results:

Dubhe Altair Spica
Time 1815 1821 1830
He 3494502 2291178 47°24'8
Ho. 34°51/3 LADA 47204
Zn 99125 09073 219°9
aL 27%00/0N 2770010 N 272000 N
an 170%10:2W 170%05:0 W 169%54'8 W

Requred.—The 1830 fix.
Answer.—1830 fix: L 27?11:5 N, X 170%00'5 W.
1707c. The 1930 DR position of a ship is lat. 29°10/5S, long. 1222354 W. The
ship is on course 320%, speed 16 knots. During evening twilight the navigator observes
a planet and two stars, with the following results:

LINES OF POSITION FROM CELESTIAL OBSERVATIONS

Saturn

1931
46?58:5
46°55/5
023°5

aL 29°00/0S
ad 122°55'0W

Required.—The 1942 fix.

Time
He
Ho
Zn

463
Regulus Rigil Kent.
1942 1951
53°04/0 24?19:5
530913 24°30/0
17002 29776
290005 2900/05
12224511 W 1222352 W

Answer.—1942 fix: L 29°05/3S, ^ 122°47/4 W.
1707d. The 0500 DR position of a ship is lat. 29%53'9N, long. 69°32/1W. The

ship is on course 130°, speed 13 knots.

a planet and two stars, with the following results:

Mars

0451
T1451
17924.:5
130?1

aL 30°00/0N
an 69?41'7W

Required.—The 0500 fix.

Time
He
Ho
Zn

Kochab
0502
38°26/2
38°19/2
353-2
30°00/0 N
692300 W

During morning twilight the navigator observes

Spica

0511

S ILD
33947/8
236.9
30°00/0 N
69°18'3 W

Answer.—0500 fix: L 29%54/0N, ^ 69°30/5 W.
1707e. The 0930 DR position of a ship is lat. 28%40/4 N, long. 125%30/4E. The

ship is on course 220°, speed 25 knots.

The navigator observes the sun and moon, and

solves each sight from the DR position at the time of sight, with the following results:

Time
He
Ho
Zn

Required.—The 0943 fix.

Sun
0936
non
54 20.5
200?2

Moon
0943
370719
87. 14.7
14276

Answer.—0943 fix: L 28?32'1 N, A 125?32'3 E.

1707f. A ship is on course 314°, speed 24 knots.

During evening twilight the

navigator observes two stars and the moon, and solves all three sights using assumed
latitude 28°00/0S, assumed longitude 41°19'5 W as the AP, with the following results:

Peacock
1855
5791216
5G 1769
194°7
Required.—The 1900 fix.

Moon
1900
66°58 12
6750172
30075

Alpheratz
1905
230015
225587
038?2

Answer.—1900 fix: L 28%03'5S, A 41?26:5 W.
1707g. The 0400 DR position of a ship is lat. 27%01/8 N, long. 51936:0 E. The

ship is on course 037°, speed 20 knots.

At 0545 the course is changed to 309°.

During

morning twilight the navigator observes two stars, with the following results:

Time
a

Zn
aL

an

Vega

0537

4.5 T
300°5
27000 N
519452 E

Alpheratz
0602

7.8 T
07577
27000 N
5195071 E

464
Required.—The 0602 fix.

Answer.—0602 fix: L 27°28/1 N, X 51?51'1 E.
1707h. The 0600 DR position of a ship is lat. 2725073 N, long. 20%58:2 W. The

ship is on course 000°, speed 20 knots.

four stars, with the following results:

Dubhe
0551
290181
28?53':4
33070
aL 28?00:0N
an 20°54'6 W

Required.—The 0600 fix.

Time
He
Ho
Zn

Kaus Aust.
0554
2175758
221167
149?7
2870010 N
219084 W

Spica

0558
37°59!4
98.0370
23353
28°00'0 N

20%56:7 W

Answer.—0600 fix: L 27°53'5N, x 20%55'0 W.
1707i. The 1815 DR position of a ship is lat. 2941/55, long. 163?52:3 W. The

ship is on course 295°, speed 18 knots.
serves three stars, with the following results:

Regulus

1810
45°18'6

45 2632
04072
30?00:0 S
163450 W

A 16325016 W.

Pollux
1815

35°50°7
36%03/4

35077

3000/05

1634918 W
Required.—(1) The 1815 fix, assuming random errors.
(2) The 1815 fix, assuming a constant error.
Answers.—(1) 1815 fix: L 29%47:2S, N 1632512 W; (2) 1815 fix: L 29%51'4 S)

LINES OF POSITION FROM CELESTIAL OBSERVATIONS

During morning twilight the navigator observes

Vega

0604
543311
5492875
05773
28000 N
20951 SW.

During evening twilight the navigator ob-

Aldebaran
1821
225018
2299791.
30095
8070070 S
163°54'0 W

1708a. The 0830 DR position of a ship is lat. 29°25!4 S, long. 9°34!7 E. The ship

is on course 326°, speed 22 knots.

at 1200, with the following results:

Time
a

Zn
alu
aN

Sun

0830
15.24
06223
2900/08
92370 E

Reguired.—The 1200 running fix.
Answer.—1200 R fix: L 2831/68, \ 8950/0 E.

1708b. The 0900 DR position of a ship is lat. 28905/6 N, long. 93?44'0 W.

Sun

1200
28.4 A
16975
2900/08
8 02 1h

The sun is observed during the morning, and again

The

ship is on course 220%, speed 20 knots, and is believed to be in a current with set of

110° and a drift of 1.5 knots. The sun is observed during the morning, and again
at 1200, with the following results:

Time
a

Zn
alu
aN

Sun

0900
112 1}
103°2
28°00/0 N
93?54/0 W

Sun

1200
17.0 A
17230
27000 N
94389 W

LINES OF POSITION FROM CELESTIAL OBSERVATIONS 465

Required.—The 1200 running fix.

Answer.—1200 R fix: L 27?19/8 N, N 94?17/5 W.

1708c. The 0715 fix of a ship is lat. 28°28/9S, long. 81%14/8 W. The ship is on
course 120°, speed 15 knots. During the morning the sun is observed twice, with the
following results:

Sun Sun
Time 0945 1200
a 94A 0
Zu 095°0 005°0

aL 29%00'08 20700 05
an 80?26:1 W 80711:2 W

Required.—(1) The 1200 running fix, allowing for current.

(2) Set and drift of the current.

(3) Course made good between 0715 and 0945.

Answers.—(1) 1200 R fix: L 29°01/08, A 80?00:2 W; (2) set 049°, drift 1.1 kn.;
(3) course made good 116°0.

1708d. The 0500 fix of a ship is lat. 28?36:5 N, long. 143%22/0 E. The courses
and speeds during the morning are as follows:

Time Course Speed
0500 047° 24 kn.
0600 102° 20 kn.
0715 038° 16 kn.
0845 075° 19 kn.
1000 030° 23 kn.
1045 085° 25 kn.
During the morning the sun is observed twice, with the following results:
Sun Sun
Time 0915 1200
a 8.8A 20.0A
Zn 125°0 1917

aL 29%00/0N 29?00:0 N
an 144%44'8E 14529/8 E

Required.—(1) The 1200 running fix, allowing for current.

(2) Set and drift of the current.

(3) Course and speed made good between fixes, assuming no change in current.

Answers.—(1) 1200 R fix: L 29°20/0N, ^ 145?33:0 E; (2) set 2002 dritte
kn.; (3) course made good 070?, speed made good 17.7 kn.

1709a. The 0400 DR position of a ship is lat. 27?41:88, long. 64?54:0 E. This
position has been run forward from a fix at 1715 the previous evening. The ship is
on course 215°, speed 19 knots, but at 0600 the course is changed to 125%. At 0715
a fix locates the ship at lat. 2823/08, long. 65?04:3 E.

Required.—Set and drift of the current between fixes.

Answers.—Set 073°, drift 1.0 kn.

1709b. The 0500 fix of a ship is lat. 27%09/0N, long. 158?09:5 W. The ship is
on course 310°, speed 14 knots. At 1155 a running fix locates the ship at lat. 28?01:2
N, long. 159%33/2W. A new dead reckoning plot is started from this position. At
1900 a star fix is obtained, locating the ship at lat. 28%57'8 N, long. 160%54:9 W.

Required —Set and drift of the average current between morning and evening
fixes.

Answers.—Set 167°, drift 1.2 kn.

CHAPTER XVIII
THE ALMANAC

1801. Introduction.—A requirement of celestial navigation is the availability of
accurate predictions of the positions of the celestial bodies used. These predictions,
with respect to the celestial equator system of coordinates (art. 1426), are contained in
three publications of the United States Naval Observatory. Recent minor modifica-
tions to these publications have not been incorporated in this printing. The solution
for a celestial line of position consists principally of the conversion of tabulated coor-
dinates to those on the horizon system of coordinates (art. 1428).

The American Ephemeris and Nautical Almanac gives, to a high precision, de- `
tailed information on a large number of celestial bodies. This annual publication is
arranged to suit the convenience of the astronomer, for whom it is primarily intended.
The ephemeris is not needed for ordinary purposes of navigation, although it contains
some information of general interest, such as various astronomical constants, details of
eclipses, information on planetary configurations (art. 1422), and miscellaneous
phenomena. Each volume of the ephemeris contains instructions for its use.

The American Nautical Almanac, an annual publication, contains the astro-
nomical information needed by the marine navigator. It is conveniently arranged to
suit his needs, and the information is tabulated to a practical degree of precision (art.
03), in general to the nearest 0/1 of arc and 1* of time, at hourly intervals. Beginning
with the edition for 1958, this volume is a joint publication of the U. S. Naval Observa-
tory and the British Admiralty, and incorporates a number of changes from previous
editions. Extracts from the Nautical Almanac for that year are given in appendix V.
These extracts, illustrating the various features of that publication, can be used in the
solution of the various illustrative and sample problems of the present volume.

The Air Almanac, published three times per year, is intended primarily for air
navigators. In general, the information is similar to that of the Nautical Almanac,
but is given to a precision of 1’ of arc and 1° of time, at intervals of 10™ (recent editions
give values for the sun and Aries to a precision of 0/1). This publication is suitable
for ordinary navigation at sea, but may lack the precision that is sometimes needed.
The Air Almanac is a joint publication of the U.S. Naval Observatory and the British
Air Council. Extracts from the Air Almanac are given in appendix W.

A highly abbreviated, long-term almanac is given in appendix X. Because of the
large intervals between entries, and the fact that no provision is made for nutation,
information taken from this almanac may be of reduced accuracy. Although this
accuracy is sufficient for most purposes of navigation, the almanac is not as convenient
to use as either of those published by the U. S. Naval Observatory, and is not recom-
mended when one of them is available. Instructions for its use are included in
appendix X.

1802. American Nautical Almanac.—The major portion of the Nautical
Almanac is devoted to hourly tabulation of Greenwich hour angle and declination, to
the nearest 0:1 of arc. On each set of facing pages, information is given for three con-
secutive days. On the left-hand page, successive columns give GHA of Aries and both
GHA and declination of Venus, Mars, Jupiter, and Saturn, followed by the SHA and
declination of 57 stars. The GHA and declination of the sun and moon, and the
horizontal parallax of the moon, are given on the right-hand page. Where applicable,

the quantities v and d are given to assist in interpolation. The quantity v is the differ-
466

THE ALMANAC 467

ence between the actual change of GHA in one hour and a constant value used in the
interpolation tables, while d is the change in declination in one hour. Both v and d are
given to the nearest 0/1. To the right of the moon data is given the LMT (art. 1911)
of sunrise, sunset, and beginning and ending of nautical and civil twilight for various
latitudes from 72? N to 60? S. The LMT of moonrise and moonset at the same
latitudes is given for each of the three days for which other information is given, and
for the following day. Magnitude (art. 1405) of each planet at GM'T 1200 of the middle
day ls given at the top of the column. "The GMT (art. 1907) of transit across the
celestial meridian of Greenwich is given as “Mer. Pass." "The value for the first point
of Aries for the middle of the three days is given to the nearest 0™1 at the bottom of
the Aries column. The time of transit of the planets for the middle day is given to
the nearest whole minute, with SHA (at GMT 0000 of the middle day) to the nearest
0:1, below the list of stars. For the sun and moon, the time of transit to the nearest
whole minute is given for each day. For the moon, both upper and lower transits are
given. This information is tabulated below the rising, setting, and twilight information.
Given there, also, are the equation of time for 0" and 12^, and the age and phase of the
moon (art. 1423). Equation of time is given, without sign, to the nearest whole second.
Age is given to the nearest whole day. Phase is given by symbol.

The main tabulation is preceded by a list of religious and civil holidays, phases
of the moon, a calendar, information on eclipses occurring during the year, and notes
and a diagram giving information on the planets.

The main tabulation is followed by explanation and examples. Next are four
pages of standard times (zone descriptions) in use in various places in the world. Star
charts are given next, followed by a list of 173 stars in order of increasing sidereal hour
angle. This list includes the stars given on the daily pages. It gives the SHA and
declination each month, and the magnitude. Stars are listed by Bayer’s name and also
by popular name where there is one. Following the star list are three pages of Polaris
tables giving the azimuth and the corrections to be applied to the observed altitude to
find the latitude. Next is a table for converting arc to time units. This is followed by
a 30-page table called ‘Increments and Corrections,” used for interpolation of Green-
wich hour angle and declination. This table is printed on tinted paper, for quick
location. Then come tables for interpolating for times of rising, setting, and twilight;
followed by two indices of the 57 stars listed on the daily pages, one index being in
alphabetical order, and the other in order of decreasing SHA.

Sextant altitude corrections are given at the front and back of the almanac.
Tables for the sun, stars, and planets, and a dip table, are given on the inside front
cover and facing page, with an additional correction for nonstandard temperature and
atmospheric pressure on the following page. Tables for the moon, and an abbreviated
dip table, are given on the inside back cover and facing page. Use of the altitude
correction tables is explained in chapter XVI. Corrections for the sun, stars, and
planets for altitudes greater than 10°, and the dip table, are repeated on one side of a
loose bookmark. The star indices are repeated on the other side.

1803. Air Almanac.—As in the Nautical Almanac, the major portion of the Air
Almanac is devoted to a tabulation of GHA and declination. However, in the Air
Almanac values are given at intervals of ten minutes, to a precision of 1'. Values are
given for the sun, first point of Aries (GHA only), the three navigational planets most
favorably located for observation, and the moon. The magnitude of each planet listed
is given at the top of its column, and the phase of the moon is given at the top of its
column. Values for the first 12 hours of the day are given on the right-hand page, and
those for the second half of the day on the back. In addition, the right-hand page has
a table of the moon’s parallax in altitude, and below this the semidiameter of the sun,

468 THE ALMANAC

and both the semidiameter and age of the moon (art. 1423). To the right of this is an
ecliptic diagram, explained in article 2209. The afternoon side of each daily page in-
cludes the LMT of sunrise, sunset, moonrise, and moonset; duration of civil twilight; and
a difference column for finding the time of moonrise and moonset at any longitude.

Critical tables for interpolation for GHA are given on the inside front cover, which
also has an alphabetical listing of the stars, with the number, magnitude, SHA, and
declination of each. The inside of the back cover has the same refraction table and
Coriolis correction table given in H.O. Pub. No. 249. The outside back cover has a
correction table for dip of the horizon, and a table of contents.

Following the daily pages are instructions for use of the almanac; a list of symbols
and abbreviations in English, French, and Spanish; a list of time differences between
Greenwich and various other places; a number of sky diagrams (art. 2212); information
on setting the astrograph (art. 2123); polar sunlight, twilight, and moonlight diagrams;
corrections to times of sunrise and sunset when observed from flight altitudes; a table `
for converting are to time; interpolation tables for finding time of moonrise and moon-
set at any longitude; a star list similar to that given on the inside front cover, but in
order of decreasing SHA; a list of the names and numbers of the stars used in H.O.
Pub. No. 249, those in H.O. Pub. No. 218, and those which can be used by declination
entry in H.O. Pub. No. 249, in addition to those listed by name; and an explanation of
the navigational star chart, and the chart itself. The inside front cover page is re-
peated on the back of the star chart. Also given there are a single Polaris correction
table, a standard aircraft astrodome refraction table, and a special refraction table for
use with H.O. Pub. No. 218.

Minor modifications and changes to some of the foregoing items have been made
in recent editions of the Air Almanac.

1804. Use of the almanacs.—The time used as an entering argument in the al-
manacs is GMT, and the information given is for the Greenwich meridian.

Tabulated information taken from the almanacs, as from any tables, should not be
recorded to a greater precision than tabulated. The units in which values are given
are shown at the tops of the columns.

The use of work forms, such as those shown in appendix Q, permits concentration
on the extraction of data, with no need for dividing one's attention between this and
thought regarding the order of work. It also simplifies the taking of all needed in-
formation from the double page to which the almanac is open, before turning to a dif-
ferent part of the almanac.

If the entering arguments are exactly those of any table, the desired value is taken
directly from the table. Often, however, this is not the case, and the detailed instruc-
tions in the following articles relate principally to the method of interpolating in the
various tables. Since Greenwich hour angle is measured in a westerly direction, the
same direction as the apparent motion of celestial bodies, the tables are customarily
entered with the next earlier tabulated time, with interpolation toward a later time.
The correction to be applied for a fractional part of an hour is then always additive. If
the sum exceeds 360°, this amount is subtracted.

In the Nautical Almanac, v is always positive unless a negative sign (—) is given.
This can occur only in the case of Venus. For the sun, the tabulated values of GHA
have been adjusted slightly to minimize the error of interpolation, so that no v value
need be given. No sign is given for tabulated values of d, which can be considered
positive if declination is increasing, and negative if it is decreasing. The sign of a y or
d value is given also to the related correction.

In the Air Almanac the tabulated declination values are those for the middle
of the interval between the time indicated and the next following time for which a value

THE ALMANAC 469

is given. It is intended that declination be taken from the tables without interpolation.

1805. Finding GHA and declination of the sun.—Nautical Almanac. Enter the
daily-page table with the whole hour next preceding the given GMT, unless this time
is itself a whole hour, and take out the tabulated GHA and declination. Record, also,
the d value given at the bottom of the declination column. N ext, enter the increments
and corrections table for the number of minutes of GMT. If there are seconds, use
the next earlier whole minute. On the line corresponding to the seconds of GMT take
the value from the sun-planets column. Add this to the value of GHA from the daily
page to find GHA at the given time. Next, enter the correction table for the same
minute with the d value, and take out the correction. Give this the sign of the d value,
and apply it to the declination from the daily page. The result is the declination at
the given time.

Example 1.—Find the GHA and declination of the sun at GMT 1824937 on
June 1, 1958, using the Vautical Almanac.

Solution.—
Sun Sun
GMT. 185249375, June 1 GMT 185247378 June 1
LS? 2290346 1350122203 54N'd.
2415375 6°09/3 corr. (4-071 (+)0/3
GHA 96°43/9 d 22903 4 DINI

The correction table for GHA of the sun is based upon a rate of change of 15?
per hour, the average rate during a year. At most times the rate differs slightly from
this. The slight error thus introduced is minimized by the method of tabulation.
The tabulated values are adjusted for half the error during the hour following the time
of tabulation. "Therefore, instead of increasing for an hour following the entry time,
the error decreases for the first half hour, to zero, and then increases during the second
half hour, and the maximum error is only about half what it would be if unadjusted
values were used. The greatest error thus introduced is about 0/1. An additional
small error may be introduced by rounding off base and correction values to the nearest
0/1. More exact values can be obtained by interpolating between the values for the
half hours, or by referring to the ephemeris.

The d value is the amount that the declination changes between 1200 and 1300 on
the middle day of the three shown.

Air Almanac. Enter the daily page with the whole 10” next preceding the given
GMT, unless this time is itself a whole 10”, and extract the tabulated GHA and decli-
nation, without interpolation. The tabulated declination is correct for the time 30”
later than that tabulated, so that interpolation during the hour following tabulation
is not needed for most purposes. Next, enter the “interpolation of GHA” table on the
inside front cover, using the “sun, etc.” entry column, and take out the value for the
remaining minutes and seconds of GMT. If the entry time is an exact tabulated value,
use the correction given half a line above the entry time. Add this correction to the
GHA taken from the daily page to find the GHA at the given time. No adjustment of
declination is needed.

Example 2.— Find the GHA and declination of the sun at GMT 18"24%37* on
June 1, 1958, using the Air Almanac.

Solution.—

18°20" 95%35'

4m37* 1°09’

GHA 96°44’
d 22%04'N

470 THE ALMANAC

1806. Finding GHA and declination of the moon.—Nautical Almanac. Enter
the daily-page table with the whole hour next preceding the given GMT, unless this
time is itself a whole hour, and take out the tabulated GHA and declination. Record,
also, the corresponding » and d values tabulated on the same line, and determine the
sign of the d value. The» value of the moon is always positive (+), and is not marked
in the almanac. Next, enter the increments and corrections table for the minutes of
GMT, and on the line for the seconds of GMT take the GHA correction from the
moon column. Then, enter the correction table for the same minute with the » value,
and extract the correction. Add both of these corrections to the GHA from the daily
page to obtain the GHA at the given time. Then, enter the same correction table
with the d value, and extract the correction. Give this correction the sign of the d
value, and apply it to the declination from the daily page to find the declination at the
given time.

Example 1.— Find the GHA and declination of the moon at GMT 21”25”44* on
June 1, 1958, using the Nautical Almanac.

Solution.—
Moon Moon
GMT 21525744" June 1 GMT 2125144" June 1
2152215901706 21511894022 9d
25"44* 6908/4 v corr. (+)1/0 (+)2/4
corr. 2:4 (4-) 5/6 d 18°47/3S

GHA 321912/4

The correction table for GHA of the moon is based upon the minimum rate at
which the moon’s GHA increases, 14%19/0 per hour. The v correction makes the ad-
justment for the actual rate. The » value itself is the difference between the minimum
rate and the actual rate during the hour following the tabulated time. "The d value is
the amount that the declination changes during the hour following the tabulated time.

Air Almanac. Enter the daily page with the whole 10" next preceding the given
GMT, unless this time is itself a whole 10”, and take out the tabulated GHA and the
declination, without interpolation. Next, enter the ‘interpolation of GHA” table on
the inside front cover, using the “moon” entry column, and take out the value for the
remaining minutes and seconds of GMT. If the entry time is an exact tabulated value,
use the correction given half a line above the entry time. Add this correction to the
GHA taken from the daily page to find the GHA at the given time. No adjustment of
declination is needed.

Example 2.—Find the GHA and declination of the moon at GMT 21*25"44* on
June 1, 1958, using the Air Almanac.

Solution.—

Moon
GMT 21°25™44* June 1
21220 2803169407

544° 1°23"
CHARRIE
d 18°47’S

The declination given in the table is correct for the time five minutes later than
tabulated, so that it can be used for the ten-minute interval without interpolation, to an
accuracy to meet most requirements. If greater accuracy is needed, it can be obtained
by interpolation, remembering to allow for the five minutes indicated above.

1807. Finding GHA and declination of a planet.—Nautical Almanac. Enter the
daily-page table with the whole hour next preceding the given GMT, unless the time
itself is a whole hour, and take out the tabulated GHA and declination! Record, also,

THE ALMANAC 471

the v value given at the bottom of each of these columns. N ext, enter the increments
and corrections table for the minutes of GMT, and on the line for the seconds of GMT
take the GHA correction from the sun-planets column. Next, enter the correction
table with the v value and extract the correction, giving it the sign of the» value. Add
the first correction to the GHA from the daily page, and apply the second correction
in accordance with its sign, to obtain the GHA at the given time. Then, enter the
correction table for the same minute with the d value, and extract the correction.
Give this correction the sign of the d value, and apply it to the declination from the
daily page to find the declination at the given time.

Example 1.—Find the GHA and declination of Venus at GMT 5'24"075 on June 2,
1958, using the Nautical Almanac.

Solution.—
Venus Venus
GMT 5247078 June 2 GMT 524075 June 2
52952128 SAN
247075 6901/8 v corr. (+) 0/4 (+) 1/0
corr. (—)0/1 (—) 0/3 d 99541 N

GHA 301°23'5

The correction table for GHA of planets is based upon the mean rate of the sun;
15° per hour. The » value is the difference between 15? and the change of GHA of
the planet between 1200 and 1300 on the middle day of the three shown. The d value
is the amount that the declination changes between 1200 and 1300 on the middle day.

Venus is the only body listed which ever has a negative v value.

Air Almanac.—Enter the daily page with the whole 10™ next preceding the given
GMT, unless this time is itself a whole 10™, and extract the tabulated GHA and declina-
tion, without interpolation. The tabulated declination is correct for the time 30™ later
than tabulated, so that interpolation during the hour following tabulation is not needed
for most purposes. Next, enter the “interpolation of GHA”’ table on the inside front
cover, using the “sun, etc.” column, and take out the value for the remaining minutes
and seconds of GMT. If the entry time is an exact tabulated value, use the correction
half a line above the entry time. Add this correction to the GHA from the daily page
to find the GHA at the given time. No adjustment of declination is needed.

Example 2.—Find the GHA and declination of Venus at GMT 5"48"45* on June 2,
1958, using the Air Almanac.

Solution.—

Venus
GMT 5^48745* June 2
54023052221
8"45* 25 V
GHA 307°33’
d 9°54’ N

The declination is taken for the next earlier tabulated time, and is correct for
GMT 5°45".

1808. Finding GHA and declination of a star.—If the GHA and declination of
each navigational star were tabulated separately, the almanacs would be several times
their present size. But since the sidereal hour angle (art. 1426) and declination are
nearly constant over several days (to the nearest 0/1) or months (to the nearest 1”),
separate tabulations are not needed. Instead, the GHA of the first point of Aries,
from which SHA is measured, is tabulated on the daily pages, and a single listing of
SHA and declination is given for each double page of the Nautical Almanac, and for an

472 THE ALMANAC

entire volume of the Air Almanac. The finding of GHAT is similar to finding GHA
of the sun, moon, and planets.

Nautical Almanac. Enter the daily-page table with the whole hour next preceding
the given GMT, unless this time is itself a whole hour, and take out the tabulated
GHAT. Record, also, the tabulated SHA and declination of the star from the listing
on the left-hand daily page. Next, enter the increments and corrections table for the
minutes of GMT, and on the line for the seconds of GMT take the GHA correction
from the Aries column. Add this correction and the SHA of the star to the GHA T of
the daily page to find the GHA of the star at the given time. No adjustment of
declination is needed.

Example 1.—Find the GHA and declination of Canopus at GMT 3*"24%33* on
June 2, 1958, using the Nautical Almanac.

Solution.—

Canopus
GMT 3^24733* June 2
3% 295048
247335 690913
SHA 264°15/0
GHA 205°29/1
d 52%40:6S

The SHA and declination of 173 stars, including Polaris and the 57 listed on the
daily pages, are given for the middle of each month, on almanac pages 268-273. For
a star not listed on the daily pages this is the only almanac source of this information.
Interpolation in this table is not necessary for ordinary purposes of navigation, but is
sometimes needed for precise results. "Thus, if the SHA and declination of 8 Crucis
(Mimosa) are desired for March 1, 1958, they are found by simple eye interpolation to
be SHA 168%40/2 and d 59%27/6 S.

If GHA 7 is desired, it is found as indicated in example 1, but omitting the addition
of SHA of a star. In the example GHA T is 295°04/8+6°09/3=301°14/1.

Air Almanac. Enter the daily page with the whole 10” next preceding the given
GMT, unless this is itself a whole 10", and extract the tabulated GHAY. Next,
enter the “interpolation of GHA” table on the inside front cover, using the “sun, etc.”
entry column, and take out the value for the remaining minutes and seconds of GMT.
If the entry time is an exact tabulated value, use the correction given half a line above
the entry time. From the tabulation at the left side of the same page, extract the
SHA and declination of the star. Add the GHA from the daily page and the two
values taken from the inside front cover to find the GHA at the given time. No
adjustment of declination is needed.

Example 2.—Find the GHA and declination of Peacock at GMT 12"17"58* on
June 1, 1958, using the Air Almanac.

Solution.—

Peacock
GMT 12*17%58* June 1
PASE 41958'

72585 2200'

SHA 54°24’

GHA 128%92/
d 56%52S

1809. Rising, setting, and twilight.—In both almanacs the times of sunrise, sunset,
o, moonset, and twilight information at various latitudes between 72° N and
DUT S are given to the nearest whole minute. By definition, rising or setting occurs
when the upper limb of the body is on the visible horizon, assuming standard refraction

SIA

THE ALMANAC 473

for zero height of eye. Because of variations in refraction and height of eye, compu-
tation to a greater precision than 1™ is not justified. For high elevations, as those
encountered on a mountain overlooking the sea, or at flight altitudes, a correction
table is provided in the Air Almanac.

In high latitudes some of the phenomena do not occur during certain periods.
The symbols used to indicate this condition are:

O Sun or moon does not set, but remains continuously above the horizon.

ma Sun or moon does not rise, but remains continuously below the'horizon.

//// Twilight lasts all night.

The Nautical Almanac makes no provision for finding the times of rising, setting,
or twilight in polar regions. The Air Almanac has graphs for this purpose. The use
of these, and other sources of such information, are explained in article 2536.

In the Nautical Almanac, sunrise, sunset, and twilight tables are given only once
for the three days on each page opening, using average declination and equation of
time. The results approximate the values for the middle day. For most purposes
this information can be used for all three days. For more accurate results, the infor-
mation can be taken from the Air Almanac, which has a table for each day. Both alma-
nacs have moonrise and moonset tables for each day.

The tabulations are in local mean time (art. 1911). On the zone meridian, this is
the zone time (ZT). For every 15’ of longitude that the observer’s position differs
from that of the zone meridian, the zone time of the phenomena differs by 1™, being
later if the observer is west of the zone meridian, and earlier if he is east of the zone merid-
ian. The local mean time of the phenomena varies with latitude of the observer,
declination of the body, and hour angle of the body relative to that of the mean sun.

Sunrise and sunset are also tabulated in the tide tables (from 76° N to 60? S) and
in a supplement to the American ephemeris of 1946 entitled Tables of Sunrise, Sunset,
and Twilight (from 75°N to 75°S). The meridian angle of any body at the time of
its rising and setting can be computed by the formulas given in article 2536. The
meridian angle of a body when its center is on the celestial horizon can be computed by
the formula

cos t=tan L tan d,
where t is the meridian angle, L is the latitude, and d is the declination. Solutions of
this formula are given in table 25, if the table is entered with a latitude 90° from the
given latitude. This table can be used for this purpose only when latitude and declina-
tion are of contrary name.

1810. Finding time of sunrise and sunset.—Nautical Almanac. Enter the table
on the daily page, and extract the LMT for the tabulated latitude next smaller than
the observer’s latitude (unless this is an exact tabulated value). Apply a correction
from table I on almanac page xxxii to interpolate for latitude, determining the sign of
the correction by inspection. Then convert LMT to ZT by means of the difference
in longitude (dX) between the local and zone meridians.

Example.—Find the zone time of sunrise and sunset at lat. 43°31/4N, long.
36°14/3 W on June 1, 1958.

Solution.—
L 43?31/4 N June 1
X 36°14/3 W

Sunrise Sunset
40% 0433 40° 1922
T I (—)11 HAL sl). 11
LMT 0422 LMT 1933
da (+)25 da (+)25

ZT 0447 Za LSS

474 THE ALMANAC

Air Almanac. The procedure is the same as that for the Nautical Almanac, except
that correction for latitude is made by linear interpolation directly from the tabulation,
since no interpolation table is provided.

The tabulated times are for the Greenwich meridian. Except in high latitudes
near the times of the equinoxes, the time of sunrise and sunset varies so little from day
to day that no interpolation is needed for longitude. If such an interpolation is con-
sidered justified, it can be made in the same manner as for the moon (art. 1812).

In high latitudes, interpolation is not always possible. For instance, on June 1,
1958, sunrise at latitude 66° N occurs at 0114, but at latitude 68° N the sun does not
set. Between these two latitudes the time of sunrise might be found from the graphs
in the Air Almanac, or by computation, as explained in article 2536. However, in
such a marginal situation, the time of sunrise itself is uncertain, being greatly affected
by a relatively small change of refraction or height of eye.

1811. Finding time of twilight.—Morning twilight ends at sunrise, and evening
twilight begins at sunset. The time of the darker limit can be found from the almanacs.
The time of the darker limits of both civil and nautical twilights (center of the sun 6°
and 12°, respectively, below the celestial horizon) is given in the Nautical Almanac.
The duration (in minutes) of civil twilight is tabulated in the Air Almanac. The bright-
ness of the sky at any given depression of the sun below the horizon may vary consid-
erably from day to day, depending upon the amount of cloudiness and other atmospheric
conditions. In general, however, the most effective period for observing stars and
planets occurs when the center of the sun is between about 3° and 9° below the celestial
horizon. Hence, the darker limit of civil twilight occurs at about the mid point of
this period. At the darker limit of nautical twilight the horizon is generally too dark
for good observations. At the darker limit of astronomical twilight (center of the sun
18? below the celestial horizon) full night has set in. The time of this twilight is given
in the ephemeris. Its approxumate value can be determined by extrapolation (art. P6)
in the Nautical Almanac, noting that the duration of the different kinds of twilight is
not proportional to the number of degrees of depression at the darker limit. More
precise determination of the time at which the center of the sun is any given number of
degrees below the celestial horizon can be determined by a large-scale diagram on the
plane of the celestial meridian (art. 1432) or by computation (art. 2536). Duration
of twilight at various angles of depression between 1?3 and 12? is given on pages A52
and A53 of the Air Almanac (not shown in appendix W).

Nautical Almanac. The method of finding the darker limit of twilight is the
same as that for sunrise and sunset (art. 1810).

Example 1.—Find the zone time of beginning of morning nautical twilight and
ending of evening nautical twilight at lat. 21?54/7S, long. 109?34'2 E on June 1, 1958.

Solution.—
L, 21854175 June 1
A 1099342 E

Nautical Nautical
twilight twilight
20951805237 20°S 1819
TI (43 des
LMT 0540 LMT 1816
d^ (—) 18 da (—) 18
ZT 0522 ZT 1758

Air Almanac. Find the ZT of sunrise and sunset as explained in article 1810,
except that correction for latitude is made by linear interpolation, since no table is
provided for this purpose. While taking the LMT from the almanac, extract, also, the
duration of civil twilight, in minutes. Subtract this value from the time SE Geer

THE ALMANAC 475

to find the time of beginning of morning civil twilight, and add it to the time of sunset
to find the time of ending of evening civil twilight.

Example 2.—Find the zone time of beginning of morning civil twilight and ending
of evening civil twilight at lat. 47%18/88, long. 879283 W on June 11958:

Solution.—
L 4718/88 June 1
A 87283 W
Sunrise Sunset
45°S 0727 45°S 1628
corr. (+)9 corr. (—)9
LMT 0736 LMT 1619
da (—) 10 dh (—) 10
ZT 0726 (sunrise) ZT 1609 (sunset)
dur. (—) 35 dur. (+) 35
ZT 0651 (twilight) ZT 1644 (twilight)

Sometimes in high latitudes the sun does not rise but twilight occurs. This
is indicated in the Air Almanac by the symbol mm in the sunrise and sunset column.
In this case the value in the twilight column indicates half the duration of twilight.
To find the time of beginning of morning twilight, subtract this interval from the time
of meridian transit of the sun; and for the time of ending of evening twilight, add it to
the time of meridian transit. The LMT of meridian transit never differs by more than
1674 (approximately) from 1200. The actual time on any date can be determined from
the almanac (art. 2104).

1812. Finding time of moonrise and moonset is similar to finding time of sunrise
and sunset, with one important difference. Because of the moon’s rapid change of
declination, and its fast eastward motion relative to the sun, the time of moonrise and
moonset varies considerably from day to day. These changes of position on the
celestial sphere (art. 1403) are continuous, as moonrise and moonset occur successively
at various longitudes around the earth. Therefore, the change in time is distributed
over alllongitudes. For precise results, it would be necessary to compute the time of the
phenomena at any given place, by the method described in article 2536. For ordinary
purposes of navigation, however, it is sufficiently accurate to interpolate between
consecutive moonrises or moonsets at the Greenwich meridian. Since apparent
motion of the moon is westward, relative to an observer on the earth, interpolation in
west longitude is between the phenomenon on the given date and the following one. In
east longitude it is between the phenomenon on the given date and the preceding one.

Nautical Almanac. For the given date, enter the daily-page table with latitude,
and extract the LMT for the tabulated latitude next smaller than the observer’s latitude
(unless this is an exact tabulated value). Apply a correction from table I of the al-
manac “Tables for Interpolating Sunrise, Moonrise, etc.” to interpolate for latitude,
determining the sign of the correction by inspection. Repeat this procedure for the
day following the given date, if in west longitude; or for the day preceding, if in east
longitude. Using the difference between these two times, and the longitude, enter
table II of the almanac “Tables for Interpolating Sunrise, Sunset, etc.” and take out
the correction. Apply this correction to the LMT of moonrise or moonset at the Green-
wich meridian on the given date to find the LMT at the position of the observer. The
sign to be given the correction is such as to make the corrected time fall between the
times for the two dates between which interpolation is being made. This is nearly
always positive (+) in west longitude and negative (—) in east longitude. Convert
the corrected LMT to ZT.

Example 1.—Find the zone time of moonrise and moonset at lat. B8 22.6N,
long. 144?07/5 W on June 1, 1958, using the Nautical Almanac.

-476 THE ALMANAC

Solution.—
L 58%23/6N June 1
A 144°07/5 W
Moonrise Moonset
582 N 2011 June 1 582 N 0314 June 1
K ESE d ba eA
LMT (G) 2014 June 1 LMT (G) 0312 June 1
58% N 2113 June 2 58% N 0401 June 2
TI (+)3 TOL en
LMT (G) 2116 June 2 LMT (G) 0358 June 2
LMT (G) 2014 June 1 LMT (G) 0312 June 1
dike) 62 diff hl
T II (+)25 T II (+)18
LMT (G) 2014 June 1 LMT (G) 0312 June 1
LMT 2039 June 1 LMT 0330 June 1
ZA 2015 unen ZT 0306

Air Almanac. For the given date, determine LMT for the observer’s latitude at
the Greenwich meridian, in the same manner as with the Nautical Almanac, except that
linear interpolation is made directly from the main tabulation, since no interpolation
table is provided. Extract, also, the value from the “Diff.” column to the right of the
moonrise and moonset column, interpolating if necessary. This “Diff.” is the difference
between the time of occurrence of the phenomenon at longitude 90° E and 90° W,
and is intended for use in both east and west longitudes. The error introduced by
this approximation is generally not more than a few minutes, although it increases with
latitude. Using this difference, and the longitude, enter the ‘‘Interpolation of Moonrise,
Moonset” table on page A54 of the Air Almanac and take out the correction. The
Air Almanac recommends the taking of the correction from this table without interpola-
tion. The results thus obtained are sufficiently accurate for ordinary purposes of navi-
gation. If greater accuracy is desired, the correction can be taken by interpolation.
However, since the “Diff.” itself is an approximation, the Nautical Almanac or computa-
tion (art. 2536) should be used if accuracy is a consideration. Apply the correction to
the LMT of moonrise or moonset at the Greenwich meridian on the given date to find
the LMT at the position of the observer. The correction is positive (+) for west
longitude, and negative (—) for east longitude, unless the “Diff.” on the daily page is
preceded by a negative sign (—), when the correction is negative (—) for west longitude,
and positive (+) for east longitude. If the time is near midnight, record the date at
each step, as in the Nautical Almanac solution.

Example 2.—Find the zone time of moonrise and moonset at lat. 58?23/6 N,
long. 144?07:5 W on June 1, 1958, using the Air Almanac.

Solution.—

L 58%23/6N June 1
A 144075 W

Moonrise Moonset

diff. (+)34 diff. (+)21

582 N 2011 582 N 0314
corr. ES corr. (—)3
LMT (G) 2014 LMT (G) 0311
corr. (++) 29 corr. (+) 16
LMT 2043 LMT 0327

dx (—)24 d^ (—) 24

UNO ZT 0303

THE ALMANAC 477

N As with the sun, there are times in high latitudes when interpolation is inaccurate
or impossible. At such periods, the times of the phenomena themselves are uncertain,
but an approximate answer can be obtained by moonlight graph in the 4ir Almanac
or by computation, as explained in article 2536. With the moon, this condition occurs
when the moon rises or sets at one latitude, but not at the next higher tabulated lati-
tude, as with the sun. It also occurs when the moon rises or sets on one day but not
on the preceding or following day. This latter condition is indicated in the Air
Almanac by the symbol * in the “Diff.” column.

Because of the eastward revolution of the moon around the earth, there is one day
each synodical month (art. 1412) when the moon does not rise, and one day when it
does not set. These occur near last quarter and first quarter, respectively. Since
this day is not the same at all latitudes or at all longitudes, the time of moonrise or
moonset found from the almanac may occasionally be the preceding or succeeding one
to that desired. When interpolating near midnight, one should exercise caution to
prevent an error.

Refer to the right-hand daily page of the Nautical Almanac for June 12, 13, 14
(app. V). On June 14 moonrise occurs at 0015 at latitude 70°N, and at 2326 at
latitude 72°N. These are not the same moonrise, the one at 2326 occurring approxi-
mately one day later than the one occurring at 0015. This is indicated by the two times,
which differ by nearly 24 hours. The table indicates that with increasing northerly
latitude, moonrise occurs earlier. Between 70? N and 72°N the time crosses mid-
night to the preceding day. Hence, between these latitudes interpolation should be
made between 0015 on June 14 and 2344 on June 13. i

The effect of the revolution of the moon around the earth is to cause the moon to
rise or set later from day to day. The daily retardation due to this effect does not
differ greatly from 50”. The change in declination of the moon may increase or
decrease this effect. The effect due to change of declination increases with latitude,
and in extreme conditions it may be greater than the effect due to revolution of the
moon. Hence, the interval between successive moonrises or moonsets is more erratic
in high latitudes than in low latitudes. When the two effects act in the same direction,
daily differences can be quite large. Thus, at latitude 72°N the moon sets at 1834
on June 13, and at 2029 on June 14. When they act in opposite directions, they are
. small, and when the effect due to change in declination is larger than that due to
revolution, the moon rises earlier on succeeding days. Thus, at latitude 722 N the
moon rises at 2344 on June 13, and at 2326 on June 14. This condition is reflected in
the Air Almanac by a negative "Diff." If this happens near last quarter or first
quarter, two moonrises or moonsets might occur on the same day, one a few minutes
after the day begins, and the other a few minutes before it ends. On June 12, 1958,
for instance, at latitude 72? N, the moon rises at 0003, sets at 1649, and rises again at
2354 the same day. On those days on which no moonrise or no moonset occurs, the
next succeeding one is shown with 24" added to the time. Thus, at latitude 70? N
the moon rises at 2358 on June 2, while the next moonrise occurs 24^21" later, at 0019
on June 4. This is listed both as 2419 on June 3 and as 0019 on June 4 (not shown in
app. V).

Interpolation for longitude is always made between consecutive moonrises or moon-
sets, regardless of the days on which they fall.

Example 3.—Find the zone time of moonrise at lat. 71%38:7 N, long. 56?21:8W
during the night of June 12-13, 1958, using the Nautical Almanac.

478 i THE ALMANAC

Solution.—
L 71°38!7N June 12-13
A 56218 W
Moonrise
70°N 0014 June 13
TI (—)16

LMT (G) 2358 June 12

70°N 0015 June 14
EZ
LMT (G) 2350 June 13
LMT (G). 2358 June 12
diff. kæ
TIE. (5)2
LMT (G) 2358 June 12
LMT 2356 June 12
dy (g-)15
ZT 2341 June 12

Interpolation for the first entry is between 0014 on June 13 (lat. 70? N) and 2354
on June 12 (lat. 72? N); for the second entry, between 0015 on June 14 and 2344 on
June 13. This solution might be more easily visualized by considering the 0014
moonrise of June 13 as occurring at 2414 on June 12, and that of 0015 on June 14 as
occurring at 2415 on June 13.

1813. Rising, setting, and twilight at a moving craft.—Instructions given in the
preceding three articles relate to a fixed position on the earth. Aboard a moving craft
the problem is complicated somewhat by the fact that time of occurrence depends
upon position of the craft, and vice versa. At ship speeds, it is generally sufficiently
accurate to make an approximate mental solution, and use the position of the vessel
at this time to make a more accurate solution. If higher accuracy is required, the
position at the time indicated in the second solution can be used for a third solution.
If desired, this process can be repeated until the same answer is obtained from two con-
secutive solutions. However, it is generally sufficient to alter the first solution by 1”
for each 15’ of longitude that the position of the craft differs from that used in the solu- :
tion, adding if west of the estimated position, and subtracting if east of it. In applying
this rule, use both longitudes to the nearest 15’.

1814. Miscellaneous.—Seztant altitude corrections are explained in chapter XVI.

Equation of time is given below the sunset and twilight information on the right-
hand daily page of the Nautical Almanac, at intervals of twelve hours. Simple inter-
polation can be used for intervening values. By convention, the sign is positive (+)
if the time in the sun's “Mer. Pass." column is earlier than 1200 (or if GHA indicates
the sun has crossed the upper branch of the celestial meridian before 1200 or the lower
branch before 0000), and negative (—) if later than 1200. In Great Britain, this
convention is reversed. A heavy line is used to indicate a change of sign between
consecutive entries, as shown between 00" and 12" on June 14, when the sign changes
from positive to negative. The equation of time is not needed for ordinary purposes
of modern navigation. Its use is explained in chapter XIX.

T ime of transit. ¡The GMT of transit of the sun across the upper branch of the
celestial meridian of Greenwich is tabulated in the Nautical Almanac, to the right of
the equation of time tables. Similar information is given for both the upper and
lower transits of the moon in the *Mer. Pass." tables below the moonset tables. On
a day when the moon does not transit the Greenwich meridian, the time for the next

THE ALMANAC 479

day is given with 24^ added. Thus, on May 31 the upper transit is at 2308. The
next transit is at 2407 on June 1, or at 0007 on June 2, as shown in appendix V. For
the four navigational planets, time of upper transit for the middle day is given below
the star list on the left-hand daily page. For all of these bodies the time is given to
the nearest whole minute. Time of transit of the first point of Aries across the upper
branch on the middle day is given to the nearest 071, below the GHA Aries column.
The tabulated times can be considered the LMT of transit at the Greenwich meridian,
since LMT at 0° longitude is GMT. The LMT of transit at the observer's meridian
can then be found by interpolation for longitude, as for moonrise and moonset (art.
1812). Eye interpolation is usually sufficient for bodies other than the moon. This
information is of little value to the navigator. It is further discussed in chapter XIX.

Moon phases are indicated symbolically in the Nautical Almanac at the lower right-
hand corner of the double-page opening. In the Air Almanac this information is given
at the top of the GHA-declination column on each daily page. An open circle is used
for full moon, and a solid black circle for new moon. The time of occurrence of each
phase is given below the list of holidays, near the front of the Nautical Almanac. The
age of the moon (art. 1423) is given between the “Mer. Pass." and phase listings in the
Nautical Almanac and at the bottom of the right-hand daily page of the Air Almanac,
near the right side.

Semidiameters of the sun and moon are given at the bottom of the sun and moon
columns of the Nautical Almanac. In the Air Almanac they are given immediately
above the age of the moon, on the right-hand daily page.

Magnitude of each planet listed is given at the top of its column on the daily pages
of each almanac.

Ecliptic diagram. The diagram at the right of each right-hand daily page of the
Air Almanac indicates the positions of the moon, navigational planets, the first point
of Aries, and certain stars, relative to the sun. This diagram is discussed in article
2209. A single Planet Location Diagram has been substituted in recent editions.

GHA and declination for following year. If an almanac for the preceding year
is available, but not for the current year, the approximate declination of the sun can
be found by entering the almanac for the previous year with a time 5'49" earlier.
The GHA of the sun can also be found in this way, if 87°15’ is added to the result.
For stars, use the declination for the preceding year, and from the GHA subtract
15/1. Every reference to the same date of the preceding year refers to the day 365
days earlier than the given date. When a February 29 has intervened, the day one
day later should be used for the preceding year.

Right ascension (art. 1426), if required, can be found by subtracting SHA from
360°, and converting it from arc to time units (art. 1904). The SHA of the stars and
planets is listed on the left-hand daily page. For the sun and moon, SHA can be found
by subtracting the GHA of Aries from the GHA of the body.

Conversion of arc to time, or vice versa, can be made by the “Conversion of Arc to
Time” tables of the almanacs, or mathematically as explained in article 1904.

Polaris tables are explained in article 2105.

Navigational star charts. These charts are explained in article 2204.

Sky diagrams of the 4ir Almanac are explained in article 2212.

Several additional items of general interest, such as a list of religious and civil
holidays, a calendar, information on eclipses, planet notes for the year, and a list of
standard times (zone descriptions) at various places throughout the world, are given
in the Nautical Almanac. Items such as symbols and abbreviations in English with
their French and Spanish equivalents, and a list of stars used in H.O. Pub. No. 249,
are included in the Air Almanac.

480 THE ALMANAC

Recent issues of the Air Almanac have been modified slightly. Beginning with `
the 1961 edition, references to H.O. Pub. No. 218, Astronomical Navigation Tables,
have been omitted and an azimuth of Polaris table added. In the 1962 edition, both
pages of tables of Corrections for Height and Depression were omitted. These two
pages were replaced by five pages of Rising, Setting and Depression Graphs, and one
page containing supplementary tables and an explanation of use of these graphs and
tables.

Problems

1805a. Find the GHA and declination of the sun at GMT 7°25™54° on June 2, 1958,
using the Nautical Almanac.

Answers. —GHA 292?01:9, d 22?07:9 N.

1805b. Find the GHA and declination of the sun at GMT 23^49704* on June 1,
1958, using the A?r Almanac.

Answers.—GHA 177°50’, d 22?05' N.

1806a. Find the GHA and declination of the moon at GMT 0^24718* on June 1,
1958, using the Nautical Almanac.

Answers—GHA 18?14'8, d 17?28'48.

1806b. Find the GHA and declination of the moon at GMT 12^01722* on June 1,
1958, using the Air Almanac.

Answers—GHA 185?40', d 18°19’S.

1807a. Find the GHA and declination of Mars at GMT 2"25"39* on May 31, 1958,
using the Nautical Almanac.

Answers.—GHA 288?25:5, d 3°53/3S.

1807b. Find the GHA and declination of Jupiter at GMT 21*06"21* on June 1,
1958, using the Air Almcnac.

Answers.—GHA 5°22’, d 7?20' S.

1808a. Find the GHA and declination of Procyon at GMT 4*25"18% on June 1,
1958, using the Nautical Almanac.

Answers—GHA 201°12/0, d 5°19/8N.

1808b. Find the GHA and declination of y Velorum at GMT 16"24"11* on May
31, 1958, using the Nautical Almanac.

Answers.—GHA 1293877, d 47°13/2S.

1808c. Find GHAT at GMT 20"25"32* on June 1, 1958, using the Nautical
Almanac.

Answer.—GHAY 196°11/6.

1808d. Find the GHA and declination of Gienah at GMT 2%53"21* on June 2,
1958, using the Air Almanac.

Answers.—GHA 109°59’, d 17?19'8.

1810. Find the zone time of sunrise and sunset at lat. 52°18/7S, long. 58%43/6 W
on June 1, 1958.

Answers.—Sunrise, ZT 0751; sunset, ZT 1554.

1811a. Find the zone time of beginning of morning nautical twilight and ending
of evening nautical twilight at lat. 16?22/7 N, long. 163?19/7 E on June 1, 1958.

Answers.—Morning twilight, ZT 0441; evening twilight, ZT 1928.

1811b. Find the zone time of beginning of morning civil twilight and ending of
evening civil twilight at lat. 55%35/6N, long. 51?13/7 W on June 1, 1958, using the
Air Almanac.

Answers.—Morning twilight, ZT 0253; evening twilight, ZT 2153.

THE ALMANAC 481

1812a. Find the zone time of moonrise and moonset at lat. 4426/35, long.
172?29:3 E on June 3, 1958, using the Nautical Almanac.

Answers.—Moonrise, ZT 1732; moonset, ZT 0743.

1812b. Find the zone time of moonrise and moonset at lat. 3927/4 S, long. 1072218
W on June 1, 1958, using the Air Almanac.

Answers.—Moonrise, ZT 1815; moonset, ZT 0554.

1812c. Find the zone time of moonrise at lat. 71°44/7N, long. 176°18/1E on
the night of June 13-14, 1958, using the Nautical Almanac.

Answer.—Moonrise, ZT 0007 June 14.

1813. The zone time of sunrise at a moving ship is desired. The first solution,
based upon an estimate of the position, is 0537. The longitude used for the solution is
51°22'2W. At 0537 the longitude will be 51°38/8 W.

Required.—The zone time of sunrise at the ship.

Answer.—Sunrise, ZT 0539.

1814a. Find the equation of time at GMT 16*21”04* on June 1, 1958.

Answer.—Eq. T(+)2"19s,

1814b. Find the zone time of transit of the moon across the upper branch of the
celestial meridian at long. 137?14'4W on May 31, 1958.

Answer.—Transit, ZT 2340.

1814c. What are the phase and age of the moon on June 2, 1958?

Answers.—Phase, full moon; age, 15 days.

1814d. What are the semidiameters of the sun and moon on June 2, 1958?

Answers.—Sun, SD 15:8; moon, SD 1671.

1814e. What is the magnitude of Jupiter on June 1, 1958?

Answer.—Mag.(—) 1.9. ;

1814f. Which of the navigational planets is nearest Aldebaran on June 2, 1958?

Answer.—Venus.

1814g. Find the GHA and declination of the sun at GMT 11*14”07* on May 31,
1959, using the 1958 Vautical Almanac.

Answers.—GHA 349°09'7, d 21%50/5N.

1814h. Find the GHA and declination of Alioth at GMT 19"25"23* on June 1,
1959, using the 1958 Nautical Almanac.

Answers.—GHA 347?48:5, d 56?11:3 N.

CHAPTER XIX
TIME

1901. Introduction.—Time serves to regulate affairs aboard ship, as it does ashore.
But to the navigator, it has additional significance. It is not enough to know where
the ship is, was, or might be located in the future. The navigator wants to know
when the various positions were or can reasonably be expected to be occupied. Time
serves as a measure of progress. By considering the time at which a ship occupied
various positions in the past, and by comparing the speed and various conditions it
has encountered with those anticipated for the future, the skillful navigator can predict
with reasonable accuracy the time of arrival at various future positions. Time can
serve as a measure of safety, for it indicates when a light or other aid to navigation
might be sighted, and if it is not seen by a certain time, the navigator knows he has
cause for concern.

To the celestial navigator, time is of added significance, for it serves as a measure
of the phase of the earth’s rotation. That is, it indicates the position of the celestial
bodies relative to meridians on the earth. Until an accurate measure of time became
available at sea, longitude could not be found.

Very small intervals of time are used in certain electronic navigational aids, such
as radar and loran.

Whatever the type of navigation, a thorough mastery of the subject of time is
important to the navigator. The use of a time diagram (art. 1427) may help in under-
standing the principles or solution of the problems of this chapter.

1902. Kinds of time.—As a measure of part of a day, time can be stated in a
number of different ways. At any given moment, the time depends upon (1) the point
on the celestial sphere used as reference, (2) the reference meridian on the earth, and
(3) the somewhat arbitrary starting point of the day.

When the sun is used as the celestial reference point, solar time results. If the
actual sun observable in the sky is used, apparent solar time is involved, and if a fictitious
mean sun is used to provide a time having an almost constant rate, mean solar time
results. Time reckoned by use of the first point of Aries (T) as the celestial reference
point is called sidereal time. Use of the moon as the celestial reference point provides
a variable-length lunar day, the basis of lunar time, which is useful in tide prediction
and analysis. Because of its application, a lunar day is sometimes called a tidal day.
It averages about 24"50™ (mean solar units) in length.

If the meridian of the observer is used as the terrestrial reference, local time is
involved. Ifa zone or standard meridian is used as the time meridian for mean solar
time over an area, zone or standard time results. Use of a meridian farther east than
would normally be used, so that the period of daylight is shifted later in the day,
produces a form of zone time called daylight saving or summer time. Time based
upon the Greenwich meridian is called Greenwich time. Greenwich mean time
(GMT) is of particular interest to a navigator because it is the principal entering
argument for the almanacs.

One complete revolution of the earth with respect to a celestial reference point is
called a day. In modern usage every kind of solar time has its zero or starting point

at midnight, when the celestial reference point is directly over the lower branch of the
482

TIME 483

terrestrial reference meridian. This has not always been so. Until January 1, 1925,
the astronomical day began at noon, 12 hours later than the start of the calendar day of
the same date. The nautical day began at noon, 12 hours earlier than the calendar day,
or 24 hours earlier than the astronomical day of the same date. The sidereal day
begins at sidereal noon, when the first point of Aries is over the upper branch of the
reference meridian. There is no sidereal date.

1903. Expressing time.—Time is customarily expressed in time units, from 0%
through 24”. To the nearest 1” it is generally stated by navigators in a four-digit unit
without punctuation. Thus, 0000 is midnight at the start of the day. One minute
later the time is 0001. Half an hour after the start of the day the time is 0030, at
one hour the time is 0100, at one hour and four minutes it is 0104, at 19 minutes after
noon (solar time) it is 1219, at four hours and 23 minutes after (solar) noon it is 1623,
etc. The term “hours” is sometimes used with the four-digit system to indicate that
the number refers to the time or “hour” of the day. However, in those few occasions
when any reasonable doubt may exist as to whether time is indicated,the fact can better
be indicated in another way. Thus, the expression “1600 hours” to indicate “1600”
or “16 hours” is not strictly correct, and is better avoided. Watch time (W), indicated
by a watch or clock having a 12-hour dial, and chronometer time (C) are expressed on
a 12-hour basis, with designations am (ante meridian) and pm (post meridian), as in
ordinary civil life ashore.

In contrast, a time interval is expressed as hours and minutes, as 5126”. When
either the time of day or a time interval is given to seconds, this same form is used,
as 21"15"18*. The kind of time may be indicated, usually by abbreviation.

When a time interval is to be added to or subtracted from a time, the solution
can be arranged conveniently in tabular form.

Example 1.— What is the time and date 14"36"53* after 21"14"18* on July 24?

Solution.—

21^14718* July 24

14°36™53°

35'51"11* July 24
=11"51"11* July 25

The fact that the sum of hours exceeds 24 is an indication that the date increases
by one. Similarly, in subtracting an interval, the date is one day earlier if 24^ must
be added to the time before the subtraction can be made. "That is, since 2400 of one
day is 0000 of the following day, one might say that 2700 on one day is 2700 —2400 —0300
on the following day. In the example above, 11"51"11* on July 25 is the same as
11"51"11*+24"00"00'=35"51"11* on July 24.

Date is sometimes expressed as an additional unit of the time sequence. Thus,
211418" on July 24 might be stated 24?21^14"18*. This system is of particular value
when an interval of several days is to be added or subtracted.

Example 2.—What is the time and date 916"35”04* before 5^11"733* on September
15?

Solution.—

159055112535
9116"35"04*
52125367295 or 12"36"29* on Sept. 5.

By this method the month and day, if of significance, are recorded separately,
or they, too, can be added to the sequence.

Example 3.—What is the time and date 3 years, 6 months, 25 days, 12 hours, 19
minutes, and 44 seconds after 7^52724* on November 14, 1958?

484. TIME

Solution.—
1958"11*14%07"52"24*
3*06725?12^] 97445

1962*06*08320^127085— 20°12™085 on June 8, 1962.
Since a month may contain a variable number of days, both the months and days
should be solved together. Thus, in the example above, the answer would be 17
months, 39 days. If 12 months are converted to one year, this becomes five months,
39 days. Since the fifth month is May, this might be stated as May 39. Since there
are 31 days in May, this is 39—31—8 days into the next month, or June 8.

A simpler method of determining the number of elapsed days between any two
dates is to use the Julian day of each date, if the information is available. This also
eliminates possible error due to change of calendar if long intervals are involved.
The Julian day is the consecutive number of the day starting at 1200 on January 1,
4713 BC. Julian day is listed in the American Ephemeris and Nautical Almanac.

1904. Time and arc.—The time of day is an indication of the interval since the
day began. One day represents one complete rotation of 360° of the earth with respect
to a selected celestial point. Each day is divided into 24 hours of 60 minutes, each
minute having 60 seconds. Thus, each day has 24 X60=1,440 minutes or 1,440 X60=
86,400 seconds. This is time regardless of the celestial reference point used, and since
the various references are in motion with respect to each other, as “seen” from the
earth, apparent solar, mean solar, and sidereal days are of different lengths. Since
they all have the same number and kind of fractional parts, these parts are themselves
of different length in the different kinds of time. Mean solar units are customarily
used to indicate time intervals. The smallest unit normally used in celestial navigation
is the second, but in some electronic equipment the millisecond (one-thousandth of a
second), microsecond (one-millionth of a second), and the millimicrosecond or nano-
second (one-billionth of a second) are used.

Time of day is an indication of the phase of rotation of the earth. That is, it
indicates how much of a day has elapsed, or what part of a rotation has been completed.
Thus, at zero hours the day begins. One hour later, the earth has turned through

360° : : ;
24 —15?. Six hours after the day begins, it has

1/24 of a day, or 1/24 of 360?, or

o

36
turned through 6/24— 1/4 day, or A —90?. Twelve hours after the start of the day,

the day is half gone, having turned through 180°. Smaller intervals can also be stated

in angular units, for since one hour or 60 minutes is equivalent to 15%, one minute of
o

m ; ; 1 i
time 1s equivalent to 60 =0°25=15’, and one second of time is equivalent to 15

60
0/25=15". Thus,

Time Arc
1°= 24^—3060?— 1 circle
60"= 1"= 15°

4n— 1°=60/
ye (kēmu
a augi

= c1

Any time interval can be expressed as an angle of rotation, and vice versa. Intercon-
version of these units can be made by the relationships indicated above.

TIME 485

To convert time to arc: `

1. Multiply the hours by 15 to obtain degrees.

2. Divide the minutes of time by four to obtain degrees, and multiply the remainder
by 15 to obtain minutes of arc.

3. Divide the seconds of time by four to obtain minutes and tenths of minutes of
arc, or multiply the remainder by 15 to obtain seconds of arc.

4. Add degrees, minutes, and tenths (or seconds).

Example 1.— Convert 14*21"39* to arc units.

Solution.—
(1) 14^ X 15=210°
(ZY AIR ease BO" (remainder 1% X15=15”)
(3) 39 — 4= 9/45” (remainder 3*X15=45”)

(4) 14°21™39°=215°24’45” —215°24/8 (to the nearest 0/1).

To convert arc to time:

1. Divide the degrees by 15 to obtain hours, and multiply the remainder by four
to obtain minutes of time.

2. Divide the minutes of are by 15 to obtain minutes of time, and multiply the
remainder by four to obtain seconds of time.

3. Divide the seconds of are by 15 to obtain seconds of time.

4. Add hours, minutes, and seconds.

Example 2.—Convert 215?24'45'' to time units.

Solution.—
(11215 ==. 15=14°20" (remainder 5°X4=20")
A lS 1™36® (remainder 9’ X4=36%)
(8) 45^ 15= 38

(4) 215°24’45” — 14^2]739*
Example 3.—Convert 161°53'7 to time units.

Solution.—
(1) 161° + 15—10^44" (remainder 11° X 4=44")
(253.7 15= 37348 (remainder 8/7 X4=34*8)

(D 161° 53-7 10473478 = 1047735".

The navigator should be able to make these solutions mentally, writing only the
answer. Asa check, the answer can be converted back to the original value. Solution
can also be made by means of arc to time tables in the almanacs. In the Nautical
Almanac the table, given near the back of the volume (app. V), is in two parts, per-
mitting separate entries with degrees, minutes, and quarter minutes of arc. The table is
arranged in this manner because the navigator is confronted with the problem of
converting arc to time more often than the reverse.

Example 4.—Convert 334°18’22” to time units, using the Nautical Almanac arc to
time conversion table.

Solution.—

9949292165
18:252 1™13°
33401812242211 7513"
The 22” are converted to the nearest quarter minute of arc for solution to the

nearest second of time. Interpolation can be used if more precise results are required,
since exact relationships are tabulated in the Nautical Almanac conversion table.

486 TIME

Example 5.—Convert 83%29'6 to time units, using the Nautical Almanac arc to
time conversion table.

Solution.— 839 — 5h39m

20:6— m 125854
83%2916—=5"33"58%4
In this solution, 58% was obtained by eye interpolation in the quarter-minute part of
the table. À
Example 6.—Convert 17*09"42* to arc units, using the Nautical Almanac arc to
time conversion table.
Solution.— 17108” — 2572?
19945 — 2515
17%09%428=257%2515
A similar table appears near the back of the Air Almanac (app. W), but values are
given only to 180°, and quarter minutes of arc are not included. For angles greater
than 180%, subtract 180% and add 12* to the result.
Example 7.— Convert 334?47:2 to time units, using the Air Almanac arc to time
conversion table.
Solution.—
334°— 180°= 154°=10°16™
4742= Ee (OM
154?47:2—10^197095
334%4712=22*19"09*
Example 8.—Convert 15°13™18* to time units, using the Air Almanac arc to time
conversion table.
Solution.—
15:12%=12%=3119%= 493
LL 19:5
951992188—' 4821956
15+18"18*=228 1055
Because the almanac conversion tables are exact relationships, interpolation in
them can be carried to any degree of precision desired without introducing an error.
1905. Time and longitude.—As indicated in the preceding article, time is a measure
of rotation of the earth, and any given time interval can be represented by a corre-
sponding angle through which the earth turns. Suppose the celestial reference point
were directly over a certain reference of the earth. An hour later the earth would have
turned through 15°, and the celestial reference would be directly over a meridian 15°
farther west. Any difference of longitude is a measure of the angle through which the
earth must rotate for the local time at the western meridian to become what it was at
the eastern meridian before the rotation took place. Therefore, places to the eastward
of an observer have later time, and those to the westward have earlier time, and the
difference is exactly equal to the difference in longitude, expressed in time units. When
a meridian other than the local meridian is used as the time reference, the difference in
time of two places is equal to the difference of longitude of their time reference meridians.
1906. The date line.—Since time becomes later toward the east, and earlier toward
the west, time at the lower branch of one’s meridian is 12 hours earlier or later depending
upon the direction of reckoning. A traveler making a trip around the world gains or
loses an entire day. To prevent the date from being in error, and to provide a starting
place for each day, a date line is fixed by international agreement. This line coincides
with the 180th meridian over most of its length. In crossing this line, one alters his

TIME 487

date by one day. In effect, this changes his time 24 hours to compensate for the slow
change during a trip around the world. Therefore, itis applied in the opposite direction
to the change of time. Thus, if a person is traveling eastward from east longitude to
west longitude, time is becoming later, and when the date line is crossed, the date becomes
one day earlier. That is, at any moment the date immediately to the west of the date line
(east longitude) is one day later than the date immediately to the east of the line, except
at GMT 1200, when the (mean time) date is the same all over the world. At any other
time two dates occur, one boundary between dates being the date line, and the other
being the midnight line along the lower branch of the meridian over which the mean
sun is located. At GMT 1200 these two boundaries coincide. In the solution of
problems, error can sometimes be avoided by converting local time to Greenwich time,
and then converting this to local time on the opposite side of the date line. Examples
are given in following articles.

1907. Zone time.—At sea, as well as ashore, watches and clocks are normally set
approximately to some form of zone time (ZT). At sea the nearest meridian exactly
divisible by 15° is usually used as the time meridian or zone meridian. Thus, within a
time zone extending 7°5 on each side of each time meridian the time is the same, and
time in consecutive zones differs by exactly one hour. The time is changed as con-
venient, usually at a whole hour, near the time of crossing the boundary between zones.
Each time zone is identified by the number of times the longitude of its zone meridian
is divisible by 15°, positive in west longitude and negative in east longitude. This
number and its sign, called the zone description (ZD), is the number of whole hours
that are added to or subtracted from the zone time to obtain Greenwich mean time
(GMT), which is the zone time at the Greenwich (0%) meridian, and is sometimes called
universal time (UT). The mean sun is the celestial reference point for zone time.

Example 1.—For an observer at long. 1419184 W the ZT is 6^18724*.

Required.—(1) Zone description.

(2) GMT.

Solution.—(1) The nearest meridian exactly divisible by 15° is 135? W, into which
15° will go nine times. Since longitude is west, ZD is (+) 9.

ZT 5192245
ZD (+)9
(2 GMT 15187245

In converting GMT to ZT, a positive ZD is subtracted, and a negative one added,
but its sign remains the same, being part of the description. The word “reversed” (rev.)
is written to the right in the work form to indicate that the “reverse?” process is to be
performed.

Example 2.—The GMT is 15*27"09*.

Required.—(1) ZT at long. 1562414 W.

(2) ZT at 39%04/8E.

Solution.— um m
1) GMT T5 24005 (2) GM 1527709» Å
WW ZD (4-) 10 (rev.) ZD (—)3 (rev.)
ZT 552 155005 ZT 1852772095

When time at one place is converted to that at another, the date should be watched
carefully. If a sum exceeds 24 hours, subtract this amount and add one day. If 24
hours are added before a subtraction is made, the date at the place is one day earlier.

Example 3.—At long. 73°29/2 W the ZT is 21"12"53* on May 14.

Required.—(1) GMT and date.

(2) ZT and date at long. 107?15:7 W.

488 i TIME

Solution.—
ZT ` 21^12753* May 14
ZD (+)5
(1) GMT 25127535 May 15
ZD (+)7 ' (rev.)
(2) ZT 19'12"53* May 14
The second part of this problem might have been solved by using the difference
in zone description. Since the second place is two zones farther west, its time is two
hours earlier. Problems involving zone times at various places generally involve
nothing more than addition or subtraction of one small number, so solutions can gen-
erally be made mentally. However, when this forms part of a larger problem, or when a
record of the solution is desired, the full solution should be recorded, including labels.
Example 4.—On November 30 the 1430 DR long. of a ship is 51?32:4 W. Ten
hours later the DR long. is 53?07:2 W.
Required.—ZT and date of arrival at the second longitude.

Solution.—
ZT 1430 Nov. 30
ZD (4-)3
GMT 1730 Nov. 30
int. 10

GMT 0330 Dec. 1
ZD (+)4 (rev.)
ZT 2330 Nov. 30

If a time zone boundary had not been crossed, there would have been no need to
find GMT. It is particularly helpful to retain this step when the date line is crossed.
This line is the center of a time zone, the western (east longitude) half being designated
(—)12, and the eastern (west longitude) half (+) 12.

Example 5.—On December 31 the 0800 DR long. of a ship is 177%23/9E. Forty
hours later the DR long. is 171%53/9 W.

Required.—ZT and date of arrival at the second longitude.

Solution.—
Alternative solution

ZT 0800 Dec. 31 ZT 31908500»
ZD (=) 1211 ZD (—) 12

GMT 2000 Dec. 30 GMT 30#20°00"
int. 40 into ls 102

GMT 1200 Jan. 1 GMT IZ U”
ZD (+)11 (rev.) ZD (+)1l1 (rev.)
ZT 0100 Jan. 1 LIA LODOS

For certain communication purposes it is sometimes convenient to designate a
time zone by a single letter. The system used is shown in figure 1907.

Use of time zones on land began in 1883, when railroads adopted four standard
zones for the continental United States. The division of the United States into time
zones was not officially adopted by Congress, however, until March 19, 1918, when a
fifth zone was also established for Alaska. The system of time zones is now used
almost universally throughout the world, although on land the zone boundaries are
generally altered somewhat for convenience. In a few places, half-hour zones are
used but these are not standard time zones.

| On land, normal zone time is usually called standard time, often with an adjective
to indicate the zone, as eastern standard time. In some areas timepieces are advanced
one or more hours during the summer to provide greater use of daylight. This “fast”
time is called daylight saving time in the United States, and summer time elsewhere.

‘GUL INSNOO 44 GINOHS LAVHO SIHL 40 NOILIGA 1SALVI AHL
'(uonrpe 8961 “Z6TS “ON HUYO OH U01j) prom 949 Jo eg ouoz OWIE “2061 Sand

489

"W31SAS 3NOZ 201 Q31d00Y
LON 3AVH HOIHM SYadv ONY S3IYINNOO

"S3NOZ ONI408H9I3N WOYJ YNOH NV JTIVH
SY33310 SWIL GYVGNVLS 383HM SIIYLNNOI =

3NOZ Q3N38WnN 00O FUEL:

3NOZ O3YISANN N3A3 ia

d

INN 31VA

$
E
E

i
As
Tw

we
SC

TIME

2021 «GET «OSI 891 »081 897 OST SET Bt

490 TIME

When time is one hour fast, the zone description is (algebraically) one less than normal.
When daylight saving or summer time is specified, an advance of one hour is under-
stood unless a greater number is indicated.

Example 6.—What is the standard time and date at Tokyo, long. 140° E, when the
daylight saving time at Washington, long. 77? W, is 1600 on Oct. 5?

Solution.—
ZT 1600 Oct. 5
ZD (+)4
GMT 2000 Oct. 5
ZD (—)9 (rev.)
ZT 0500 Oct. 6

During hostilities daylight saving time may be kept all year long throughout a
nation, and designated war time (WT).

1908. Chronometer time (C) is time indicated by a chronometer. Since a chro-
nometer is set approximately to GMT, and not reset until it is overhauled and cleaned,
perhaps three years later (art. 1514), there is nearly always a chronometer error (CE),
either fast (F) or slow (S). The change in chronometer error in 24 hours is called
chronometer rate, or daily rate, and designated gaining or losing. With a consistent
rate of 1* per day for three years, the chronometer error would be approximately 18".
Since chronometer error is subject to change, it should be determined from time to
time, preferably daily at sea. Chronometer error is found by radio time signal (art.
1909), by comparison with another timepiece of known error, or by applying chro-
nometer rate to previous readings of the same instrument. It is recorded to the nearest
whole or half second. Chronometer rate is recorded to the nearest 0°1.

Example 1.—At GMT 1200 on May 12 the chronometer reads 12*04%21% At
GMT 1600 on May 18 it reads 4047255,

Required —(1) Chronometer error at both comparisons.

(2) Chronometer rate.

(3) Chronometer error at GMT 0530 on May 27.

Solution.—

GMT 12*00”00* May 12
C 12^0472]*
(1) CE (F) 47215

GMT 16^00"00* May 18
C 4^047255
(1) CE (F) 42255
GMT 12912"

GMT 1816"
diff. 6904^— 642

CE (F) 4721* 1200 May 12
CE (F) 4725* 1600 May 18
diff. 4* gained
(2) daily rate 0:6 per day, gaining. (49-632)

GMT 18316^00»

GMT 27305^30»
diff. 8413^30»— 845 i
CE (F) 4"25* 1600 May 18

corr. (+) 5° (895 <0%6 per day)
(3) CE (F) 4730* 0530 May 27

TIME 491

Because GMT is stated on a 24-hour basis, and chronometer time on a 12-hour
E basis, a 12-hour ambiguity exists. This is ignored in finding chronometer error. How-
ever, if chronometer error is applied to chronometer time to find GMT, a possible 12-
hour error can result. This can be resolved by mentally applying zone description
to local time to obtain approximate GMT. A time diagram can be used for resolving
doubt as to approximate GMT and Greenwich date. If the sun for the kind of time
used (mean or apparent) is between the lower branches of two time meridians (as the
standard meridian for local time, and the Greenwich meridian for GMT), the date at
the place farther east is one day later than at the place farther west.

Example 2.—On August 14 the DR long. of a ship is about 124? E, and the zone time
is about 0500. Chronometer error is 12™27® slow.

Required.—GMT and date when the chronometer reads 8"44"225,

Solution.—
approx. ZT 0500 Aug. 14
ZD (—)8
approx. GMT 2100 Aug. 13
C 8'447223

CE (S) 121975
GMT 205567495 Aug. 13

The A chronometer, usually the best (having the most nearly uniform rate), is
compared directly with the time signal (art. 1909). Other chronometers, designated
B, C, etc., may then be compared with the 4 chronometer.

Example 3.—At GMT 1400 chronometer A is checked by time signal, and found
to read 1"57"09*. A little later, when it reads 2"05"00*, chronometer B reads 2511™38°.

Required.—(1) Error of chronometer A.

(2) Error of chronometer B.

Solution.—

GMT 14*00”00*
Ca 1757709"

(1) CE, (S) 27511
C, 2*05=00°
GMT 14*07"51*
Cs: 2711738?

(2) CE, (F) 347°

If time signals are not available at the chronometer, a good comparing watch (art.
1515) should be compared with the radio signal, and this watch used to determine
chronometer error, as indicated in example 3, substituting the watch for chronometer 4.

1909. Time signals.—The usual method of determining chronometer error and
daily rate is by radio time signals, popularly called time ticks. Most maritime nations
broadcast time signals several times daily from one or more stations, and a vessel
equipped with radio receiving equipment normally has no difficulty in obtaining a time
tick anywhere in the world. The times of emission of signals transmitted by the U.S.
are the same to about 05001 as those of Argentina, Australia, Canada, Japan, U.K.,
Republic of South Africa, and Switzerland. The time transmitted is maintained
virtually uniform with respect to atomic clocks but follows GMT closely. The dif-
ference seldom amounts to 05050. The time, as received by a vessel, may be considered
to be GMT to 071. Radio Navigational Aids, H.O. Pubs. Nos. 117-A and 117-B, lists
all time signals, together with their hours of transmission, system used, frequency, and
other useful information.

492 TIME

At sea the chronometer should be checked daily by radio time signal, and in port
daily checks should be maintained, or begun at least three days prior to departure, if
conditions permit. Error and rate are entered in the chronometer record book (or
record sheet) each time they are determined.

Prior to the development of radio time signals, chronometers were checked in
port by visual signals which consisted of dropping a time ball or shape by telegraphic
action, or firing a gun. Visual signals are still used in some ports. If a gun is used,
the flash marks the correct time, as the report may not reach the observer until several
seconds after the gun is fired.

The various time signal systems used throughout the world are explained in detail
in H.O. Pubs. Nos. 117-A and B. Only the United States signals are discussed here.

The U. S. Naval Observatory at Washington, D. C., controls the transmissions
of time signals from U. S. Naval radio stations. Beginning at 5 minutes before each
even hour of GMT, dashes are transmitted on every second, except the 29th and certain
others near the end of each minute, as shown in the following diagram:

Minutes Seconds

51 52 53 56 57 58 59

DE
ILLIS

sue
Bese:

The seconds marked “60” indicate the start of the next minute. The final dash,
marking the hour, is considerably longer than any of the others. The number of
dashes in the group near the end of any minute indicates the number of minutes before
the hour. This is known as the United States system. In all cases the beginnings
of the dashes indicate the beginning of the seconds, and the ends of the dashes are
without significance.

Station WWV, near Washington, D. C., broadcasts continuous time signals
obtained from the U. S. Naval Observatory time service. Station WWVH in Hawaii
broadcasts the same signals, except for certain periods during which the station is off
the air to compare its standards with those of WWV and to obtain ionospheric sound-
ings. The signals broadcast by these stations are intended primarily for measurement
of time intervals, and checking of frequencies of two standard audible tones, but signals
can also be used for checking time. The system used is fully explained in H.O. Pubs.
Nos. 117—A and 117-B.

1910. Watch time (W) is time indicated by a watch. This is usually an approxi-
mation of zone time, except that for timing celestial observations it is good practice to
set a comparing watch (art. 1515) to GMT. If the watch has a second setting hand,
the watch can be set exactly to ZT or GMT, and the time is so designated. If the
watch is not set exactly to one of these times, the difference is known as watch error
(WE), labeled fast (F) or slow (S) to indicate whether the watch is ahead of or behind
the correct time, respectively.

If a watch is to be set exactly to ZT or GMT, it is set to some whole minute slightly
ahead of the correct time, and stopped. When the set time arrives, the watch is
started. It should then be checked for accuracy.

Example 1.—A chronometer 97463 fast on GMT reads approximately 7°23™. At
the next whole five minutes of GMT a comparing watch is to be set to GMT exactly.

TIME 493

Required.—(1) What should the watch read at the moment of starting ?
(2) What should the chronometer read ?
Solution.—
C 7*23"00*
CE (F) 97465
GMT 7*13214s
(1) GMT 7715005 (next whole 5")
CE (F) 9468
(2) C 72446"

The GMT may be in error by 12", but if the watch is graduated to 12 hours, this
will not be reflected. If a watch with a 24-hour dial is used, the actual GMT should
be determined.

If watch error is to be determined, it is done by comparing the reading of the watch
with that of the chronometer at a selected moment. "This may be at some selected
GMT, as in example 1.

Example 2.—If, in example 1, the watch had read 7514"48* at the moment the
chronometer read 7^24"465*, what would be the watch error on GMT?

Solution.—

GMT 715"00*
W 7*14748*
WE (S) 12*

A more convenient chronometer time might be selected, as a whole minute. .

Example 3.—A watch is set to zone time approximately. The longitude is about
48? W. The watch is compared with a chronometer which is 19"44* fast on GMT.
When the chronometer reads 5"22"005, the watch reads 2°01™53°.

Required.—Watch error on zone time.
Solution.—
C 5522m90*
CE (F) 19744"
GMT 50271 6*
ZD (4-)3 (rev.)
ZT 25029165
W 22012535
WE (S) 23°

The possible 12" error is not of significance. When such a watch is used for
determining GMT, however, as for entering an almanac, the 12-hour ambiguity is
important. Unless a watch is graduated to 24 hours, its time is designated am before
noon and Pw after noon.

Example 4.—On January 3 the DR long. is 94?14:7 E. An observation of the
sun is made when the watch reads 12*16"23* pm. The watch is 22° fast on zone time.

Required —GMT and date.

Solution.—
W 12*16"23* PM Jan. 3
WE ($0) 225
ZT 125167015
ZD (—)6

GMT 6^16?01* Jan. 3

Note that between 1200 and 1300 watch designations are PM. Between 0000
and 0100 they are AM.

494 TIME

Comparison of a watch and chronometer should be made carefully. If two
observers are available, one can give a warning “stand-by” a few seconds before the
selected time, and a “mark” at the appointed moment, while the other notes the time
of the watch. A single observer can make a satisfactory comparison by counting
with the chronometer. Chronometers beat in half seconds, with an audible “tick.”
Ten seconds before the selected time (perhaps a whole minute), the observer starts
counting with the beats, as he watches the chronometer second hand, “50, and, 1, and,
D abd5929nd; siet oae 9, and, mark." During the count the observer shifts his view
from the chronometer to the second hand of the watch, continuing to count in cadence
with the chronometer beats. At the “mark,” the second, minute, and hour hands of
the watch are read in that order, and the time recorded. A comparison of this time
with the GMT or ZT corresponding to the selected chronometer time indicates the
watch error. i

Even though a watch is set to zone time approximately, its error on GMT can
be determined and used for timing observations. In this case the 12-hour ambiguity
in GMT should be resolved, and a time diagram used to avoid possible error. This
method requires additional work, and presents a greater probability of error, without
compensating advantages.

Still another method of determining GMT, generally used before zone time came
into common use at sea, is to subtract watch time from chronometer time, to find
C-W. This is then added to the watch time of an observation to obtain chronometer
time (C—W+W=C). Chronometer error is then applied to the result to obtain
GMT. A time diagram should always be used with this method, to resolve the 12-hour
ambiguity and to be sure of the correct Greenwich date, unless an auxiliary solution is
made using approximate ZT and ZD. This method has little to recommend it.

If a watch has a watch rate of more than a few seconds per day, watch error should
be determined both before and after a round of sights, and any difference distributed
proportionally among observations.

If a stop watch is used for timing observations, it should be started at some con-
venient GMT, as a whole 5” or 10". The time of each observation is then this GMT
plus the reading of the watch.

1911. Local mean time (LMT), like zone time, uses the mean sun as the celestial
reference point. It differs from zone time in that the local meridian is used as the
terrestrial reference, rather than a zone meridian. Thus, the local mean time at each
meridian differs from that of every other meridian, the difference being equal to the
difference of longitude, expressed in time units. At each zone meridian, including
0% LMT and ZT are identical.

Example 1.—At long. 12493712 W the LMT is 17"24"18* on March 21.

Required.—(1) GMT and date.

(2) ZT and date at the place.

Solution.—

LMT [/524* 157 sy Mare 2
A 8"18"29* W
(1) GMT 1429478 Mar. 22
AS (rev.)
(2) 20 17427475 Mar. 21

In navigation the principal use of LMT is in rising, setting, and twilight tables.
The problem is usually one of converting the LMT taken from the table to ZT. At
sea, the difference between these times is normally not more than 30™, and the conver-

TIME 495

sion is made directly, without finding GMT as an intermediate step. This is done by
applying a correction equal to the difference of longitude (dA). If the observer is west
of his time meridian, the correction is added, and if east of it, the correction is subtracted.
If Greenwich time is desired, it is found from ZT.

Example 2.—At long. 63°24/4 E the LMT is 0525 on January 2.

Required.—(1) ZT and date.

(2) GMT and date.

Solution.—
LMT 0525 Jan. 2
dS (as)
(1) ZT 0511 Jan. 2
ZD (—)4

(2) GMT 0111 Jan. 2

On land, with an irregular zone boundary, the longitude may differ by more
than 7°5 (30™) from the time meridian.

If LMT is to be corrected to daylight saving time, the difference in longitude
between the local and time meridian can be used, or the ZT can first be found and
then increased by one hour.

Conversion of ZT (including GMT) to LMT is the same as conversion in the
opposite direction, except that the sign of dh is reversed. This problem is not normally
encountered in navigation.

1912. Apparent time utilizes the apparent (real) sun as its celestial reference, and
a meridian as the terrestrial reference. Local apparent time (LAT) uses the local
meridian. The LAT at the 0° meridian is called Greenwich apparent time (GAT).

The LAT at one meridian differs from that at any other by the difference in
longitude of the two places, the place to the eastward having the later time, and
conversion is the same as converting LMT at one place to LMT at another.

Use of the apparent sun as a celestial reference point for time results in time of
nonconstant rate for at least three reasons. First, revolution of the earth in its orbit
is not constant. Second, motion of the apparent sun is along the ecliptic, which is
tilted with respect to the celestial equator, along which time is measured. Third,
rotation of the earth on its axis is not constant. The effect due by this third cause is
extremely small.

For the various forms of mean time, the apparent sun is replaced by a fictitious
mean sun conceived as moving eastward along the celestial equator at a uniform speed
equal to the average speed of the apparent sun along the ecliptic, thus providing a
nearly uniform measure of time equal to the approximate average apparent time. At
any moment the accumulated difference between LAT and LMT is indicated by the
equation of time (Eq. T), which reaches a maximum value of about 1674 in November.
This quantity is tabulated at 12-hour intervals at the bottom of the right-hand daily
page of the Nautical Almanac. In the United States, the sign is considered positive
(+) if the time of sun’s “Mer. Pass.” is earlier than 1200, and negative (—) if later
than 1200. If the “Mer. Pass.” is given as 1200 (as on June 12-14, 1958), the sign is
positive if the GHA at GMT 1200 is between 0° and 1°, and negative if it is greater
than 359°. The sign is correct for conversion of GMT to GAT. In Great Britain,
this convention is reversed. Since GMT is the entering argument for the almanacs,
interconversion of apparent and mean time should preferably be made from Greenwich
time, rather than from local time.

Example —Find the LAT and date at ZT 15"10”40* on May 31, 1958, for long.
73?18'4 W.

406 TIME

Solution.—

ZT 15^10740* May 31
ZD (+) 5

GMT 20*10"40* May 31

Eq. T (+) 2™27°

GAT 20°13"07* May 31

A 4*537148 W
LAT 153197535 May 31

In conversion from apparent to mean time, a second solution may be needed if
the equation of time is large and changing rapidly, using the GAT for entering the
almanac for the first solution, and using the GMT from this solution as the almanac
entry value for the second solution.

Apparent time can also be found by converting hour angle to time units, and
adding or subtracting 12 hours. If LAT is required, but not GAT, conversion of arc
to time should be made from LHA, rather than GHA, to avoid the need for conversion
of longitude to time units. Equation of time can be found by subtracting mean time
from apparent time at the same meridian. This method of finding apparent time and
equation of time is the only one available with the Air Almanac, which does not tabulate
equation of time.

The navigator has little or no use for apparent time, as such. However, it can be
used for finding the time of local apparent noon (LAN), when the apparent sun is on
the celestial meridian.

The mean sun averages out the irregularities in time due to the variations of the
speed of revolution of the earth in its orbit and the fact that the apparent sun moves
in the ecliptic while hour angle is measured along the celestial equator. It does not
eliminate the error due to slight variations in the rotational speed of the earth. When
a correction for the accumulated error from this source is applied to mean time, ephem-
eris time results. This time is of interest to astronomers, but is not used directly by
the navigator.

1913. Sidereal time uses the first point of Aries (vernal equinox) as the celestial
reference point. Since the earth revolves around the sun, and since the direction of
the earth's rotation and revolution are the same, it completes a rotation with respect
to the stars in less time (about 35676 of mean solar units) than with respect to the sun,
and during one revolution about the sun (one year) it makes one complete rotation more
with respect to the stars than with the sun. "This accounts for the daily shift of the
stars nearly 1? westward each night. Hence, sidereal days are shorter than solar
days, and its hours, minutes, and seconds are correspondingly shorter. Because of
nutation (art. 1417) sidereal time is not quite constant in rate. "Time based upon the
average rate is called mean sidereal time, when it is to be distinguished from the
slightly irregular sidereal time. "The ratio of mean solar time units to mean sidereal
time units 1s 1:1.00273791.

The sidereal day begins when the first point of Aries is over the upper branch of
the meridian, and extends through 24 hours of sidereal time. "The sun is at the first
point of Aries at the time of the vernal equinox, about March 21. However, since the
solar day begins when the sun is over the lower branch of the meridian, apparent solar
and sidereal times differ by 12 hours at the vernal equinox. Each month thereafter,
sidereal time gains about two hours on solar time. By the time of the summer solstice,
about June 21, sidereal time is 18 hours ahead or six hours behind solar time. By the
time of the autumnal equinox, about September 23, the two times are together, and by
the time of the winter solstice, about December 22, the sidereal time is six hours ahead
of solar time. There need be no confusion of the date, for there is no sidereal date.

TIME 497

Local sidereal time (LST) uses the local meridian as the terrestrial reference. At
the prime meridian this is called Greenwich sidereal time (GST). The difference
between LST at two meridians is equal to the difference of longitude between them
the place to the eastward having the later time. Local sidereal time is LHA Tv
expressed in time units. To determine LST at any given moment, find GHAT by
means of an almanac, and then apply the longitude to convert it to LHAT. Then
convert. LHA Y in arc to LST in time units.

Example.—Find LST at ZT 8*25"51* on May 31, 1958, for long. 103°16/3 E.

Solution.— ZT 8"25"51" May 31
ZD (—)7
GMT 1^25751* May 31
k 2637016
25"51* 6288
GHAT 269°30/4
A 103°16/3E
LHAT 129467
LST 05517075

Unless GST is required, conversion from arc to time units should be made from
LHA T, rather than from GHA 7, to avoid the need for converting longitude from arc
to time units.

Conversion of sidereal to solar time is the reverse. Local sidereal time is converted
to arc (LHA T), and the longitude is applied to find GHA Y. This is used as an argument
for entering the almanac to determine GMT, which can then be converted to any other
kind of time desired. "This is similar to one method of finding time of meridian transit,
described in article 2104. Normally, the problem is not encountered by the navigator.

Sidereal time, as such, is little used by the navigator. It is the basis of star charts
(art. 2204) and star finders (art. 2210), and certain sight reduction methods (notably
H.O. Pub. No. 249), but generally in the form LHA T. This kind of time is used for
these purposes because its celestial reference point remains almost fixed in relation to the
stars. Sidereal time is used by astronomers to regulate mean time. Timepieces
regulated to sidereal time can be purchased.

1914. Time and hour angle.— Both time and hour angle are a measure of the phase
of rotation of the earth, since both indicate the angular distance of a celestial reference
point west of a terrestrial reference meridian. Hour angle, however, applies to any
point on the celestial sphere. Time might be used in this respect, but only the apparent
sun, mean sun, the first point of Aries, and occasionally the moon are commonly used.

Hour angles are usually expressed in arc units, and are measured from the upper
branch of the celestial meridian. Time is customarily expressed in time units. Sidereal
time is measured from the upper branch of the celestial meridian, like hour angle, but
solar time is measured from the lower branch. Thus, LMT=LHA mean sun plus or
minus 180°, LAT—LHA apparent sun plus or minus 180°, and LST=LHA T.

As with time, local hour angle (LHA), based upon the local celestial meridian, at
two places differs by the longitude between them, and LHA at longitude 0? is called
Greenwich hour angle (GHA). In addition, it is often convenient to express hour angle
in terms of the shorter arc between the local celestial meridian and the body. This is
similar to measurement of longitude from the Greenwich meridian. Local hour angle
measured in this way is called meridian angle (t), which is labeled east or west, like
longitude, to indicate the direction of measurement. A westerly meridian angle is
numerically equal to LHA, while an easterly meridian angle is equal to 360°—LHA;
also, LHA=t (W), and LHA=360°—t (E). Meridian angle is used in the solution of
the navigational triangle (art. 1433).

408 TIME

Example 1.—Find LHA and t of the sun at GMT 3^24716* on June 1, 1958, for
long. 118?48:2 W.

Solution.—
Gre GMT 3*24"16* June 1

3^ 225%36:0

24916 6?04:0

GHA 231400
X 118%48!2 W

LHA 112%51:8
t 112?51:8 W

Example 2.—Find LHA and t of Kochab at ZT 18"24™47° on May 31, 1958, for
long: D5 2733 W.

Solution.— K och ab
ZT 18^24747* May 31
ZD

GMT 2224475 May 31
22h 218°53/4

24m475 651258
SHA 13221712
GHA 52235

A 55273 W
LHA 306%56/1
t 53%03/9 E
Problems

1903a. What is the time and date 9"13"29* before 3"16"34* May 9?

Answer.—T 18"03"05* May 8.

1903b. What is the time and date 4%19*22%50* after 9"31"04* on December 25?

Answer.—T 4*53%54* on Dec. 30.

1903c. What is the time and date 2 years, 11 months, 16 days, 10 hours, 23 minutes,
and 48 seconds before 2"46"17* on October 4, 1958?

Answer.—T 16*22"29* on Oct. 17, 1955.

1903d. What is the time and date 412 days, 15 hours, 6 minutes, and 56 seconds
after 22"27"03* on March 16, 1958?

Answer.—T 13°33759° on May 3, 1959.

1904a. Convert 6*28"31* to arc units, without use of a conversion table.

Answer.—97?07'45" or 97%07/8.

1904b. Convert 217?28'8 to time units, without use of a conversion table.

Answer.—14"29"55*2 or 145299555.

1904c. Convert 196?21/46" to time units, without use of a conversion table.

Answer.—13^05727*] or 135059275.

1904d. Convert 107%49'44” to time units, using appendix V.

Answer.—7*11%195,

1904e. Convert 211373 to time units, using appendix V.

Answer.—14*06"29%2.

1904f. Convert 8497335 to arc units, using appendix V.

Answer.—132%23'2.

1904g. Convert 251%09/2 to time units, using appendix W.
Answer.—16^447375.

TIME 499

1904h. Convert 23^07738* to time units, using appendix W.

Answer.—346%54/5.

1907a. For an observer at long. 97”24'6E the ZT is 19^10726*.

Required.—(1) Zone description.

(2) GMT.

Answers.—(1) ZD (—) 6, (2) GMT 13*10"26s,

1907b. The GMT is 11"32"07s,

Required.—(1) ZT at long. 133°24/7 W.

(2) ZT at long. 111%43/9E.

Answers.—(1) ZT 2^327075, (2) ZT 183207.

1907c. At long. 165?18:2E the ZT is 17^08"51* on July 11.

Hequired.—(1) GMT and date.

(2) ZT and date at long. 125°36/7 W.

Answers.—(1) GMT 6^08751* on July 11, (2) ZT 22^08751* on July 10.

1907d. On January 26 the 0800 DR long. of a ship is 128%03/2E. Twenty-six
hours later the EP long. is 125%01/4 E.

Reguired.—ZT and date of arrival at the second longitude.

Answer.—ZT 0900 Jan. 27.

1907e. On April 1 the 1200 running fix long. of a ship is 179%55/2W. Eight hours
later the DR long. is 178°48/9 E.

Required.—ZT and date of arrival at the second longitude.

Answer.—ZT 2000 Apr. 2.

1907f. Inch'ón, long. 137? E, uses ZD (—) 830" for standard time. Find the
standard time and date at San Francisco, long. 122? W, when the summer time at
Inch’dn is 2000 on August 9.

Answer.—ZT 0230 Aug. 9.

19084. At GMT 1400 on July 2 the chronometer reads 1"42"28*. At GMT 0800
on July 12 it reads 742740",

Required.—(1) Chronometer error at GMT 1400 on July 2.

(2) Chronometer error at GMT 0800 on July 12.

(3) Chronometer rate.

(4) Chronometer time at ZT 1800 July 20, at long. 153?21:7 W.

Answers.—(1) CE 17732* slow, (2) CE 177208 slow, (3) rate 1*2 gaining, (4) C
Get Sie Lë

1908b. On March 5 the DR long. of a ship is about 151°E, and the zone time
is about 1800. Chronometer error is 6™40° fast.

Required.—GMT and date when the chronometer reads 8^02723*.

Answer.—GMT 7*55"43* on Mar. 5.

1908c. On November 7 the EP long. of a ship is about 71? W, and the zone
time is about 1900. Chronometer error is 17181 slow.

Required.—GMT and date when the chronometer reads (1) 11°55™20°, (2) 11550250*.

Answers.—(1) GMT 23°56™38* Nov. 7, (2) GMT 0°01™08° Nov. 8.

1908d. At GMT 2200 a comparing watch is checked by time signal, and found to
read 105009055. The chronometer errors are then determined by means of the com-
paring watch. When the watch reads 10"06"00*, chronometer A reads 10°11™17°, and
when the watch reads 105087005, chronometer B reads 9"59"06=.

Required.—(1) Watch error.

(2) Error of chronometer A.

(3) Error of chronometer B.

Answers.—(1) WE 55 fast on GMT, (2) CE, 5"22* fast, (3) CEs 8"49* slow.

500 TIME

1910a. A chronometer 72225 slow on GMT reads approximately 3"45". About
two minutes later, when the GMT is a whole minute, a comparing watch will be set
to GMT exactly.

Required.—(1) Reading of the watch at starting.

(2) Reading of the chronometer.

Answers.—(1) W 3^54"005, (2) C 3°46™38°.

1910b. A chronometer 57105 fast on GMT reads approximately 5"50™. About one
minute later, when the GMT is a whole minute, a comparing watch with a 24-hour
dial will be set to GMT exactly. The ZT is approximately 1145 and the long. 94° W.

Required.—(1) Reading of the watch at starting.

(2) Reading of the chronometer.

(3) Watch error if, instead of being set to GMT, the watch setting is unchanged
and the watch reads 17"45"32* at comparison.

Answers.—(1) W 175467008, (2) C 5517108, (3) WE 28° slow on GMT.

1910c. A watch is set to zone time,approximately. The long. is about 160%E. The
watch is compared with a chronometer which is 3”16* fast on GMT. When the
chronometer reads 1"48"00*, the watch reads 12^45702*.

Reguired— Watch error on zone time.

Answer. —WE 18° fast on ZT.

1910d. On February 14 the DR long. is 63%46/1W. An observation of Dubhe is
made when the. watch reads 6"07"30* pm. The watch is 11* slow on zone time.

Reguired.—GM T and date.

Answer.—GMT 225077418 Feb. 14.

1910e. On December 11 a watch is set to zone time, approximately. The long. is
137°W. The chronometer is 3"36* fast on GMT. When the chronometer reads
4"40"00*, the watch reads 7*36"06* pm.

Required.—(1) Watch error on GMT.

(2) GMT and date about 20 minutes later, when the watch reads 75557525.

Answers.—(1) WE 2^59742? fast on GMT, (2) GMT 4*^56710* Dec. 12.

1910f. Shortly before taking morning sights on January 17 the navigator compares
his watch with the chronometer. When the chronometer reads 2"30"00s, the watch
reads 6"13"12* am. The chronometer is 17715? fast on GMT. The long. is 118? W.

Reguired.—(1) C-W.

(2) GMT and date a little later when Regulus is observed at W 6"28"47* am.

Answers.—(1) C-W 8^16"48*, (2) GMT 14*28=20* Jan. 17.

1911a. At long. 138?09'3 E the LMT is 0'09%57% on April 23.

Reguired.—(1) GMT and date.

(2) ZT and date at the place.

Answers.—(1) GMT 14'5720* Apr. 22, (2) ZT 2357720 Apr. 22.

1911b. At long. 157%18/4 W the LMT is 1931 on June 29.

Required.—(1) ZT and date.

(2) GMT and date.

Answers.—(1) ZT 2000 June 29, (2) GMT 0600 June 30.

1911c. At long. 99°35'7 W the daylight saving time is 21"29"45* on August 31.

Required.—(1) Standard time and date.

(2) LMT and date.

Answers.—(1) Standard time 20°29™45° Aug. 31, (2) LMT 20"51"22 Aug. 31.

1912a. Find the LAT and date at ZT 5"26™13° on June 12, 1958, for long. 9°28/1 E.

Answer.—LAT 5^04731* June 12.

TIME 501

1912b. At long. 77°15'5 W the LAT is 1500 on June 13, 1958.

Required.—(1) ZT.

(2) LMT.

Answers.—(1) ZT 15^08"565, (2) LMT 14"59™548,

1912c. Using the Air Almanac, find (1) LAT at long. 117°55’ W, and (2) the Eq.
T, at ZT 20*43"09* on June 1, 1958.

Answers.—(1) LAT 20^53^445, (2) Eq. T (+) 22155,

1913a. Find LST at ZT 19"24"26> on June 1, 1958, for long. 87°51/2 E.

Answer.—LST 11%53"565,

1913b.—Find the ZT at LST 215207078 on May 31, 1958, for long. 54°21/3 W.

Answer.—ZT 4^24"135.

1914. Find LHA and t of the moon at GMT 9^257075 on May 31, 1958, (1) for
long. 43?19:0 W, and (2) for long. 43?19/0E. Use appendix V.

Answers.—(1) LHA 118°54/8, t 118”54'8 W; (2) LHA 205%32/8, t 154°27/2E.

CHAPTER XX
SIGHT REDUCTION

2001. Introduction.— The process of deriving from a celestial observation the in-
formation needed for establishing a line of position is called sight reduction. "The
observation itself consists of measuring the altitude of a celestial body and noting the
time. Although special methods may be used for finding certain coordinates such as
latitude or longitude, the modern navigator generally thinks in terms of lines of posi-
tion without regard to any special significance of these lines. The process of finding `
such a line of position may be divided into six steps:

. Correction of sextant altitude (ch. XVI).

. Determination of GHA and declination (ch. XVIII).

. Selection of assumed position and finding meridian angle at that point.
. Computation of altitude and azimuth.

. Comparison of computed and observed altitudes (ch. XVII).

6. Plot of the line of position.

Broadly speaking, tables which assist in any of these steps can be considered
sight reduction tables. However, the expression is generally limited to tables in-
tended primarily for computation of altitude and azimuth. A great variety of such
tables exists. In chapter XXI various methods of sight reduction, including graphical
and mechanical solutions, are contrasted. All are based, directly or indirectly, upon
solution of the navigational triangle (art. 1433). "Thus, the process of sight reduction,
in its limited sense, is one of converting coordinates of the celestial equator system
(art. 1426) to those of the horizon system (art. 1428).

The U. S. Navy Hydrographic Office publishes a set of sight reduction tables
giving tabulated solutions of the navigational triangle, intended primarily for use with
the Nautical Almanac aboard ship. These Tables of Computed Altitude and. Azimuth,
popularly known by their publication number, “H.O. 214," are widely used among
mariners of various nations. In addition to the United States printing, editions are
published by Great Britain, Spain, and Italy. "They are suitable for reduction of
nearly all observations made aboard ship, and will be used to explain the principles
of sight reduction as given in this chapter. Extracts from H.O. Pub. No. 214 are
given in appendix AA.

2002. Preliminary computation.—Certain computations precede the use of sight
reduction tables. The correction of the sextant altitude (hs) to find observed altitude
(Ho), as explained in chapter XVI, is usually performed first, but not necessarily so.
If any form of time other than GMT is used for timing the observation, it is first con-
verted to GM'T because this is the kind of time used for entering the almanacs. From
the almanac, the GHA and declination are determined, as explained in chapter XVIII.

To enter H.O. Pub. No. 214 and most other sight reduction tables, the following
variables are needed:

1. Latitude (L).

2. Declination (d).

3. Meridian angle (t).

The latitude to use in entering the tables is that of the assumed position (AP).
This latitude is usually called the assumed latitude (aL). The assumed position should

502

cU Hm GO D ra

SIGHT REDUCTION 503

be in the general vicinity of the actual position, which, of course, is usually un-
known. Several methods of selecting an AP are in use. The dead reckoning position
or estimated position might be used. However, when H.O. Pub. No. 214 and certain
other methods of sight reduction are used, unnecessary interpolation can be avoided
by selecting an AP that will result in two of the three variables being exact entry values.
In H.O. Pub. No. 214, altitudes and azimuths are given for each whole degree of latitude.
Therefore, it is customary to select an AP on the nearest whole degree of latitude to the
DR or EP at the time of sight.

Declination is taken from the almanac, as explained in chapter XVIII. This value
is used without adjustment to simplify the solution.

Meridian angle is the angular distance that the celestial body is east or west of
the celestial meridian. It is found from local hour angle (LHA), which, in turn, is
found from Greenwich hour angle by adding east longitude or subtracting west longitude.
A time diagram (art. 1427) is useful in visualizing this relationship.

Example 1.—The GHA is 168%42/6.

Required.—The LHA and t at (1) long. 137°24/6 W, and (2) 158?24'7 E.

Solution.—
(1) GHA 168%42'6 (2) GHA 168°42'6
A 137°24'6 W ^ 158224/7 E
SHA 73171820 LHA 327%07/3
te 3191840 W (32524 Ë

In west longitude, if GHA is less than longitude, add 360% to GHA before subtract-
ing. In east longitude, if the sum exceeds 360°, subtract this amount. If LHA is
less than 180°, it is numerically equal to meridian angle, which is labeled W (west).
If LHA is greater than 180°, t is 360°—LHA and is labeled E (east).

In HO Pub. No. 214, t (labeled ““H.A.”) is given at intervals of 1°. If t is to
be a whole degree, the longitude of the assumed position, called assumed longitude (a),
must be selected so that no minutes of arc will remain after it is applied to GHA.
This means that in west longitude the minutes of ak must be the same as those of
GHA; while in east longitude the minutes of ak must be equal to 60’ minus the minutes
of GHA.

Example 2.—The GHA is 57°1879.

Required.—The LHA, t, and AP for use with H.O. Pub. No. 214 without inter-
polation for t or L, if the DR position is (1) lat. 11?48:8 N, long. 151°53'3W; and
(2) lat. 62?2177 N, long. 4?31:3 E.

Solution.—
(1) GHA 57718:9 (2) GHA 57?18:9
ax 152°18'9 W an 4%41:1E
LHA 265%00'0 LHA 62%00/0
t 95°00/0E t 62°00/0 W
aL 12°00/0N aL 62%00/0N
ax 152%18:9W GN 4 411

2003. Tables of Computed Altitude and Azimuth (H.O. Pub. No. 214).—These
popular sight reduction tables are published by the U. S. Navy Hydrographic Office
in nine volumes, each covering 10? of latitude in increments of 1%. For each degree
of latitude there is a series of tables, with cutaway tabs providing quick reference to
the first page of the tables for that latitude. Declination entries are given at intervals
of 0°5 from 0? to 29°. Beyond this, 37 selected declination entries are given to provide
solutions for all of the stars listed on the daily pages of the almanacs, and most of the
additional stars listed near the back of the Nautical Almanac. A total of 96 declination

504 SIGHT REDUCTION

entries are given for each latitude, arranged eight to a page. Each declination entry
is given at the top of a column. The third variable, meridian angle, is given in the
column at the extreme left and right sides of each page. These columns are labeled
“H.A.”, the abbreviation for “hour angle,” the expression formerly used for meridian
angle, but replaced because of confusion with local hour angle, Greenwich hour angle,
etc. Meridian angle entries are given at intervals of 1° from 0° at the top of the page
to the maximum value at which the altitude is 5% or greater.

At most page openings, separate tables are given for declination having the same
name (N or S) as the latitude and those having contrary name (one N, the other S).
That is, declination values on the left-hand page (same name) are duplicated on the
right-hand page (contrary name). A maximum of ninety-one meridian angle entries
(0°-90°) are given on the left-hand page (same name). As either the declination or the
latitude increases, the number of same-name entries increases, and the number of
contrary-name entries decreases. When the same-name entries exceed 90° of meridian
angle, the additional ones are placed on the right-hand page, below the contrary-name
entries. At extreme values of declination and latitude there are no contrary-name
entries, the same-name entries occupying both pages.

In each declination column there are four sets of figures. The first, given in bold
type, is the altitude (labeled “Alt.”) to the nearest 0/1. Following this is Ad in small
type. This is the change of altitude for a unit change of declination. Except when
the value is 1.0, entries are given in hundredths of a unit, although the position of
the decimal point is not shown. Following Ad, and also in small type, is At, the change
of altitude for a unit change of meridian angle. This is given in the same form as Ad.
The last set of figures in the column is the azimuth angle (labeled ‘‘Az.’’), to the nearest
OA:

At latitude 0° the arrangement is modified because there is no “same” or “con-
trary’ name of declination. Here a single set of declination entries is given. Decli-
nation replaces latitude as the prefixdabel for azimuth angle.

Following the altitude-azimuth section of each latitude is a two-page star identifi-
cation table. The use of this table is explained in article 2213.

On the inside front cover and its facing page is a speed-time-distance table, which
is useful in advancing or retiring lines of position, as well as for other purposes. This
table contains information similar to that in table 19 of this publication, but in some-
what different form. Volume VIII and older printings of other volumes have sextant
altitude correction tables on these pages.

Following the speed-time-distance table is an arc to time conversion table.

Following the title page and preface are given a description of the tables, and sample
problems.

On the inside back cover and facing page is given a “multiplication table” to
multiply Ad or At by the number of minutes between the declination or meridian
angle and the value used for entering the main table. This is used in interpolating
the altitude for declination or meridian angle.

On the two pages next preceding the multiplication table is given a somewhat
similar table to provide easy interpolation for latitude.

The use of the various parts of H.O. Pub. No. 214 is explained in articles 2004-2007
and 2213. The primary purpose of H.O. Pub. No. 214 is to provide an easy method
of sight reduction for use with the Nautical Almanac aboard ship. It may also be
used with the Air Almanac, and for solution of any spherical triangle for which entry

values are given. Therefore, it can be used in great-circle sailing for determining the
initial course and the distance.

SIGHT REDUCTION 505

In the British edition (H.D. 486) the main tables are identical to those of H.O.
Pub. No. 214, being a reproduction of the United States tables, but arranged with 15° of
latitude in each of six volumes. The explanation has been rewritten to suit British
usage. The Spanish edition is identical to H.O. Pub. No. 214, except that the ex-
planation is in Spanish. The Italian edition is based on H.O. Pub. No. 214.

2004. H.O. Pub. No. 214 solution by Ad only.—If interpolation is made for all
three variables—latitude, declination, and meridian angle—a triple interpolation is
needed. A simpler solution, almost universally used with H.O. Pub. No. 214, is to
select an assumed position that will eliminate interpolation for latitude and meridian
angle, leaving a simple interpolation for declination.

Example.—Find computed altitude (Hc) and azimuth (Zn) if aL is 41°00/0 N,d
is 22?14:3 N, and t is 36°00/0 W.

Solution.—

t 36?00:0W

d 22%14/3N d diff. 1473
aL 41?00:0N

ht 54%16/8 Ad (+)0.65 Z N111°0W
corr. (+) 9/3

Hen454726: 1
Zn 249°0

The main table is entered with the three variables, t, d, and aL (being sure to
note whether d and aL are of same or contrary name); and the values of ht (tabulated
altitude, labeled “Alt.” in H.O. Pub. No. 214), Ad, and Z are taken directly from the
table, without interpolation. The tabulated altitude (ht) is the computed altitude
(He) for the values used for entering the table. The designation ht is used to dis-
tinguish it from the Hc obtained by applying a correction to the value taken from the
table.

The declination entry argument used should be the tabulated entry nearest the
declination for which a solution is sought, normally differing by not more than half
a degree. The difference between this value and the actual declination is recorded
as “d diff." No sign (+ or —) is assigned to this value. It is good practice to show
Ad as a decimal, even though it is not tabulated in this way. Thesign of this value should
be determined carefully by inspection of the main table of H.O. Pub. No. 214. Inter-
polation of altitude for declination is made between the base value taken from the
table and the value given on the same line in the next column to the right or left.
The choice of the second column depends upon the actual declination. If it is greater
than the value used for entering the table, use the next column to the right, and if less,
use the next column to the /eft. If the value in the second column is greater than the
base value, the sign is plus (+), and if less, the sign is minus (—). The accuracy of
this important step can be checked by comparing the computed altitude (Hc) with
the altitudes given in the main table of H.O. Pub. No. 214. If Ad has been given the
correct sign (and applied correctly), Hc should lie between the tabulated altitudes in
the columns for tabulated declination next smaller and next larger than the actual
declination.

The azimuth angle is given a prefix N or 5 to agree with the latitude, and a suffix
E or W to agree with the meridian angle. For this reason it is good practice to label
these values when they are recorded.

'The next step is to multiply Ad by d diff., to interpolate between the altitude
entries for consecutive declination columns. In most instances, the easiest way to do
this is to use the multiplication table on the inside back cover of H.O. Pub. No. 214 and
its facing page, entering separately with minutes and tenths of minutes of Ad and

506 SIGHT REDUCTION

adding the two parts. The correction, which is recorded below ht, is given the sign of
Ad. The correction is then added or subtracted, in accordance with its sign, to ht.
The answer is computed altitude (Hc).

Azimuth (Zn), which is recorded below He, is found by converting azimuth angle
(Z) in accordance with its labels, as explained in article 1428. Usually, azimuth
angle is found without interpolation. For exceptions to this practice, see article
2007.

If Ad is changing rapidly, or when it changes sign (at the maximum altitude for
the given meridian angle and latitude), interpolation may be somewhat less accurate
than in other parts of the tables, but this should not introduce a large error unless the
celestial body is near the zenith, when the method of H.O. Pub. No. 214 is not recom-
mended.

2005. H.O. Pub. No. 214 solution by Ad and At is similar to that using Ad only,
but with the additional step of interpolating between the altitude entries for consecutive
meridian angle entries, in a similar manner to interpolation for declination.

Example.—Find computed altitude and azimuth if aL is 41?00:0 N, d is 20748778,
and t is 22°14/0K.

Solution.—
t 22%14'0E t diff. 14/0 t corr. (—) 4/2
d 20%48:7 S dūdūt alt d corr. (+) 10/8
aL 41%00/0N corr. (+) 6/6
ht 249?43^T Ad (+) 0.95 At (—) 0.30 Z N 15724 E
corr. (+) 6‘6
He 24°49/7
Zn Ww T5774

In this solution, t diff. is the difference between the meridian angle and the nearest
whole degree of t used for entering the table. The t corr. is t diff. X At, found by
using the same multiplication table used for the d corr. The sign of At is found by
inspection of the main table. In this example interpolation is between the base alti-
tude for t 22?, and the altitude for t 23?. Since the altitude for t 23? is less than that
for t 22?, the correction should be subtracted, so that the interpolated value will lie
between the two values between which interpolation is being made. The sign of Ad
is found by comparing the altitude for d 21°00’ with that for d 20°30’. The total
correction 1s the algebraic sum of the t corr. and d corr.

The principal advantage of this solution is that a round of sights can be worked and
plotted from the same assumed position. However, this advantage is offset by the
additional length of the solution. The method is little used.

2006. H.O. Pub. No. 214 solution by Ad, At, and AL.—Tf the altitude and azimuth
at a particular place are desired, interpolation should be made for all three variables, t,
d, and L, if needed. The change in altitude for a change of latitude of 1^ (AL) is not
tabulated. The table on the two pages preceding the multiplication table of H.O.
Pub. No. 214 is used for finding the correction for latitude.

Example.—Find computed altitude and azimuth if aL is 41?12/88, d is 21?32/58
and t is 8952/3 W. |:

Solution .— J- E
Dee Kl SET ss t corr. 2'4
12153255 d diii. 245 d corr. 2/4

aL 4112/85 dir" 1228 L corr. E

ht 69°04/0 Ad (+)0.94 At (+)0.32 sum 4/8 eko,
cor —)'070 corr. (—)6:9

He 68°57/1 Zi 515620 W

Zn 336%0

-

-
N

SIGHT REDUCTION 507

The corrections for meridian angle and declination are found as explained in
articles 2004 and 2005. The L corr. is found by entering the correction table with
azimuth angle and L diff., the difference between the latitude of the assumed position
and the nearest whole degree used for entering the main table. It is customary to inter-
polate in this table, where applicable, but the error introduced by not doing so is always
less than 0:3 if the nearest whole degree of azimuth angle is used. The sign of the
latitude correction is determined by the rules given at the bottom of the correction
table. The total correction is the algebraic sum of the three individual corrections.

All of these are altitude corrections. The azimuth is that corresponding to the
values used for entering the main table. If the exact value at the place is desired, it
can be found by interpolation, as explained in article 2007. If such an interpolation is
made, the interpolated value should be used for entering the latitude correction table
for altitude interpolation.

2007. Interpolation for azimuth.—In sight reduction for plotting lines of position,
it is not customary to interpolate for azimuth angle when H.O. Pub. No. 214 is used.
However, if greater accuracy is desired, as for determining compass error, triple interpo-
lation should be made. This is customarily accomplished by entering the main table
of H.O. Pub. No. 214 with the nearest values of t, d, and L, and taking out the corre-
sponding tabulated value. Simple eye interpolation is then used to determine separately
the correction for each of the three variables. The algebraic sum of these is the cor-
rection applied to the base value. The Ad, At, and AL corrections are not used because
these refer to the altitude, not the azimuth. Corrections are made to azimuth angle
before it is converted to azimuth.

Example.—Find the azimuth by interpolation if Lis 41°25'9 S, d is 22?19:6 N, and
t is 17°22'4 E.

Solution.—
te =
t 1724 E Beni TE Zami, (AV 150. t corr. 0?4
d SN aloni 092 tegt 4d corr: —
L 41°48 Li ditt. 024 eut 052 cor
tabam 16257 sum 0?1 0°4
corr. (—)0°3 corr. (—)0?3
Z $162%4E
Zn 01776

The corrections are determined by inspection. In this example the tabulated
value used as a base is compared with the value for the same d and L, but t 18°, to
determine the t corr. Similarly, it is compared with the value for the same t and L,
but d 22° to determine the d corr.; and with the value for the same t and d, but L 42°
to determine the L corr. Interpolation is between whole degrees of t and L, but be-
tween half degrees of d. For declinations of more than 29°, the d interpolation interval
varies.

If azimuth is needed to a greater precision than the nearest tenth of a degree, it
should be determined by H.O. Pub. No. 260 or 261 (art. 2126), or by computation
(art. 2125).

2008. Complete solution.—The complete solution includes all of the parts listed
in article 2001. Because of the various alternatives available for the separate parts,
a large number of variations might be used in the complete solution. The following
examples combine some of the most commonly used variations.

Example 1—On May 31, 1958, the 1425 DR position of a ship is lat. 40^39:6 N,
long. 64917/2 W. At watch time 2"25"51* pm the navigator observes the lower limb of

An cm PM

508 SIGHT REDUCTION

the sun with a marine sextant having an IC of (—)2:0, from a height of eye of 36 feet.
The watch is 23° fast on zone time. The hs is 56%10:9.
Required.—The a, Zn, and AP, using H. O. Pub. No. 214 (Ad only) and the Nautical `

Almanac.

Solution.—
May 31 Sun UO Uds
W 2525™51° PM 1899195571 N* d IC 21D
WE (F) 23* eorr. (+)0/1 (+)0:3 D 518
- ZT 14525m985 d 21 055.2 N o 15:3
ZD (+)4 sum 15:3 7:8
GMT 18^25"28* May 31 corr. (+)7:5
18» 90?36:8 hs 56?10:9
257928 6922'0 Ho 56918/4
GHA 96?58:8
ar 63588 W
LHA 33°00/0
t 33°0010 W
d 21%55:2N d diff. 418
aL 41?00:0 N
ht 5092272 Ad (—)0.67 Z N114?22W
COIT. (—)3'2
Hc 56719'0
a 0.6A aL 41?00:0N
Zn 245?8 an 63?58:8W

It is good practice to have a standard work form. If this is not printed, or on
a rubber stamp, it should be copied in its entirety before the solution is started. The
first step should then be to fill in the known information. If the solution for observed
altitude is made first, this value can then be copied in the main solution at the left of
the form, so that it will be ready for comparison when Hc is determined. The best
form to use is that which the individual navigator finds most logical and least likely to
result in errors. Those shown in appendix Q, and used here, are slight modifications
of forms developed at the United States Naval Academy, where they evolved as a
result of long experience. Their use reduced materially the number of mistakes
made in solutions. Some navigators include a time diagram (art. 1427) in the form,
immediately below the name of the celestial body, as a check both on the time and
meridian angle computation. |

There is a growing tendency among navigators to keep the navigational watch set
to GMT. This is particularly helpful when a number of observations are made, as
during twilight, to eliminate the need for repeated application of watch error and zone
description, and determination of Greenwich date. The use of a GMT watch is
illustrated in the following example of a complete sight of the moon:

Example 2.—On June 2, 1958, the 0420 DR position of a ship is lat. 41°07/6 N,
long. 131?51:2 W. At GMT 13"24752* the navigator observes the upper limb of the
moon with a marine sextant having an IC of (+)1 /5, from a height of eye of 29 feet.
The hs is 7°40/1.

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad only) and the Nautical
Almanac.

Solution.—

June 2

GMT 1324525 June 2

13*

24™52°
corr.

185°38/0

5°56/0 v
2'5 (+) 6/0

GHA 191°36'5
an 131?36:5W

LHA
t

d

aL
ht

COIT.

60?00:0

60?00:0W
19%09'6S
41%0010 N

8?14:0

(—) 7:3

8706:7
8712:0

5.3T
23578

SIGHT REDUCTION

Moon
13" 19%09/5S' d
corr. (+) 0/1 (+)0/3

d 19%09'6S

d diff. 9/6

Ad (—)0.75

aL 41?00:0N
a^ 131?36:5W

509
+ € -

A CSS
D 540

C 61/0

Uy 476
add’! 30/0
sum 6751 35:2
COIT (+) 31:9
hs 7940/1
Ho 9921970
Z N124?2W

Occasionally it is desired to solve an observation for the estimated position of the

ship.

Example 3.—During morning twilight on June 1, 1958, the 0624 EP of a ship is lat.
41%12:'3 S, long. 178?39:2 E. At ZT 6"24757* the navigator observes Saturn with a

marine sextant having an IC of (—) 1:0, from a height of eye of 53 feet.

20?52'3.

The hs is

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad, At, AL) and the
Nautical Almanac.

Solution.—
June 1
LLE 624257"
ZD(—)12
GMT 18'24"57* May 31
18* 20995153
242515 60 1455 d
corr. (+) 1:1 (4) 2°7
GHA 262%06:7
aN 178°39/2 E
LHA 80%45:9
t 80?45/9 W
d 21950775
aL AS
ht 20°48/5
corr. (+)7:4
He 2025519
Ho 2094147.
a 14.2 A
Zn 25874

Saturn
1821 50750,
corr. 0205020
d 21650575

t diff. 14:1
d diff; 973
Eech

Ad(—) 0.60 At(+) 0.74

aL 41%12:35
ad 178?39:2 E

+ S —
IC 1/0
D Ea
*-P 245
sum 1016
corre, E 10:
hs 2095225
Ho DOS
SR e
Corr 005
d corr. 096
L corr. 2:5
Sum 13:09 55/0
COIT. (4-)7:4
ZES TS A W.

510 SIGHT REDUCTION

The local date is used as the heading of the first column of the solution. The
Greenwich date is recorded opposite GMT. In this example, the two dates are dif-
ferent. Even when they are the same, it is good practice to record both dates, to
avoid possible error. It is desirable to show all closely related information on the
same line, as t, t diff., and t corr. This is not always possible because of interference
of other information. When this occurs, the form is changed in a way to cause the
least upset to the usual form. Thus, in this example, it would be desirable to show ht,
Ad, At, and Z on the same line and in the order these values are taken from H.O. Pub.
No. 214. However, the sum of the t, d, and L corrections is at the logical place for Z,
which is therefore kept in the same column, but moved down two spaces.

Example 4.—During evening twilight on June 1, 1958, the 1730 DR position of a
ship is lat. 40?39/2 S, long. 75°01/2E. At GMT 12^31717* the navigator observes
Arcturus with a marine sextant having no IC, from a height of eye of 38 feet. The
hs is 5502:

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad only) and the Air
Almanac.

Solution.—

i June 1 Arcturus + k —
GMT 12"31"17* June 1 IC — —
122305 76°59’ D 6’

¡EE 19’ R Ve
SHA 146°33’ sum — ts
GHA 223951" corr. (—)13%
an 75°09’ E hs i Sor
LHA 299°00’ Ho 7°42"
t 61°00’ E
d. .19%94N d dub 6’
aL. 410045
ht 7°14/0 Ad (+)0.75 Z 5123286
corr. (+)4'5
Hc 791815
Ho 79242'
a 246 aL 41°00’S
Zn 05622 ar 75°09’ E

Both ht and its correction are shown to tenths of a minute of arc, to avoid a
possible error of 1’ in the algebraic sum, Hc.

There is no significance to the type of solution and almanac used with the various
celestial bodies shown in the examples above. The combinations used for examples 1
(sun) and 2 (moon) are most commonly used by marine navigators, but the other two
are shown to illustrate variations sometimes used at sea.

2009. Precomputation.—Sometimes it is desired to determine computed altitude
before the observation, generally for the purpose of obtaining a line of position quickly
after the observation has been completed. This is called precomputation. When it is
done, sextant altitude corrections are generally applied with reversed sign to He to obtain
precomputed altitude (Hp), which is then compared directly with hs to obtain the
altitude difference for plotting a line of position. Where altitude is needed for entering
correction tables, the computed altitude (He) is used. The error introduced by this
practice is negligible except at low altitudes, where the corrections should be adjusted
by using the Hp to reenter the tables. If greater accuracy is required, limit precom-
putation to Hc and Zn, and apply corrections to the sextant altitude after observation.

SIGHT REDUCTION all

Example.—On June 2, 1958, the 1025 DR position of a ship is lat. 42%21/4 S
long. 118%47.1W. The navigator plans to observe the lower limb of the sun at this
time with a marine sextant having an IC of (+)2/5, from a height of eye of 25 feet.

Required.—(1) Precomputed altitude by H.O. Pub. No. 214, Ad only, (2) the a
Zn, and AP if hs is 22?23/6. Use Nautical Almanac. | i

Solution.—
June 2 Sun OE
ZT 10"25"00 1589991174 NU 1005750
ZD (+)8 corr. (+)0/1 (+)0/3 D 4:9
GMT 18*25%00* June 2 tl PRON IN| OS
18" 90%32'3 sum 16/2 4/9
25"00* 6°15/0 corr. (+)11/3
GHA 96%47/3
ar 118%47'3 W
LHA 338°00/0
E 22°00/0 E
d 22%11/5N ddi
aL 4200/08
ht 2295015 Ad (—)0.95 Z S157?9E

corr. (—) 11/0
He 2278905

corr. (+) 1113 (rev.)
(1) Hp 2259812
hs PA

(2) a 4.6 A aL 42°00/0S
Zn 022°1 ar 118947/3 W

At the AP used in the calculation, Hp is correct only for the time used. However,
if the observation is made early or late, the same Hp and Zn can be used by moving
the AP along the parallel of latitude, eastward for early observations, or westward for
late observations, a distance equal to 0/25 of longitude for each second (15/0 for each
minute) difference between actual and predicted times. This adjustment is based
upon the assumptions that the apparent motion of the body is westward at the rate
of 15° per hour, and the declination is constant. Over the seconds or minutes likely
to be involved, these assumptions and the possible increased length of the plotted lines
do not introduce a significant error, except possibly for the moon.

2010. Low altitudes.—When Hc is determined by inspection tables such as H.O.
Pub. No. 214, a minimum tabulated altitude may be available. In H.O. Pub. No. 214,
altitudes below 5° are not given. These tables can be used for low-altitude observations
by selection of an AP that will result in He being 5° or greater. To do this, proceed as
follows: At the time of observation, note the approximate azimuth of the celestial body.
Plot the azimuth line through the DR or EP and measure off, toward the celestial body,
a distance equal to 6?—hs (or 6?— Ho). Select the AP in relation to this point as if it
were the DR or EP. Occasionally it may be necessary to use 7°—hs (or 7°—Ho).
The increased length of the altitude difference line does not introduce a significant
error over the distance that a rhumb line can be considered identical to a great circle.
Only in high latitudes is this a problem, and here the error can be virtually eliminated
by using a chart projection on which a great circle plots as a straight line or approxi-
mately so. The error introduced by using a rhumb line to represent the circle of equal
altitude (the line of position) is not increased because the AP selected is near the

azimuth line.

512 SIGHT REDUCTION

Example.—On June 1, 1958, the 1625 DR position of a ship is lat. 43739778,
long. 15°07/0W. At GMT 17^24722* the navigator observes the lower limb of the
sun as it breaks out below an overcast, shortly before setting. He uses a marine sextant
having no IC, and makes his observation from a height of eye of 52 feet. The hs is
1%00/8, air temperature (art. 1614) 24°F, and the atmospheric pressure (art. 1615)
30.16 inches. The sun's azimuth is approximately 305°. À

Required.—The a, Zn, and AP using H.O. Pub. No. 214 (Ad only), the Nautical
Almanac, and tables 23 and 24.

Solution.—
June 1 Sun ` + „OV
GMT 17%24=22* June 1 17* 22°03/1N d IC — —
bi eege See corr. (+)0/1 (+)0:3 D 7:0
294900: UNO ZZ SUS UN sum — 7/0
GHA 81402 corr. (—)7:0
an 20?40:2W hs 1?00:8
LHA 61°00/0 hr 095855
t 61°00°0 W
d$22*03:2:N ddi 32 © 9/1
aL 4100/08 40 168
Dto 52178 Ad(—)0.75 ZS125°5W B 0:3
eorr. (—) 2:5 sum — 10:7
Hc 571913 corr. (—)10°7
Ho 0?43'1 hr US ME.
ü TODA aL 41°00/0S Ho- su 0135
Zn 30525 a^ 20402 W

Refer to figure 2010. From the 1625 DR position, the approximate azimuth of
305° is plotted, as shown by the broken line. Along this line a distance of 6%00/0—
0?43:1—5?16:9, or 316.9 miles, is measured, locating the point labeled A. The AP is
selected with respect to this point as if it were the DR position. The sight is plotted
from this AP as in any observation. If it makes the plot easier, record a in the solution
in degrees and minutes of arc instead of in miles (5%19/3—0%43/1=436/2=276/2=
276.2 miles).

Large altitude differences can be avoided by using a method of solution that
provides for low altitudes. Among such methods are H.O. Pub. No. 249; nearly any
trigonometric method such as the cosine-haversine formula, H.O. Pub. No. 208, or H.O.
Pub. No. 211; and most graphical and mechanical methods. All of these methods are
discussed in chapter XXI. If a trigonometric method is used, the signs of the various
functions (or special rules) should be used if there is a possibility of He being negative.
The rules needed for H.O. Pub. No. 208 and H.O. Pub. No. 211 are given in articles
2110 and 2111, respectively. The need for special care can be eliminated by using
an assumed position about half a degree or more from the DR position or EP, in the
direction of the celestial body, if the altitude is less than 0°30’.

By any method of solution, if either He or Ho (but not both) is negative, the
altitude difference is found by numerically adding the two altitudes. Thus, if He is
(+) 0°12°6 and Ho is (—)0%03/2, the altitude difference, a, is 15/8, or 15.8 miles. The
positive altitude is greater than the negative one. Therefore, the a in this case is
away. If both He and Ho are negative, the difference is found by subtraction, but in
this case the one which is numerically smaller is the greater altitude. Thus, if He is
(—) 090916 and Ho is (—) 0%04'3, the altitude difference is 5.3 T.

SIGHT REDUCTION 513

21 W 20 W 19*W o o
AN | 18* W 17°W 16°W 15°W

41°S

41'S

42°s 42*S

43°S

43°S

44*S
21*W 20°W 19°W 18°W 17°W 16°W 15°W

Figure 2010.—Selecting an AP for low-altitude solutions by H.O. Pub. No. 214.

2011. High altitudes are usually avoided for at least two reasons. First, bodies
near the zenith are difficult to observe. A star or planet is difficult to “bring down”
to the horizon. It is not always easy to determine the azimuth accurately, and when
near the zenith, a body may be changing azimuth rapidly. On the other hand, such
observations are little affected by astronomical refraction. The second reason for
avoiding high altitudes is one of geometry. As the altitude increases, the radius of
the circle of position decreases. For a body near the zenith, the radius is so small
that the use of a straight line to approximate the circle may introduce serious error.

With higher altitudes, it is good practice to avoid use of lines of position extending
a considerable distance from the azimuth line. Since the decrease in radius is gradual,
there is no one altitude at which the curvature becomes excessive. However, a safe
general rule, if one is needed, is to use the DR position or EP as the assumed position,
and interpolate for azimuth angle, for all altitudes greater than 70°. The purpose of
this is not primarily to decrease the altitude difference, as sometimes suggested, but to
decrease the length of the line of position.

Within perhaps three degrees of the zenith, the curvature of the circle of position
becomes so great that even for a short distance a straight line is not an adequate repre-
sentation of the circle. At these altitudes, it is good practice to plot the line of position
as a circle. This is done by using the geographical position (GP) of the celestial body
as the center, and the zenith distance as the radius. Hence, no sight reduction tables

514 SIGHT REDUCTION

are needed. The same body can be used for obtaining a fix from two observations
separated by several minutes. In celestial navigation, as in piloting, a circle of position
is advanced or retired by moving its center. A^ "T in
Example.—On May 31, 1958, the 1224 DR position of a ship is lat. 20 17:4 N,
long. 50°07/4W. The ship is on course 127°, speed 18 knots. Using a marine sextant
having no IC, the navigator observes the lower limb of the sun twice, from a mu
eye of 65 feet. The first observation is made at GMT 15"15”15*, and hs is 88%01:1.
The second observation is made at GMT 15524™138, and hs is 87%34/7. The GHA of
the sun at GMT 15"15™15* is 49%25/9. Use the same declination as at GMT 15°24™13°.
Required.—The 1224 fix.

Solution.—
May 31 Sun + Q —
GMT 15^15715* May 31 d 21°54/1N IC t CONSES im
o y: 4
GHA 49°25/9 DH is
GPL, 21°54/1N sum 15/9 7/8
GP Md 49?25:9W corr. (+) 811
radius 110.8 mi. hs 88°01/1
Ho 88°09/2
Z 1?50'8
May 31 Sun OIE
GMT 15'24713* May 31 15 21954 "0N d IQ. n E
155104593701 corr. (+)0/1 (+)0/3 AE 7:8
24^13* 6903/3 d 21%4'1N M T -
GHA 51?40/4 Mc P.
GRICE? oN hs 87347
GPA, 51%40'4 W Ho 87?42'8
radius 137250 Z 251762

Answer.—1224 fix: L 20%09/0N, x 50%06:0W.

The plot of this problem is shown in figure 2011. No significant error would be
introduced by assuming the same declination and sextant altitude correction for both
observations, and a change of GHA equal to the are equivalent of the time difference
between observations (art. 1904). In east longitude the GP longitude would be
360°—GHA.

Problems

2002a. The GHA is 51%47/3.

Required.—The LHA and t at (1) long. 138°14/1 W, and (2) 65%11/7E.

Answers.—(1) LHA 273?33'2, t 86%26/8E; (2) LHA 116°59/0, t 116%59'0W.

2002b. The GHA is 135%17'3.

Required.—The LHA, t, and AP for use with H.O. Pub. No. 214 without interpola-
tion for t or L, if the DR position is (1) lat. 71%36/9 N, long. 137%25/3W, and (2)
lat. 8214/15, long. 96?41'7 E.

Answers.—(1) LHA 358°00/0, t 290010 E, aL 72?00:0 N, ad 137%17'3 W; (2) LHA
232°00/0, t 128°00/0B, aL 8700/05, ad 96%42'7 E.

SIGHT REDUCTION 515
52* W 51°W 50° W 49°W

GP, 22°N
Q GP

aw | Sg

BON eegent da, Gi Zut ee kā 20°N
52*W 51*W 50*W 49*W

FicurE 2011.—Plotting high-altitude observations.

2004. Find computed altitude (Hc) and azimuth (Zn) if aL is 42°00/05, d is
21%09/5N, and t is 11?00:0 E.

Answers.—He 26°01'6, Zn 01174.

2005. Find computed altitude and azimuth if aL is 41°00°05, d is 20°49/1S, and
tus 37?11:3 W.

Answers.—Hc 52°40/1, Zn 29193.

2006. Find computed altitude and azimuth if aL is 41%53/4N, d is 19%45/8S,
and t is 189127 W.

Answers.—He 26°05/1, Zn 198°8.

2007. Find the azimuth by interpolation if L is 41%33/7 N, d is 2018/75, and t is
56?40:5 E.

Answer.—Zn 12775.

2008a. On June 1, 1958, the 0425 DR position of a ship is lat. 41?07:3 N, long.
153903/9E. At GMT 18'25"16* (May 31) the navigator observes Saturn with a ma-
rine sextant having no IC, from a height of eye of 30 feet. The hs is 9%13:4.

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad only) and the Nautical
Almanac.

Answers.—a 2.0 A, Zn 230?3, aL 41°00’N, a^ 152?48:6 E.

2008b. On June 2, 1958, the 0625 DR position of a ship is lat. 40?38'18, long.
24908/3E. At watch time 6^24748* am the navigator observes the upper limb of the
moon with a marine sextant having an IC of (—)2:7, from a height of eye of 56 feet.
The watch is 19° slow on zone time. The hs is 147388.

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad, At) and the Nautical

Almanac.
Answers.—a 7.1A, Zn 257°9, aL 41°00/08, a^ 24?08:3 E.

516 SIGHT REDUCTION

2008c. During the morning of June 2, 1958, the 1025 DR position of a ship is `
lat. 4191238, long. 13%45/7W. At GMT 11"25"42 the navigator observes the lower
limb of the sun with a marine sextant having an IC of (+)1/0, from a height of eye
of 38 feet. The hs is 23?37:3.

Required—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad, At, AL) and the
Nautical Almanac.

Answers.—a 16.5 T, Zn 022?3, aL 41°12'3S, a^ 13%45:7 W.

2008d. During evening twilight on June 1, 1958, the 2100 DR position of a ship
is lat. 40°47/3N, long. 67%28/7W. At ZT 21"08"01* the navigator observes Arcturus
through a break in the clouds, with a marine sextant having no IC, from a height of
eye of 42 feet. "The hs is 65?31'8.

Required.—The a, Zn, and AP, using H.O. Pub. No. 214 (Ad only) and the Ai
Almanac.

Answers.—a 7T, Zn 146?8, aL 41?00' N, ad 67°33’ W.

2009. On June 3, 1958, the 0625 DR position of a ship is lat. 41?03'78, long.
104%25/6E. The navigator plans to observe the upper limb of the moon at this time
with a marine sextant having no IC, from a height of eye of 57 feet.

Required.—(1) Precomputed altitude by H.O. Pub. No. 214 (Ad, At, AL). (2)
The a, Zn, and AP if hs is 19?09:8. Use Nautical Almanac.

Answers.—(1) Hp 19%0711;(2)74112.7 T, Zn 26176, aL 41°0377S, aX 10472550 BI

2010a. On June 2, 1958, the 0725 DR position of a ship is lat. 45%07'3S, long.
48°05'8E. At GMT 4"25"21* the navigator observes the lower limb of the sun shortly
after the upper limb disappears behind an overcast, soon after sunrise. He uses a
marine sextant having an IC of (4-) 1:2, and makes his observations from a height of
eye of 35 feet. The hs is 0%45:2, air temperature 30°F, and the atmospheric pressure
29.74 inches. The sun bears approximately 050°.

Required.—The a, Zn, and AP using H.O. Pub. No. 214 (Ad only), the Nautical
Almanac, and tables 23 and 24.

Answers.—a 289.1A, Zn 053°8, aL 42°00/0S, ad 53°06/0E.

2010b. If Hc is 590912 and Ho is (—) 0?03/4, find a.

Answer. 591216 A, or 312,64.

2010c. If He is (—)0?18:4 and Ho is (—)0%01/3, find a.

Answer.—a 17.1 T.

2011. On June 2, 1958, the 1225 DR position of a ship is lat. 23%47/8N, long.
130%13/2E. The ship is on course 200°, speed 20 knots. Using a marine sextant
having an IC of (—) 2/2, the navigator observes the lower limb of the sun twice, from
a height of eye of 43 feet. The first observation is made at GMT 3^107355, and hs is
87%34"8. The second observation is made at GMT 3°25™108, and hs is 87?13/4. The
GHA of the sun at GMT 3*10"35* is 228°12’6. Assume no change in declination
between observations.

Required.—The GP at the time of each observation, the radius of each circle of
position, and the 1225 fix.

Answers.—GP L, 22%6/5N, GP X, 131%47'4 E, "GPL, 1229065 Ny GP
128%08'7 E; radius; 137.9 mi., radius, 159.3 mi.; 1225 fix: L 23%52'5N, 130°17/1 E.

| CHAPTER XXI
COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

2101. Introduction.— Before the development of a means of determining accurate
time at sea (art. 127), longitude could not be found by celestial observation. Celestial
bodies were used for determination of latitude, and as an indication of direction, often
in a very general way. 'The development of the marine chronometer opened up a
whole new vista to the navigator. Immediately, methods began to appear to utilize
this new dimension of navigation. During the two centuries that have elapsed, many
of the best minds have been directed to the problem of providing easier or more adequate
methods of “reducing” the observations to a form suitable for determination of position.

2102. Kinds of methods.—Various "special" methods have been devised to take
advantage of some unique relationship to provide a simplified solution. The most
widely used are latitude methods for determination of latitude by meridian altitude
or observation of Polaris, and longitude methods for determination of longitude by
observation of a body near the prime vertical. Both latitude and longitude methods
have now been largely superseded by the altitude method, based upon the discovery
of the altitude difference, or intercept, by the Frenchman Mareq St.-Hilaire (art. 131).
Most modern methods are of this type, although some latitude and longitude methods
are still in use.

The most commonly used methods utilize computation for determining certain
information which is then plotted as a line of position, two or more such lines being
needed for a fix. The “method” might consist of one or more formulas to be solved
by general mathematical tables, a set of special tables conveniently arranged for use
with the formulas, or a set of tables constituting a list of computed answers. A method
which determines latitude or longitude separately requires no plot. In fact, a plot
would be misleading unless the celestial body were almost exactly on the celestial
meridian or prime vertical, or unless the azimuth were considered. While a number of
methods determine latitude and longitude by computation, without plotting, other
methods substitute a graphical or mechanical solution for computation.

2103. Meridian altitudes.—If a celestial body is on the celestial meridian at the
time of observation, a modification of the high-altitude method (art. 2011) can be used
at any altitude, without plotting the GP. Both GP and observer are on the same
meridian, and the difference of latitude between them is the zenith distance of the body
(909— Ho). The direction of the GP is the direction faced during observation (unless
a backsight is made). "The line of position is a latitude line.

Example 1.—At GMT 16"24715* on June 2, 1958, the navigator observes the lower
limb of the sun on the celestial meridian, bearing north. He makes the observation
with a marine sextant having an IC of (+) 2:6, from a height of eye of 33 feet. The hs
is 29%14:6.

Required.—The latitude.

517

518 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Solution.—

June 2 Sun 2209 =

GMT 16524715* June 2 1622107 wa IC 2:6
corr. (+)0/1 (+)0/3 D 5/6

GP L 22%10/8N d 22210/8N © 14/3
l 60°34/1S sum 16/9 5:6
L 88823495 COIT. (+) 11:3
hs 29°14'6
Ho 29259
Z 60°34/1

Since the observer faces north, he is south of the GP. The GP latitude is equal to
the declination, and the difference of latitude is equal to the zenith distance of the body.
Since the body is known to be over the meridian, a knowledge of the longitude is not
needed. Neither is a knowledge of the approximate latitude of the observer needed,
but this information is useful, as it provides a check to prevent a gross error. Also, it
can serve as the basis for precomputation, most of the solution being made before
observation. The time is needed only for determining declination. If the body is
observed at lower transit, the latitude is equal to observed altitude (Ho) plus polar
distance (p=90°—d) of the body: L=Ho +p.

If an observation is made near but not exactly at meridian transit, it can be solved
as a meridian altitude, with one modification. Enter table 29 with the approximate
latitude of the observer and the declination of the body, and take out the altitude
factor (a). This is the difference between meridian altitude and the altitude one minute
of time later (or earlier). Next, enter table 30 with the altitude factor and the difference
of time between meridian transit and the time of observation, and take out the correc-
tion. Add this value to Ho if near upper transit, or subtract it from Ho if near lower
transit. Then proceed as for a meridian altitude, remembering that the value obtained
is the latitude at the time of observation, not at the time of meridian transit. This
method should not be used beyond the limits of table 30 unless reduced accuracy is
acceptable. This process is called reduction to the meridian, the altitude before
adjustment an ex-meridian altitude, and the observation an ex-meridian observation.
It requires knowledge of the meridian angle, which depends upon knowledge of longitude.
If reasonable doubt exists regarding the longitude, the azimuth of the body at the time
of observation should be determined, and the line of position drawn perpendicular to it
(through the point defined by the “observed” latitude and the assumed longitude),
rather than as a latitude line. There are alternative methods available. A correction
to latitude can be applied, using the factor f from table 26. In 1899 A. A. Vilkitskiy, a
captain in the Russian Navy, developed a mechanical device for determining the cor-
rection to be applied for reduction to the meridian.

Several hundred years ago, when longitude could not be found accurately, and
logarithms had not been invented, the finding of latitude furnished the only reliable
navigation available on long sea voyages. Since most of these were in a generally
easterly or westerly direction, it became common practice to sail first to the latitude of
destination (“run down the latitude”) and then to follow this parallel until landfall was
made. The meridian observation of the sun at local apparent noon was the most
important navigational event of the day, and became a well-established routine. On
the basis of this observation at “high noon,” clocks were reset, and a new day, the
nautical day, began. intentional meridian altitudes of other celestial bodies were not
as widely used as those of the sun.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 519

As accurate time became available at sea, and then more convenient tables and
more accurate almanacs appeared, the noon sight lost its importance. Since the modern
inspection table has been available, the use of meridian altitudes has decreased rapidly,
and reduction to the meridian has all but disappeared. True, the solution of a meridian
altitude is simple and quick, but this is more than offset by the need for determining the
time at which to make the observation (art. 2104), the dislike of many mariners for
having to make an observation at a predetermined time, the inconvenience sometimes
experienced when local apparent noon occurs at a time when other activities conflict
with observation, and the possibility of missing the observation because of overcast
conditions. The practice of observing a body when a line of position is desired, and
solving those which happen to have a meridian angle of 0° or 180° in the same manner
as other observations, is a growing practice that eliminates the need for remembering a
separate procedure for bodies on the celestial meridian. The modern navigator thinks
primarily in terms of lines of position, rather than of latitude and longitude observations.

Example 2.—On June 2, 1958, the 1225 DR position of a ship is lat. 41?21:2 S,
long. 127207:3 W. At GMT 20*25%48* the navigator observes the lower limb of the sun
with a marine sextant having no IC, from a height of eye of 40 feet. The hs is 26°20/1.

Required.—(1) The a, Zn, and AP, using H.O. Pub. No. 214 (Ad only) and the
Nautical Almanac.

(2) The latitude at the time of observation.

Solution.—
June 2 Sun + Q —
GMT 20*25748* June 2 DUI ONSE IC — ==
20 120 32.1 corr. (+)0/1 (+)0:3 D 6:1
25249 Al) d 22212 TIN Cat Aal
GHA 126°59/1 sum 14/1 6/1
ar 126%59/1 W corr. (+) 8/0
LHA 09?00:0 hs 26°20/1
t 090010 Ho 26?28'1
(11822512 IN aia
aL 41%00/0S
ht 27°00/0 Ad (—)1.0 Z 8180?0 (E or W)
corr. (—) 12/1
He 26479
Ho03268-23*1
(Da . 198A aL 41°00/0S
Zn 000?0 an 126°59'1 W

(2 L 41°19/8S

Since the azimuth is 000°, the line of position is a latitude line. It is 19:8 south
(away from 000°) of the assumed latitude of 41°00°0, or latitude 41?19'8 S. i

When Ad is 1.0, the altitude changes one minute for each one minute change of decli-
nation. Therefore, the correction to ht is numerically equal to d diff. For this reason,
no entry is given in the “multiplication table” for a A value of 100 (1.0). A A value
of 1.0 should not be confused with one of 0.01 or 0.10.

2104. Finding time of meridian transit.—If a meridian altitude is to be observed,
other than by chance, a knowledge of the time of transit of the body across the meridian
is needed. í

On a slow-moving vessel, or one traveling approximately east or west, the time
need not be known with great accuracy. The right-hand daily page of the Nautical

520 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Almanac gives the GMT of transit of the sun and moon across the Greenwich meridian
(approximately LMT of transit across the local meridian) under the heading “Mer.
Pass." In the case of the moon, an interpolation should be made for longitude. This
is performed in the same manner as finding the LMT of moonrise and moonset (art.
1812). In the case of planets, the tabulated accuracy is normally sufficient without
interpolation. The time of transit of the navigational planets is given at the lower
right-hand corner of each left-hand daily page of the Nautical Almanac. The tabulated
values are for the middle day of the page. These times are the GMT of transit across
the Greenwich meridian, but are approximately correct for the LMT of transit across
the local meridian. Observations are started several minutes in advance and continued
until the altitude reaches a maximum and starts to decrease (a minimum and starts
to increase for lower transit). The greatest altitude occurs at upper transit (and the
least at lower transit). This method is not reliable if there is a large northerly or
southerly component of the vessel’s motion, because the altitude at meridian transit
changes slowly, particularly at low altitudes. At this time the change due to the vessel’s
motion may be considerably greater than that due to apparent motion of the body
(rotation of the earth), so that the highest altitude occurs several minutes before or
after meridian transit.

If the moment at which the azimuth is 000° or 180° can be determined accurately,
the observation can be made at this time. However, this generally does not provide
a high order of accuracy.

If the longitude is known with sufficient accuracy, the time of transit can be
computed. A number of methods of computation have been devised, but perhaps the
simplest is to consider the GHA of the body equal to the longitude if west, or 360%—X
if east, and find the time at which this occurs.

Example.—Find the zone time of meridian transit of the sun at longitude 156°
44:2 W on May 31, 1958.

Solution.—
May 31
A 156?44:2 W
GHA 156°44/2
22 150?36/4
24™318 as
GMT 2224"31* May 31
ZD (+)10 (rev.)
ZT 12^24m3]*

This solution is the reverse of finding GHA. The largest tabulated value of
GHA that does not exceed the desired GHA is found in the tabulation for the day, and
recorded, with its time. The difference between this value and the desired GHA is
then used to enter the “Increments and Corrections" table. The time interval cor-
responding to this value is added to the time taken from the daily page. If there is a v
correction, it is subtracted from the GHA difference before the time interval is deter-
mined. For such bodies, the Air Almanac solution is easier, but not as precise by a
fraction of a second of time. The GMT can be converted to any other kind of time
desired. If the Greenwich date differs from the local date at the time of transit (for
the sun this can occur only near the 180th meridian), a second solution may be needed.
This possibility can often be avoided by making an approximate mental solution in
advance. As the basis for this approximate solution, it is convenient to remember that
the GMT of Greenwich transit (GHA 0°) is about the same as the LMT of local transit.
To find the time of transit of a star, subtract its SHA from the desired GHA to find the

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 521

desired GHA Y. Determine the time corresponding to GHA T, as explained above for
the sun.

Aboard a moving vessel, the longitude at transit usually depends upon the time
of transit. An approximate mental solution may provide a time sufficiently close.
In the absence of better information, use ZT 1200 for thesun. Find the time of transit
for the position at this time, and then make an adjustment, if necessary, for the sun
between 1200 and the time found by computation. This adjustment is equal to four
seconds for each minute of longitude involved. If the ship is west of the 1200 position
at the computed time of transit, add the correction; and if east, subtract it. For high
accuracy a second adjustment may occasionally be needed, but this is seldom justified
because of the uncertainty of the vessel’s position.

The time of transit of the sun can also be found by means of apparent time (art.
1912). Meridian transit occurs at LAT 12^00"00*. This can be converted to any
other kind of time desired.

2105. Latitude by Polaris.—Another special method of finding latitude, available
in most of the northern hemisphere, utilizes the fact that Polaris is less than 1° from
the north celestial pole. As indicated in
article 1432, the altitude of the elevated A
pole above the celestial horizon is equal to
the latitude. Since Polaris is never far from
the pole, its observed altitude (Ho), with
suitable corrections, is the latitude.

Three corrections are commonly applied.
The first, and principal one, is illustrated in
figure 2105. In this figure, P is the north
celestial pole, and the circle is the path fol-
lowed by Polaris as it circles the pole daily.
When Polaris is directly above the pole, at
A, on the upper branch of the celestial merid-
ian, the polar distance (90°—d) is subtracted
from Ho to obtain latitude. At B, on the

lower branch of the celestial meridian, this 3
value is added. At C and C”, with meridian |
angle approximately 90? E or W (see below), Figure 2105.— Latitude by Polaris.

there is no correction. At any other point,

such as D, the correction is between these extreme values, being equal to the polar
distance multiplied by the cosine of the meridian angle (approximately). This is
shown at D'P.

The second correction corrects for the tilt of the diurnal circle of Polaris with
respect to the vertical. Refer again to figure 2105. Zero correction occurs at C and
©’, when Polaris is at the same altitude as the north celestial pole. Thus, point C,
P, and C’ are all on a parallel of altitude, which is a small circle everywhere the same
angular distance above the celestial horizon. However, a meridian angle of 90*E
or W occurs when Polaris is on an hour circle 90? from the celestial meridian. "These
90? hour circles are not horizontal, like the circle of equal altitude, but are tilted down-
ward toward the celestial horizou, which they cross at the prime vertical. "Therefore,
these 90° hour circles (EPE/) do not intersect the diurnal circle of Polaris at C and
C' but at E and E”, which are at a lower altitude than the pole. "The discrepancy
between these points (C-E and C'-E") increases as the latitude increases from zero
at the equator to a maximum at the pole.

522 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The third correction is needed because Polaris, being near the celestial pole, has a
relatively large change in coordinates due to precession of the equinoxes (art. 1419)
and aberration (art. 1417). The correction is the difference between actual coordi-
nates and those used for the first correction.

In the Polaris correction tables of the Nautical Almanac, a constant is added to

n

each correction so that all tabulated values are positive. The sum of the constants is |

1°. Therefore, this value (1°) is subtracted from the result. The table at the top of
each Polaris correction page is entered with LHA Aries, and the first correction (do)
is taken out by single interpolation. The second and third corrections (a; and as,
respectively) are taken from the double entry tables without interpolation, using the
LHA Aries column with the latitude for the second correction and with the month
for the third correction. |

Example.—During morning twilight on June 2, 1958, the 0525 DR position of a
ship is lat. 15%43/6N, long. 110°07/3W. At watch time 5"24749* am the navigator
observes Polaris with a marine sextant having an IC of (—)3'0, from a height of eye
of 44 feet. The watch is 23° slow on zone time. The hs is 1692410.

Required.—The latitude.

Solution.—
June 2 Polaris + + —
W 59247495 AM + Se IC 3:0
WE (S) 23* 05 Oo a D 6:4
ZT 525123 di US *-P DEO
ZD (+)7 (02 U3 sum (—) 1217
GMT 1225512" June 2 add” 60/0 corr. (=) 1217
205 7099740 sum 33:8 60/0 hs 16 2170
252125 691910 corr. (—) 26/2 Ho TO 11:4

GHAT 76°46/0
A 1102073 W
LHA Y B20 Saar
Ho 162113
corr. (—) 26:2
L 15945 ^N

Since LHA T is an entering value in all three correction tables, and since this is
affected by the longitude, other observations, if available, should be solved and plotted
first, to obtain a good longitude for the Polaris solution. For greater accuracy, par-
ticularly in higher latitudes, and especially if considerable doubt exists as to the longi-
tude, it is good practice to find the azimuth of Polaris and draw the line of position
perpendicular to it, through the point defined by the latitude found in the computation
and the longitude used in the solution. The azimuth at various latitudes to 65% N is
given below the Polaris corrections. This table can be extrapolated to higher latitudes,
but Polaris would not ordinarily be used much beyond latitude 65°. In the example
given above the azimuth is 000?9.

The Air Almanac provides only the first correction, which it designates Q.

Polaris observations can be solved like those of other celestial bodies, using the dec-
lination and SHA given in the tabulation near the back of the Nautical Almanac, if a
method of solution providing for such a high declination is available. H.O. Pub. No.
214 is not designed for solution of Polaris observations.

Like other special solutions, latitude by Polaris has lost much of its popularity since
modern inspection tables have become available. Being of magnitude 2.1, Polaris
is not a bright star. It is normally considered available to the mariner only during
twilight, when the azimuths of various celestial bodies relative to each other are of

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 523

more interest than an “easy” solution which is little, if at all, simpler than the usual
solution by inspection table. If provision were made for solution of Polaris sights by
inspection table, the special method would no longer be needed for ordinary navigation.

2106. Longitude methods.—A celestial observation for a line of position, whether
reduction is to be by longitude method or by latitude method, consists of measurement.
of the altitude of a body with the noting of the time. If sight reduction is to be by the
longitude method, the latitude must be known, or the best estimate used. With
altitude, latitude, and declination (from the almanac), one is able to solve the naviga-
tional triangle (art. 1433) for meridian angle. This is converted to local hour angle.
The Greenwich hour angle at the time of observation is determined by means of the
almanac. The difference between the GHA and LHA is the longitude. A time dia-
gram (art. 1427) is useful in establishing the correct relationship.

Longitude can also be determined by establishing the exact time of meridian
transit, at which time the GHA (or 360°—GHA) is the longitude (art. 2104).

If the latitude is known accurately, the longitude method provides a direct and
relatively simple solution for position. However, since latitude is rarely known to
the desired accuracy, a line of position is usually needed. This is obtained by either
(1) solving for longitude at two or more assumed latitudes, and drawing a straight
line through the points thus found (the Sumner method), or (2) solving for longitude
at one point, determining the azimuth at this point, and drawing the line of position
through the single point thus found, perpendicular to the azimuth of the body.

The error introduced in the computed longitude as a result of an inaccurate latitude
used in the solution increases as the celestial body departs from the prime vertical.
If it is learned that an incorrect latitude has been used in the solution, a correction
can be applied, using the factor F from table 26. If the body is near the celestial merid-
ian, a small error in the latitude introduces a large error in the longitude. At any
location, the azimuth of the body can be determined by observation or computation,
and a line of position drawn perpendicular to it, through the position defined by the
latitude used in the computation, and the calculated longitude. Alternatively, solution
can be made at two or more latitudes, and the line of position drawn through the two
positions. It was the use of this second method in 1837 by Captain Thomas H.Sumner,
when his latitude was in doubt, that led to the discovery of the line of position from
celestial observation (art. 131).

No longitude method is more accurate than the GMT used for timing the observation.
Before chronometers (art. 1514) and time signals (art. 1909) were available, relatively
few navigators attempted to determine longitude, and it was never established reliably.
The search for a method of “discovering” longitude at sea was primarily a search for a
means of determining time at the Greenwich meridian (arts. 126, 127).

If the longitude is to be determined, most accurate results are obtained by ob-
servation of a body on the prime vertical. The observation having been made, sight
reduction can be made by time sight or, more conveniently, by an ordinary solution
for a line of position, using an inspection table such as H.O. Pub. No. 214. Any general
method of sight reduction can be used, without need for a special solution. Å

Solution by the longitude method is usually called a time sight. The various
longitude methods are all basically the same, differing only in choice of formulas and
arrangement of tables. The basic formula is
sin h—sin L sin d

cos L cos d

3 em

in which t is the meridian angle, h is the altitude, L is the latitude, and d is the declina-
tion. Early tables for solution of meridian angle were called horary tables.

524 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The time sight came into use following the development of the marine chronometer `

in 1763. Solution for meridian angle is usually by the formula

hav t=sec L csc p cos s sin (s—h),

in which p=90°—d if L and d have same name, and 90%+d if L and d have contrary

names; and s=% (h+L-+p).
When azimuth angle is used with the method, it is usually computed by one of the
formulas
sin Z=sin t cos d sec h
or
hav (180%—Z)=sec h sec L cos s cos (s— p).

There are no rules with this method, but it is subject to possible large errors in
high latitudes or if the body has a high declination. "Various special tables have ap-
peared for solution of the time sight:

Cassini. The first “inspection tables" were probably prepared by M. Cassini, a
Frenchman, in 1770. These “horary tables" provided tabulated solutions for meridian
angle.

Lalande. The horary tables prepared in 1793 by Jerome Lalande, a Frenchman,
provided tabulated solution for meridian angle for the sun and stars for all latitudes
to 61°.

Lynn Horary Tables, by Thomas Lynn, a commander of the East India Company
Service, were published in 1827. These 242-page tables consisted of tabulated solutions
of meridian angle computed by the time sight formula. Two years later they were
followed by a volume of 364 pages of azimuth angle (Lynn Azimuth Tables) computed
by the haversine azimuth formula. Entries are given for whole degrees of latitude to
60°, declination to 24°, end altitude to 60° (later 90°). The tables are accurate and
well arranged, but the triple interpolation is tedious.

Hommey. Louis Hommey’s Table d’angles horaires (horary tables), published in
two volumes in France in 1863, contained more than 40,000 hour angles calculated for
“all latitudes.” These tables were an improvement on those of Cassini and Lalande.

Martelli. In 1873 a small volume of 49 pages by G. F. Martelli, an Italian, was
published in New Orleans. This book, called simply Tables of Logarithms, provided a
relatively short, fast solution for meridian angle, with very few rules and only one
interpolation. Martelli abandoned the inspection table and provided five short tables
for a four-place logarithmic solution by the formula

cos (L=d)—cos z

ad 2 cos L cos d

Solution reguired six book openings, six table entries, and four mathematical steps.
Hour angles were given only to eight hours, and no provision was made for azimuth.
This method proved very popular, and is still used among navigators of several
countries. A 1932 edition was published in Glasgow, Scotland, with explanations in
French, Dutch, Italian, and Spanish, as well as in English. A 1944 edition added
provision for finding azimuth angle, and for solution by the altitude method.
Thomson. A table of only nine pages by Sir William Thomson, better known as
Lord Kelvin, was published in London in 1876 to provide a solution for the longitude
method. This very thin volume, called Tables for Facilitating Sumner's Method at Sea,
contains the first known solution by dividing the navigational triangle into two right
triangles. In 1849 Towson (art. 2126) had divided the triangle in the same manner,
but his solution was for reduction to the meridian. Lord Kelvin divided the triangle
by dropping a perpendicular from the celestial body to the celestial meridian of the

AA A

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 925

observer, as shown in figure 2111. He used a for the length of the perpendicular v,
b for x, and b’ for w (of fig. 2111). His solution uses the formulas

m sin a
sin t= ;
os d

sin d

cos b= ,
cos a

The tables are entered with half the colatitude (using colatitude to the nearest
whole degree) in column b. With a pair of dividers, search is made in the “cohypo”
column for two numbers, one agreeing with the altitude, and the other with the dec-
lination. The number in column A opposite the altitude in the cohypo column is the
azimuth angle, and that opposite the declination is the meridian angle, interpolation
being used if needed. The line of position is adjusted for the difference between the
interpolated altitude and the observed altitude.

Although the tables are among the shortest of the various methods, their manipula-
tion is difficult. In 1880 Kortazzi, a Russian astronomer, attempted to modify the
tables to provide an easier solution, but without great success.

Davis’ Chronometer Tables, providing a solution for the longitude method, were
published in 1897 in London. They are similar to Lynn's tables, using his values but
providing assistance in interpolation by adding values of change with latitude, declina-
tion, and altitude. As with Lynn, a separate volume is given for azimuth angle, in
which there is no interpolation. Originally Davis’ tables were limited to latitude 50°
and declination 24°, but later tables were published for declinations 23° to 64°.
A limited number of altitude entries is given.

Blackburne. Tables by H. S. Blackburne, a New Zealander, were published in
London in 1914 under the title The Excelsior Azimuth and Position Finding Table.
The tables, providing a solution by the longitude method, are similar to Lynn Horary
Tables and Davis’ Chronometer Tables but with a new determination of azimuth based
upon the ratio of variation of latitude to variation of meridian angle. Azimuth angles
(ten pages) are given in a separate tabulation in the same volume with meridian angles
(242 pages).

Blackburne’s arrangement is more modern than that of Davis. This was the
first publication to include columns for variations of t for 1’ of declination, latitude,
and altitude. Meridian angles are given to 0*1. Latitude is limited to 30°, and
declination to 23°.

Rust. In 1918 the Practical Tables for Navigators and Aviators, by Captain
Armistead Rust, USN, were published in Philadelphia. This small volume of 37 pages
of tables reverted to a logarithmic solution, as did Martelli’s, using the following formula
for determining meridian angle:

log hav t=log sec L+log sec d+log } [cos (L=d)—sin h].

The volume has three tables. Table A tabulates log secants for obtaining the
first two terms of the formula. Table B is a double-entry table giving log [cos (Ld)
—sin h]. Table O gives log haversines. Values are given to four places.

Azimuth angle is obtained from an original diagram computed from the well-known

formula
sin Z=sin t cos d sec h.

526 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

This diagram had been given in a volume of ex-meridian tables by Rust published in

1908. Inthe Practical Tables an auxiliary diagram was added to indicate the meridian
angle when the celestial body is on the prime vertical. The purpose of the diagram is to
resolve possible ambiguities when the azimuth angle is near 90°. The Rust azimuth
diagram was used later by Goodwin and Weems, and in the Italian Tavole H (art. 2110).

Goodwin. The Alpha, Beta, Gamma Navigation Tables of H. B. Goodwin, an
Englishman, were first published in London in 1921. This is a small volume having
two tables with a total of 34 pages. Meridian angle is found from the formula

_Cos (L~d)—cos z

ver t
cos L cos d

Table I has two values, o being the angle in seconds of arc, and 8 being four-place
natural cosines multiplied by 1,000 to eliminate the decimal. Table II provides 7,
the logarithms for the values of versine t.

The Rust diagram is used for determining azimuth angle.

Instructions are included for use of the tables for altitude method of solution,
and for reduction to the meridian.

H.O. Pubs. Nos. 203 and 204 (Littlehales), The Sumner Line of Position of Celestial
Bodies, were published by the U. S. Navy Hydrographic Office in 1923. These tables,
prepared by George W. Littlehales, provide in two large volumes (847 and 675 pages,
respectively) tabulated solutions of the meridian angle and azimuth angle, using the
general time sight formulas. The arrangement is similar to that of Davis and Black-
burne, but t and Z are tabulated together in consecutive columns. Latitude is limited
to 60°, and declination to 27° in H.O. Pub. No. 203 and to 64° in H.O. Pub. No. 204.
Interpolation for latitude is avoided by using the nearest whole degree, and shifting
the line of position for the difference between the altitude at this latitude and the
observed altitude.

These publications are no longer in print.

Soule and Dreisonstok. In 1932 these two Americans prepared a small volume
providing a logarithmic solution of the longitude method, using the formulas

1 secs csc (s—h)
hav t sec L esc p

and
1 . Sec s sec (s— p)
hav (180%—Z) ` sec Lsech ’

where s=% (h+L+p) and p=90°+d.

The “azimuth” determined in this way is the direction of the line of position
(43:90?) rather than that of the celestial body.

Weems' Secant Time Sight was published in 1944 by Captain P. V. H. Weems,

USN (Ret.), to provide a short solution based entirely upon secants and cosecants,
using the formulas

sec s esc (s—h)

2.17
GE
sec L sec d
and
esc t sec d
csc T= a,
sec h

where s=% (h+L+p). A Rust azimuth diagram is included for those who prefer a
diagrammatic solution.

2107. Finding time on prime vertical.—Best results by time sight are obtained
when the celestial body is on the prime vertical. As explained in article 1432, a celestial

48 ^ AAA u^

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 527

body having a declination of opposite name to the latitude crosses the prime vertical
below the horizon. Its nearest visible approach is at the time of rising and setting.
E If a celestial body has a declination of the same name as the latitude, but is numer-
ically greater, it does not cross the prime vertical. Its nearest approach (in azimuth)
is at the point at which its azimuth angle is maximum. At this point the meridian
angle is given by the formula |

sec t=tan d cot L,
and its altitude by the formula

esc h=sin d esc L.

A celestial body having a declination of the same name as the latitude, and numer-
ically smaller, crosses the prime vertical at some point before it reaches the celestial
meridian, and again after meridian transit. At these two crossings of the prime
` vertical, the meridian angles are equal and are always less than 90%. "They are given
by the formula

cos t—tan d cot L.

The altitudes are also equal, and are given by the formula
sin h=sin d csc L.

Meridian angle and altitude of bodies on the prime vertical, and similar data for
the nearest approach (in azimuth) of those bodies of same name which do not cross the
prime vertical, are given in table 25 for various latitudes, and for declinations from 0? to
23?, inclusive. Similar information can be determined by means of H.O. Pub. No.
214, entering with latitude and declination, and finding the meridian angle and altitude
corresponding to an azimuth angle of 90? (or the maximum azimuth angle for nearest
approach). Since this information is generally not required to great accuracy, inter-
polation is not needed.

To find the time of crossing the prime vertical, convert t to LHA, and add west
longitude or subtract east longitude to find GHA. The GMT at which this GHA occurs
can be found, as explained in article 2104, and converted to any other time desired.

Example.—Determine (1) the approximate zone time, and (2) the approximate
altitude of the sun when it crosses the prime vertical during the afternoon of May 30,
1958, at lat. 51°32/3 N, long. 160°21/7 W, using table 25 and the Nautical Almanac.

Solution.—
May 30
t 7176 W (from table 25)
LHA 71?6
A 160°4 W
GHA 232?0
527 7220.0
26” 6:4

GMT `` 0326 May 31
ZD(+)11 (rev.
(1) ZT 1626 May 30
(2) h 28?4 (from table 25)

At the time of crossing the prime vertical, or at nearest approach (in azimuth), a
celestial body is changing azimuth slowly, and therefore this is considered a good time
to check compass deviation or to swing ship.

The prime vertical at any place is the celestial horizon of a point 90? away, on the
same meridian. "Therefore, a celestial body crosses the prime vertical at approximately

528 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

the same time it rises and sets at the point 90° away. ‘Thus, if one is at latitude
35° N, the sun crosses his prime vertical at about the same time it rises or sets at `
latitude 55? S. If time of sunrise and sunset are to be obtained accurately by this
method, corrections must be applied for semidiameter and refraction.

2108. Altitude methods, like longitude methods, require an accurately timed `
observed altitude of a celestial body. Usually, in both types of solution, the naviga-
tional triangle is solved, but in the altitude method, t, d, and L are used in solving for -
altitude. The method is based upon the concept of circles of equal altitude explained `
by Commander Marcq St.-Hilaire, a Frenchman, in 1875 (art. 131). For this reason
it is often called the Mareq St.-Hilaire method. It may also be called the altitude
intercept method because it uses the difference between computed and observed alti- :
tudes, a value sometimes called an altitude intercept.

The altitude method has largely replaced the latitude and longitude methods,
although some navigators still prefer the older methods. The principal advantage of
the altitude method is that it provides a universal solution that is equally reliable in
all latitudes, with all values of declination, and with all values of meridian angle.
Even for observations of celestial bodies near the zenith the altitude method is appli-
cable, although in this case an arc of the circle itself is plotted, without the use of the
altitude difference (art. 2011). However, the formulas selected for some of the “short
methods" do impose some limitations when those methods are used.

For many years following introduction of the altitude method, the concept was
termed the “new navigation," an expression now seldom heard. At first, an attempt
was made to adapt existing tables to the altitude method. Some were more readily
adaptable than others. In due course, various methods designed for use with the
altitude method made their appearance. These methods may be grouped in six classi-
fications: those which do not divide the triangle, those which divide it by dropping a
perpendicular from each of the three vertices, those which do not use the navigational
triangle, and the modern “inspection table." However, not all inspection tables are
for altitude methods. In practice, the dropping of a perpendicular from the pole has
not been used except in great-circle sailing (art. 822). This would result in dividing
both the meridian angle and zenith distance into two parts, a condition that has not
proved attractive.

2109. Altitude methods, triangle not divided.— The basic formula for solution of
the undivided navigational triangle is

sin h=sin L sin d + cos L cos d cos t,

derived from the law of cosines. A number of special tables have been prepared for
solution of the undivided triangle:

Davis' Requisite Tables, published in London in 1905, introduced the cosine-

haversine formula to navigation, although it had been used previously by astronomers.
This formula is

hav z—hav (Ld) --cos L cos d hav t,
in which z is zenith distance (90°—h). This is sometimes written
hav z=hav (L=d)+hav 6,
in which hav 6=cos L cos d hav t. It might also be written entirely in haversines:
hav z=hav (d—L)+hav t [hav (180°—L—d)—hav (d— L)].

In this formula the sign of d is reversed if L and d are of contrary name. "The haversine
of an angle is positive whether the angle is positive or negative.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 529

These tables were the first to give log haversines and natural haversines in one
table. j The method was little used at first, but later proved very popular, and as
haversines became available from additional sources, the formula was used even more
widely. Davis' original tables made no provision for azimuth.

Since the cosine-haversine formula can be used for solution with tables 33 and 34,
an example is given below, with solution of azimuth by the formula

sin Z=sin t cos d sec h.

Example.—A celestial body a little to the south of west is observed, with the
following results: t 80%45/9 W, aL 41%12/38, d 21°50/7S.

Required.—The Hc and Zn by the formulas given above.

Solution.—

t 80°45/9 W l hav 9.62300 lsin 9.99434
aL 4112/38 l cos 9.87643
d.21950/7 S l cos 9.96764 Leos 9.96764
0 — l hav 9.46707 n hav 0.29313
L~d 19?21/6 n hav 0.02827
z 69%04/3 n hav 0.32140
He;20%55''7 l sec 10.02964
Zn 25828 7578470 W lsin 9.99162

This is typical of logarithmic solutions, except that there are no “rules” for the
altitude computation. In this example the coordinates are the same as those of
example 3, article 2008, where solution is by H.O. Pub. No. 214, using Ad, At, AL.
The slight differences are due to the interpolation and rounding oft of different
quantities. As pointed out in article 2125, the formula used for azimuth angle does
not indicate whether the body is north or south of the prime vertical.

Ball. In 1907 Rev. Frederick Ball's Altitude or Position Line Tables were pub-
lished in London. There are two volumes of 244 and 240 (later 313) pages, respec-
tively, the first volume having tables for latitude 0° to 30°, and the second, 31° to
60° (later editions 24° to 60°). These were the first inspection tables for the altitude
method. The tabulated altitudes were computed by the haversine formula. The
assumed position is selected so that latitude and meridian angle are the nearest whole
degree, but no assistance is given for interpolation of altitude for declination.

Azimuth angle is not tabulated, being found by the altitude tables, interchanging
altitude and declination, and finding azimuth angle (in hours and minutes) in the
meridian angle columns. Since declination is limited to 24° in the first edition and
60° in later editions, this method is not available for azimuth if altitude is greater
than this amount. In this case azimuth angle is found by the formula
sec LXAh (for 8")

120 |

This formula had not previously been used in navigation.

Davis’ Alt-Azimuth Tables were published in London in 1917. This volume
lists both altitude and azimuth together for the first time. Latitudes included are
from 30° to 64°, and declinations from 0° to 24%. In 1921 a second volume was pub-
lished for latitudes 0° to 30°. Entries are for each whole degree of latitude and decli-
nation, and for each 4” (1°) of meridian angle. However, for each meridian angle,
altitude or azimuth angle is given alternately. Thus, azimuth angle is given for
meridian angles of 0™, 8", 16™, 24”, etc., and altitude for meridian angles of 4”, 12”,
207, 28", etc. Altitudes are given in bold type. All declination entries (0° to 24°)
are given on facing pages. Tables for latitude and declination of the same name are

sin Z=

530 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

given in the first part of the book and those for contrary names in the last part, the

^: o aut iret

two parts being separated by several auxiliary tables. Altitude is given to the nearest `
1’, and azimuth angle to the nearest 0?1. Altitudes are carried down to the horizon, `

and the local apparent times of sunrise and sunset are also given, with the azimuth
angle at these times. Because of the 8” interval between altitude entries, and the
use of an assumed position to avoid interpolation for change in meridian angle, large
altitude differences sometimes arise.

H.O. Pub. No. 201, Simultaneous Altitudes and Azimuths of Celestial Bodies,
was published by the U. S. Navy Hydrographic Office in 1919. In this volume of
606 pages, altitudes and azimuths were tabulated in parallel columns for the first time.
Latitude is limited to 60° and declination to 24°. Virtually all altitudes above the
horizon are included. The tables are well arranged and very legible, but no assistance
is given for interpolation of altitude or azimuth angle for a change of declination.
Meridian angles are given at intervals of 10" (2°5). Since the assumed position is
selected to avoid interpolation of altitude or azimuth for meridian angle, large altitude
differences result in some instances. This publication is no longer in print.

Yonemura. In 1920 S. Yonemura's Tables for Calculating Altitude and Azimuth
of Celestial Bodies were published in Japan. This small table of 39 pages contains
logarithms of haversines and secants, arranged for convenient solution of the formulas

hav (90°—h)—hav (L=d)=hav 6,
1 1
log eerst? (log sec L+log sec d) —log haw
log ese Z=log ese t+log sec d— log sec h.
The method is similar to that of Davis’ Requisite Tables but includes solution for
azimuth angle. The table is included in the book of Ogura’s tables (art. 2110).
Braga. The Tdboas de Alturas by Roméo Braga, a Brazilian, were published in

1924 in Paris. This is a table of natural haversines arranged for solution of the
formula

hav h=A-+B, .
in which A=hav t—[hav (L+d) hav t]
and B=hav (L—d)—[hav (L—d) hav t].

The first table of 108 pages is for solution for A and B. The second table of nine pages
is for finding h.

The assumed latitude is selected so that (L+d) is a whole degree. The assumed
longitude is selected so that t is a whole degree.

No provision is made for azimuth.

Japanese H.O. Pub. No. 601, Celestial Navigation Computation Tables, was pub-
lished in 1942. The method is similar to that of Yonemura, the triangle not being
divided and a modification of the cosine-haversine formula being used for altitude.
| Waller. In 1946 George W. D. Waller, a naval officer on duty as a navigation
instructor at the U. S. Naval Academy, proposed a solution by means of Gaussian
logarithms, commonly called “addition and subtraction logs.” The formula

BY ak: esc d ese L
1+ 20630 d ese L
sec d sec L sec t
was derived from the basic formula given above,
and esc yx ane
sec h

was derived from the time and altitude azimuth formula given in article 2125.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 531

A single table of 30 pages would contain in consecutive columns the following values:

A =log secant

B =log cosecant

C — —log (cosecant-4- 1) —log cosecant
C+=log cosecant—log (cosecant— 1).

All values would be multiplied by 100,000 to eliminate decimals. One additional page
would contain A and B values for all whole degrees from 0? to 180°. The values C+
and C— are the Gaussian logs.

The method is reasonably short and simple. Its publication as the “A, B, C
Method,” with suitable explanation, was prevented by the untimely death of its
originator.

Hugon. Nouvelles Tables Pour le Calcul de la Droite de Hauteur a Partir du Point
Estimé, by the French hydrographic engineer, Professor P. Hugon, were published in
1947. This logarithmic solution is based upon the fundamental formula

sin h=sin L sin d+c0s L cos d cos t,
from which the following is derived:

hav z=Xy+Yx
in which
X=hav (180?—t) —cohav t
y=hav (d—L)
X= havit

x—hav [180?— (d+L)]=cohav (d+L).
The formula for z may then be written
hav z=A+B
in which
log A=log X--log y
log B=log Y+log x.

Solution is by means of a table of 90 pages which lists in parallel columns values of
log cohav, log hav, and natural hav for every minute of arc from 0° to 180°. The solu-
tion requires six book openings, seven table entries, and five mathematical steps.

Azimuth is found from a diagram in a pocket on the inside back cover. This
diagram is designed to solve the formula

M=oaX+68Y,
in which M=cos h cos Z
a=sin (d—L)
X=cos? 5
B=sin (d+L)
Y=sin? $.

Chiesa. About 1948 the Tavole nautiche e Tavole dei Semisenoversi of the Italian
Stefano Chiesa were published in Genova, Italy. These include tables for computation
of altitude by the cosine-haversine formula, and “A, B, C” tables for computation of
azimuth angle by the formula

hav Z=[hav p—hav(L—h)] sec L sec h.

532 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Rose. In 1952 the Nautische Tafeln of G. Rose were published in Germany.

~ Arii

This volume has a convenient table for computation of the altitude by the cosine- `

haversine formula. It also includes the “A, B, C” azimuth tables of Lecky (art. 2126).
Various other tables are included, a number of them having been taken from an earlier

work of the same name by Dr. Otto Fulst, published in numerous editions since 1860. `

Doniol. The Miniature Navigation Table for Altitude and Azimuth, by R. Doniol,

a Frenchman, was published in 1955. This is undoubtedly the shortest of all sight `

reduction tables, consisting of only two pages. The formula for altitude was derived
from the basic formula given above. The formula used is

sin h=n—(n+m) a,

in which n=cos (L—d), m=cos (L+d), and a=hav t.
The formula for Z was derived from the formula

tan d cos L—cos t sin L
cot Z= : :
sin t

'The formula used is

tan 7 008 d

H

tan kt, "qi cot %t
2 Sin ol Zen:

in which Y=fAm+f'An. In this expression, f=

1”, and Ay=sin (d— L) sin 1’.

The first of the two tables gives sines and cosines for each half degree, and tangents
for half degrees of 45? and more. Interpolation is performed by means of a tabulated
A value which is the change of sine or cosine for 1”. Interpolation is minimized by
selecting an assumed position so that t and either (L+d) or (L— d) are an exact half
degree.

The second table gives the value of t in degrees, minutes, and seconds, and the
values of f and f' corresponding to selected values of a (natural haversines). The
interval between consecutive tabulated
values of haversine varies from 0.0002 to
0.005.

The solution is generally accurate to
0:1 of altitude and 0?1 of azimuth, but the
method requires a number of relatively
simplemathematical steps, making it some-
what longer than most “short” solutions.

2110. Altitude methods, perpendicu-
lar from zenith.—In figure 2110 the naviga-
tional triangle is shown in heavy lines on
a diagram on the plane of the celestial
meridian (art. 1432). The broken line is
a perpendicular from the zenith to the
hour circle of the celestial body. This
perpendicular may fall outside the tri-
angle. In figure 2110 it divides both the

FIGURE 2110.—Navigational triangle with azimuth angle (at Z) and the codeclina-
perpendicular from zenith to hour circle, tion side into two parts. The length of

» Au=sin (d+L)sin

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 533

the perpendicular is designated v and the two parts of the codeclination are designated

w and z. By means of Napier’s rules (art. 042), the following basic formulas can
be derived:

sin v=cos L sin t (1)
cos w=sin L sec », or tan w=cot L cos t (2)
sin Z’=sin w sec L, or cot Z'=sin L tan t (3)
sin h=cos v cos x (4)
sin Z’’=sin z sec h, or cos Z/'—tan v tan h, (5)

in which x=90%—(d+w).

This basic method has been modified in a number of ways, having proved the
most popular altitude method.

Souillagouet, a French professor of hydrography, was the first to divide the
navigational triangle by dropping a perpendicular from the zenith. His Tables du
Point Auxiliare were published in France in 1891. He designates various parts of the
diagram of figure 2110 as follows:

v is designated a

w is designated b

x is designated 90?— (d —b).

His formulas for altitude are
tan b=cot L cos t
sin &—cos L sin t
sin h=cos a sin (db).
For azimuth angle, the perpendicular is dropped from the celestial body to the

celestial meridian, a being the perpendicular and b that part of the celestial meridian
from the pole to the foot of the perpendicular. The following formulas are used:

tan b=cos t cot d
sin a=sin t cos d

cot Z=cos (L+b) cot a.

The assumed position is selected so that latitude is the nearest 15’ and meridian
angle is the nearest 1" or 15’ (2% or 30’ for latitudes greater than 60%). There are
four separate tables with a total of 408 pages. The method requires five book open-
ings, seven table entries, and six mathematical steps. Interpolation is not needed.

Bertin. A French professor of hydrography, Charles Bertin, devised tables similar
to those of Souillagouet, which were published in Paris in 1919 under the title Tablette
de Point Sphérique. Bertin used Souillagouet’s formulas for altitude, but for azimuth
angle he dropped the perpendicular from the zenith, as for altitude, and used the
following formulas:

sin Z,—sin e sec L

cot Z,=sin b tan (ed)
1= ZD + a.

534 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

In these formulas, b and c are substituted for the a and b, respectively, of Souillagouet.
This is the first method in which Z is divided into two parts, found separately.

| The assumed position is selected so that latitude and meridian angle are each

to the nearest 20”. The tables are shorter than those of Souillagouet, having 324

pages, but still bulky for this type solution. The method has fewer steps and requires

only two book openings, but interpolation is needed in two steps.

Ogura. In 1920 the New Altitude and Azimuth Tables by Sinkiti Ogura, Japanese
hydrographic engineer, were published in Tokyo. The solution for altitude is generally
similar to that of Souillagouet, a perpendicular being dropped from the zenith, but
Ogura introduced secants and cosecants for the first time in this type solution. His
solution for azimuth is similar to that of Blackburne (art. 2106) and Lecky (art. 2126).

The assumed position is selected so that latitude and meridian angle are each
to the nearest whole degree. The altitude is determined by means of two tables (A
and B-C) of a total of 27 pages, and azimuth by means of three additional tables (D,
E, F) of a total of 29 pages. The altitude can be obtained to an accuracy of 0:6 with-
out interpolation. Latitude and declination are limited to 65°. The rules are numerous
and complicated.

Both the Ogura and Yonemura (art. 2109) tables are given in the same book,
the Japanese Hydrographic Office Pub. No. 225. An English edition, with slight
modifications in the Ogura method, was published in 1924.

The Ogura tables have been widely copied.

Smart and Shearme's Position Line Tables were published in London in 1922,
based upon a division of the triangle by a perpendicular from the zenith. The altitude
formulas of Souillagouet were used, but the arrangement of the earlier tables was
improved. It is somewhat similar to that of Ogura, but with the positions of meridian

angle and latitude interchanged, providing a better arrangement when solutions of

several observations are made simultaneously. Solution requires a log sine table which
is not provided. There is no solution for azimuth. The assumed position is selected
so that the meridian angle and latitude are each the nearest whole degree. No inter-
polation is needed.

Newton and Pinto. The Navegação Moderna of J. A. Newton and J. C. Pinto was
published in Lisboa, Portugal, in 1924, providing a solution by dropping a perpendic-
ular from the zenith. The method is based upon ideas expressed by Newton in 1912
and 1913. The formulas for altitude are almost the same as those of Souillagouet.
The method of finding azimuth angle resembles somewhat the method of Bertin, but
with the use of auxiliary angles. There are only two tables, the first occupying 120
pages, and the second two pages. The assumed position is selected so that latitude
and meridian angle are each to the nearest 30’. No interpolation is needed, but the
rules are somewhat complicated.

Weems’ Line of Position Book, published in 1927, combines the Ogura altitude
tables and the Rust azimuth diagram (art. 2106).

H.O. Pub. No. 208 (Dreisonstok), Navigation Tables for Mariners and Aviators,
was published by the U. S. Navy Hydrographic Office in 1928 to provide a solution by
the method of dropping a perpendicular from the zenith. The method, devised by
Lieutenant Commander J. Y. Dreisonstok, USN, is similar to Ogura’s. For altitude,
it uses the Souillagouet formula inverted so as to be in secants and cosecants. For
azimuth angle the formula is similar to that of Newton and Pinto, except that it does
not use the parallactic angle at the celestial body. In the first edition the latitude was
limited to 65°. There were two tables, one of 45 pages and the other of 18 pages.
Later, a 23-page addition to the first table extended the coverage to the poles.

i
|

\

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 535

The assumed position is selected so that the latitude and meridian angle are each
the nearest whole degree. The method requires four book openings, eight table entries,
and six mathematical steps. Although values are usually obtained by relatively easy
interpolation, altitude accuracy of 0/5 can be obtained without interpolation.

As with H.O. Pub. No. 211 (art. 2111), the rules for this method were made on
the assumption that only bodies above the celestial horizon would be obseryed. The
rules may be restated to allow for both positive and negative altitudes, as follows:

If t is less than 90°, give b same name as latitude.

If t is greater than 90°, give b opposite name to latitude, and mark Z’ minus.

If (d+b) is numerically greater than 90°, mark Z” minus.

æ 1i (d+b) is contrary name to latitude, the altitude is negative; use the supplement
of Z”.

If Z is minus, subtract from 360° and mark plus.

The value labeled “t” in the tables is actually LHA. Ift, east or west, is used, as
in modern practice, the printed values greater than 180% can be ignored. The rules
can be stated in abbreviated form on alternate pages, as follows:

At the top of each left-hand page of table I:

t <90°, b same name as L.
At the top of each right-hand page of table I:
t >90°, b contrary name to L, Z’ (—).

At the top of each left-hand page of table IT:

(d+b) >90°, Z” (—).
At the top of each right-hand page of table II:

Z (—), use 360°—Z.
At the bottom of each page of table II (if desired):

(d+b) contrary name to L, He (—): use 180°— Z”.

If the D+B value used for finding Z” exceeds 10,000, it is reduced by this amount,
the remainder being used for entering table II. If desired, this can be stated in abbre-
viated form at the bottom of alternate pages of table II, as follows:

(C+D) >10,000, use (C+ D) — 10,000.

Like H.O. Pub. No. 211 (art. 2111), H.O. Pub. No. 208 has been largely superseded
by H.O. Pub. No. 214 (art. 2113).

Gingrich. The Aerial and Marine Navigation Tables, by Lieutenant John E.
Gingrich, USN, were published in 1931 to provide another solution by the method of
dropping a perpendicular from the zenith. The formulas for altitude are similar to those
of Ogura, and the formulas for azimuth are similar to those of Perrin (art. 2126). The
first two tables, of 31 and seven pages, respectively, are similar to those of Ogura. A
single third table of 13 pages is given for azimuth. The general arrangement is in many
respects similar to that of H.O. Pub. No. 208, and as with the earlier method, the assumed
position isselected so that latitude and meridian angle are each to the nearest whole degree.
The precision of tabulation of K, an auxiliary function, is not consistent. Consequently,
if the tables are used without interpolation, errors as great as 0:5 can arise in the
computed altitude.

536 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

PLU

Weems’ New Line of Position Tables are sometimes called the Manuscript Å
Tables because they were in manuscript form from 1932 until they were published in |

1943. They are similar to his earlier tables but arranged with the position of latitude
and meridian angle values interchanged so that values for several observations can be
taken from the tables with a single book opening. The latitude values are extended
from the 65° given in earlier tables to 90°. As in the earlier edition, the Rust azimuth
diagram (art. 2106) is included, but provision is also made for computation of azi-
muth angle. One part is found in terms of latitude and meridian angle, using the

formula of H.O. Pub. No. 208, and the other part is found in terms of altitude and the.

perpendicular from the zenith. If the azimuth is required to a greater precision than
0°5, interpolation is needed. The assumed position is selected so that the latitude
and meridian angle are each the nearest whole degree.

Collins. The I. C. S. Altitude and Azimuth Tables for Air and Sea Navigation, `

by Elmer B. Collins, formerly of the U. S. Navy Hydrographic Office, were published
by the International Correspondence Schools in 1934. The tables and method of
solution are generally similar to those of H.O. Pub. No. 208.

F-Tafel, published by the German Oberkommandos der Kriegsmarine about 1937,
divides the triangle by a perpendicular from the zenith. The formulas of Souillagouet
are used for altitude. Azimuth is found by the familiar formula

sin Z=sin t cos d sec h.

There are four tables. Latitude, declination, and altitude are limited to 70°. The
assumed position is selected so that latitude and meridian angle are each to the nearest
whole degree.

Comrie. In 1938 the Hughes’ Tables for Sea and Air Navigation, by L. J. Comrie,
former Superintendent, H. M. Nautical Almanac Office, were published in London.
These tables are similar to those of H.O. Pub. No. 208, but arranged with the positions
of latitude and meridian angle interchanged as in the Weems’ New Line of Position
Tables.

Myerscough and Hamilton. The Rapid Navigation Tables, by W. Myerscough
and W. Hamilton, were published in London in 1939. A perpendicular is dropped
from the zenith to the hour circle of the celestial body. With slight modification, the
altitude formulas of Souillagouet and the azimuth formula of Gingrich are used. Six
quantities are tabulated in a single table of 90 pages. Both altitude and latitude are
limited to 70°.

Ageton’s Manual of Celestial Navigation, published in 1942, combines the first
table of Weems’ New Line of Position Tables as table I, and H.O. Pub. No. 211 (art.
2111) as table II. The basic formulas are restated in terms of secants and cosecants.
The result is a short, easy solution without interpolation, involving four book openings,
eight table entries, and four mathematical steps. Since the H.O. Pub. No. 211 table
is included, the book can be used for Ageton’s earlier method.

Benest and Timberlake. The Astro-Navigation Tables for the Common Tí angent
Method by two British professors, E. E. Benest and E. M. Timberlake, were published
in 1945. In three tables of 61, 18, and 12 pages is given a logarithmic solution for
altitude only, by dropping a perpendicular from the zenith. The formulas are slight
modifications of those of Ogura.

The location of the line of position is somewhat similar to the method sometimes
used in longitude method solutions such as H.O. Pubs. Nos. 203 and 204 (art. 2106).
Two assumed positions are selected, usually 1° apart on the same meridian. The
altitude difference at each position is determined, and a circle, or arc of a circle, is
drawn with the assumed position as the center, and the altitude difference as the radius.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 537

The line of position is the common tangent to the two circles. Since there are four
common tangents, the general direction of the body is required. Where doubt exists
as to which of two or more answers is the correct one, additional solutions from other
assumed positions may resolve the ambiguity. If the celestial body is near the me-
ridian, the two assumed positions are better taken on the same parallel of latitude.
Even with these precautions, there is danger of selection of the wrong line.

Tavole H (I. I. 3113), published by the Istituto Idrografico della Marina of
Italy in 1947, combines table I of Ogura and table II of Weems' New Line of Position
Tables, including, also, the Rust azimuth diagram (art. 2106). This table is a modi-
fication of an earlier Tavole F.

2111. Altitude methods, perpendicular from body.—Figure 2111 is a diagram on the
plane of the celestial meridian (art. 1432), with the navigational triangle shown in
heavy lines. A perpendicular from the celestial body, M, to the celestial meridian
divides the triangle into two right spherical triangles. In figure 2111 the length of the
perpendicular is designated v and the two parts of the colatitude are designated w and
x. By means of Napier's rules (art. O42), the following basic formulas can be derived:

sin ?— cos d sin t (1)
cos w=sin d sec v, or sin w=cot t tan v (2)
sin h=cos v cos x (3)
sin Z=sin v sec h, or cos Z=tan zx tan h (4)

Since z—90?— (w+L), formula (3) can be written in terms of latitude, and w found
from equation (2). Thus, both h and Z can be determined by means of t, d, and L
and auxiliary functions found from them.

William Thomson (Lord Kelvin) was the first to divide the navigational triangle
as shown in figure 2111 for sight reduction, but his method (art. 2106) was for deter-
mination of longitude. "Various later methods made such a division for determination
of altitude.

Fuss. The Tables to Find Altitudes and Azimuths, devised by V. E. Fuss, an
astronomer at the Kronstadt (Russia) Naval Observatory, were published in 1901.
In these tables a perpendicular is dropped from the celestial body, the following notation
being used (fig. 2111):

v is designated a

w is designated 90%—b

x is designated B-90°

B=90°—L-+b (if v falls between Z and Q).

Solution is by the following formulas:

sin a=cos d sin t
cot b=cot d cos t
sin h— cos a sin B
cot Z=cot a cos B.

The assumed latitude is selected to provide the nearest 15’ value of B. The
assumed longitude is selected so that t will be the nearest whole 1” (02253. The
tables are entered twice, first with t and d to find a and b, interpolating for d, and then
with B and a to find h and Z, interpolating for a. The method involves two book
openings, eight table entries, four interpolations, and ten mathematical steps. There
are 144 pages of tables. a

Aquino. The Altitude and Azimuth Tables of Radler de Aquino, a Brazilian naval
officer, were first published in 1909. These were followed the next year by his Sea and

538 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Air Navigation Tables. Several later edi- `
tions of both publications appeared with `
some modification, principally of the aux-
iliary material given. Aquino dropped a
perpendicular from the celestial body to
the celestial meridian, and used the same
formulas as Fuss and generally the same `
arrangement, except that longitude is as-
sumed so as to provide a meridian angle
to the nearest whole degree.

H.O. Pub. No. 209 (Pierce), Position
Tables for Aerial and Surface Navigation,
was published by the U. S. Navy Hydro- |
graphic Office in 1930. These tables were
devised by Commander M. R. Pierce,

Na USN, in 1925, when he was navigator of

Figure 2111.—Navigational triangle with per- the dirigible USS Los Angeles. ; The meth-

pendicular from celestial body to celestial od is based upon a triangle divided by a

ursi perpendicular from the celestial body. It

is generally similar to those designed by Fuss and Aquino, but the arrangement is

somewhat different, requiring 206 pages of tables. This method was never widely
used, and is now out of print.

H.O. Pub. No. 211 (Ageton), Dead Reckoning Altitude and Azimuth Table,
was published by the U. S. Navy Hydrographic Office in 1931. This method, designed
by Lieutenant Arthur A. Ageton, USN, while a student of the Post Graduate School,
then at Annapolis, Maryland, is based upon a triangle divided by dropping a per-
pendicular from the celestial body. It is generally similar to those of Fuss and Aquino.
However, Ageton modified the formulas so as to include only secants and cosecants.
In terms of figure 2111, his notation is as follows:

Q'

v is designated R
w is designated 90?—K
x is designated K~L
K=x+L.

Ageton's formulas are
csc R=csc t sec d

csc d
esc K=

` sec R
esc h=sec R sec (K —L)

CSC ponite

sec h
A single table of 36 pages gives five-place log cosecants (labeled A) and log secants
(labeled B), both multiplied by 100,000 to eliminate the decimal. These values are
given in parallel columns for each 0/5 of angle from 0° to 180°. The table is well
arranged and indexed for quick reference. The rules are relatively simple and well
presented. The method can be used for solution from the dead reckoning or any other
assumed position. The method is intended for use without interpolation. "These

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 539

features combined to make this a popular method, although solution is somewhat
tedious, and large errors may be encountered if t is near 90°. The method has been
largely superseded by H.O. Pub. No. 214 (art. 2113):

E. If a celestial body near the visible horizon is observed, it may be below the celestial
7 horizon (zenith distance greater than 90°), because of refraction and dip. Under these
conditions the computed altitude, He, is negative (art. 2010). In the solution by H.O.
Pub. No. 211, He is negative if K is of the same name as L and greater than (90°+L)
or if K is of contrary name to L and greater than (90°—L). Under the second of d
conditions, Z is less than 90? and should be taken from the top of the table if K is
greater than (180°—L).

Fontoura da Costa and Penteado's Tabuas de Altura e Azimute were published in
Lisboa, Portugal, in 1936. "These consist of 26 pages of log secant and log cosecant
tables similar to those of H.O. Pub. No. 211. The method and formulas are shght
modifications of those of H.O. Pub. No. 211.

Tillman. The Altitude Tables for Mariners and Aviators, by E. Tillman, were
published in 1936 in Sweden. Solution is by three tables using the basic formulas
given above.

USSR tables. About 1940 the USSR replaced the Fuss tables with a method
that is similar but uses a much shorter table. However, the solution is about the same
length as with the Fuss tables, requiring six book openings, nine table entries, and
five mathematical steps. Visual interpolation is used.

Japanese H.O. Pub. No. 602, Brief Celestial Navigation Table, was published in
1942. A perpendicular is dropped from the celestial body, as in figure 2111. Side
w is designated K, and the following formulas are derived from the basic formulas

given above:
log tan K=log cot d+log cos t

log cot Z=log cot t+log ese K+log cos (K +L)
log cot h=log cot (K +L) +log sec Z.

These formulas result in a simple solution, at the expense of some duplication in the
three tables of 49 pages.

Hickerson. In 1944 Thomas F. Hickerson, professor of applied mathematics
at the University of North Carolina, published a small volume called Navigational
Handbook with Tables, in which the tables of H.O. Pub. No. 211 are given with the
interval between entries reduced to 0/2. All values are given on 45 pages, by tabulating
values only to 45° and interchanging the A and B values for angles between 45° and
90°. In 1947 a second edition was published under the title Latitude, Longitude and
Azimuth by the Sun or Stars.

2112. Altitude methods without use of navigational triangle.—The navigational
triangle is composed of arcs of three great circles: the celestial meridian of the observer,
the hour circle of the celestial body, and the vertical circle of the celestial body. Ares
of other great circles might also be used in forming spherical triangles that can be
solved to find altitude and azimuth.

Kotlarié. In 1956 Stjepo M. Kotlarié, technical assistant, Hydrographic Institute
of the Yugoslavian Navy, proposed a method based upon the solution of three right
spherical triangles composed of arcs of great circles, as follows:

triangle 1—celestial horizon, hour circle, and celestial equator;

triangle 2—celestial horizon, hour circle, and vertical circle;
triangle 3—celestial horizon, hour circle, and celestial meridian (lower branch).

540 i COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The formulas are derived from Napier’s rules:
tan (Z+F)=— sin L tan t
tan M=cot L cos t
cos C=cos L sin t
tan F=cos C tan (M +d)
sin Hc—sin C sin (M+d)
Z=(Z+F)—F,

in which F, M, and C are auxiliary parts.

Four tables totaling about 200 pages would be needed with the method, although
table ITI is not needed if the assumed position is selected so that latitude and meridian
angle are the nearest whole or half degree. The size of the tables could be reduced
considerably if half degrees were dropped. With an assumed position selected as indi-
cated above, the method requires only four table entries and four mathematical
steps. The rules are few and simple.

2113. Modern inspection tables may contain lists of altitude or azimuth, or both.
Another type tabulates the information needed for finding longitudes. Values are
taken directly from the tables, without the need for logarithms, auxiliary functions,
or mathematical solutions (except interpolation). Inspection tables are not new, the
horary tables of Cassini in 1770, Lalande in 1793, Lynn in 1827, and Hommey in 1863
(art. 2106) being of this type. Other inspection tables include Davis’ Chronometer
Tables, Blackburne, H.O. Pubs. Nos. 203 and 204, Ball, Davis’ Alt-Azimuth Tables,
and H.O. Pub. No. 201 (arts. 2106 and 2109). None of these tables is used to any
extent today, largely because interpolation is difficult, and coverage is limited. A
short logarithmic solution with wide coverage has often proved more popular.

In contrast, the modern inspection table, made practicable by recent developments
in computation techniques, has largely replaced the trigonometric solution. The
principal modern inspection tables are:

H.O. Pub. No. 214, Tables of Computed Altitude and Azimuth, were published by
the U.S. Navy Hydrographic Office between 1936 and 1946, in nine volumes. Between
1951 and 1953 the British Admiralty published identical tables (H.D. 486) in six
volumes, with altered explanation to suit British practice. The first volume of an
identical Spanish edition was published in Spain in 1953, and the second volume in
1956. Several volumes of an Italian edition based on H.O. Pub. No. 214 have also
been published. The H.O. Pub. No. 214 series is described in detail in chapter XX.

British Air Pub. 1618 (H.O. Pub. No. 218), Astronomical Navigation Tables,
were published by the British Admiralty between 1938 and 1944 in 15 volumes (lat.
0°-79°). In 1941 the first 14 volumes (lat. 0°-69°) were republished by the U. S.
Navy Hydrographic Office as H.O. Pub. No. 218. The tables are intended primarily
for aviators.

These tables are similar to H.O. Pub. No. 214, but with several differences. In A.P.
1618 values are given to the nearest whole minute for altitude, and the nearest
whole degree for azimuth. The altitude values include allowance for refraction at a
height of 5,000 feet. The minimum altitude in most cases is 10°. Provision is made
for interpolation for declination only, and this always from the nezt smaller whole
degree, instead of from the nearest whole degree. Declination is given for each whole
degree from 0° to 28° only. In addition, values of altitude and azimuth are given for
the declination (in 1940) of 22 stars. This part of the table is entered with the star
name (or an arbitrarily-assigned number), so the declination of the body need not be

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 541

known. An auxiliary table provides a correction for changes in declination during the
| years following 1940 (to the year 2000).

During World War II these tables were widely used by aviators. Some marine
navigators also used them. Since publication of H.O. Pub. No. 249, their use has
declined.
| Japanese H.O. Pub. No. 351, Celestial Navigation Observation Table, was pub-
lished in 1940-42, in seven volumes for latitudes 0°-70°. The original printing was
classified "secret." The tables are similar to British Air Pub. 1618, with several differ-
ences. In H.O. Pub. No. 218 all star-name entry tables are given first, followed by
all declination entry tables. In Pub. No. 351 the declination entry table for each degree
of latitude is followed by the star-name entry table. Altitudes, including refraction
at 4,000 meters (13,123 feet), are tabulated to a minimum value of 2°. Declination
is extended to 29°. The latitude-declination contrary-name entries are inverted so
that meridian angles increase upward on the page as in H.O. Pub. No. 260 (art. 2126),
resulting in better utilization of space on the pages having both “same name” and
“contrary name” entries. Twenty stars are used, the selection differing somewhat
from that of H.O. Pub. No. 218. In H.O. Pub. No. 218 the stars are listed and num-
bered alphabetically. In Pub. No. 351 they are given in order of declination, from
Dubhe, listed as 62°03’ N, to Sirius, listed as 16°38’S.

Hoehne. In October 1941 George G. Hoehne, an American, proposed a set
of tables similar to the star section of H.O. Pub. No. 218, except that a value approxi-
mating LHA T would replace meridian angle of the star as an entering argument, and
a maximum of ten stars would be given in parallel columns for each whole degree of
entering value. The value used for entering the tables would be determined by adjust-
ing LHAT by an amount tabulated for each year for each star used. This would
prevent the tables from becoming inaccurate because of precession of the equinoxes
(art. 1419). Refraction at altitude 5,000 feet would be included as in H.O. Pub. No.
218. One volume of these tables (volume II, lat. 20? N to 39? N) was published in 1943.

Japanese H.O. Pub. No. 603, Simplified Celestial Observation Table, was published
in 1943. This publication is virtually the same as Pub. No. 351, except that eight addi-
tional stars are given, all farther south than those of Pub. No. 351. This extends
the list to a Crucis (Acrux), given as declination 62?48' S.

Altitude and Azimuth Almanac was published by the Japanese Hydrographic
Office, beginning in 1944. Originally, this was a secret publication. Several different
versions were printed, and there were some modifications after the first editions. In
each, however, the functions of almanac and sight reduction tables were combined. For
each of several specific locations, the altitude and azimuth of one or more celestial
bodies are tabulated for the date and time, usually at ten-minute intervals. In the
earlier editions, the locations selected were important points in the western Pacific.
From this practice, these publications are sometimes called "destination tables."
Later editions used positions differing in latitude by 5?. These tables provided a quick
solution for observations made at the tabulated times. On a worldwide basis such a
system would involve a very voluminous tabulation each year, or cumbersome cor-
rections. The Altitude and Azimuth Almanac is no longer published.

Hohentafeln nach Sternzeit, an official German table, was published in
1944 as an experimental edition with a very limited range of latitude. The tables
were similar to those of Hoehne, but with six stars listed for each minute of local
sidereal time.

'Mēnēclier and Chevalier. The Cálculo del Punto of Víctor Ménéclier and Roberto
Chevalier was published in 1945-49 by Aeronáutica Argentina. There are six volumes
for latitudes 0° to 59° south. At intervals of 4" LST (or 1° LHA T) the altitude,

542 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

a correction factor, and azimuth (not azimuth angle) of selected stars are tabulated.
Twelve columns are provided, but a number of blank areas appear, resulting in an `
average of about nine altitude-azimuth entries for each time entry. In most cases,
altitudes are carried to a minimum value of 5%, and azimuth to the horizon. These
tables are similar to those of Hoehne and volume I of H.O. Pub. No. 249.

H.O. Pub. No. 230 (Goetz), High Latitude Celestial Navigation Tables, designed
in 1945 by Roy F. Goetz, was published by the U. S. Navy Hydrographic Office in 1946.

The first section, called “Star Tables," is entered with the latitude to the nearest
1° from 70°N to 89°N, the name of the star (for ten selected stars), and LHA f at
intervals of 2? for latitude 70° to 79°, 5° for 80? to 84°, and 10° for 85° to 89°. Altitude
is tabulated to the nearest 1’ and azimuth (not azimuth angle) to the nearest 0?1. A
“AH” value is given for use with an auxiliary table to interpolate for precession of the
equinoxes (art. 1419).

In the second section, called “Declination Tables," declination is substituted for
the name of the star. A separate table is given for each 1° declination from 0° to 28°.
For each degree a “same name" section is given first, followed by a “contrary name"
section (to declination 19°). The minimum altitude is 1°. The declination tables
give “d” in place of “AH” for use with an auxiliary table to interpolate for declination.

Only 400 of these tables were published. They were intended only for use in
military aircraft operating beyond the latitude range of H.O. Pub. No. 218. After
H.O. Pub. No. 249 became available, H.O. Pub. No. 230 was canceled.

H.O. Pub. No. 249, Sight Reduction Tables for Air Navigation, in three volumes, are
published by the U. S. Navy Hydrographic Office. A preliminary edition of volume I

for selected stars was published in 1947 under the title Star Tables for Air Navigation,
using the principles and features of tables proposed previously by George G. Hoehne,
Commander C. H. Hutchings, USN, and others. The altitudes of this edition were ad-
justed for refraction at a height of 10,000 feet. By the time the “first” edition was printed
in 1951, for epoch 1955.0, more than 20,000 copies of the preliminary edition had been
distributed. The 1951 edition dropped the refraction adjustment feature from the
altitudes, and had an improved selection of stars. It was followed in 1952 with two
volumes for declination entry at 1° intervals from 0° to 29°. In 1952 and 1953 a
British edition was published with identical tables (A. P. 3270) but altered explanation.
The tables have been accepted as standard by the air forces of Great Britain, Canada,
and the United States. They are in limited use by mariners. Extracts from these
tables (1957 edition, for epoch 1960.0) are given in appendix CC.

Volume I contains tabulations of altitude (to the nearest 1’) and azimuth (to the
nearest 1°) in parallel columns. For each 1° of latitude a two-page table (one-page
above 69°) is given. For each 1° (2° beyond latitude 69°) of LHA Tr, altitude and azi-
muth are given for seven stars carefully selected with regard to azimuth, magnitude,
altitude, and continuity. Stars of the first magnitude are shown in capital letters, and
those of second and third magnitude in lower case with initial capital. After each 15
entries a break occurs and a new listing of stars is given, whether or not there are any
changes from the previous list. Stars are listed in the order of increasing azimuth at
the beginning of each period. A total of 41 stars is used, 19 of which are of the first
magnitude, 17 of the second magnitude, and 5 of the third magnitude. The tables
are intended for use with an assumed position selected so that latitude and LHA Y
are each the nearest whole degree (nearest even degree of LHAT at latitudes higher
than 69°).

Tabulation by name of star eliminates the need for finding the declination, but
for strict accuracy, a correction for precession of the equinoxes (art. 1419) and nutation
(art. 1417) may be needed. This is given in an auxiliary table (tab. IV). Since it is

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 543

anticipated that the tables will be recomputed at five-year intervals, it will probably be
possible for aviators to ignore this correction. However, it may reach a value of as
much as 3”, and should not be neglected if the tables are used by mariners. This
correction is applied to the fiz, not to each altitude.

Tabulation of azimuth (not azimuth angle) eliminates the need for conversion.

Tabulation by LHA Y instead of meridian angle of the star eliminates the need
for finding and applying SHA. It also makes of the tables a star finder for the seven
stars given, since all values given for any entry of LHAY are for the same time. In
the air it is common practice, when H.O. Pub. No. 249 is used, to observe the stars at
intervals of exactly four minutes. Solution is made for only one observation (usually
the middle of three), altitude and azimuth entries being found on consecutive lines
(neglecting the small difference between solar and sidereal time during a four-minute
period), and all are plotted from the same assumed position, selected so that latitude and
LHA T are the nearest whole degree, and adjusted as necessary for the motion of the
observer between observations. If the time selected for the observation to be
solved is a whole 10" of GMT, and the navigational watch is set to GMT, the GHAT
can be taken directly from the Air Almanac without interpolation. With addition or
subtraction of only one longitude, a person has all the information needed for entering
H.O. Pub. No. 249 for solving three observations. If the navigator had a watch set
to read GHA T in arc, the almanac would not be needed for solving an observation.
Wing Commander E. W. Anderson and Dr. D. H. Sadler, both of Great Britain, have
suggested a ruler for use with a Mercator chart of certain scales, and a circular computer
for use with any projection and scale, to permit quick conversion of sidereal to solar
units if observations are made at greater intervals.

Example 1.—During evening twilight on June 2, 1958, the 1724 DR position
of a ship is lat. 40?39:2 S, long. 128?01:2 E. At GMT 824703? the navigator ob-
serves Canopus with a marine sextant having no IC, from a height of eye of 38 feet.
The hs is 55%57/1.

Required.—The a, Zn, and AP, using H.O. Pub. No. 249 (epoch 1960.0), vol. I,
and the Air Almanac.

Solution.—
June 2 Canopus d oue
GMT 824703! June 2 IC — —
$220" ` 15°18 D 6’
47035 1901" R d
GHA T 16°19’ sum — 11
019127941" E corr. oen T
CHAT 144900" hs 5S
aL 41°00’S Ho 552501
Hc 558454
Ho 55850:
7.4 5T ali 41°00'S
Zn 2803 TAN NAD

This problem is similar to that of example 4, article 2008. A comparison of the
two indicates that the H.O. Pub. No. 249 solution reduces the number of table entries
over the number required by H.O. Pub. No. 214 solution by four, and the number
of mathematical steps also by four. The use of a whole 10” of GMT would elimi-
nate one more table entry and one mathematical step. If three observations were
made at 4” intervals, two more table entries and two mathematical steps would be
eliminated from the three solutions. Whether or not these “wrinkles” are used, all
values needed for a fix are together on one page, and are extracted without interpolation.

544 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Volumes II and III are somewhat similar in many respects to H.O. Pub. No. 214.
Altitude and azimuth angle are given in parallel columns for every whole degree of
latitude (0° to 89°), every whole degree of declination (0° to 29°), and every whole
degree (2° beyond lat. 69°) of LHA for all values at which the altitude is greater than
several degrees below the celestial horizon (to allow for large values of dip at aircraft
heights, and for considerable difference between assumed position and the position of
the craft at the time of observation). The values for latitude and declination con-
trary name are tabulated with values of meridian angle (LHA less than 180°) increasing
upward on the page, as in some older tables such as H.O. Pub. No. 260 (art. 2126).
This permits better utilization of space where same- and contrary-name tabulations
are given on the same page. It also serves to emphasize the difference between the
same- and contrary-name tabulations, the contrary-name tabulation being given in a
“contrary” manner on the page. A more convenient arrangement of declination
entries is provided by having the “top” of each page of the tables along the left side,
requiring the turning of the page through 90°. l

A “d” value is tabulated between the altitude and azimuth angle to facilitate
interpolation of altitude for declination. No interpolation is needed for latitude and
LHA because the assumed position is selected so that these are the nearest whole
degree (nearest even degree of LHA beyond latitude 69°). The “d” value is the dif-
ference in minutes, with sign, between the accompanying altitude and that for declina-
tion 1° greater, at the same latitude and LHA. It is used for entering an auxiliary
table (tab. III) for determining the correction to be applied to altitude for minutes of
declination, in a manner similar to using Ad and the “multiplication table” of H.O.
Pub. No. 214. Interpolation is normally made in the direction of increasing declination.

Volume II covers latitudes 0° to 39°, and volume III contains similar information
for latitudes 40° to 89°. Since these tables are entered with LHA of the celestial body,
they do not become inaccurate in succeeding years, and no correction is needed for
precession and nutation, as in volume [. These volumes are intended for solution of
observations of the sun, moon, planets, and any stars within the declination range.

Example 2.—During morning twilight on June 2, 1958, the 0724 DR position of
a ship is lat. 40?39:2S, long. 131%01/2E. At GMT 22*24703* (June 1) the navigator
observes Alpheratz with a marine sextant having no IC, from a height of eye of 38 feet.
The hs is 20°15/3.

Required.—The a, Zn, and AP, using H.O. Pub. No. 249, vol. III, and the Air
Almanac. ;

Solution.—
June 2 Alpheratz + + —
GMT 22^24»035 June 1 IC — —
DODAS BS" D 6'
4035 STA R 34
SHA 358°26’ sum — 9’
GHA 224990" corr, E ECH
a^ 130?40' E hs 20515.
LHA 3559?00' Ho 20°06’
d 28 cK) d diff. 52’
aL 41°00’S
ht 209514 "d" (—)60 Z S175? E
corr. (—)52’
He 19°59’
Ho 20°06’
a E aL 41%00'S

Zn 005° ar 130%40'E

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 545

This problem is similar to those of example 4, article 2008, and example 1 above.

All volumes of H.O. Pub. No. 249 are intended for use with the Air Almanac.

Experimental Air Navigation Tables. During the early part of World War II
the British Royal Air Force felt the need for an inspection table that would be faster
than Air Pub. 1618 (H.O. Pub. No. 218), but free from the limitations of the astro-
graph (art. 2123). Wing Commander R. C. Alabaster suggested the addition of SHA
to the hour angle (measured eastward) of the stars given in Air Pub. 1618, converted
to time at the sidereal rate of 15%02/5 per hour. This would give the time inter-
val until the next meridian transit of the vernal equinox. Before observation, the
time of passage of the vernal equinox across a convenient meridian would be marked
on the chart or plotting sheet. After observation, the tables would be entered with
assumed latitude and the nearest tabulated altitude. The (SHA-+ HA) corresponding
to this altitude would be added to GMT at the time of observation. The result should
be close to the time marked on the chart. The difference would be converted to arc
units (or a time scale would be marked on the chart or plotting sheet) and the corre-
sponding longitude determined. This point would serve as the assumed position.
The difference between the observed altitude and that used for entering the table
would be the altitude difference to be used with the azimuth for plotting the line of
position.

Squadron Leaders A. Potter and A. J. Hagger suggested a method of printing a
time scale on the chart or plotting sheet with an auxiliary table to assist in locating the
assumed position.

Various modifications and conventions were later added to avoid negative values
and other complications. As the method finally emerged, a quantity known as “scale
time" was adopted. This value, designated T, would be equal to 26 hours plus the GMT
of the next transit of the vernal equinox occurring after 0600 during the night of the
flight. The GMT of observation would be designated t. The quantity T—t would be
the value tabulated.

Further attempts were made to simplify the conversion of mean to sidereal time
so that the single setting might be used during an entire flight. One of these, called
the “Astro-Scales,”” was suggested by Wing Commander E. W. Anderson in 1945.
In 1953 he and D. H. Sadler suggested an improved version.

Although a considerable amount of thought was given to this method, and ex-
perimental tables were published for a limited band of latitude, the limitations of a
longitude method and the inconvenience of converting mean time to sidereal time
resulted in the method being discarded in favor of the less restrictive H.O. Pub. No.
249 method.

Ashton. In 1943 Philip Ashton proposed a set of tables called Astrograph-time
Star Tables for Air Navigation, based upon the principle of the Experimental Air
Navigation Tables. A permanent table would be entered with the name of the star,
latitude, and “astrograph mean time” (art. 2123), and altitude and azimuth would
be taken from the table. A set of tables issued each year would list the values to be
used with GMT each night to determine the astrograph mean time. Before take-off,
the chart or plotting sheet would be marked to agree with the astrograph mean time,
and a metal tape would then be used to convert mean time to sidereal time for finding
the assumed position.

Heard. About 1950 John F. Heard, associate professor of astronomy at the
University of Toronto, prepared a modification of the Experimental Air Navigation
Tables. The tabulation would be altered so that altitude would be given in the left-
hand column at intervals of 20’. A delta (““diff.”) value would be tabulated and this
used with the difference between entering and observed altitudes to enter an auxiliary

546 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

table to determine a correction to be applied to T—t so that the altitude difference
need not be plotted. A correction for 60 minus seconds of 7' would also be applied.
The “bearing” of the line of position (azimuth plus or minus 90°) would also be tab-
ulated. The line of position would be plotted through the assumed position, in the
direction indicated by the “bearing.” For any given time three stars differing in
azimuth by approximately 120° would be given. The part of the table to use would
be determined by a rough computation of T—t.

2114. Azimuth methods.—Nearly all methods proposed for obtaining a line of
position are based upon the use of altitudes. The azimuth might also be used if an
instrument becomes available for measuring it to the required accuracy. The accuracy
needed would depend upon the acceptable error of the line of position. The error
would be proportional to the cosine of the altitude. For a celestial body on the celestial
horizon an error of 1’ in the azimuth would introduce an error of one mile in the line
of position, the same as it does in an altitude observation. For any altitude greater
than 0°, the error would be less.

Each method of determining a line of position by altitude has its counterpart in
the azimuth problem. Thus, if it can be determined that a celestial body is exactly
on the celestial meridian, the west longitude is the same as the GHA of the body.
If the body is exactly on the prime vertical, the latitude can be computed. As a more
general case, two points on a given azimuth line can be computed and joined by a
straight line, by assuming two latitudes or two longitudes. However, if one such posi-
tion is known, the azimuth line of position can be drawn through it in the direction of
the azimuth. If the celestial body is sufficiently high, or if a small scale is acceptable
and allowance is made for chart distortion, the azimuth line can be plotted directly,
just as the circle of position can be drawn if the altitude is known. The difference be-
tween the observed azimuth and that computed for an assumed position can be used
in a manner similar to the altitude difference. The azimuth difference in minutes
multiplied by the cosine of the altitude would be the “intercept” measured off from the
assumed position in a direction perpendicular to the computed azimuth. Through the
point thus determined, a line would be drawn in the direction of the observed azimuth.
For small differences, the line could be drawn perpendicular to the line from the assumed
position. The relative values of the observed and computed azimuths would indicate
the direction (right or left) to draw the line from the assumed position.

If the altitude and azimuth were both known to sufficient accuracy, a single celestial
body would suffice for determining position by any combination of altitude and azimuth
methods or by direct computation of latitude and longitude. The two lines of position
would always be perpendicular to each other.

Double altitudes. For a stationary observer the longitude can be determined by
observing the altitude shortly before meridian transit (either upper or lower), and noting
the time when the altitude has returned to exactly the same value after meridian transit.
If there has been no change in declination between observations, the mid time represents
the moment of meridian transit, at which time the azimuth is 000° or 180°. The GHA
(or 360? — GHA for east longitude) is the longitude of the observer: This method might
be considered as either a longitude or an azimuth method. A variation is to observe
a number of altitudes shortly before and after meridian transit. These are then plotted
against time on cross-section paper and a smooth curve plotted through them. The
time corresponding to the maximum altitude (minimum altitude for lower transit) is
the moment of meridian transit.

| Quilter. Ir 1950 Commander E. S. Quilter, USN, suggested a method based upon
azimuth difference. He would measure and compute azimuth to the nearest 0201 (when
the means for doing so became available) and express the azimuth difference to the

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 547

same precision. A table would be provided to list values of K, a constant by which the
azimuth difference would be multiplied for any given altitude to determine the “inter-
cept” to measure off from the assumed position.

2115. Determination of latitude and longitude.—Most methods provide informa-
tion needed for plotting a line of position. The fix is at the common intersection of two
or more such lines. A line of position might be plotted in one of several ways. In the
latitude and longitude methods, the lines are plotted at the computed coordinate.
When one coordinate has been determined, the other can be computed without plotting.
Thus, the longitude determined by time sight is generally correct only for the latitude
used in its solution, and the plotting of a longitude line is misleading, unless the celestial
body is on the prime vertical. A better procedure is to compute two points, using differ-
ent latitudes (or longitudes, if latitude is being computed). These two points are on the
line of position. A straight line connecting them is a good approximation of the circle
of equal altitude. This was the method used by Captain Sumner when he discovered the
line of position (art. 131), and the method of H.O. Pubs. Nos. 203 and 204 (art. 2106).

Another method is to compute one point and the azimuth (or Zn+90°), and plot
the line of position through the point. This is the method used by Soule and Dreison-
stok (art. 2106).

If only the altitude difference is computed for two points, the line of position is a
common tangent of circles of radius equal to the altitude difference at these two points.
This is the method of Benest and Timberlake (art. 2110).

The most common modern method of plotting the line of position is by means of
the assumed position, altitude difference, and azimuth. If this information is available
for two observations solved for the same assumed position, the position of the fix can
be determined by computation instead of by plot, using the following formulas:

d2—a, cos A
tane
a, sin A

)

and

a’=a, sec B,
in which A is the difference in azimuth of the two celestial bodies, B is the difference
between the azimuth of the first celestial body and the direction of the “position vector"
(the line connecting the common assumed position with the fix), a, is the altitude dif-
ference of the first celestial body, az is the altitude difference of the second celestial
body, and a’ is the length of the position vector.

If A is greater than 90°, the minus sign in the numerator of the first formula is
replaced with a plus sign. The common intersection of the two lines of position (the
fix) is a’ miles from the common assumed position, in a direction B degrees from the
azimuth of the first observation. Since B is always between the azimuths of the two
celestial bodies observed, it will always be added to the first azimuth if the left-hand
body is considered the “first” one.

With the information a’ and B one can find the latitude and longitude of the fix
by (1) plot, (2) table 3, or (3) computation. If method (2) or (3) is used, the problem
is the same as that encountered when course and distance from a known position is
given, and point of arrival is desired. This can be solved by a combination of plane
and parallel sailing, as explained in articles 813 and 815. r

It is possible, too, to plot circles of position by using the geographical position of
each body as the center of its circle, and the zenith distance as its radius. This is the
method used for high-altitude observations (art. 2011), but is generally not practical
for ordinary altitudes because of the small scale that would be needed, and the error
that would be introduced by chart distortion, unless plotting were done on the surface
of a sphere (art. 2124).

548 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The use of a circle of equal altitude is similar to the use of a circle of position around
a landmark of known range. The bearing of such a landmark also furnishes a line of
position. Similarly, a line of position can be obtained by plotting the azimuth line of a
celestial body, and a fix by plotting two such lines. This is generally not done because
of the scale and chart limitations mentioned above, and also because the needed ac-
curacy in observation is beyond the capability of equipment generally available to the
navigator. Errors in both compass and measurement of azimuth are involved.

Various methods of determining position by computation from observations of
two or more celestial bodies or four observations of a single celestial body are discussed
in articles 2116 and 2117.

2116. Computed position from observation of two or more bodies.—Several
methods have been proposed for computing the position directly from the observation
of two or more celestial bodies. These generally consist of some combination of lati-
tude and time sight methods. One form of automatic celestial navigation, proposed
by Collins Radio Company, uses the principle of the planetarium in reverse, two bodies
serving to position a horizontal-stabilized sphere (in principle) for latitude and local
sidereal time. If the device is accurately set to Greenwich sidereal time, longitude is
indicated.

Fox. In 1951 Charles Fox, associate professor of mathematics at McGill Uni-
versity, Montreal, proposed formulas for computing latitude and longitude if certain
star pairs are observed, the two stars of each pair having almost the same SHA. Pre-
sumably, simultaneous observations would be needed. Five such star pairs are listed.
Four of the stars in three of these pairs are dimmer than the third magnitude, and are
not listed in the almanacs, either in the main tabulation or among the additional stars.
More involved formulas are suggested for use of the method with any three celestial
bodies.

de Jonge. In 1945 Joost H. Kiewiet de Jonge, a lieutenant in the Netherlands
East Indies Army Air Force, proposed a method of determining position from the ob-
servation of three stars. The U.S. Navy Hydrographic Office published experimental
tables for several star pairs for latitudes 20° to 30° under the title Three Star Position
Tables for Aerial Navigation. It was anticipated that if the method proved popular,
all possible three-star combinations (of the stars in the main tabulation of the almanacs)
would be given, so that the navigator would not be limited in his selection.

No assumed position is needed with the method. Three stars are observed at
intervals of three minutes, the stars being observed in the order of listing in the main
table. Table I is entered with the three altitudes, h,, h», and hz, and for each a value
is taken from the table. These values are labeled H,, H;, and Hs, respectively. They
are combined to form H,+H,=H,,, and H,+H;=H,3. These combined values, H;2
and Hz, are then used to enter the main table, from which local sidereal time (in arc
units) and latitude are obtained. Greenwich sidereal time minus local sidereal time
equals longitude (measured westward). Delta values and auxiliary tables provide
corrections for motion of the observer and observation intervals differing from three
minutes. Mean corrections for both atmospheric refraction and Coriolis are included
in the tables, which are limited to altitudes between 20? and 75?, and azimuth difference
between consecutive stars to 1652,

Dozier. In 1949 Charles T. Dozier proposed a method based upon the simul-
taneous observation of two celestial bodies and the solution of two spherical triangles,
with vertices as follows:

triangle 1—the two celestial bodies and the elevated pole,

triangle 2—the two celestial bodies and the zenith.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 549

The method involves the successive solution of seven formulas:

cos D=sin ES sin d;--cos d, cos d; cos S (1)
sin ENS (2)
rēt sin h, tan hy
bs f aeos h; sin D^ tan D (3)
} X,= (X, +41) FA, (4)
sin L=sin d; sin h,+ cos d, cos h; cos X, (5)
sin t, In X; cos h;
OS a (6)
\=GHA,+t, (7)

in which D is the great-circle distance (angular) between the two celestial bodies, d, is
the declination of the first body, d; is the declination of the second body, S is the differ-
ence of SHA of the two bodies, X, is the parallactic angle of the first body, 4, is the angle
at the first body between its vertical circle and the great circle between it and the second
body, h, is the altitude of the first body (Ho is used), h, is the altitude (Ho) of the
second body, L is the latitude of the observer, t, is the meridian angle of the first body,
X is the longitude of the observer, and GHA is the Greenwich hour angle of the first
body.

If the great circle joining the two celestial bodies is on that side of the zenith
opposite the elevated pole (if Z is within the angle formed by the vertical circle and
hour circle of the first body), (Xı +4) is used in formulas (2) and (4), the sign in formula
(3) 1s positive (4-), and the sign of A, in formula (4) is negative (—). These signs are
all reversed if the line adjoining the celestial bodies is on the opposite side of the zenith
(Z outside the angle). If the great circle joining the two bodies passes almost through
the zenith, an error might be made in the selection of the sign, and it is well to select
another star pair. In formula (7) the sign is positive if the first celestial body is east
of the observer's celestial meridian, and negative if it is west. The answer is in longi-
tude measured westward from the Greenwich meridian. If the value exceeds 180?, it
is subtracted from 360%, and the longitude is east.

If the quadrant of angle (X,+A;) or if t; is in doubt, the following formulas are
suggested to replace (2) or (6):

cot (X PEM à Esta d; tan pe d; cos S eN
CoU este d; tan AE d; cos X, dio

In the presentation of the method it was suggested that simultaneous observations
be obtained by a two-star tracker mounted on a stable platform, or by a double sextant.
Several such sextants have been proposed, but none is in common use. Other possi-
bilities would be to have two observers or to adjust the value of one observation for
the change in altitude due to its apparent motion and the motion of the observer between
observations.

It was proposed that values obtained by solution of formula (1) be published in a
permanent table, since these values for various star pairs would be constant except for
the very slight change due to proper motion (art. 1418). Since the values obtained by
formula (2) change slowly with precession of the equinoxes (art. 1419), 1t was proposed
that the angle (X,--.4:) for a number of star pairs be published annually, perhaps in
the almanacs. The other formulas would be solved after observation of the celestial

bodies.

550 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

Kotlarié. In 1956 Stjepo M. Kotlarié (art. 2112), of Yugoslavia, proposed a
method based upon computation of the same quantities suggested by Dozier. In the
Kotlarié method most of the computation would be done in advance and published in
tables divided into volumes for different latitude bands. This would generally elimi-
nate the need for two answers for each set of altitudes, for the two intersections of the
two circles of position would ordinarily be so far apart that only one solution would
fall in the tabulated latitude band. Each volume would have a two-page index listing
the stars used for each 5? latitude band and 15° LHA T band, based upon the selection
used in H.O. Pub. No. 249, Vol. I (art. 2113).

Similar tables were proposed for use with two observations of the sun or moon
taken 45? of GHA apart. In this case, the first observation would be corrected (be-
fore the tables were entered) for the change in altitude due to motion of the craft
between observations.

A separate table would be provided for each pair of observations. The tables
would be entered with the altitudes, to the nearest 0?5, and the latitude of the observer;
and the meridian angle of the second celestial body would be taken directly from the
table. The meridian angle and GHA (from the almanac) would then be combined to
find longitude. Delta values and a “multiplication table" would provide corrections
for (1) the differences between observed and tabulated altitudes, (2) the difference
between actual and tabulated declinations, and (3) the difference between the actual
and tabulated SHA (or GHA) difference of the two celestial bodies. In the case of
stars, the corrections for (2) and (3) are primarily due to precession of the equinoxes
(art. 1419). If star observations were not taken simultaneously, a correction would
be applied (before the tables were entered) to the first altitude to obtain the value it
would have if made at the time of the second observation.

Uribe-White. A unique method of using two stars was suggested in 1952 by
Enrique Uribe-White, of Colombia. A bubble sextant would be used to measure the
altitude of one star, while a small, marine-type sextant attached to the bubble sextant
would be used to measure simultaneously the angle at the star between the vertical cir-
cle and the great circle through this star and a second one. Prepared tables would
give the great-circle distance between the two stars and also the angle between the
great circle joining them and the hour circle of the first star. This angle, combined
with the inclined angle which would be measured, constitute the parallactic angle
(art. 1433). With this value, the observed altitude, and tbe declination of the first
body, the latitude of the observer and the meridian angle of the first star could be com-
puted by relatively simple formulas or by a mechanical computer proposed by the
originator of the method. Meridian angle could be compared with GHA to deter-
mine longitude.

2117. Position from observation of single body.—If azimuth could be determined
and plotted to sufficient accuracy, the altitude and azimuth of a single body could be
used for establishing a fix. Any combination of altitude and azimuth methods (arts.

2108 and 2114) might be used, or the position could be computed without plotting. The
following formulas might be used:

sin t=sin Z cos h sec d
tan K,=cos t cot d
tan K,=c0s Z cot h

L=90°—(K,+K,) (Approximate latitude must be known)

r A single body can be used for a running fix, of course, and if the body is near the
zenith, à relatively short time might be needed. This is the case for high-altitude

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 551

observations (art. 2011) and has been used by a submarine measuring azimuth through
its periscope when the sun is near the zenith (art. 2404).

Willis. Another method of determining position by a single body is by the use
of altitude and rate of change of altitude. Three methods of doing this were suggested
by Edward J. Willis in 1928.

Prime vertical observation. It can be shown by the use of differential calculus
(art. 044) that

cos L-% csc Z ; (1)

dh . a ;
when de P the rate of change of altitude with respect to time, specifically the change of

altitude in minutes of arc during a one-minute-of-arc (four-seconds-of-time) change of
hour angle of the body. However, to obtain latitude accurately in this way it is neces-

ax. dh Å
sary to determine dt to an accuracy of perhaps four decimal places, and Z to an ac-

curacy of perhaps one minute of arc. Two possible methods of obtaining dh are given

dt
below, but present instrument limitations do not permit measurement of azimuth to
the required accuracy. However, the cosecant of 90? is unity, so that if the observation
is made when the celestial body is on the prime vertical, the formula becomes

dh
cos L8 (2)

Relatively little error is introduced if the body is within 1? of the prime vertical.
The determination of position consists of the following steps:

1. Observe the altitude (h) and rate of change of altitude GI when the celestial

body is within 1° of the prime vertical.

2. Compute latitude (L) by formula (2).

3. Determine longitude by any standard method, such as H.O. Pub. No. 214 or
other line of position method, or by time sight (art. 2106).

Perpendicular lines of position. The great circle through the zenith and the celestial
body (the vertical circle or azimuth line) furnishes an azimuth line of position that can
be established if rate of change of altitude can be accurately determined. This line is
perpendicular to the circle of equal altitude and therefore nearly perpendicular to the
line of position determined in the usual manner. The intersection of the two lines
is the position of the observer. The method involves the following steps:

1. Observe the altitude (h) and rate of change of altitude (E)

2. Compute the direction of the great circle through the zenith and the celestial
body (the vertical circle) at the point where the great circle crosses the celestial equator.
This is the complement of the latitude of the vertex and so can be found from a modifica-
tion of formula (2), which gives the latitude of the vertex:

sin Z= (3)

3. Compute the longitude (Ao) at which the vertical circle crosses the celestial
equator, using the formula

sin (o X) — tan Zo tan d (4)

The value X, is the longitude of the geographical position of the celestial body.

552 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

4. Solve for the latitude (L) at which the azimuth line of position crosses the
meridian of the dead reckoning position, or for longitude (X) at which the line crosses
the parallel of latitude of the dead reckoning position, using one of the following formulas:

tan L=cot Zo sin (Xy Apr) (5)
or sin (Ao -A)=tan Zo tan Lpr . (6 )

in which Lpr and Apr are the DR latitude and longitude, respectively. Any assumed
position in the vicinity can be used in place of the DR. In general, it is preferable to
use (5) if azimuth angle is between 45° and 135°, and (6) if it is outside these limits.

5. Solve for the direction (Z) of the azimuth line of position at the point determined
in step (4), using the formula

sin Z=sin Zo sec L (7)

If the DR position or the AP is near the actual position, the azimuth can be considered
the same at both without appreciable error.

6. Plot the azimuth line of position through the point found in step (4), in the
direction found in step (5).

7. Compute a and Zn by any method and plot the resulting line of position. The.
intersection of the two lines of position is the fix.

Latitude and longitude by computation. This method is independent of a dead
reckoning position, and requires no plotting. It is free from limitations except that
observations near meridian transit should be avoided. At this time the rate of change of
altitude decreases to zero and then reverses, introducing a possible error. The steps
by this method are:

1. Observe the altitude (h) and rate of change of altitude (Æ)

2. Compute Zo, using formula (3).
3. Compute the latitude (L) of the observer by the formula

sin L=cos Zo cos [ hæsin”! ( sin d ] (8)
cos Zo
sin d
cos Zo
from h. The cosine of this angle is then multiplied by cos Zo, and the result is the sine
of the latitude of the observer. The sign is positive (+) unless L is greater than d and
has the same name, when it is negative (—). However, if d is of the same name and
greater, the angle to be added may be greater than 90°.
4. Compute the meridian angle of the observer by the formula

In the solution of this equation, the angle whose sine is is added to or subtracted

sin t=sin Zo cos h sec d sec L (9)

5. Determine GHA for the time of observation.
6. Convert t to LHA, and compute longitude (A) by the formula

A=GHA-—LHA (10)
If X is greater than 180°, subtract it from 360° and label it E (east).

Formulas (8) and (10) yield a position on the circle of equal altitude regardless of
the value of Zo used. The correct position is given only if the correct value of Zo is used.
Any of the three methods requires determination of F Two methods are proposed:
In the first, the time needed for the sun (or moon) to change altitude an amount
egual to its own diameter is measured. If the body is rising, the upper limb of the
reflected image is brought a short distance below the horizon. As it makes contact
with the horizon, a stop watch is started. When the lower limb makes contact with the

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 553

horizon (usually between 127.8 seconds, the minimum for a stationary observer, and
ten minutes after the first contact) the watch is stopped, and the time is read to the
nearest tenth of a second, if possible. If the body is setting, the lower limb of the
reflected image is brought a short distance above the horizon and the watch started
when the lower limb makes contact and stopped when the upper limb makes contact
with the horizon. At sunrise or sunset no sextant is needed. Any lag in starting or
stopping the watch will not affect the result if it is the same at both ends of the period.
The diameter of the body, in minutes of arc, divided by one-fourth the number of

gluten aie Å
seconds is is Since semidiameter is tabulated, the most convenient procedure for

Hine. dh;
determining as probably to solve the equation

dh 8SD

MIRI
where SD is the semidiameter of the body in minutes and T is the time interval in
seconds. The semidiameter is given to the nearest 0/1 in the Nautical Almanac.
More accurate results will be obtained if the value is taken from the Ephemeris, where
semidiameter is given to the nearest 0701.

The motion of the observer introduces an error which can be corrected as follows:
multiply half the run of the vessel between upper and lower limb contacts, expressed
in nautical miles, by the cosine of the angle between the course of the vessel and the
azimuth of the celestial body at the mid time of observation. If this angle is less than
90°, the correction is added to the tabulated semidiameter if the body is setting, and
subtracted if it is rising. If the angle is greater than 90°, the correction is added if the
body is rising and subtracted if it is setting.

Some practice may be needed to obtain an accurate measurement of the time inter-
val. This practice might be obtained by making a number of observations at a known
position and comparing these with values obtained by computation, using the formula

T=8 SD cos h sec d sec L esc t,

using He for h.

The time of an observation is at the middle of the interval between contacts.
In correcting hs, the reading of the sextant, to obtain Ho, omit the correction for
semidiameter. This might be done by correcting in the usual manner, with an addi-
tional correction equal to the semidiameter. The additional correction is negative
(—) if the lower limb correction is applied, and positive (+) if the upper limb correction
is applied. Another way is to apply neither the lower nor upper limb correction, but
a value equal to the algebraic average of both.

The second method of determining a is given as the more accurate of the two.

It consists of observing three altitudes of the celestial body at exactly equal intervals
of from 15 to 30 minutes. A shorter interval may result in too great an error in rate,
while a longer one increases the time without advantage. If h, ho, and h are the three
altitudes and t, and t4 are the meridian angles at the times of the first and third ob-

servations, respectively, gà can be computed by means of the formula
EET %(h,—h3) cos Mib: +h3) esc X(t; —t5) sec hy.

If difficulty is experienced in making an accurate observation at a given time,
better results might be obtained by computing the time for the third observation, by
adding the interval between the first two observations to the time of the second ob-
servation, and then making several observations starting shortly before the computed

554 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

time. These can then be plotted on cross-section paper with altitude as one coordinate
and time as the other. The altitude indicated by the intersection of the line represent-
ing the required time and a line faired through the plotted points is used as the third
altitude. A similar procedure might increase the accuracy of the first two observa-
tions. A quicker but less accurate way of determining the third altitude is to take one
observation shortly before the required time and another shortly after it, and interpolat-
ing to find the altitude at the required time. Another variation is to take an altitude
at about the required time and adjust the second altitude to the corresponding value
midway between the first and third observations, using the mean value found by
interpolating from the first or third observation and extrapolating (art. P6) from the
other. The time and altitude are those of the second observation.

This method assumes no change of declination between observations, and no change
in the position of the observer. When the observer is not stationary, a correction is
applied to h, and h; to convert them to the equivalent values at the position of the
second observation. Assuming constant course and speed, this correction in minutes
of arc is equal to the vessel's run between consecutive observations multiplied by the
cosine of the angle between the course of the vessel and the average azimuth of the
body. If the angle is less than 90°, the correction is added to h; and subtracted from hs.
If the angle is greater than 90°, the correction is subtracted from h, and added to ha.

A possible variation of either method of determining E would be to make a com-

paratively large number of observations (10 to 15) at short intervals and plot the
altitudes versus time on cross-section paper. A point near each end of the line faired
through the plotted points would then be corrected for the run of the vessel, as in the
second method. Two points might then be selected, one near each end of the altitude-
time line. The change in altitude, in minutes, divided by the number of seconds
between the two points is = If preferred, three points might be selected at equal
intervals and the formula of the second method used.

Rate determined by two individual observations a few minutes apart would not
be sufficiently accurate for practical navigation.

None of the methods employing rate of change of altitude have proved popular,
probably because of the difficulty of obtaining an accurate value of CH The use of
azimuth and rate of change of azimuth, altitude and rate of change of azimuth, or
azimuth and rate of change of altitude have been even less attractive because of the
even greater difficulty of obtaining accurate measurements of azimuth or rate of change
of azimuth. With the further development of automatic devices for continuously
measuring altitude or azimuth, with allowance for motion of the observer, such methods
might prove more attractive.

2118. Use of unique situations.—Various unique situations might be used for
determining position or a line of position. As a general rule these have not been
attractive because they could be used only when the conditions were met. As an ex-
ample, if a celestial body of known coordinates were known to be in the zenith, the
declination of the body would be the same as the latitude of the observer. His longitude
would be the same as GHA of the body (360°—GHA in east longitude).

Near the geographical poles, the poles can be used as the assumed position. Here
the declination of the body is the same as the computed altitude, and GHA replaces
azimuth.

Meridian altitudes (art. 2103) and latitude by Polaris (art. 2105) are examples of
methods depending upon unique situations. These have both been used extensively,

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 555

but are decreasing in popularity because of their reliance upon unique conditions,
without adequately compensating advantages.

Shchetkin. In 1899 N. O. Shchetkin proposed a method of computing latitude
and meridian angle from measurement of the times at which two or more pairs of stars
have the same altitude. Each star pair would provide, in effect, a single great-circle
line of position. Variations of the method were proposed by Zinger, Pewzow, and
W. W. Kawraisky, a Russian. The necessary tables for latitude 60% N to 809 N were
published by the Astronomical Institute of Russia in 1936. A similar method was
prepared by Simon Swahn in 1943.

Collins. In 1946 Oliver C. Collins, an astronomer at the University of Nebraska,
proposed a variation of the method of Shchetkin, and extended it to include observa-
tions when two celestial bodies have the same azimuth.

McKee. In 1951 Lieutenant Merlin A. McKee, USMS, proposed a graphical
solution of the same-altitude method of Collins.

Pierce. About 1951 Rear Admiral M. R. Pierce, USN (Ret.), suggested a method
of establishing a line of position perpendicular to the course line when the altitude of
a celestial body is observed at the moment it crosses the great circle through the
observer and his destination.

2119. Graphical and mechanical solutions.—All of the methods described above
require tables, either for a mathematical solution or to extract computed values of
altitude and azimuth. The total number of possible tabular solutions must be very
great. The number of graphical and mechanical solutions is almost endless. The
ones selected for mention below are representative of the types that have been prepared
or made available.

Graphical solutions are almost as old as tabular ones, having existed at least since
1790, when Margetts’ Horary Tables appeared in graphical form. These were intended
“for shewing by Inspection the Apparent Diurnal Motion of the Sun, Moon, and Stars,
the Latitude of a Ship and the Azimuth, Time, or Altitude corresponding with any
Celestial Object." They were intended primarily for use with the longitude method
of laying down a line of position.

In general, graphical and mechanical solutions have not proved popular, for several
reasons: First, they generally involve a small scale, yielding results of less accuracy
than desired, even with careful work. Second, some of the methods must be used as
a whole, and cannot be divided into parts to increase the scale. Third, such methods
usually do not provide a record of the solution, and it is often difficult to check the
results. Fourth, solutions requiring instruments are subject to errors due to lack of
proper adjustment or mechanical damage which may not be apparent. Fifth, the
required diagrams or instruments may be quite bulky, requiring considerable space
for stowage and manipulation. Finally, in some cases the necessary instruments are
expensive.

2120. Altitude and azimuth angle by graph.—One type of graphical solution is
by means of a diagram that solves an equation.

d’Ocagne. Typical of such diagrams is that prepared by Maurice d’Ocagne, a
Frenchman. Both altitude and azimuth angle can be found by means of this diagram,
which is based upon the following formulas:

hav z=hav (L—d)+(hav [180?— (L4-d)] — hav (L—d)) hav t,
hav (90°+d)=hav (L—h)--[hav [180?— (L+h)]— hav (L—h)) hav Z,

in which z=90%—h.

556 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The sides of a square are divided according to the haversines of angles, from 0°
to 180°, and the corresponding graduations of opposite sides are connected with straight
lines, forming a diagram as shown in figure 2120a. The graduations on the two sides
run in opposite directions. To find the zenith distance, locate the value corresponding
to (L—d) along the left of the diagram, and the value corresponding to (L+d) along
the right of the diagram. Draw a straight line through these points. Locate the
intersection of this line with the vertical line corresponding to meridian angle. A
horizontal line from this intersection to the left edge indicates the zenith distance.

t-A
DEGREES
360 340 330 320 310 300 290 280 270 260 250 240 230 220 210 200 180
0 20 30 40 50 60 70 LN 90 100 110 120 130 140 250,160.19.
miss eee sossa d
210 150 ut y ELI ru" =»

220 140 i

I
230 130 : H |
240 120 | +—+ | es

even IET

[= — p) | Tl

z 260 100 | m: = dlls d |
H

DEGREES 270 9 ==

H

L=\ a HHHH HA > |

99-0 MI D |
290 70

Hk.

H
H

|
d
=

E
H
BEE
PE

Sm L+D

£

270 DEGREES

Lan

EE
3
^o
ES

S
Es

i

+

EE
Pa
F
===
P:

lA lala ll TTU 136
ES T
| Lil]
310 50 130 230
| Ki I | CTT
e adi CIE EE EHE ze
330 30 < 1 ii | —— NT 150 210
340 20 +H [rxs dus ee AOS A E) a STIK IÐ Í í |
si == === SO ees (a
1 2 3 4 5 6 7 8 9 10 1112
HOURS
d

Ficure 2120a.— The d'Ocagne diagram as H.O. Chart No, 2776.

To find azimuth angle, draw a straight line between (L—h) at the left and (L+h)
at the right. Locate the intersection of this line and the horizontal line corresponding
to (90°—d). A vertical line from this intersection to the top of the diagram indicates
the azimuth angle.

If the altitude, latitude, and declination are known, the first solution can be made
in reverse for meridian angle, for a longitude method solution.

The diagram was first published in 1899 in Traité de Nomographie by d'Ocagne.
Similar diagrams have since been published under the name Spherical Triangle Nomo-

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

gram by Wimperis, and under the
title Altitude, Azimuth, and Hour
Angle Diagram by Littlehales in
1906, and by the U. S. Navy Hy-
drographic Office in 1917.

Favé and Rollet de l'Isle.—
If a perpendicular is dropped from
the celestial body to the celestial
meridian, a diagram can be pre-
pared to solve the basic formulas
given in article 2111, or others de-
rived from these. Such a diagram
is shown in figure 2120b. This
diagram was devised by the French
engineers Favé and Rollet de l'Isle
in 1892. The diagram represents
only one-eighth of a sphere, addi-
tional sections being needed. An
alternative is to show additional
labels, as in figure 2120b. This
results in three “cases” and sev-
eral rules similar to those used with
some logarithmic solutions. Solu-
tions for both altitude and azimuth
angle are made in two steps, plus
one addition or subtraction. This
diagram was reproduced by the
Frenchman M. E. Pereire in 1894
and by another Frenchman, P.
Constan, in 1906 as a method of
finding azimuth.

Jernzes.—In 1953 Leiv Jernes,
a Norwegian, invented a device he
called a “Nauticator,”” which con-

EIFE:
E
7

557
KE 90
= » Y 80
CEJA ase di
a ETE
ES SEI
y euim
E So 9l SJ A
e |
C = 50
d | N
ELIAS s
xd N | Ch 40
al PS
SAS
= (AZ 30
H AH pet LK < e xS BS OO A
ME NK N o
ti SX
IR
LT Ea] 10
afloja E
adek ad 17] i
INTSYHNDCMEUPUDINTISPUCUTIMES
11077 120 130" 140 150. 160. 170 180, — IE
250 240 230 220 210 200 Fir

270 260

Case 1.

Case 2.

Case 3.

8

3' =p +(90*-L)

Land D same Name —t<90°
Read [> on scale II

Azimuth from upper pole, E or W as star is E or W of
meridian

Land D same name —t>90°
Read (180? —t) instead oft
Read (3 on scale I

Azimuth from upper pole, E or Was star is E or W of
meridian

L and D opposite names
Read (5 on scaleI

Azimuth from lower pole, E or Was star is E or W of
meridian

Figure 2120b.— The Favé diagram.

sists of various scales in a semicircle with radial scales on a plastic arm pivoted at

the center of curvature of the semicircle.

The device is used with a pair of dividers

to solve various problems of spherical trigonometry to an accuracy of about 15”.

Bertin.

In 1955 Rev. Maurice Bertin, a Frenchman, devised a graphical

solution for the longitude method, using the formulas:

tan? Y t=tan % (90°—a) tan % (90? — B) (1)
! tan 1⁄2 (90? — a)
and tan? 4 Z—.— y (9058) (2)
in which tan 4 a=tan X (h+d) tan X (90 —L)
tan % (h—d
and tan % 8 AN

— tan X (909—L)

598 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The diagram consists of three families of straight lines, one vertical, one horizontal,
and the third at an angle of 45° to the others. The accuracy depends upon the scale
of the diagram, but a large one is needed for navigational accuracy.

2121. Altitude and azimuth angle by computer.—Slide rules, like diagrams, have
been devised to solve formulas. In the case of the navigational triangle, both suffer
from the need for a scale that can be read to a subdivision at least as small as 1'. A
number of such slide rules have been devised for use in reducing celestial observations.

Richer. In 1791 Jean Francisco Richer, a Frenchman, constructed a device
composed of six arms, some hinged and some sliding, which won a prize offered by the
Paris Academy of Science for a simple method of “clearing” lunar distances (art. 131)
in the solution for longitude. The device solved a formula devised by the French
mathematician Joseph Louis Lagrange, and was capable also of solving other problems
involving spherical triangles, such as those related to time sight solution (art. 2106),
computation of altitude, and great-circle sailing problems (art. 819).

Poor. A slide rule invented by Professor Charles L. Poor is shown in figure 2121a.
This device, called the “Line of Position Computer,” was designed to solve the cosine-
haversine formula (art. 2109). Eight concentric circular scales are engraved on a
metal disk about 15 inches in diameter. A plastic arm and circular sheet are pivoted
at the center of the disk. The arm may be clamped to the plastic sheet. The seven

FIGURE 2121a.— The Poor Line of Position Computer.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 559

FIGURE 2121b.—The Bygrave slide rule.

outer scales are used in solving for altitude. The altitude scale is graduated at intervals
of 10’, and further subdivisions can be estimated. The inner scale is used for deter-
mining azimuth angle. Several rules are needed, and the number of scales adds to the
possibility of error.

Bygrave. A cylindrical slide rule was designed by the Englishman Bygrave to solve
the navigational triangle divided by dropping a perpendicular from the celestial body
to the celestial meridian (fig. 2111). This device, shown in figure 2121b, consists of
three concentric tubes. The inner one has a spiral scale of logarithmic tangents, the
middle one a spiral scale of logarithmic cosines, and the outer one a pointer for each
scale. Solution is simple and relatively fast, but altered procedures are required if the
azimuth angle is near 90°, or the meridian angle or declination is very small. The
overall dimensions are about 2% inches in diameter by nine inches long. An accuracy
of about 1’ or 2’ is generally attainable.

Bertin. In 1955 Rev. Maurice Bertin devised an 18-inch slide rule to provide a
solution of the longitude method to an accuracy of about 1°, using the formulas upon
which his graphical solution (art. 2120) is based. He also devised a solution of the
same formulas by a circular slide rule consisting essentially of two spirals. The inner
one is on a disk 23 centimeters (9.2 inches) in diameter, and the outer one is on an
annular ring 39 centimeters (15.6 inches) in outside diameter. The graduations are
proportional to the log cotangents of half-angles. A window on a cover is provided
with a radial line to serve as an index. Solution is facilitated if an approximation of
the answer is known in advance. An accuracy of better than 3’ is claimed for this
device. Still another solution proposed at the same time is by a computer consisting

560 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

of a strip four centimeters (1.6 inches) wide and 12 meters (nearly 40 feet) long, wound
on two rollers and engraved with three sets of graduations. An accuracy of better
than 1’ is claimed, but several arithmetical steps are required. in |

LeSort. A computing device based upon solution of formulas for a divided navi-
gational triangle was designed by Commander LeSort of the French Navy. l Logarith-
mic scales are placed on eight films wound on rollers. The films operate in pairs so
arranged that the two films of any pair can be locked together at any point. Alternate
films carry log cosine and log tangent scales. Although an accuracy of about 0/2 can
be obtained, the method is comparatively long and has no apparent advantage over
modern inspection tables.

Desk computers. Several desk-type computers have been designed to solve the
navigational triangle, but none has proved popular.

2122. Altitude and azimuth angle by map projection.—If the observer were to
move along his meridian to the nearer pole, and the navigational triangle were tc
move with him without its proportions being changed, his zenith would coincide with
the pole, and the vertical circle would coincide with some celestial meridian. Zenith
distance or altitude could be read directly. Since both great circles forming the
azimuth angle would now coincide with celestial meridians, the azimuth angle could
also be determined directly.

Littlehales. To accomplish this with a sphere, to a useful accuracy, would require
a sphere of impractical size for use by the navigator. However, the solution can be
made by means of a map projection. George Littlehales, of the U.S. Navy Hydro-
graphic Office, used the stereographic projection (art. 318) and a 12-foot sphere for
this purpose. The projection is divided into 368 overlapping sheets which, with a
key diagram, are bound together. An accuracy of about 1’ or 2’ can be ovtained by
a rapid and simple process, but the volume is bulky and not particularly convenient.

Veater. Commander Veater of the British Royal Navy used the transverse Mer-
cator projection (art. 309), with the observer’s meridian as the fictitious equator.

Hyatt. A similar principle is utilized in the diagram on the plane of the celestial
meridian (art. 1432). A mechanical device based upon this diagram can be made by
drawing a hemisphere by equatorial orthographic (art. 319) or stereographic projection
and pivoting at its center an identical hemisphere on transparent material. If the top
hemisphere is rotated until the arc between poles of the two hemispheres is equal
to the colatitude of the observer, the lines of one hemisphere represent coordinates of
the celestial equator system (art. 1426), and those of the other, coordinates of the
horizon system (art. 1428). Thus, if a body is located by meridian angle and declina-
tion on one set of lines, its altitude and azimuth angle can be read from the other set.
If altitude and declination are used to locate the body, meridian angle can be read from
the diagram. In the United States such a device, on both the orthographic and stereo-
graphic projections, has been prepared by Commander Delwyn Hyatt, USN, under
the titles “Celestial Coordinator” and “Coordinate Transformer.” It has also been
produced in other countries, notably in Germany, France, and Russia, where, in addi-
tion to such a device, precision instruments based upon the same principle have been
constructed. The scale of the German instrument is so small that an accuracy of
about 5’ is about the best that can be expected. The Bastien-Morin (French) and
Kavroyskyy (Russian) instruments might yield results of slightly greater accuracy.
The plastic device, if carefully made, might be generally accurate to half a degree.
It has been used primarily for instructional purposes.

h Brown-Nassau. The Brown-Nassau “Navigational Computer” utilizes the same
principle, but uses the azimuthal equidistant projection (art. 320) and increases the

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 561

scale by limiting the device to an octant of the sphere, with separate solutions for alti-
tude and azimuth, and various rules.

True. In ņa Celestial Navigator for Aviators, printed about 1943, Clarence H. True,
of the Canal Zone, uses a single diagram on the HE) projection. This serves as
the basis for a Trees by construction, claimed to be of sufficient accuracy for use in
lifeboats. Various rules are needed.

Pierce. A series of diagrams on the azimuthal equidistant projection have been
devised by Rear Admiral M. R. Pierce, USN (Ret.). The method is based upon the
principle that angles are correctly delent at the point of tangency of this projection,
and radial lines from this point represent great circles along which distances are repre-
sented by a uniform scale. A protractor is used for measuring the azimuth angle.
Attached to the protractor is an arm with a linear scale graduated so that altitude can
be read directly. "The whole device
iscalleda “Cadameter.” The meth-
od is easy to use, and about as fast
as modern inspection tables. With
great care an accuracy of 1’ can be E

rot ||
obtained. The method suffers from = SERDAR
-—

LATITUDE

the need for a number of diagrams
which are somewhat bulky and more
susceptible to damage than a book.

2123. Latitude and longitude
by diagram.—A number of graphical
and mechanical solutions have been
devised to yield latitude and longi-
tude directly.

Beij. One proposed in 1924 by
K. Hilding Beij, of the U. S. Bureau
of Standards, was based upon the
fact that latitude and local sidereal
time are completely defined by the
simultaneous altitudes of two celes-

LOCAL SIDEREAL TIME
LOCAL SIDEREAL TIME

tial bodies whose declination and LATITUDE

SHA are known. A page of his ALTITUDES OF REGULUS R— 60°
proposed diagrams is shown in figure ALTITUDES.OF BETELGEUX Bësse?
2123a, in which latitude is the ab- Fiatre 2123a.—The Beij two-star diagram.

scissa, and LST is the ordinate. Po-

sition on the graph is located by the intersection of the curves representing the altitude
of the two celestial bodies observed. The vertical line through the intersection
indicates the latitude, and the horizontal line the LST. The difference between
GST and LST is the longitude. If a timepiece keeping GST is available, not even
an almanac is needed.

The method is accurate, fast, and direct. The individual sheets can be drawn
to any scale and cut to any size (AR For a large scale with sheets of a convenient
size, a great many diagrams would be needed, but these might be bound together in
convenient-size volumes, or placed on a tape wound around rollers, as originally proposed.
A weakness of the method is the requirement for simultaneous observations. For
nonsimultaneous observations a table might be provided to indicate the change in
altitude during the interval between observations. Since the positions of the curves
depend upon the declination and SHA of the body, the method is limited to celestial

562 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

bodies whose coordinates are nearly constant, unless the curves are intended only for a
particular time. Even for stars, the diagrams become out-of-date in a few years. The
method is limited to the particular bodies for which curves are shown, although the
number of curves need not be limited to two. This is a form of precomputation, since
the computation is performed in locating the curves, rather than by the navigator.
In a sense, it might be considered a graphical form of H.O. Pub. No. 249 (art. 21 13).

Weems. If the Beij diagram is rotated through 90°, the parallels of latitude be-
come horizontal, as customary on a chart. If they are spaced according to the Mercator
projection, azimuth is indicated by the normal to a curve. This is the arrangement
used by Captain P. V. H. Weems, USN (Ret.), in his Star Altitude Curves, the first
volume of which was published in 1928. Later he added a third star, using a different
color for each star, and included a correction for refraction at sea level. A separate
volume is used for each 10° of latitude, and a correction is provided for precession of
the equinoxes. Coverage extends from latitude 50°S to 70? N, with a separate volume
for latitude 70°-90°N. The curves for 80°-90°N are on the polar stereographic
projection. Any orthomorphic projection (art. 302) could be used at any latitude.

Lines representing observations at different times can be advanced or retired as
on any chart of the same projection. In addition to the adjustment due to motion of
the craft between observations, the lines are shifted right or left for the elapsed time
between observations. An accuracy of about 1’ is attainable by interpolation between
curves for each 10’ of altitude.

The star altitude curves are undoubtedly the most widely used of all the graphical
and mechanical methods. Two-star curves similar to Weems’ first edition were
published in Germany in 1940.

Pritchard and Lamplough. In 1940 H. C. Pritchard and F. E. Lamplough, of
the British Royal Aircraft Establishment, devised a method of reducing the work in-
volved in the adjustment for elapsed time between observations. They placed the
star altitude curves on film which is used in a projector called an astrograph. The
curves are projected onto a Mercator plotting sheet and can be moved across it to allow
for rotation of the earth. The adjustment is critical, the setting of the projector some-
what involved (a special “astrograph mean time” being needed), and a bulky and ex-
pensive projector is needed to prevent distortion. Because of these disadvantages and
the fact that any advantage over short tabular methods is slight, the astrograph
decreased in popularity following World War II.

Longley. In 1943 Flight Lieutenant C. D. N. Longley, RAF, suggested a “Star
Computer” based upon the principle of the astrograph. A circular disk serving as a
base plate would have a mean time scale around its circumference. Altitude curves
of a limited number of stars would be printed on a template for each latitude. The
circumference of each template would also carry a mean time scale. A radial cursor
would aid in reading the device, which is set by means of the GMT at which LHA T is
0° at some convenient longitude, the time of observation, and observed altitude.
Longitude is determined within a 10° band, the ambiguity being resolved by means of
the dead reckoning position. With a modification of the procedure, the device can be
used with the altitude method.

Baker. As early as 1919 Commander T. Y. Baker, RN, prepared altitude curves
and their orthogonals (normals) on transparent tape which is wound on rollers in the
“Baker Navigating Machine” (fig. 2123b). The transparent tape is moved across a
Mercator plotting sheet, being oriented by means of a time scale set with respect
to a meridian. The line of position is transferred to the plotting sheet by means of
carbon paper. A single tape has curves for several stars, and a separate tape for each
4° of declination from 24°N to 24°S permits use of the device with the sun and other

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 563

bodies of the solar system. A rule attached to the machine (shown at the top of fig.
2123b) provides a correction for declination differing from that of the curves.

Davies. The principle of the Baker Navigating Machine was used by Com-
mander T. D. Davies, USN, in 1947 in a device for use in the antarctic. A chart on
the polar azimuthal equidistant projection (art. 320) is printed on plastic material.
A set of altitude curves is printed on a second sheet and placed under the chart, being
pivoted at the south pole. A slot in the material bearing the altitude curves permits
adjustment for any declination between 8°S and 18°S, the values the sun was to
have had during the original period of use. Additional sets of curves could be provided
for other declination ranges, or the slot increased in length. In the use of the device,
the curves are oriented for GHA and declination, and a short segment of the curve
representing the observed altitude is traced on the chart.

Weems. In 1955 Captain P. V. H. Weems, USN (Ret.), prepared a somewhat
similar device called a “Polar Computer,” using his star altitude curves.

Leick. In 1911 Dr. A. Leick, a German, prepared a diagram by which latitude
and LST could be obtained by altitudes of Polaris and one other star. The diagram
can be used for finding the
correction to apply to the
altitude of Polaris to de-
termine the latitude, and
then to find the LST in a
second step.

Favé. In 1901 Favé
devised a graphical solu-
tion based upon the Marcg
St.-Hilaire principle (art.
2108). Achart on the ster-
eographic projection (art.
318) is used. Tables of
computed altitude and az-
imuth for the point of
tangency are needed. The
chart is on transparent ma-
terial. An additional sheet FIGURE 2123b.— The Baker Navigating Machine.
has a set of arcs of circles,
with a straight azimuth line drawn normal to them. The chart is placed over the curves
with the straight azimuth line through the point of tangency and oriented in the
direction of the celestial body. A large circle on the chart assists in this orientation.
The chart is then moved along the azimuth line until the curve representing the com-
puted altitude at the point of tangency is under that point. The curve representing
the observed altitude is then correctly placed and a segment of it can be traced on the
chart. However, due to chart distortion, error is introduced in this way. It can be
removed by means of a nomogram which indicates the correct curve to use. A mark is
placed on the chart at the intersection of the azimuth line and the curve representing the
observed altitude. The chartis then moved along the azimuth line a second time until
the correct curve is in place, and the arc is traced. This process is repeated for each
celestial body observed. For stars, a one-page set of curves can be used instead of
tables for determining altitude and azimuth at the point of tangency. Favé recom-
mended use of five separate charts with points of tangency at 0?, 30?, 459, 75%, and 90°,
respectively. Each chart could be used as a plotting sheet for any longitude at the
same latitude, requiring computed altitude and azimuth for only five places. Favé

564 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

later put his method into instrumental form and used a special protractor and curved
ruler.

Brill. In 1909 Dr. Alfred Brill, a German, invented a device based upon the
same principle used by Favé, as shown in figure 2123c. In this device the plotting
sheet is on the azimuthal equidistant projection (art. 320) and covers about 10° of
latitude. Two sets of curves on separate sheets of tracing cloth are mounted below the
plotting sheet. A handle turns the plotting sheet to the correct azimuth. l <

Voigt. The same principle used by Favé and Brill was used in the Voigt “Orion”
instrument constructed in Germany in 1911. A plotting sheet on the azimuthal equi-
distant projection is engraved on aluminum. Each of the three plotting sheets,
centered on latitudes 42°, 50°, and 55°, respectively, covers a spread of 10? of latitude.
The line of position is drawn by means of a flexible ruler mounted on a bridge that can
be clamped at any position over the plotting sheet. The curvature is controlled by
means of gears, a scale being provided to indicate the correct value.

Vucetic. In 1921 a device called
a ''Toposcope" was prepared by
Vucetic, a Frenchman. The device
is identical with the Brill instrument
except that a single set of curves is
prepared and these are cut through
the material as slots, and placed over
the top of the plotting sheet.

Littlehales in 1918 suggested a
method similar to that of Favé, but
with a polyconic projection (art. 315).

Kahn. In 1928 Louis Kahn, a
French naval architect, prop osed that
a set of navigational charts be pre-
pared on the oblique Mercator pro-
jection (art. 310), a separate chart
being provided for the great circle
between various places on the earth.
On each chart the small circles on the
earth directly below the parallels of

FIGURE 2123c.— The Brill device. declination (that is, the daily paths
of the geographical positions) of var-
10us navigational stars would be shown. These circles would be graduated in Greenwich
sidereal time, so that the GP at any GST would be indicated. The distance from any
assumed position to the GP at the instant of observation would be the zenith distance,
and the direction of the line would be the azimuth. By comparing the observed
zenith distance with that at the assumed position, the navigator could obtain the
altitude difference, and plot the line of position. The common intersection of two or
more such lines of position, advanced or retired to a common time if necessary, would
define the position of the observer. The method would be limited to zenith distance
within the range of the chart. A later version would produce greater accuracy, but
with a little more trouble in making the measurements, by substituting the gnomonic
projection (art. 317) for the oblique Mercator projection.

Dusinberre. In 1944 Lieutenant Commander H. W. Dusinberre, USN, suggested
a method using star diagrams. A diagram for each 1° of latitude and 1° of LHA Y
would be provided. Each diagram would consist of a series of radial lines extending
in the directions of the prominent stars favorable for observation. The 22 stars of

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 565

H.O. Pub. No. 218 (art. 2113) were suggested. Until changed by precession of the
equinoxes (art. 1419) the common origin of these lines would represent a definite
altitude for each star. The altitude at the next higher whole degree or half degree,
adjusted for refraction, would be indicated by a tick on the appropriate azimuth line.
After observation, a transparent plotting board would be properly oriented over the
appropriate star diagram, using LHA Y and adjusting for the run between observations.
The line of position would then be drawn at the correct point, perpendicular to the
azimuth line, using the tick as a guide. An LHAY computer was proposed for de-
termining LHA T at the time of each observation from a single LHA Y for a time near
the start of each set of observations. When all lines of position were plotted, the
fix would be transferred to the chart or plotting sheet.

2124. Solution by sphere.—Solution of a spherical triangle directly on a spherical
surface, or by means of arcs representing great circles on the surface of an imaginary
sphere, must have occurred to man quite early. Pictures of ancient navigators sur-
rounded by their instruments and accessories invariably show a sphere. Solution
by sphere is still suggested from time to time. Although this method is relatively simple
and easy, the problem of scale is even more acute than in the graphical solutions.

Spherical methods can be classified in three groups: (1) those which solve the
navigational triangle for a single line of position, (2) those which solve two or more
observations for a fix, and (3) those which combine observation and solution for
a fix.

The first group constructs the navigational triangle with arcs of great circles.
Essentially, such a device consists of three arcs. The one representing the celestial
meridian is usually fixed and a part of the frame. The base to which it is attached
usually carries the azimuth scale. Movable arcs are provided for the vertical circle
and the hour circle. If the latitude, meridian angle, and declination are properly set,
the three arcs form the navigational triangle, and altitude and azimuth angle can be
read from their scales. If altitude is used for constructing the triangle, meridian angle
can be read from the instrument for a longitude solution.

Willis. A large number of teaching aids has been based upon this design or one of
the many possible variations of it. Several precision instruments have been proposed or
actually constructed. In 1932 such an instrument designed by Edward J. Willis, an
American engineer, was constructed in Scotland. The marine version, weighing about
27 pounds, is graduated to 1’; and the aeronautical version, weighing between seven
and eight pounds, is graduated to 5'. The longest dimension of either version is 11
inches.

Japanese Navy. During World War II, the Japanese Navy used an instrument
virtually in the form described above. Results were accurate to approximately 1’.

MeMillen. Of the various methods of determining a fix by sphere, the most ob-
vious is that of providing an actual sphere as a plotting surface, with provision for
striking arcs equal to the zenith distances, using the geographical positions of the
celestial bodies as centers. In 1943 such a method was proposed by D. A. McMillen,
a United States businessman in Sáo Paulo, Brazil. His sphere, of a little more than 14
inches in diameter, had a scale of 8° (480 nautical miles) per inch along a great circle.

Hiltner. In 1945 Dr. W. F. Hiltner, a professor at Lehigh University, suggested
a similar method using arcs of spheres and a billiard ball. This, in effect, sets up two
navigational triangles, locating the observer at the common zenith of both triangles.
Simultaneous observations are needed. ie i

U. S. Navy Training Device Center. About the same time, the Training Device
Center of the U. S. Navy prepared a device called the “Sphereman Craft Positioner,”
combining the functions of the devices of both McMillen and Hiltner, and providing a

566 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

plotting surface for dead reckoning. A line of position from a single observation can
be drawn on the 17-inch aluminum globe, or the triangle of position from the observa-
tion of three stars can be mechanically set up. Provision is made for advancement or
retirement of lines due to motion of the craft. The device was intended for training
purposes.

Zerbee. In 1951 Louis J. Zerbee, of Bellfontaine, Ohio, proposed a device similar
to that of Hiltner, but without the billiard ball. His instrument was called the '"Zerbee
Celestial Fix Finder." Like the Hiltner device, that of Zerbee makes no provision
for nonsimultaneous observations (unless one of them is corrected to the value it would
have if observed simultaneously with the other) or for a check by observation of addi-
tional bodies. Observations of bodies near the meridian or taken from high latitudes
cannot be accommodated.

Combined sextant and computer. At least as early as 1895 an attempt was made
to combine in a single instrument the functions of sextant and computer. Such instru-
ments are fundamentally the same as those described above, except that they are set
by alignment with one or more celestial bodies. If the instrument is level and ac-
curately aligned with the meridian at the time of observation, the miniature sphere is
oriented to the celestial sphere and the earth. If both the altitude and azimuth are
used, a fix can be obtained by means of a single celestial body. If two bodies are ob-
served simultaneously, accurate directional reference by compass is not needed.

The weakness of such methods is the need for a stable platform and either accurate
directional reference or the need for observing two bodies simultaneously.

Beehler. In 1895 Lieutenant W. H. Beehler, USN, invented an instrument he
called the “Solarometer,” which was designed to furnish a position from observation
of the sun. It requires a heavy cast iron base rigidly attached to the ship, with a
bowl set in gimbals and filled with mercury. A float resting on the mercury carries
the sighting instrument.

Hagner. In 1936 Fred Hagner, of San Antonio, Tex., invented a similar instru-
ment he called the “Hagner Position Finder.” This is a portable instrument operating
on the same principle as the Solarometer, but obtaining the vertical by being hung from
a suitable support, and therefore acting as a pendulum. This is reminiscent of the
ancient astrolabe (art. 124).

Bedell. In 1953 A. L. Bedell, of St. Louis, Mo., proposed an instrument based
upon simultaneous observation of two celestial bodies. The horizontal would be
defined by spirit level.

Zenith photography. A number of suggestions have been made for eliminating
a miniature sphere and locating the zenith among the stars. Several methods of doing
this have been proposed, but the usual suggestion is to use a stabilized camera to photo-
graph a portion of the sky in the vicinity of the zenith, which would be marked by a
small cross within the camera. Use of a quick-developing method would reduce the
delay. The position of the craft would be determined by comparison of the developed
picture with a graduated star chart. Another suggestion is to reverse this process by
comparing a previously made photograph with the actual sky.

Automatic celestial navigation. The principal weakness of methods requiring
stabilization is the high order of accuracy needed. An error of 1’ introduces an error
of one mile in the position. Such accuracy aboard a moving craft subject to various
accelerations has been elusive. If stabilization of the required accuracy is available,
it can be utilized with automatic star trackers to provide automatic celestial navigation.
Such a system has been proposed. By means of the star trackers, the device would be
continually oriented to two celestial bodies, and if the device were set for sidereal time,
latitude and longitude would be indicated continuously on dials. The only setting

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 567

required would be the shifting from one star to another when the altitude of the first
one became too low for convenient use of the body.

What would seem to be the “final” step in the development of such methods
would be the scheduling of a voyage or flight in advance and the automatic comparison
of preset values with automatically observed values, any discrepaney being used to
actuate controls to change the heading or speed of the craft so that it would be auto-
matically guided along the prescribed track on a preselected schedule. Several such
methods, either singly or in combination with inertial or Doppler methods (art. 809),
have been proposed for use in guided missiles. They could be adapted for use aboard
ship, but are very expensive.

2125. Azimuth.—Most of the methods described above provide for determination
of both altitude and azimuth angle. Several provide only for altitude. The number
of tables, diagrams, and devices providing solution for azimuth only is very great,
approaching the number providing solution for both altitude and azimuth. The reason
for this is that azimuth is needed for other purposes than sight reduction. One common
use is for checking the compass. Since modern inspection tables have provided parallel
columns of computed altitude and azimuth or azimuth angle, separate azimuth tables
have decreased in popularity.

Azimuth can be determined by computation or by amplitudes (tab. 27, 28), as
well as by azimuth table. The method of computation depends somewhat upon the
information available. There are three general approaches:

Time azimuth is the name given an azimuth or azimuth angle computed with merid-
ian angle (a function of time), latitude, and polar distance (or declination) as the
known quantities. Solution can be made by the following formula:

DAY, Ld Gy hay OL S (541),

in which tan X=sin D esc S cot % t
and tan Y —cos D sec S cot } t.
Further, DE [p~(90°—L)]
and s= 1⁄2 [p+ (90? —L)].

If S is less than 90°, use Z=X +Y if p is greater than (90°—L), or Z=X ~Y if p
is less than (90°—L).

If S is greater than 90°, use Z=180°— (X~ Y).

To convert Z to Zn, label Z north or south to agree with the latitude, and east or
west to agree with the meridian angle.

Altitude azimuth is an azimuth or azimuth angle computed with altitude, latitude,
and polar distance as the known quantities. Solution can be made by the formula:

hav Z=sin (s—L) sin (s—h) sec h sec L,
in which s=% (h+L-+p).

Azimuth angle is labeled N or S to agree with the latitude, and E or W as the
celestial body is east or west of the celestial meridian. |

Time and altitude azimuth is computed with meridian angle, declination, and al-
titude as the known quantities, the most common formula being

sin Z=sin t cos d sec h.

568 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

The weakness of this method is that it does not indicate whether the celestial body
is north or south of the prime vertical. Usually there is no question on this point, but
if Z is near 90°, the quadrant may be in doubt. If this occurs, either the meridian
angle or altitude when on the prime vertical can be determined from table 25 or by
computation, using the formula

cos t=tan d cot L
or sin h=sin d ese L.

If the altitude is Jess, or the meridian angle is greater than the value when the body is
on the prime vertical, the azimuth angle should be labeled N or S to agree with the
latitude. If h is greater or t is less than when on the prime vertical, Z should be given
the contrary name (N or S) to that of the latitude.

Amplitudes. For checking the compass, a low altitude is desirable because it can
be measured easiest and most accurately. If a celestial body is observed when its
center is on the celestial horizon, the amplitude (art. 1428) can be taken directly from
table 27. It is given a prefix E (east) if rising or W (west) if setting. It is given a
suffix N or S to agree with the declination of the body. When the center of the sun
is on the celestial horizon, its lower limb is about two-thirds of a diameter above the
visible horizon. When the center of the moon is on the celestial horizon, its upper
limb is on the visible horizon. When planets and stars are on the celestial horizon,
they are a little more than one sun diameter above the visible horizon.

If the body is observed when its center is on the visible horizon, the observed value
should be corrected by the value from table 28, using the rules given with the table,
before comparison with the value taken from table 27. If preferred, the correction
can be applied with reversed sign to the value taken from table 27 and compared with
the uncorrected observed value. This is the procedure used if amplitude or azimuth
is desired when the celestial body is on the visible horizon.

Example.—The DR latitude of a ship is 51°24’6N, at a time when the declination
of the sun is 19°40/4N. l

Required.—(1) The amplitude (A) when the center of the setting sun is on the
celestial horizon.

(2) The amplitude when the center of the setting sun is on the visible horizon.

(3) The azimuth when the center of the setting sun is on the visible horizon.

Solution.—

(1) A W 32°6 N(tab. 27)

LZS 1°1 S (Rev.)—applied to tabulated amplitude
(2) A W33°7N
(3) Zn 303?7

2126. Azimuth tables are numerous. Originally, they were designed primarily
for use in determining compass error. Since the sun was the celestial body customarily
used for this purpose, most of the tables were designed with the sun in mind. Meridian
angle is commonly expressed in terms of local apparent time, in intervals varying from
about one to 20 minutes. In many of the tables, meridian angle increases upward
from the bottom of the page.

The following are some of the principal azimuth tables:

Wakeley. The first known azimuth tables for use of the navigator were The
Regiment of the Pole Star by Andrew Wakeley. These tables were part of the author's
The Marmer's Compass Rectified, published in London in 1665. These tables show
the “true hour of the day” at which the sun is at the various points of the compass.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 569

k Lynn Azimuth Tables, by Thomas Lynn (art. 2106), were published in 1829.

E 364-page table gives azimuth angle computed by the haversine formula of article

Towson and Atherton. The Tables to Facilitate the Practice of Great Circle Sailing,

by the Englishmen John Thomas Towson and J. W. Atherton, were designed primarily

for great-circle sailing, but since they indicate the course, they were easily adapted to
finding azimuth angle. They were published in England in 1847.

Burdwood. The Tables of Sun's True Bearing or Azimuth, by Staff Commander
John Burdwood, RN, were first published in 1852, with additional parts being added
in 1858, 1862, 1864, and 1866. Captain John E. Davis, RN, and Percy L. H. Davis, of
the British Nautical Almanac Office, later added to the tables, making them complete
for all values of altitude and for declination between 649 N and 64°S. These tables
were standard in Great Britain for more than a century. They have now been largely
replaced by H.D. 486 (H.O. Pub. No. 214) for mariners and A.P. 3270 (H.O. Pub.
No. 249) for aviators. Burdwood used modifications of the time azimuth formula.

Labrosse. Azimuth tables by the Frenchman F. Labrosse were published in
London in 1868, and later in Paris. In 275 pages this Table des Azimuts du Soleil
covers latitudes from 61°N to 61°S, and declinations from 0° to 30°N or S. The
following formula was used:

cot e ae L cot t.
sin t
Fifteen editions had been published by 1920.

Shortrede. In 1869 Captain Robert Shortrede’s Azimuth and Hour Angle for
Latitude and Declination and Tables for Finding Azimuth at Sea were published in
London.

John E. Davis. The first azimuth tables by Captain John E. Davis were published
in 1875. These were published as an extension of the Burdwood tables.

Perrin. In Paris the Nouvelles Tables Destinées a Abréger les Calculs Nautiques,
by Ensign de Vaisseau E. Perrin, French Navy, were published first in 1876. These
consist of three tables of nine, seven, and six pages, respectively, providing elements for
determination of azimuth by a short computation. Several editions were published.

Kortazzi, a Russian, produced a volume appropriately called Modification des
Tables d' Azimuth de Thomson (art. 2106). These were published in Paris in 1880.

H.O. Pub. No. 66 (Schroeder and Wainwright), Arctic Azimuth Tables. Lieu-
tenants Seaton Schroeder and Richard Wainwright, USN, prepared azimuth tables for
use of the USS Rodgers in her search for the arctic steamer Jeanette. These were
published in 1881. Azimuths to the nearest 1’ are given for each 10” meridian angle
between Ap and 7%, for latitudes between 70° and 88°, declination 0? to 23°, same name.

Decante. In 1882 Lieutenant de Vaisseau E. Decante, of the French Navy, pre-
pared Table du Cadran Solaire Azimutal, which was published in 1904, in eight volumes
for latitudes 1° to 66° and declinations 0° to 48°.

H.O. Pub. No. 260 (Schroeder and Southerland). The Azimuths of the Sun were
prepared in 1882 by Lieutenant Seaton Schroeder, USN, and Master W. H. H. Souther-
land, USN. These are popularly called “Red Azimuth Tables,” because of the red
binding used for most printings. This designation distinguishes them from the “Blue
Azimuth Tables” (H.O. Pub. No. 261). After 15 editions, these tables are still in use.
Azimuth angles are given to the nearest 1’, at 10™ intervals of local apparent time
from “sunrise” to “sunset” (middle of the sun on the celestial horizon), with the LAT
and the azimuth angle of these phenomena given at the bottom of each column. A
separate table is given for each 1° of latitude from 0° to 70°. The first part of the

570 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

book is a table for latitude 0°. The second part is devoted to tables of latitude and
declination “same name.” The third part gives “contrary name” tables. Declina-
tion entries are given at 1° intervals from 0° to 23°, with the approximate dates on
which this is the declination of the sun. Extracts from these tables are given in appendix
Y. Values are customarily taken by triple interpolation, using the right-hand “pm”
LAT column as meridian angle, as shown in the following example:

Example 1.—Find the azimuth of a celestial body when its meridian angle is
71°24'3 W and its declination is 18°23/2N, if the latitude is 2391611 N.

Solution.— |
diff. for diff. corr. for + =
t 44576 W 10» (+) 48’ 474 212
d 1894 N 18 (—) 62’ 0°4 254
L 23°3N 19 (+) 25’ 0°3 EN
tab. 79°13’ sum 29’ 25!
COIT. EE COIT. (+)4'
Z (GS tea a
Zn 28027

In the solution, the meridian angle is expressed in time units to the nearest 071,
and the declination and latitude in arc to the nearest 091. The “diff. for” is the unit
of the entering argument. The “diff.” is the difference in minutes of arc between the
tabulated value for the nearest values of t, d, and L, and the next value for the t, d,
or L on the opposite side of the actual value. The “corr. for” is the difference
between the actual value of t, d, and L and that used for entering the table. The
correction for each element is found from this tabulation. For instance, the correction
48’ x4™4

107
find Z, labeled N or S to agree with the latitude, and E or W to agree with the meridian
angle. In entering the table, one should keep in mind that values of t increase upward
from the bottom of the page. Care should be used in locating meridian angle, for the
manner of labeling the values can easily be misunderstood. For latitude 0°, Z is
labeled N or S to agree with declination. Interpolation is made for t and d only, and
the value converted to Zn. The Zn at latitude 1° is then computed, and interpolation
for latitude is made between the two values of Zn.

Blackburne. The New Zealand nautical almanac for 1883 carried the 177-page
“A and B” azimuth tables, by H. S. Blackburne. By 1911, after several modifications,
these emerged as “A, B, C" Tables for Azimuth, Great Circle Sailing, and Reduction to
the Meridian. The range of both the latitude and declination is from 90°N to 90°S.

Lecky. In 1892 Captain S. T. S. Lecky, an Englishman, modified the Blackburne
tables and produced another set of “A, B, C” tables which have been widely used.

Ebsen. The Azimut-Tabellen of Julius Ebsen, published in Germany in 1896,
uses the same formula as Labrosse, and is arranged like H.O. Pub. No. 260, except
that azimuth angles are given to the nearest 0°1, and the time and azimuth angle of
sunrise and sunset are given at the top of the table, in place of the dates of H.O. Pub.
No. 260. In two volumes, coverage is for latitudes 72° N to 72° S, and declinations
0° to 29°. Tables are for same name only, contrary-name situations being handled
by using the supplement of meridian angle, and using the supplement of the value taken
from the table, as in H.O. Pub. No. 261.

Johnson. A Combined Time and Altitude Azimuth Table for latitudes and declina-
tions from 0° to 80°, by A. C. Johnson of the British Royal Navy, was published in
London in 1900. In the same year, his Short, Accurate, and Comprehensive Altitude-

for t is =21'. The total net correction is applied to the tabulated value to

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 571

Azmuth Tables were published. This publication consists of three tables for computa-
tion of azimuth for each degree of latitude and altitude from 0° to 75°, and each degree
of declination from 30°N to 30°S.

Zhdanko. The Russian Tables of Azimuth of the Sun, by M. Zhdanko, published
in 1900, supplied computed azimuth angles for latitudes between 61° and 759. These
were later expanded by Yustchenko.

Percy L. H. Davis. In 1900 Percy L. H. Davis took over the work previously
done by Burdwood and John E. Davis, continuing to improve and extend the tables.

H.O. Pub. No. 261, Azimuths of Celestial Bodies, published by the U. S. Navy
Hydrographic Office in 1902, extend the H.O. Pub. No. 260 tables by providing informa-
tion in similar form (but with meridian angle increasing downward on the page) for dec-
linations 24° to 70%. These are popularly called “Blue Azimuth Tables,” from their
blue binding. Tables for “same name” only are given. If latitude and declination
are of contrary name, the tables are entered with the supplement of the meridian
angle. The value taken from the table is then the supplement of the azimuth angle,
which is labeled N or S to agree with the latitude and E or W to agree with the meridian
angle. Extracts from H.O. Pub. No. 261 are given in appendix Z.

Example 2.—Find the azimuth of a celestial body when its meridian angle is
49°31‘6E and its declination is 57?41'4 N, if the latitude is 51°25/5S.

Solution.—
LESE BAREND diff. for diff. corr. for + —
1800—t — 8^4179 107 (—)75’ 199 14'
Woe EN 19 (+)36' 023 11’
L 51°48 1° (+) 14’ 0°4 6’ e
tab. 26°57’ sum 17’ 14’
corr. (+) 3’ corr. (+) 3’

180°—Z 27°00’
Z S153%00'E
Zu 027°0

One step can be eliminated by considering the corrected value Z instead of 180°—Z,
and labeling it N or S to agree with the declination. Jn this example the body is below
the horizon, showing that a solution is no assurance that a body is visible. X

Symonds. The Nautical Astronomy, with New Tables, by W. P. Symonds, British
Survey Commissioner, Bombay, includes azimuth tables. It was published in 1912.

Goodwin. An Equatorial Azimuth-Table, by H. B. Goodwin, was published in 1921.

Purey-Cust. Azimuth by Logs, by Admiral Sir H. E. Purey-Cust, RN , was pub-
lished in England in 1929. It consists of a three-page table of the logarithms of the
six principal trigonometric functions at 10’ intervals (5’ below 10°) for solution of the
time azimuth and altitude azimuth formulas.

Yustchenko. In 1935 A. Yustchenko, a Russian, extended the Zhdanko tables
to all latitudes, in the work entitled Azimuty Svetil (Azimuths of Celestial Bodies).
For each 10° of latitude (5°, 15°, 25°, etc., to 85°) complete azimuth tables (to the
nearest 0°1) are given for each 1™ of meridian angle and each 30’ of declination from 0°
to 30°. At the bottom of each page are given corrections for 1° of latitude. This value
is multiplied by the number of degrees between the actual latitude and the latitude
for which the table was computed. | ;

Cugle. Cugle's Two-Minute Azimuths, by Charles H. Cugle, were printed in
1935 in two large volumes. Coverage is for latitude 0° to 65° and declination 0° to
239. The arrangement is almost identical with that of H.O. Pub. No. 260, except that

572 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

meridian angle increases downward on the page. The number of entries is multiplied
by five, values being given for each 2™ of meridian angle.

Table 902. Azimuts, published in Paris in 1953, with the concurrence of the
Marine Hydrographic Service, contains azimuth angles to the nearest 0°1 for each
whole degree of latitude from 70° N to 70° S, each whole degree of declination from 0°
to 30°, and each 10™ of meridian angle. The arrangement is similar to that of H.O.
Pub. No. 260, except that meridian angle increases downward on the page.

2127. Azimuth diagrams have appeared in various forms, in addition to the
general graphical and mechanical solutions discussed above. A graphical solution is
generally more acceptable for azimuth than for altitude, because the accuracy require-
ment for azimuth is usually less.

Godfrey. A graphical solution has been available at least since 1858 when the
Time Azimuth Diagram of Hugh Godfrey was published in London.

Weir. The Azimuth Diagram devised by Captain Patrick Weir, of the British
Merchant Navy, was published in London in 1890, and by the U. S. Navy Hydro-
graphic Office in 1891, under the title Time Azimuth Diagram.

Molfino. In 1901 the Nomograma degli Azimut del Sole of Molfino was published.

Constan. In 1906 P. Constan’s Tables Graphiques d’Azimut were published in
Paris. This was a reproduction of the graph of Favé and Rollet de l'Isle (art. 2120).

Alessio. The Diagrammi Altazimutali of A. Alessio was published in 1908 in
Italy.

Rust. In 1908 the diagram of Lieutenant Commander Armistead Rust, USN,
(art. 2106) was published. This diagram was later used by Goodwin (art. 2106)
and Weems (arts. 2106 and 2110), and in the Italian Tavole H (art. 2110).

Cornet. The Graphique d’Azimut of Cornet was published in 1927.

Romanovsky. About 1933 A. A. Romanovsky, a Russian, devised a simple nomo-
gram for determining azimuth.

German Oberkommendos der Kriegsmarine. A large volume called Azimut-
diagramme, containing sets of diagrams for each whole degree of latitude (2° beyond 80°)
for all azimuth angles and for all altitudes to 80°, was published by the German
Oberkommandos der Kriegsmarine in 1944.

Hugon. The azimuth diagram of Professor P. Hugon (art. 2109) was published
in 1947.

Hilsenrath. About 1948 Joseph Hilsenrath, of the University of Maryland, pro-
duced a mechanical device for solving azimuth angle by the method of Weir’s diagram.

2128. Summary.—The methods of sight reduction discussed in this chapter
are undoubtedly only a small fraction of the number of methods that have been pro-
posed. They are considered representative of the effort that has been made to reduce
the work of the navigator. Individual preferences have largely dictated the use of
the various methods. Presentation and description of a method have been important
factors in the relative popularity of various methods.

There is no single “best” method for all circumstances and all navigators. The
one which produces the desired results easiest and with least possibility of mistake is
the one that should be selected. However, two practical precautions should be observed.
First, one should be thoroughly familiar with the limitations or weaknesses of the method
he selects. Second, a prudent navigator will never limit himself to a single method,
particularly one requiring a special table that might some day be unavailable, or a
device that is subject to mechanical damage or loss. The slight bending of an are
might be too insignificant to be noticed, yet might introduce intolerably large errors in
the result. A wise practice is to memorize, or write on something always carried,
fundamental formulas that can be used when no “special” tables are available.

COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION 573

Problems

k 2103a. At GMT 10^25722* on June 1, 1958, the navigator observes the lower
limb of the sun on the celestial meridian, bearing south. He makes the observation
with a marine sextant having no IC, from a height of eye of 50 feet. The hs is 41°58/7.

Required.—The latitude by meridian altitude.

Answer.—L 69%54'1 N.

2103b. At GMT 14^15"21* on June 1, 1958, the sun is estimated to be on the
upper branch of the celestial meridian. At this time the sun is obscured by clouds,
but several minutes later it breaks out, and at GMT 1424225 the navigator observes
the lower limb, facing in a northerly direction. He makes the observation with a
marine sextant having an IC of (—) 2/5, from a height of eye of 33 feet. The hs is
70?46:9. The approximate latitude is 3° N.

Required.—(1) The latitude by reduction to the meridian. (2) The latitude if
the navigator learns that his ship was 1/2 of longitude farther west than assumed for
computation of the time of meridian transit, and the azimuth angle at the time of ob-
servation was N 620W. Use table 26.

Answers.—(1) L 3%04'1 N, (2) L 3°04/0N.

2103c. On June 1, 1958, the 1225 DR position of a ship is lat. 40?45/7 N, long.
1422019 W. At GMT 21^25736* the navigator observes the lower limb of the sun with
a marine sextant having an IC of (+) 3/3, from a height of eye of 29 feet. The hs is
71%06/8.

Required.—(1) The a, Zn, and AP, using H.O. Pub. No. 214 (Ad, At, AL, and
interpolating for Z) and the Nautical Almanac.

(2) The approximate latitude at the time of observation.

Answers.—(1) a 1.8 T, Zn 17998, aL 40?45'7 N, ah 142°01'9 W; (2) L 40?43:9 N.

2104a. Find the watch time of meridian transit of the sun at longitude 68084 E
on June 1, 1958, 1f the watch is 27* fast on zone time.

Answer.—W 12*25"31".

2104b. Find the zone time of meridian transit of the moon at longitude 1662312 E
on June 13, 1958, using the Nautical Almanac, GHA method.

Answer.—ZT 8525™42°.

2104c. Find the GMT of meridian transit of Nunki at longitude 157°52'2 W
on June 1, 1958, using the Air Almanac.

Answer —GMT 12*46"11*.

2104d. On June 1, 1958, the 1200 DR position of a ship is lat. 57?21:9 N, long.
21953/2 W. The ship is on course 065°, speed 22 knots. Find the zone time of meridian
transit of the sun at the ship.

Answer.—ZT 12^24"10*.

2104e. Find the zone time of transit of the sun at longitude 47?23:4 E on June 2,
1958, using apparent time and the Nautical Almanac.

Answer.—ZT 11°48™13°.

2105. During evening twilight on May 31, 1958, the 2325 EP of a ship is lat.
58°38/4 N, long. 165°34/3 W. At watch time 11^25"01* pm the navigator observes
Polaris with a marine sextant having no IC, from a height of eye of 42 feet. The
watch is 6* fast on zone time. The hs is 57%54/4.

Required.—(1) The latitude, (2) the azimuth of Polaris.

Answers.—(1) L 58%35'6 N, (2) Zn 001°0.

2106. On June 2, 1958, the 0725 EP of a ship is lat. 7?31:25, long. 225050 W.
At GMT 9"24"425 the navigator observes the lower limb of the sun with a marine sextant
having an IC of (+) 2/0, from a height of eye of 47 feet. The hs is 2915.0.

Required.—(1) The longitude by time sight.

574 COMPARISON OF VARIOUS METHODS OF SIGHT REDUCTION

(2) The longitude if the navigator learns that his ship was 2.1 miles farther north
than assumed for computation, and the azimuth at the time of observation was 062°0.
Use table 26.

Answers.—(1) ^ 22%38/1 W, (2) ^ 22?39:2 W.

2107a. Determine (1) the approximate zone time, and (2) the approximate altitude
of the sun at its nearest approach to the prime vertical during the morning of June 1,
1958, at lat. 1221477 N, long. 35°16/1 W, using table 25 and the Nautical Almanac.

Answers.—(1) ZT 0826, (2) h 3397.

2107b. Determine (1) the approximate zone time, and (2) the approximate altitude
of the sun when it crosses the prime vertical during the afternoon of May 31, 1958,
at lat. 41°17/2 N, long. 154°37/4 W, using H.O. Pub. No. 214 and the Nautical Almanac.

Answers.—(1) ZT 1625, (2) h 3418.

2109. The dead reckoning latitude of a vessel is 10?23:8 S. The navigator
observes a star having a declination of 28?51:5 N and a meridian angle of 27?17:4 E.
He notes that it is in the northeast quadrant of the sky.

Required.—The (1) He by cosine-haversine formula and (2) azimuth by the
formula sin Z —sin t cos d sec h.

Answers.—(1) Hc 42°43/4, (2) 033*1.

2113a. During evening twilight on June 1, 1958, the 1740 DR position of a ship
is lat. 41?28/5 S, long. 82?17:6 W. At ZT 17”41”08* the navigator observes Rigel
Kent. with a marine sextant having an IC of (—)1‘2, from a height of eye of 55 feet.
The hs is 44°05/2.

Required.—The a, Zn, and AP, using H.O. Pub. No. 249, vol. I (epoch 1960.0), and
the Air Almanac.

Answers.—a 13 T, Zn 140°, aL 41?00' S, ad 82°11’ W.

2113b. During morning twilight on June 2, 1958, the DR position of a ship is
lat. 41?08:2 N, long. 5?11:5 E. At GMT 3^45"11* the navigator observes Fomalhaut
with a marine sextant having an IC of (4-)0'8, from a height of eye of 49 feet. The
hsastos l3.

Required.—The a, Zn, and AP, using H.O. Pub. No. 249, vol. III, and the Azr
Almanac.

Answers.—a 10 À, Zn 152°, aL 41?00' N, ad 5?27' E.

2125. The DR latitude of a ship is 15%11/3S when the declination of the sun is
18%36:5N.

Required.—(1) The amplitude (A) when the center of the rising sun is on the
celestial horizon.

(2) The amplitude and azimuth when the center of the rising sun is on the visible
horizon.

Answers.—(1) A E 19?3 N; (2) A E 19?1 N, Zn 070299.

2126a. The dead reckoning latitude of a vessel is 23°53/6S. The navigator
observes a celestial body having a declination of 20°26/2S and a meridian angle of
18?37'4 E.

Required.—Azimuth by H.O. Pub. No. 260.

Answer.—Zn 08222.

2126b. The dead reckoning latitude of a vessel is 51?46:5 N. The navigator
observes a celestial body having a declination of 49?42/7 N and a meridian angle of
115?37:2 W.

Required. Azimuth by H.O. Pub. No. 261.

Answer.—Zn 319?9.

CHAPTER XXII
IDENTIFICATION OF CELESTIAL BODIES

. 2201. Introduction.—A basic requirement of celestial navigation is the ability
to identify the bodies observed. This is not difficult because relatively few celestial
bodies are commonly used for navigation, and various aids are available to assist in
their identification, as explained in this chapter.

Many navigators consider it a matter of professional pride to have a more extensive
acquaintance with the heavens than required by the relatively simple demands of
navigation.

2202. Bodies of the solar system.—No problem is encountered in the identification
of the sun and moon. However, the planets can be mistaken for stars. A person
working continually with the night sky recognizes a planet by its changing position
among the relatively fixed stars. He identifies the planets by noting their positions
relative to each other, the sun, the moon, and the stars. He knows that they remain
within the narrow limits of the zodiac (art. 1420) but are in almost constant motion
relative to the stars. The magnitude and color may be helpful. The information he
needs is found in the Nautical Almanac. The “Planet Notes" near the front of that
volume are particularly useful.

Sometimes the light from a planet seems steadier than that from a star. This
is because fluctuation of the unsteady atmosphere causes scintillation or twinkling of
& star, which has no measurable diameter with even the most powerful telescopes.
The navigational planets are less susceptible to twinkling because of the broader
apparent area giving light.

Planets can also be identified by the Air Almanac ecliptic diagram (art. 2209), star
finder (art. 2210), sky diagram (art. 2212), or by computation (art. 2213).

2203. Stars.— The average navigator regularly uses not more than perhaps 20
or 30 stars. The Nautical Almanac gives full navigational information on 19 first
magnitude stars and 38 second magnitude stars, in addition to Polaris. Abbreviated
information is given for 115 more. Additional stars are listed in The American Ephem-
eris and Nautical Almanac and in various star catalogs. About 6,000 stars of the sixth
magnitude or brighter (on the entire celestial sphere) are visible to the unaided eye on
a clear, dark night.

Stars are designated by one or more of the following:

Name. Most names of stars, as now used, were given by the ancient Arabs and
some by the Greeks or Romans. One of the stars of the Nautical Almanac, Nunki,
was named by the Babylonians. Only a relatively few stars have names. Several of the
stars on the daily pages of the almanacs had no name prior to the 1953 edition, and were
given coined names so that all stars listed on the daily pages might have names. The
pronunciation, meaning, and other information of general interest regarding Polaris
and the 57 stars listed on the daily pages of the Nautical Almanac are given in
appendix H.

Bayer's name. Most bright stars, including those with names, have been given
a designation consisting of a Greek letter followed by the possessive form of the name

575

576 IDENTIFICATION OF CELESTIAL BODIES

of the constellation, as o Cygni (Deneb, the brightest star in the constellation Cygnus,
the swan). Roman letters are used when there are not enough Greek letters. Usually,
the letters are assigned in order of brightness within the constellation, but in some cases
the letters are assigned in another order, where it seems logical to do so. An example
is the big dipper, where the letters are assigned in order from the outer rim of the bowl
to the end of the handle. This system of star designation was suggested by John Bayer
of Augsburg, Germany, in 1603. All of the 173 stars included in the list near the back of
the Nautical Almanac are given by Bayer's name as well as regular name, where there
is one.

Flamsteed’s number. A similar system, accommodating more stars, numbers
them in each constellation, from west to east, the order in which they cross the celestial
meridian. An example is 95 Leonis, the 95th star in the constellation Leo, the lion.
This system was suggested by John Flamsteed (1646-1719), who was the first British
Astronomer Royal. S

Catalog number. Stars are sometimes designated by the name of a star catalog
and the number of the star as given in that catalog, as A. G. Washington 632. In
these catalogs stars are listed in order from west to east, without regard to constellation,
starting with the hour circle of the vernal eguinox. This system is used primarily for
dimmer stars having no other designation. Navigators seldom have occasion to use
this system.

The ability to identify stars by position relative to each other is useful to the
navigator. A tabulation of the relative positions of the 57 stars given on the daily
pages of the Nautical Almanac, and Polaris, is given in appendix G. A star chart
(art. 2204) is helpful in locating these relationships and others which may be useful.
This method is limited to periods of relatively clear, dark skies with little or no overcast.
Stars can also be identified by the Azr Almanac ecliptic diagram (art. 2209), star finder
(art. 2210), H.O. Pub. No. 249 (art. 2211), sky diagram (art. 2212), or by computation
(art. 2213).

2204. Star charts are based upon the celestial equator system of coordinates,
using declination and sidereal hour angle (or right ascension). The zenith of the ob-
server is at the intersection of the parallel of declination equal to his latitude, and the
hour circle coinciding with his celestial meridian. This hour circle has an SHA equal
to 360°—LHAY (or RA=LHA T). The horizon is everywhere 90° from the zenith.
A star globe is similar to a terrestrial sphere, but with stars (and often constellations)
shown instead of geographical positions. Star globes are used by British navigators,
but not customarily by Americans. The combined Nautical Almanac includes instruc-
tions for using this device. On a star globe the celestial sphere is shown as it would
appear to an observer outside the sphere. Constellations appear reversed. Star
charts may show a similar view, but more often they are based upon the view from
inside the sphere, as seen from the earth. On these charts, north is at the top, as with
maps, but east is to the left and west to the right. The directions seem correct when the
chart is held overhead, with the top toward the north, so that the relationship is similar
to that in the sky. Any map projection (ch. III) can be used, but some are more
suitable than others.

The Nautical Almanac has four star charts. The two principal ones are on the
polar azimuthal equidistant projection (art. 320), one centered on each celestial pole.
Each chart extends from its pole to declination 10° (same name as pole). Below each
polar chart is an auxiliary chart on the Mercator projection, from 30° N to 30° S.
On any of these charts, the zenith can be located as indicated above, to determine which
stars are overhead. The horizon is 90° from the zenith. The charts can also be used

IDENTIFICATION OF CELESTIAL BODIES 577

to determine the location of a star relative to surrounding stars. The Air Almanac
has a fold-in chart at the back, on the rectangular projection (art. 311). This projec-
tion is suitable for indicating the coordinates of the stars, but excessive distortion
occurs in regions of high declination. The celestial poles are represented by the top
and bottom horizontal lines the same length as the celestial equator. To locate the
. horizon on this chart, first locate the zenith as indicated above, and then locate the
four cardinal points. The north and south points are 90° from the zenith, along the
celestial meridian. The distance to the elevated pole (having the same name as the
latitude) is equal to the colatitude of the observer. The remainder of the 90° (the
latitude) is measured from the same pole, along the lower branch of the celestial meridian,
180° from the upper branch containing the zenith. The east and west points are on
the celestial equator at the hour circle 90° east and west (or 90° and 270° in the same
direction) from the celestial meridian. The horizon is a sine curve (fig. O40b) through
the four cardinal points. Directions on this projection are distorted.

The star charts shown in figures 2205-2208, on the transverse Mercator projection
(art. 309), are designed to assist one in learning the stars listed on the daily pages of the
Nautical Almanac, and Polaris. Each chart extends about 20° beyond each celestial
pole, and about 60° (four hours) each side of the central hour circle (at the celestial
equator). Therefore, they do not coincide exactly with that half of the celestial sphere
above the horizon at any one time or place. The zenith, and hence the horizon, varies
with the position of the observer on the earth, and also with the rotation of the earth
(apparent rotation of the celestial sphere). The charts show all stars of fifth magnitude
and brighter as they appear in the sky, but with some distortion toward the right and
left edges.

The transparencies add certain information of use in locating the stars. Only
Polaris and the 57 stars listed on the daily pages of the Nautical Almanac are named on
the charts. The almanac star charts should be used for locating the additional stars
given near the back of the Nautical Almanac. When a transparency is correctly
placed over its accompanying chart, the information given is properly oriented to the
chart. The broken lines connect stars of some of the more prominent constellations.
The solid lines indicate the celestial equator and certain useful relationships among
stars in different constellations. The celestial poles are marked by crosses, and labeled.
By means of the celestial equator and the poles, one can locate his zenith approximately
along the mid hour circle, when this coincides with his celestial meridian, as shown in the
table below. At any time earlier than those shown in the table the zenith is to the
right of center, and at a later time it is to the left, approximately one-quarter of the
distance from the center to the outer edge (at the celestial equator) for each hour that
the time differs from that shown. The stars in the vicinity of the north pole can be
seen in proper perspective by inverting the chart, so that the zenith of an observer in
the northern hemisphere is wp from the pole.

Fig. 2205 Fig. 2206 Fig. 2207 Fig. 2208

Local sidereal time 0000 0600 1200 1800

LMT 1800 Dec. 21 Mar. 22 June 22 Sept. 21
LMT 2000 Nov. 21 Feb. 20 May 22 Aug. 21
LMT 2200 Oct. 21 Jan. 20 Apr. 22 July 22
LMT 0000 Sept.22 Dec. 22 Mar. 23 June 22
LMT 0200 Aug. 22 Nov. 22 Feb. 21 May 23
LMT 0400 Juw 2 Owi 2 san. 21, Apr. 22

LMT 0600 June 22 Sept.21 Dec. 22 Mar. 23

578 IDENTIFICATION OF CELESTIAL BODIES

2205. Stars in the vicinity of Pegasus (fig. 2205).—In autumn the evening sky has
few first magnitude stars. Most of these are near the southern horizon of an observer
in the latitudes of the United States. A relatively large number of second and third
magnitude stars seem conspicuous, perhaps because of the small number of brighter
stars. High in the southern sky three third magnitude stars and one second magnitude
star form a square with sides nearly 15° of arc in length. This is Pegasus, the winged
horse, although to many modern men it more nearly resembles a baseball diamond,
complete with catcher, pitcher, batter, umpire, base umpire near second base, infield
and outfield; although there does seem to be a large number of outfielders. One may
even see the next batter, bat boy, and coach.

Only Markab at the southwestern corner (third base) and Alpheratz at the north-
eastern corner (first base) are listed on the daily pages of the Nautical Almanac. Al-
pheratz is part of the constellation Andromeda, the princess, extending in an arc toward
the northeast and terminating at Mirfak in Perseus, legendary rescuer of Andromeda.

A line extending northward through the eastern side (first-second base line) of the
square of Pegasus passes through the leading (western) star of M-shaped (or W-shaped)
Cassiopeia, the legendary mother of the princess Andromeda. The only star of this
constellation listed on the daily pages of the Nautical Almanac is Schedar, the second
star from the leading one as the configuration circles the pole in a counterclockwise
direction. If the line through the eastern side of the square of Pegasus is continued
on toward the north, 1t leads to second magnitude Polaris, the north star (less than 12
from the north celestial pole) and brightest star of Ursa Minor, the little bear. Kochab,
a second magnitude star at the other end of the little dipper, is also listed in the alma-
nacs. At this season the big dipper is low in the northern sky, below the celestial pole.
A line extending from Kochab through Polaris leads to Mirfak, assisting in its identi-
fication when Pegasus and Andromeda are near or below the horizon.

Deneb, in Cygnus, the swan, and Vega are bright, first magnitude stars in the
northwestern sky. They are discussed in article 2208. Capella, a bright star in the
northeastern sky, is discussed in article 2206.

The line through the eastern side of the square of Pegasus (first-second base line)
approximates the hour circle of the vernal equinox, shown at Y on the celestial equator
to the south. The sun is at T on or about March 21, when it crosses the celestial
equator from south to north. If the line through the eastern side of Pegasus is extended
southward and curved slightly toward the east, it leads to second magnitude Diphda.
A longer and straighter line southward through the western side (home plate-third base
line) of Pegasus leads to first magnitude Fomalhaut. A line extending northeasterly
from Fomalhaut through Diphda leads to Menkar, a third magnitude star, but the
brightest in its vicinity. Ankaa, Diphda, and Fomalhaut form an isosceles triangle,
with the apex at Diphda. Ankaa is near or below the southern horizon of ob-
servers in latitudes of the United States. Four stars farther south than Ankaa may be
visible when on the celestial meridian, just above the horizon of observers in latitudes of
the extreme southern part of the United States. These are Acamar, Achernar, Al Na’ir,
and Peacock. These stars, with each other and with Ankaa, Fomalhaut, and Diphda,
form a series of triangles as shown in figure 2205. Almanac stars near the bottom of
figure 2205 are discussed in succeeding articles.

Two other almanac stars can be located by their positions relative to Pegasus.
These are Hamal in the constellation Aries, the ram, east of Pegasus, and Enif, west
of the southern part of the square, identified as shown in figure 2205. The line leading
to Hamal, if continued, leads to the Pleiades, not used by navigators for celestial ob-
servations, but a prominent figure in the sky, heralding the approach of the many
conspicuous stars of the winter evening sky, figure 2206.

IDENTIFICATION OF CELESTIAL BODIES

FIGURE

580 IDENTIFICATION OF CELESTIAL BODIES

2206. Stars in the vicinity of Orion (fig. 2206).—As Pegasus leaves the meridian
and moves into the western sky, Orion, the mighty hunter, rises in the east. With
the possible exception of the big dipper, no other configuration of stars in the entire
sky is as well known as Orion and its immediate surroundings. In no other part are
there so many first magnitude stars.

The belt of Orion, being nearly on the celestial equator, is visible by an observer
in virtually any latitude, rising and setting almost on the prime vertical, and dividing
equally its time above and below the horizon. Of the three second magnitude stars
forming the belt, only Alnilam, the middle one, is listed on the daily pages of the Nautical
Almanac.

Four conspicuous stars form a box around the belt. To the south is Rigel, one
of the hottest and bluest of the stars, in contrast with relatively cool, red, variable
Betelgeuse, at approximately an equal distance to the north. Bellatrix, bright for a
second magnitude star but overshadowed by its more brilliant neighbors, is a few
degrees west of Betelgeuse. Neither the second magnitude star forming the south-
eastern corner of the box, nor any star of the dagger, is listed on the daily pages of
the Nautical Almanac.

A line extending eastward from the belt of Orion and curving toward the south
leads to Sirius, the brightest star in the entire heavens, having a magnitude of (—)
1.6. Only Mars and Jupiter at or near their greatest brilliance, and the sun, moon,
and Venus are brighter than Sirius. This is part of the constellation Canis Major,
the large hunting dog of Orion. Starting at Sirius a curved line extends northward
through first magnitude Procyon, in Canis Minor, the small hunting dog; first magnitude
Pollux and second magnitude Castor (not listed on the daily pages of the Nautical
Almanac), the twins of Gemini; brilliant Capella in Auriga, the charioteer; and back
down to first magnitude Aldebaran, the follower, which trails the Pleiades, the seven
sisters. Aldebaran, brightest star in the head of Taurus, the bull, may also be found
by a curved line extending northwestward from the belt of Orion. The V-shaped
figure forming the outline of the head and horns of Taurus points toward
third magnitude Menkar. At the summer solstice the sun is between Pollux and
Aldebaran.

If the curved line from Orion's belt southeastward to Sirius is continued, it leads
to a conspicuous, small, nearly equilateral triangle of three bright second magnitude
stars of nearly equal brilliancy. This is part of Canis Major. Only Adhara, the
westernmost of the three stars, is listed on the daily pages of the Nautical Almanac.
Continuing on with somewhat less curvature, the line leads to Canopus, second brightest
star in the heavens and one of the two stars having a negative magnitude (—0.9). With
Suhail and Miaplacidus, Canopus forms a large, equilateral triangle which partly en-
closes the false southern cross. The brightest star within this triangle is Avior, near
its center. Canopus is also at one apex of a triangle formed with Adhara to the north
and Suhail to the east, another triangle with Acamar to the west and Achernar to the
southwest, and another with Achernar and Miaplacidus. Acamar, Achernar, and
Ankaa form still another triangle toward the west. Because of chart distortion, these
triangles do not appear in the sky in exactly the relationship shown on the star chart.
Other daily-page almanac stars near the bottom of figure 2206 are discussed in succeeding
articles.

During the winter evening sky the big dipper is east of Polaris, the little dipper is
nearly below it, and Cassiopeia is west of it. Mirfak is northwest of Capella, nearly
midway between it and Cassiopeia. Hamal is in the western sky. Regulus and Alphard

are low in the eastern sky, heralding the approach of the configurations associated with
the evening skies of spring.

IDENTIFICATION OF CELESTIAL BODIES

Ficure 2206.—Stars in the vicinity of Orion.

582 IDENTIFICATION OF CELESTIAL BODIES

2207. Stars in the vicinity of Ursa Major (fig. 2207).—Asifto enhance the splendor
of the sky in the vicinity of Orion, the region toward the east, like that toward the west,
has few bright stars, except in the vicinity of the south celestial pole. However, as
Orion sets in the west, leaving Capella and Pollux in the northwestern sky, a number of
good navigational stars move into favorable positions for observation. l

The big dipper, part of Ursa Major, the great bear, appears prominently above
the north celestial pole, directly opposite Cassiopeia (only partly shown in fig. 2207),
which appears as a W just above the northern horizon of most observers in latitudes of
the United States. Of the seven stars forming the big dipper, only Dubhe, Alioth, and
Alkaid are listed on the daily pages of the Nautical Almanac. :

The two second magnitude stars forming the outer part of the bowl of the big
dipper are often called the pointers because a line extending northward (down in spring
evenings) through them points to Polaris. The little dipper, with Polaris at one end and
Kochab at the other, is part of Ursa Minor, the little bear. Relative to its bowl, the
handle of the little dipper curves in the opposite direction to that of the big dipper.
Other almanac stars near the top of figure 2207 are discussed elsewhere.

A line extending southward through the pointers, and curving somewhat toward
the west, leads to first magnitude Regulus, brightest star in Leo, the lion. The head,
shoulders, and front legs of this constellation form a sickle, with Regulus at the end
of the handle. Toward the east is second magnitude Denebola, the tail of the lion.
On toward the southwest from Regulus is second magnitude Alphard, brightest star
in Hydra, the sea serpent. A dark sky and considerable imagination are needed to
trace the long, winding body of this figure.

A curved line extending the are of the handle of the big dipper leads to first mag-
nitude Arcturus. With Alkaid and Alphecca, brightest star in Corona Borealis, the
northern crown, Arcturus forms a large, inconspicuous triangle. If the are through
Arcturus is continued, it leads next to first magnitude Spica and then to Corvus, the
crow, which appears most like a gaff mainsail of a schooner. The brightest star in this
constellation is Gienah, but three others are nearly as bright. At autumnal equinox
the sun is on the celestial equator, about midway between Regulus and Spica.

A long, slightly curved line from Regulus east-southeasterly through Spica leads to
Zubenelgenubi (zoo-bén'él.jé-nü'be) at the southwestern corner of an inconspicuous
box-like figure called Libra, the (weighing) scales.

Returning to Corvus, a line from Gienah, extending diagonally across the figure
and then curving somewhat toward the east, leads to Menkent, just beyond Hydra.

Far to the south, below the horizon of most northern-hemisphere observers, a
group of bright stars is a prominent feature of the spring sky of the southern hemisphere.
Cruz, the southern cross, is about 40? south of Corvus. This is a small figure and a poor
cross, and hence disappointing to many who view it for the first time. The “false cross”
to the west is a better but less conspicuous cross. Acrux at the southern end of the
southern cross, and Gacrux at the northern end, are listed on the daily pages of the
Nautical Almanac.

The triangles formed by Suhail, Miaplacidus, and Canopus, and by Suhail, Adhara,
and Canopus, are west of the southern cross, Suhail being in line with the horizontal
arm of the southern cross at this time. A line from Canopus, through Miaplacidus,
curved slightly toward the north, leads to Acrux. A line through the east-west arm
of Cruz, eastward and then curving toward the south, leads first to Hadar and then to
Rigil Kentaurus, two very bright stars. Continuing on, the curved line leads to small
Triangulum Australe, the southern triangle, the easternmost star of which is Atria.

Scorpius, the scorpion, Kaus Australis, and Peacock, in the southeastern sky of
the southern hemisphere, are discussed in article 2208.

IDENTIFICATION OF CELESTIAL BODIES

Sigil Kentaun
x #

4 "Canopus
5

E EEN dÉ 3u Ana Bth.
Ficure 2207.—Stars in the vicinity of Ursa Major. Scale of magnitudes: 15 Li 2n *_ 8 AE

584 IDENTIFICATION OF CELESTIAL BODIES

2208. Stars in the vicinity of Cygnus (fig. 2208).—As the celestial sphere continues
in its apparent westward rotation, the stars familiar to a spring evening observer sink
low in the western sky. By midsummer the big dipper has moved to a position to the
left of the north celestial pole, and the line from the pointers to Polaris is nearly hori-
zontal. The little dipper is standing on its handle, with Kochab above and to the left
of the celestial pole. Cassiopeia is at the right of Polaris, opposite the handle of the
big dipper.

The only first magnitude star in the western sky is Arcturus, which forms a large,
inconspicuous triangle with Alkaid, the end of the handle of the big dipper, and
Alphecca, the brightest star in Corona Borealis, the northern crown. _

The eastern sky is dominated by three very bright stars. The westernmost of
these is Vega, the brightest star north of the celestial equator, and third brightest
star in the heavens. Its magnitude is 0.1. Having a declination of a little less than
39°N, this star passes through the zenith along a path across the central part of the
United States, from Washington in the east to San Francisco on the Pacific coast.
Vega forms a large but conspicuous triangle with its two bright neighbors, Deneb to
the northeast and Altair to the southeast. The angle at Vega is nearly a right angle.
Deneb is at the end of the tail of Cygnus, the swan. This configuration is sometimes
called the northern cross, with Deneb at the head. To modern youth it more nearly
resembles a dive bomber while it is still well toward the east, with Deneb at the nose
of the fuselage. Altair has two fainter stars close by, on opposite sides. The line
formed by Altair and its two fainter companions, if extended in a northwesterly direc-
tion, passes through Vega, and on to second magnitude Eltanin. The angular dis-
tance from Vega to Eltanin is about half that from Altair to Vega. Vega and Altair,
with second magnitude Rasalhague to the west, form a large equilateral triangle.
This is less conspicuous than the Vega-Deneb-Altair triangle because the brilliance
of Rasalhague is much less than that of the three first magnitude stars, and the triangle
is overshadowed by the brighter one.

Far to the south of Rasalhague, and a little toward the west, is a striking con-
figuration called Scorpius, the scorpion. The brightest star, forming the head, is red
Antares. At the tail is Shaula. Å

Antares is at the southwestern corner of an approximate parallelogram formed by
Antares, Sabik, Nunki, and Kaus Australis. With the exception of Antares, these
stars are only slightly brighter than a number of others nearby, and so this parallelogram
is not a striking figure. At winter solstice the sun is a short distance northwest of
Nunki.

Northwest of Scorpius is the box-like Libra, the (weighing) scales, in which
Zubenelgenubi marks the southwest corner. j Å

With Menkent and Rigil Kentaurus to the southwest, Antares fornis a large but
unimpressive triangle. For most observers in the latitudes of the United States,
Antares 1s low in the southern sky, and the other two stars of the triangle are below
the horizon. To an observer in the southern hemisphere Cruz, the southern Cross, 1s
to the right of the south celestial pole, which is not marked by a conspicuous star. A
long, curved line starting with the now-vertical arm of the southern cross and extending
northward and then eastward passes successively through Hadar, Rigil Kentaurus,
Peacock, and Al Nair. |

| Fomalhaut is low in the southeastern sky of the southern hemisphere observer, and
Enif is low in the eastern sky at nearly any latitude. With the appearance of these
stars it is not long before Pegasus will appear over the eastern horizon during the
evening, and as the winged horse climbs evening by evening to a position higher in the
sky, a new annual cycle approaches.

IDENTIFICATION OF CELESTIAL BODIES

Ficure 2208.—Stars in the vicinity of Cygnus.

586 IDENTIFICATION OF CELESTIAL BODIES

2209. Ecliptic diagram.—On each right-hand page of the daily tabulations of
the Air Almanac (app. W) an ecliptic diagram shows a band of the sky 105 wide (the
zodiac, art. 1420), with the sun at the center. Shown in correct position relative to
the sun (except when very close to it) are the moon, selected planets and stars, and
the vernal eguinox. This diagram is useful for planning purposes and for locating the
planets. That part of the diagram to the left of the sun is east of it, approximately
coinciding with the visible part during evening twilight. That part to the right, or
west, of the sun coincides approximately with the visible portion during morning
twilight. The two ends are that point in the sky 180° from the sun. These diagrams
were replaced in 1965 by a single Planet Location Diagram.

2210. Star finders.—Various devices have been invented to help an observer
locate and identify individual stars. The most widely used is the Star Finder and
Identifier published by the U. S. Navy Hydrographic Office. The current model,
H.O. 2102-D, as well as the previous 2102-C model patented by E. B. Collins, formerly
of that Office, employs the same basic principle as that used in the Rude Star Finder,
which was patented by Captain G. T. Rude, USC&GS, and later sold to the Hydro-
graphic Office. Successive models reflect various modifications to meet changing con-
ditions. and requirements.

The star base of H.O. 2102-D consists of a thin, white, opaque, plastic disk about
8% inches in diameter, with a small peg in the center. On one side the north celestial
pole is shown at the center, and on the opposite side the south celestial pole is at the
center. All of the stars listed on the daily pages of the Nautical Almanac are shown
on a polar azimuthal equidistant projection (art. 320) extending to the opposite pole.
The south pole side is shown in figure 22104. Many copies of an older edition, H.O.
2102-C, showing the stars listed in the almanacs prior to 1953, and having other
minor differences, are still in use. These are not rendered obsolete by the newer
edition, but should be corrected by means of the current almanac. The rim of each
side is graduated to half a dezree of LHA (or 360°—SHA).

Ten transparent templates of the same diameter as the star base are provided.
There is one template for each 10? of latitude, labeled 5°, 15°, 25°, ete., plus a tenth
(printed in red) showing meridian angle and declination. The older edition (H.O.
2102-C) did not have the red meridian angle-declination template. Each template
can be used on either side of the star base, being centered by placing a small center hole
in the template over the center peg of the star base. Each latitude template has a
family of altitude curves at 5° intervals from the horizon (from altitude 10° on the
older H.O. 2102-C) to 80%. A second family of curves, also at 5° intervals, indicates
azimuth. The north-south azimuth line is the celestial meridian. The star base,
templates, and a set of instructions are housed in a circular leatherette container.

Since the sun, moon, and planets continually change apparent position relative
to the “fixed” stars, they are not shown on the star base. However, their positions at
any time, as well as the positions of additional stars, can be plotted. To do this, deter-
mine 360°—SHA of the body. For the stars and planets, SHA is listed in the Nautical
Almanac. For the sun and moon, 360°—SHA is found by subtracting GHA of the
body from GHAT at the same time. Locate 360°—SHA on the scale around the
rim of the star base. A straight line from this point to the center represents the
hour circle of the body. From the celestial equator, shown as a circle midway be-
tween the center and the outer edge, measure the declination (from the almanac)
of the body toward the center if the pole and declination have the same name (both
N or both S), and away from the center if they are of contrary name. Use the scale along
the north-south azimuth line of any template as a declination scale. The meridian
angle-declination template (the latitude 5° template of H.O. 2102-C) has an open slot

IDENTIFICATION OF CELESTIAL BODIES

"m vr pa On TOT
R) EK Ch Ai 9 M "yl Wun,
N NOS d Ge 3 x GC Viju,
NN g k 1
RS e,
S ona "eu
Sy gr dr
5 KH
E
es 27
% 9 Ku,
% t
a,
SE
Fei
Yo
Yo
ez
A
es kØ
=$ Z
= t 6:
= 5 =
zu $ =
= e g=
= o &-
=8 =
= = R=
E i S
: 2 k=
= "i E
=a =
= Ne
$e
"S RS
eS
ENS
p E SES
>. R
O Ko
m Schedar BN
7, . N
Ki E T SIN
Up, šā: aries) Æ »
ly $ N
/, a- E : NN

l; 5 Sek
IT MP : à d | DA
à QUIT DIA I TS ud

FiGurE 2210a.— The south pole side of the star base of H.O. 2102-D

with declination graduations along one side, to assist in plotting positions, as shown in
figure 2210b. In the illustration the celestial body being located has a 360°—SHA of
285°, and a declination of 14?5 S. It is not practical to attempt to plot to greater
precision than the nearest 0?1. Positions of Venus, Mars, Jupiter, and Saturn on June
1, 1958, are shown plotted on the star base in figure 2210c. It is sometimes desirable
to plot positions of the sun and moon, to assist in planning. Plotted positions of stars
need not be changed. Plotted positions of bodies of the solar system should be replotted
from time to time, the more rapidly moving ones oftener than others.
interval for each body can be determined by experience. It is good practice to record

the date of each plotted position of a body of the solar system, to serve later as an
indication of the interval since it was plotted.

The satisfactory

To orient the template properly for any given time, proceed as follows: enter
the almanac with GMT, and determine GHA Y at this time. Apply the longitude to
GHA 1, subtracting if west or adding if east, to determine LHAT. If LMT is sub-
stituted for GMT in entering the almanac, LHA T can be taken directly from the al-

manac, to sufficient accuracy for orienting the star finder template. Select the tem-

588 IDENTIFICATION OF CELESTIAL BODIES

a

\ suis 1 =- SEU NL p R 4 \ N. A
!ü; SK x S R, E
et RD a e Sa KC "NS
S >
s N y ` x N 2 ZA

Lead ;
E She ge Ae E \ k E
Ss / SUC c
= ÀX V NS

E 32007 \ \ A \ E
E. y 4 2
SE LL geg

I iere E

E =á) el ` R=!

Eg 2 ; | =

E i 1 us | VÆ

Eg nm, 1—-—31 31-88)

S ez; | NEL

si | a Y $ EI

` Ze 2

E K E e, dé j E 4

gas | > DuBbeE
, 4 & @ I Á =
| Js E MES
: "RT CE

Sh =/
(0) es
P Bl
dh MN
$4 3
x "Se
po LS
X RSS
LS
x / i
X AV
Se
BS
e
KEE
T :
t I S
; n Æ ap sE T MS
' MD | Tri Jeria dd Hu

Ficure 2210b.—Plotting a celestial body on the star base of H.O. 2102-D.

plate for the latitude nearest that of the observer, and center it over the star base,
being careful that the correct sides (north or south to agree with the latitude) of both
template and star base are used. Rotate the template relative to the star base until
the arrow on the celestial meridian (the north-south azimuth line) is over LHA Y on
the star base graduations. The small cross at the origin of both families of curves now
represents the zenith of the observer. The approximate altitude and azimuth of the
celestial bodies above the horizon can be read directly from the star finder, using eye
interpolation. Consider Polaris, not shown, as at the north celestial pole. For more
accurate results, the template can be lifted clear of the center peg of the star base, and
shifted along the celestial meridian until the latitude, on the altitude scale, is over the
pole. This refinement is not needed for normal use of the device. It should not be
used for a latitude differing more than 5° from that for which the curves were drawn.
If the altitude and azimuth of an identified body shown on the star base are known, the

template can be oriented by rotating it until it is in correct position relative to that
body.

IDENTIFICATION OF CELESTIAL BODIES 589

NVO VOU VJL PHI En
WM | TN
MS $ E À : pus CMT
H ji
aww Ei A M oS) y,
N A VIJ) o
SS S (say) ESA
S , : 4
N jeuX
T N N V [OR 2$ /
SN S a GH. S d 27
SSS T me
D Ke Om, ty, d
Sr e a.
e e
5$ ES +
E šās ake
= ey = [o3 Ø
a Ø
Ey DEER LOS e
E e d
4 es 3QUTITA.I > ue
E LATITUDE 35'N z
A Be
= oer OB o =
= E 350 o E Sc =
: a
EN g E =
= E o% =
3 5 ý =
E lo) E z
= [3 R=
= $ =
== o 3 TE
= šo 8=
—5 =
= =
aA =
—B SO om
: p BS
Za, -ð CS ees
e S
Z NĒ SES RS
> § N E L_loalso NES
OE KR 3 ee eai e i BS
a N k N R y E L On 1 NS
e ĀDĀ as
© ` =< f vel: NS
do. 4 S r l” GE <
UN EE E Fas | mE. S.
4 P Se saitā m M
$ (rees? te Sta A CAE? e
4%. Ss Sli = à
4%. Oe — 0 | oGacrux_> —
ole O
155. ^ Q^
/ 60°
/if Jee LH Wo sE
Hip, s YS 180" 185 10
Willd Lala a

FIGURE 2210c.—A template in place over the star base of H.O. 2102-D.

Customarily, H.O. 2102-D is used in either of two ways:

1. To make an advance list of celestial bodies available for observation at a given
time.

2. 'To identify an unknown celestial body which has been observed.

Example 1.—During evening twilight on June 1, 1958, the GMT 2324 DR
position of a ship is lat. 34%12/5 N, long. 57?46:8 W.

Required.—The approximate altitude (ha) and azimuth of each first magnitude
star, and any planets, between altitudes 15? and 75?.

Solution (fig. 2210c).—(1) Plot the positions of the planets, as shown. The
values used are those for GMT 1200 on June 1, as follows:

Planet 360? —SHA Dec.
Venus 28?5 9?6 N
Mars 356?7 3.0.9
Jupiter 201°1 C35
Saturn 262°8 21°8S

590 IDENTIFICATION OF CELESTIAL BODIES

(2) Determine LHA T by means of the Nautical Almanac, as follows:

GMT 2324 Junel
232 934955'/0

245. + 620140
GHA T 240?56:0
A 57?46:8W

LHAT 183?09:2

(3) Select the template for latitude 35°, place it over the north side of the star
base with “LATITUDE 35° N” appearing correctly, and orient it to 18372. It is
customary to list the bodies in order of increasing azimuth, as follows:

Body ha Zn
Vega (Ki 054°
Arcturus 59° EK
Jupiter 45° 155°
Spica 42° 157°
Regulus 53° 240°
Procyon 20° 262°
Pollux 33° 284°
Capella Ius 316?

Example 2.—At the time and place of example 1, an unidentified celestial body is
observed through a break in the clouds. Its sextant altitude is 15?27'8, and its azimuth
is 085°.

Required.—Identify the celestial body.

Solution (fig. 2210c).—Orient the template as in example 1. By means of its
altitude and azimuth, identify the star as Rasalhague.

If no body appears at the measured altitude and azimuth, place the red meridian
angle-declination template over the altitude-azimuth template and read off, by in-
spection, the declination and the 360°—SHA value of the body, and from this, determine
its SHA. Using the SHA and declination, enter the list of stars near the back of the
Nautical Almanac, and identify the body. If it is not found in this list, and no error
has been made, one of the stars not listed in the almanac, or possibly the planet Mercury,
has been observed. Unless a copy of The American Ephemeris and Nautical Almanac
or another book containing the required information is available, the observation can-
not be used. If right ascension (art. 1426) of the body is available, but not its SHA,
the value taken from the star finder (3609— SHA) is converted to time units (art. 1904)
and used directly, since RA=360°—SHA.

Example 3.—At the time and place of example 1 an unidentified celestial body is
observed through a break in the clouds. Its altitude is 52°58/9, and its azimuth is
1709:

Required.—Identify the celestial body.

Solution (fig. 2210c).—Orient the template as in example 1. Since no celestial
body appears at the place indicated by its altitude and azimuth, the red meridian angle-
declination template is placed over the altitude-azimuth template. The declination
is found to be about 1? S. The 360°—SHA value is about 190°, and SHA is therefore
about 170°. From the star list near the back of the Nautical Almanac, the star is
identified as y Virginis.

2211. Sight Reduction Tables for Air Navigation (H.O. Pub. No. 249).—Volume I
of H.O. Pub. No. 249 can be used as a star finder for the stars tabulated at any given

IDENTIFICATION OF CELESTIAL BODIES 591

time. Ë For these bodies the altitude and azimuth are tabulated for each 1° of latitude
and 1° of LHAT (2° beyond latitude 699). The principal limitation is the small
. number of stars listed.

2212. Sky diagram.—Near the back of the 4ir Almanac are a number of sky
diagrams. These are azimuthal equidistant projections (art. 320) of the celestial sphere
on the plane of the horizon, at latitudes 70°N, 50°N, 30? N, 10°N, 1098, and 3008,
at intervals of two hours of local mean time each month. A number of the brighter
stars, the visible planets, and several positions of the moon are shown at their correct
altitude and azimuth. These are of limited value because of their small scale ; the
large increments of latitude, time, and date; and the limited number of bodies shown.
However, in the absence of other methods, particularly a star finder, these diagrams
can be useful. Allowance can be made for variations from the conditions for which
each diagram is constructed. Instructions for use of the diagrams are included in the
Air Almanac.

2213. Identification by computation.—If the altitude and azimuth of the celestial
body, and the approximate latitude of the observer, are known, the navigational
triangle (art. 1433) can be solved for meridian angle and declination. The meridian
angle can be converted to LHA, and this to GHA. With this and GHA of Aries at
the time of observation, the SHA of the body can be determined. With SHA and
declination, one can identify the body by reference to an almanac. Any method of
solving a spherical triangle, with two sides and the included angle being given, is
suitable for this purpose. ‘Short’ methods such as H.O. Pubs. Nos. 208 and 211 include
instructions for star identification by the tables provided. A large-scale, carefully-
drawn diagram on the plane of the celestial meridian, using the refinement shown in
figure 1432f, should yield satisfactory results. Perhaps the simplest method of actual
computation is by H.O. Pub. No. 214. Following the tables of computed altitude and
azimuth for each latitude, a two-page star identification table is given, as shown in
appendix AA. The example given below is based upon this extract.

The steps in solution by H.O. Pub. No. 214 are:

1. Convert Zn to Z.

2. With Z and ha (usually the approximate value taken from the sextant, without
correction) enter the H.O. Pub. No. 214 star identification pages for the nearest whole
degree of latitude, and extract the declination and meridian angle, t (given as H.A. in
the table). If the declination is given in roman type, above the heavy line, it has the
same name as the latitude. If the declination is given in italics, below the heavy line,
it has the contrary name to that of the latitude. When interpolating between roman
and italic declinations, consider the italic value negative, using the arithmetical sum as
the algebraic difference needed for interpolation. Extract values to the nearest whole
degree.

3. Convert t to LHA.

4. Apply the longitude to LHA to find GHA, adding if in west longitude, and
subtracting if in east longitude.

5. Enter the Nautical Almanac with GMT, and determine GHA Y.

6. Subtract GHA T from GHA* to find SHA (since GHAx =GHA T+SHA).

7. With the approximate SHA and d enter the Nautical Almanac star list and
identify the body, checking first the SHA and then the declination. Do not overlook
the possibility of having observed a planet or a star not listed in the almanac. For
a planet, check first the declination. If this is approximately correct, check the GHA.
It is not necessary to find the SHA of a planet.

592 IDENTIFICATION OF CELESTIAL BODIES

Example.—On May 31, 1958, the 0425 DR position of a ship is lat. 41%13:6N,
long. 140?41/7 W. About this time the navigator observes an unknown star through
a break in the clouds, as follows: GMT 13^247465, hs 15?01:5, Zn 232°.

Required.—Identify the unknown celestial body, using H.O. Pub. No. 214.

Solution.—
May 31
GMT 13^24"46* May 31 Zn 232°
195€ 8823132 Z N128?W
924946*«1:09 1215 ha 153
GHAT 89°43/7 (subtract) d 16°S (from H.O. Pub. No. 214)
GHAx 193? t 52°W (from H.O. Pub. No.214)
SHAx 1039 . LH Am 20529
d 16°S A 141° W
Body Sabik GHA 193°

Problems

2210a. During morning twilight on June 3, 1958, the GMT 1825 (June 2) DR
position of a ship is lat. 26°21'4N, long. 157%10:4E.

Required.—The approximate altitude and azimuth of each first magnitude star,
and any planets, between altitudes 10° and 80°, using H.O. 2102-D.

Answer .—
Body ha Zn
Venus 279 092?
Mars a 128°
Fomalhaut JAS 160°
Saturn 14° 291.
Altair 592 2479
Vega 505 SOT
Deneb 672 304°

2210b. At the time and place of problem 2210a an unidentified celestial body is
observed through a break in the clouds. Its sextant altitude is 21°04/1 and its azimuth
is 044°.

Required.—Identify the celestial body, using H.O. 2102-D.

Answer.—Mirfak.

2210c. The dead reckoning latitude of a ship is 25?06/4S. Two stars are observed
in quick succession, as follows:

Star ha Zn
Antares 572 1002
Unidentified 52° 3012

Required.—Identify the unknown celestial body, using H.O. 2102-D.

Answer.—e Virginis.

2213. On June 2, 1958, the 1725 DR position of a ship is lat. 41%27/38, long.
158?36:9 E. About this time the navigator observes two unknown celestial bodies
through breaks in the clouds, as follows: (1) GMT 6"24"15*, hs 16%04/9, Zn 334°;
(2) GMT 6^25753*, hs 30%38/1, Zn 071%. The second body appears to be of the first
magnitude, with a bright but somewhat dimmer body above it and slightly to the right.

Required.—Identify the unknown celestial bodies, using H.O. Pub. No. 214.

Answers.—(1) Pollux, (2) Jupiter.

PART FIVE
THE PRACTICE OF NAVIGATION

PART FIVE

THE PRACTICE or NAVIGATION

Page
CnHaPrER XXIII. The Practice of Marine Navigation----------------------—- 595
CHAPTER XXIV. Submarine Navigation_______________ DAA Incem 607
CHAPTER XX V. Polar Navigation DT SUL ME O A 612
CHAPTER XX VI. Lifeboat Navigation... o. EE 645
CHAPTER XXVII: Land Navigation: ts S a S 664
CHAPTER -XAXAVIIL Air Navigation — C ee 670

CHAPTER XXIX. Navigational Error: Maa 678

CHAPTER XXIII
THE PRACTICE OF MARINE NAVIGATION

2301. Introduction.—In the preceding 22 chapters, the various elements of naviga-
tion are discussed separately. In this chapter the interrelationship of the various parts
is discussed. However, the most important element of successful navigation cannot be
acquired from this book—nor from any book or instructor. The science of navigation
can be taught, but the art of navigation must be acquired. Modern navigation is a
blending of the two—a scientific art. The truly successful navigator is one who supple-
ments his knowledge with judgment, utilizing every opportunity to improve his judg-
ment through experience. Even with knowledge and judgment, the navigator cannot
expect to be fully reliable unless he is alert, constantly evaluating the situation as it
develops, avoiding dangerous situations before they arise, or recognizing them if they
do occur, and always keeping “ahead of the vessel." The elements of successful
navigation, then, are knowledge, judgment, and alertness. To the person possessing
these, navigation can be a pleasure. A person who tries to navigate without them is at
best a doubtful asset. He may be a menace to his vessel and shipmates.

It is not wise to attempt to reduce navigation to a series of steps that can be followed
mechanically. The methods and techniques to be used are those which are applicable
to the type of vessel, the equipment available, the training and experience of the
navigator and any assistants, the local situation, etc. The navigation of a small craft
proceeding up the Choptank River, for instance, might be quite different from that of an
ocean liner entering New York harbor. Both might differ from the navigation of a
naval vessel approaching an assigned anchorage. It is important that a navigator
make an “estimate of the situation” and use the methods and techniques that are best
adapted to the conditions at hand.

The discussion that follows is generally applicable to any vessel under average
conditions, but is written primarily for an average ship which might be planning and
executing an ocean voyage.

2302. Advance preparation.—Before starting a voyage, the navigator should
familiarize himself with his equipment and the conditions to be encountered. Any
defective or questionable instruments should be repaired or replaced. The necessary
charts and publications should be on hand. If the voyage is to extend beyond the time
range of any publication, such as an almanac or tide tables, the volume for the next
period should be included, or provision should be made to acquire it before the expira-
tion date of the current volume. Charts and light lists should be checked to see that
they have been corrected through the latest Notice to Mariners.

When all equipment is on hand and in suitable condition, the navigator should
study his charts and publications. He should determine which soundings are in feet,
which in fathoms, and whether other units are used (app. L). It is good practice to
underline or circle with a colored pencil the statement of units as given on each chart.
The various notes on the chart should be read, and applicable ones marked. The latitude
and longitude scales should be observed and the units noted. The channels, currents,
shoals, aids to navigation, and natural landmarks should be studied so that the general
arrangement is familiar. Useful natural ranges should be located and marked. Where
needed, turning bearings, danger angles, and danger bearings should be determined.

595

596 THE PRACTICE OF MARINE NAVIGATION

The tides and currents to be encountered should be determined from the tables and
charts. The advice and warnings given in coast pilots or sailing directions should be
read and pertinent parts marked or copied out. The light list should be studied, and
circles of visibility for the usual height of eye drawn in. Characteristics should be
written on the chart, if not printed there, or in a notebook, to assist in identification.
Useful radar targets, radiobeacons, loran rates, etc., should be noted if equipment to
utilize them is available. If a danger sounding is useful, it should be drawn in. The
bottom configuration should be studied for distinctive features that will prove helpful
in locating the position of the vessel, or keeping it in safe water. If foreign charts
are to be used, the symbols should be understood.

The extent of the preliminary study depends somewhat upon the navigator's
previous knowledge of the area. But however familiar he may be with local conditions,
the navigator should not overlook the need for checking his equipment to be sure it is
complete and up-to-date, nor to refresh his memory regarding critical items of informa-
tion. The prudent navigator leaves nothing to chance and assumes nothing that can be
verified.

In pilot waters with limited maneuvering space, the desired track might well be
plotted in advance, and the predicted time between buoys, turns, etc., determined.
Where repeated runs are made over the same routes, the entire track may be plotted
in ink. Courses, distances between lights, visibility circles, and other useful informa-
tion might be prominently indicated. When this practice is followed, a positive routine
should be set up to apply corrections and to bring these to the attention of all concerned.

2303. Getting underway.—Shortly before the ship gets underway the necessary
charts, publications, and plotting equipment should be placed on the chart table. A
check should be made to be sure that all marks (except those permanently plotted in
ink or colored pencil) relating to a previous voyage have been erased from the charts.
The navigator's binoculars should be checked to see that they are properly secured
in their accustomed place on the bridge. The gyro compasses should be started suf-
ficiently in advance to insure proper operation, and should then be compared with the
repeaters and the magnetic compass on the bridge. A check should be made to see
that the latest deviation tables are available, and that magnetic gear has not been left
near the compass. Azimuth circles and peloruses should be in place and checked.
The standard and emergency steering gear should be checked, as well as communication
and signaling equipment. If practical, the mechanical log and electronic equipment
such as radar, loran, radio direction finder, and echo sounder should be started and
checked. The hand lead should be placed at a convenient location ready for immediate
use. The anchor windlass should be tested. The sextant, chronometers, almanac,
and tables should be checked to see that they are in their proper places. It is good
practice for the navigator to prepare a check-off list to insure that nothing is over-
looked. The checks should be made carefully by a responsible person.

Before getting underway the navigator should see that all navigational personnel
are at their assigned stations and that each understands his duties. It is good practice
to acquaint each person with the general plan of operation, for an informed person is
less likely to make mistakes, and more likely to detect mistakes made by others.

2304. Leaving port.—In a harbor, the largest scale chart should be used for
greatest accuracy and detail. The dead reckoning should be started as soon as the
vessel steadies on its first course. If the desired track has not been plotted in ad-
vance, the dead reckoning is run ahead a short distance. In either event, the predicted
time of arrival at the next turning bearing, or of passing the next aid to navigation
is recorded on the chart. Predicted times of arrival at various points are of great
importance in interpreting the information received and in avoiding dangerous situa-

THE PRACTICE OF MARINE NAVIGATION 597

tions. It is good practice to use all available information, and not rely solely upon a
single aid. A good position should be maintained at all times. Fog may set in rapidly
and without warning, obscuring landmarks before a round of bearings can be observed.
Lights should be timed and identified by their characteristics. Ata distance, the color
and shape of buoys may not be apparent. Sometimes a sailboat can be mistaken for a
buoy. Buoys may be out of position. Bearings and ranges on fixed objects are
better than on floating aids which do not remain at fixed points. Soundings should be
taken continuously in the vicinity of shoal water. It is good practice to check the
compass at convenient opportunities, as when on a range. Ranges are of great value
for checking position or keeping on the desired track, and should be used whenever
available.

By skillful navigation, one may be able to save many miles of steaming. However,
it is possible to allow insufficient margin of safety. The navigator should always keep
in mind the possibility of failure of some item of equipment, unexpected fog, or the need
for maneuvering room if another vessel approaches too close. He should remember,
too, that in pilot waters currents may be strong and variable.

A detailed record should be kept in a notebook. Entries should be made showing
bearings and ranges, important soundings, all changes of course and speed, the times
of passing important aids to navigation, and other pertinent information. The record
should leave nothing in doubt, indicating whether bearings are true or by magnetic
compass, whether soundings are in feet or fathoms, etc. This record is useful in
preparing the ship’s log, providing guidance for future runs over the same area, establish-
ing position if fog sets in, and in providing an acceptable record if the vessel experiences
a mishap resulting in a later investigation.

The chart, also, should present a neat and intelligible record of the passage. Course
lines and lines of position should be drawn lightly and neatly, and should be no longer
than needed. Labels should be used wherever they contribute to an understanding of
the plot. They should be so placed and worded that no doubt is left as to their ap-
plicability and meaning. If possible, lines and labels should not be drawn through
chart symbols.

Outside the harbor, if the course is parallel to the coast, there may be advantages in
remaining close enough to utilize major aids to navigation and other landmarks. How-
ever, a set toward the beach, particularly off the entrance to an estuary, can endanger
the safety of a vessel. Many ships have grounded because a course was set too close
to off-lying dangers.

2305. Taking departure.—When a vessel reaches the open sea and is about to leave
the land astern, a last accurate position is obtained by means of landmarks available.
This process is called taking departure. It marks the end of piloting and the beginning
of the next phase of the navigation. The work of the navigator becomes less hurried,
and fixes are obtained less frequently. Soundings become of less interest. The hand
lead is secured. The position may be transferred from the chart to a plotting sheet.
Courses and speeds will be maintained over relatively long periods. The sea routine
begins. Even if the vessel is to follow the coast, it generally does so at such a distance
that danger is some distance away, and navigation is an intermittent process rather
than a continuous one.

2306. Navigation at sea, like piloting, varies somewhat from vessel to vessel
depending upon the equipment available and the individual preferences of the navigator.
A daily routine, called the day’s work, is established by the navigator and carried out
with such variations as dictated by circumstances. While details vary with the
navigator, a typical minimum day’s work is:

1. Plot of dead reckoning throughout the day.

598 THE PRACTICE OF MARINE NAVIGATION

2. Observation and reduction of celestial observations for a fix during morning
twilight.

3. Winding of chronometers and determination of chronometer error. ve. Bi

4. Observation of the sun for a morning sun line (on or near the prime vertical if
made at about the same time as 5).

5. Azimuth of the sun for a compass check. This may be an amplitude observa-
tion at sunrise, but is more commonly made at about the same time as a morning sun
line observation. )

6. Observation of the sun at or near noon. This is crossed with a morning sun
line, advanced, or with an observation of the moon or Venus to obtain a noon (ZT 1200)
position.

7. Computation of the day's run (noon to noon, or midnight to midnight).

8. Observation of the sun during the afternoon (on or near the prime vertical if
made at about the same time as 9). This is primarily for use with the advanced noon
sun line, or with a moon or Venus line, if the skies are overcast during evening twilight.

9. Azimuth of the sun for a compass check. This is commonly made at about the
same time as an afternoon sun observation, but may be an amplitude observation at
sunset.

10. Computation of the time of sunset, sunrise, and twilight, and preparation of
a list of stars and any planets in favorable positions for observation during each twi-
light period, with the approximate altitude and azimuth of each body.

11. Observation and reduction of celestial observations for a fix during evening
twilight.

12. Computation of the time of moonrise and moonset (if required).

13. Use of loran and any other available electronic aid on a regular schedule, as
every hour.

The list of celestial bodies available for observation is customarily prepared with
the aid of a star finder such as H.O. 2102-D (art. 2210). This list is particularly
helpful during evening twilight, when one desires to know where to look for the brightest
stars or planets before the general pattern of stars becomes visible. Some navigators
list or make a simple plot of the relative azimuths of the bodies, to assist in locating
them. The brightest bodies may be visible at about the time of sunset, or even
a little before. In general, it is good practice to observe the brightest bodies as
they appear in the evening, while the horizon is clear and sharp, and the dimmest
first in the morning, before they fade from view. Several observations should be made
of each body, each sight being taken quickly to avoid eye fatigue. In general, it is
better to use one good observation than to average several of questionable accuracy.
At least five or six bodies should be observed. If the three most favorably situated ones
provide a good fix, additional sights need thot be reduced, but if doubt remains, in-
formation for obtaining additional lines is available. It is better to observe bodies all
around the horizon than in the same semicircle. Thus, three bodies separated by 120°
are better than three separated by 60°, for in the former case any constant error in
altitude will be neutralized.

If a comparing watch is used, it should be compared with the chronometer or a
time tick every time celestial observations are made. The index correction should be
determined each time the sextant is used. If the horizon is used for this purpose, the
measurement should be made before evening twilight observations and after morning
twilight observations, while the horizon is sharp. If the horizon is not equally sharp
in all directions, the best part should be used.

When skies clear after a prolonged period of overcast, or when clouds threaten to
obscure the heavens, additional observations should be made, if available. During

THE PRACTICE OF MARINE NAVIGATION 599

the day a series of sun lines might be obtained and advanced to a common time, or the
moon or Venus might be available at a favorable azimuth. Sometimes observations
can be made during the night, either by use of moonlight to illuminate the horizon, or
by dark-adapting the eyes. At this time the moon, and bodies having an azimuth nearly
the same as the moon, should be avoided because of the probability of false horizons
on the illuminated water.

Sights may be reduced by any reliable method. The one most widely used by
mariners is H.O. Pub. No. 214, used in conjunction with the Nautical Almanac. If a
check is needed, a good practice is to use a different method and a different almanac, so
that mistakes will not be repeated.

Before the development of modern sight reduction methods, celestial navigation
was largely a matter of determining latitude by observation of bodies on or near the
celestial meridian (including Polaris) and longitude by observation of bodies on or near
the prime vertical. Longitude was computed by time sight. Frequently, this method
of navigation was inconvenient. Often it produced misleading results, as when a
north-south “longitude” line was used instead of the true line of position which might
differ in direction by as much as 30° or more. Errors were introduced when an incor-
rect longitude was used for solving a reduction to the meridian, or an incorrect latitude
for solving a time sight of a body some distance from the prime vertical. The use of
azimuth with a time sight was an improvement, but was not well adapted to observa-
tions of celestial bodies near the celestial meridian. The modern navigator is freed
from these restrictions. He is able to obtain a line of position extending in the correct
direction almost any time a celestial body can be observed. He places no special
significance upon latitude and longitude lines, and solves all sights by a common
method of sight reduction.

It is good practice to use a workbook for the various solutions made at sea. This
provides a valuable record which may be of inestimable value in the future. Entries
should be neat, orderly, and intelligible to another navigator. All original data and
computations should be included. The use of standard work forms is recommended.
Those given in appendix Q are slight modifications of forms developed at the United
States Naval Academy and used widely at sea. They are considered adequate but,
for sight reduction of celestial observations, there is merit in using a form which uses
a single column, so that several sights can be reduced in parallel columns. The best
form for anyone to use is one he thoroughly understands and finds logical and least
confusing. If an alteration in a work form reduces the number of errors made, it is
a desirable change. Because of the difference of opinion among marine navigators, and
the tendency to follow mechanically an established form without fully understanding
the principles involved, a work form standardized for all navigators is probably undesir-
able, although such is widely used by air navigators, who use celestial navigation some-
what intermittently. When one has established the work forms he desires to use, he
can have a rubber stamp made, or have the forms reproduced by printing. The former
is probably preferable because it permits use of a bound workbook. However, printed
forms can be punched for retention in a looseleaf binder.

At sea it is good practice to run the dead reckoning from fix to fix, determining
set and drift of the current at each fix. The use of single lines of position and current
to establish estimated positions is a matter of judgment. The ability to predict the
difference between dead reckoning positions and fixes, which ability may be developed
when the need is not apparent, can serve as a valuable asset when fixes are not available.
In the U. S. Navy, the best position available is recorded in the log at 0800, 1200, and
2000. A typical plot of part of a day’s run at sea (omitting possible loran fixes) is
shown in figure 2306.

THE PRACTICE OF MARINE NAVIGATION

600

Kn

62

"(sexy u'e1o[ ƏJqIssod Surjjruio) Bes Je

30[d umuHulul peordé T —'90ez AUNDIA

Buipees 8/9419 veino
əsn pue sey uJni
apne uinog soy

dI 0002
YO 0002.

"(01140 008)
(6+) 40 006)

8
Lui bread een bra buda]

LU

40 0080

d1 0080

N 804
EE oat

Morada UL

a ea S SO NIelelO Id -NOI LIS O

8

mala]

8e

062

THE PRACTICE OF MARINE NAVIGATION 601

It is good practice to compare the gyro repeaters with the steering magnetic
compass each half hour and after each change of course at sea, to detect any discrepancy
which may arise through malfunction. In making the comparison, one should not
overlook changes in variation and deviation. The master gyro compass should be
compared with its repeaters from time to time.

One of the duties of the navigator is to inform the captain of the expected time
of crossing time zone boundaries. The change of time is usually made at a convenient
whole hour near the time of crossing a boundary, or during the night. Aboard some
merchant ships the change is distributed equally through several watches, as 20 minutes
during three consecutive watches.

It is common practice for the captain to maintain a night order book. Standing
orders such as the conditions under which the captain is to be called, and the admonition
to keep a sharp lookout, are usually given on the inside front cover. The orders for
each night, if any, are recorded in order, over the captain's signature. They include
items such as courses to be steered, speeds to be used, times and bearings of lights
expected to be sighted, and any other pertinent navigational information. The
navigator provides the captain with such information as he may require.

2307. Landfall.—After a voyage at sea, the first contact with land is of considerable
importance. The accuracy with which one predicts the time and place of sighting land
depends upon the accuracy of navigation. If consistent loran fixes have been obtained
at frequent intervals, and these positions are confirmed by a recent fix from celestial
observations or other information, the prediction should be highly accurate. But if no
fix has been available for several days, considerable doubt may surround the landfall.

Often the approximate distance offshore, if not the position, can be determined
by means of soundings. Along most of their coasts the continents have a continental
shelf of relatively shoal water extending outward for a varying distance. A similar
insular shelf extends outward from many island groups. At the outer edge, called the
continental talus (or insular talus), a sharp increase in depth occurs. This is usually
at about the 100-fathom curve. Therefore, the crossing of this curve is often quite
abrupt, and gives information on the distance offshore. The position of this and other
depth curves may be indicated on the chart.

The place of making landfall has a definite relationship to the safety of the vessel,
particularly in an area where shoaling is not uniform along the beach. For some time
before making a landfall in such an area, it may be advisable to maintain both a dead
reckoning and estimated position plot. The best obtainable position should be deter-
mined. Methods which are acceptable a thousand miles from land may not provide
sufficiently exact data when a landfall is expected.

Only judgment, based upon existing circumstances, can determine the existence
of a dangerous situation. If the water has shoaled to a dangerous degree, for instance,
and the position of the vessel is seriously in doubt, one may have no recourse but to
stand off or anchor and await daylight, improved visibility, or better information.

When contact is made with land, the first step should be to identify the point of
contact. The anticipated point of making contact should be of assistance, but one
should be alert to the possibility of similarly appearing land at other points within a
reasonable distance on each side. The position of the vessel relative to land might be
established even before land is sighted. Soundings, radio bearings, and radar may be
used for this purpose. h

2308. Entering port, Before entering port, the navigator should have reliable
information regarding the draft of his vessel. He should also have a reliable position
relative to the land. Preparations for entering are similar to those for getting under-
way. The tide and tidal current tables, light list, coast pilot or sailing directions, and

602 THE PRACTICE OF MARINE NAVIGATION

M
WC

TRACK |?
\ PRINTED ONT:

19

¿Gp FI(FS)

,Kannon
di 8!

+ iM
18

X^ t$. dy) ` Cs ANE
DR TETAS O AN
C ĶurībamaS ji: KURIHAMA WAN _ e^ | X ay
4 DAEL, md e BER me RO "x
iy Sebds S | | ra Spera: ab
kam JS ARS ei
io PASIE äer, ds
AA 7 No Säi
; ZS -
as ana 7
vis T

: ð `
Submepted Obstructions

et

: Kakari Ne: d
z í 19 N27
(s "KANEDĀSWAN

-

IN "a DO ES
3 (7217 E
W525 OR —

Kann

269

Amen ` AAA

Wed 5
AN Storm Sig =.

E
SUME
Ë Gei ges Wee
Gg | | i u AA
(Dos! e Å = 5 2 —,

2144 7 SE
à x TOs yy
Bre T: f SE

g >a Ba. Y)
SLAN
EEN

„(dies | f PR
Qs) ü

hy

ÆN

FIGURE 2308.—Typical plot in pilot waters.

THE PRACTICE OF MARINE NAVIGATION 603

charts should all be broken out and studied so that one is familiar with conditions to
be encountered. The time of entering might be selected to take advantage of favorable
currents, and to arrive at the assigned berth at slack water. One should have a mental
picture of what to expect when approaching from seaward under the anticipated con-
ditions of lighting and visibility. The characteristics of all aids to navigation by day
or night, as appropriate, and fog signals should be known or immediately available.
In entering a strange port the navigator should carefully select the most suitable aids
to use, with substitutes if these prove inadequate, or if there is any doubt as to their
identity. Useful ranges, natural or artificial, should be noted. Danger bearings and
danger circles should be drawn in and labeled, if this has not already been done. A
danger sounding should be selected and drawn on the chart, if needed. Any shoal
areas, wrecks, areas of unusually swift current, etc., should be noted.

The courses to be steered and the distance on each should be determined and
recorded, or drawn and labeled on the chart. The identification of each turning point
should be indicated. Definite courses should be steered, and changes made only
when established positions indicate a departure from the planned track, or when
necessitated by trafic. Course changes should occur at preselected points having
definite identification. The position should not be permitted to be in doubt at any
time, even in ports which are familiar to the navigator and considered easy to enter.
Most avoidable groundings are caused by erroneous assumptions which should have
been verified. The position should be checked frequently, using the most reliable
information available. This may seem to be an unnecessary refinement, but in an
emergency a position might be needed at a time when it cannot be obtained. When
changes of course are ordered, itis good practice to indicate the amount and direction of
change, or the new course, to avoid the possibility of having one's attention diverted at
the moment the order should be given to check the swing or steady on the new course.
In general, course changes are best made when a given aid to navigation or other
landmark is abeam, or when the ship is on a range.

If it becomes necessary to pass between visible dangers without suitable marks for
obtaining fixes, a track midway between dangers can be followed by eye more accurately
than one closer to either side. If a vessel is to pass near reefs or shoals, it is sometimes
possible to observe these from a position aloft, particularly if the sun is astern.

The actual navigation while entering port is similar to that when leaving port.
A typical plot in pilot waters is shown in figure 2308. The entering of pilot waters
should be accompanied by a mental reorientation and an increased alertness. The use
of a local pilot, unless this is a mandatory requirement, is a matter which should be
decided in each case. Whether or not a pilot is used, local harbor regulations should
be followed, for the presence of a pilot does not relieve the master of his responsibility.
One should not forget to note the time of entering the area where local or inland rules
of the road apply.

Speed in the vicinity of wharves, construction work, dredges, small boats, etc.,
should be carefully controlled to avoid damage to them.

If the vessel anchors, the anchorage should be selected carefully, considering local
regulations as well as suitability and safety, including the holding qualities of the bot-
tom. If there is any doubt as to the depth of water, a boat might be sent in ahead to
take soundings. If space is limited, the approach to the anchorage should be planned
and executed carefully. As soon as the anchor is let go, the position should be de-
termined accurately, preferably by horizontal sextant angles. Bearings of a number
of prominent landmarks and lights should be measured and recorded, as a guide in
determining whether or not the vessel drags anchor.

604 THE PRACTICE OF MARINE NAVIGATION

2309. Fog.—During periods of reduced visibility, the navigator's work is more
difficult. At sea he is prevented from making celestial observations. Even when the
fog is so shallow that celestial bodies are visible, the horizon is not available as a refer-
ence. An artificial-horizon sextant may prove of some value at such a time, but unless
the sea is almost a flat calm, the results are likely to be less reliable than the dead reckon-
ing. Radio aids to navigation are affected little by fog. Unless the vessel is ap-
proaching land, there is generally no cause for concern regarding the navigation, the
principal danger being one of collision with other vessels. Usually the navigator merely
waits for the fog to lift.

When a coast is approached, however, a wait may be impractical. The safety of
the vessel requires reliable positional information. Along a coast where the shoaling
is gradual, the echo sounder or sounding machine can be of great assistance in indicating
the distance off. But along a coast having abrupt shoaling, the first indication of
shallow water may be obtained so close to the beach that action to avoid grounding is
not possible. If radio aids such as loran, radio direction finder, and radar are available,
they can provide useful information. If the vessel is near enough to a shore with steep
cliffs, the echo of the vessel’s whistle may provide indication of the distance off.

The decision of whether to enter a fogbound harbor should be made carefully.
Once committed to the channel, the vessel may have no alternative but to continue on
to the anchorage or wharf, for in some areas there is not room to turn back, and anchor-
ing is unsafe. It is sometimes wiser to stand off or anchor for a few hours than to risk
danger of grounding or collision.

If the decision is made to enter, one should be prepared for any reasonable eventu-
ality. The proximity of danger and the presence of currents make necessary the main-
tenance of a good position at all times. Fog limits the number of objects that can be
used for fixing position, and destroys the overall view of the area. The radio direction
finder and radar, both shipborne and shore-based, have done much to reduce the hazard
due to fog, but they have not eliminated it. The need for special precautions and
increased vigilance is still present.

During periods of reduced visibility the practice of steering exact courses, with
precise changes at definite points, is of great assistance in pilot waters. If the vessel
is following a channel, each buoy should be located successively. If the fog is dense,
this requires careful steering and attention to all details, such as indications of current,
changes of wind, etc. If a single buoy is missed, consideration should be given to an-
choring and waiting for improved visibility.

With the possible exception of radar, the most important navigational aid during
fog in pilot waters is the echo sounder, sounding machine, or hand lead. Continuous
soundings, compared with the chart, can provide valuable information on the position
and safety of the vessel. The decision as to whether to plot a line of soundings on trans-
parent material, or along the edge of a piece of paper, and compare this with the chart is
a matter of judgment. In general, the procedure is valuable when approaching a
harbor or proceeding in an open part of a large bay, but in a channel or other restricted
waters the method is not needed and might prove distracting.

During fog one should keep a sharp lookout for any objects that might appear
momentarily through thin places in the fog. It is well to have a lookout stationed
aloft, and another in the bow, for the visibility may vary with height.

The lookouts and all persons on the bridge should listen intently for fog signals.
As soon as such a signal is heard, an effort should be made to identify its source and
determine its bearing. However, experience in the use of sound signals indicates that
they are not wholly reliable. In particular, relative intensity of a sound is not a reliable
indication of its distance, or whether the distance is increasing or decreasing. A signal

THE PRACTICE OF MARINE NAVIGATION 605

may be totally inaudible in certain areas close to its source. Neither is its apparent
direction always a correct indication of its actual direction. A fog signal may not be
in operation when fog is present a short distance from a station but is unobserved from
it. Transmission of sound through water is subject to uncertainties due principally to
differences in density in different parts of the sea, causing the sound to be deflected.

It is well to remember that at reduced speed the relative effect of current is cor-
respondingly greater, since the effect of current is proportional to time, not to the
speed of the vessel.

2310. Navigation of small craft.—In principle, the navigation of small craft is
the same as that of a large ship, but because of the shallower draft, greater maneuver-
ability, and possible limitations of equipment of small craft, there are important dif-
ferences. Small craft spend most of their time within sight of land, where navigation is
largely a matter of piloting. They generally skirt the beach close enough to be able
to reach safety in case of storm or fog, and since most of them are used primarily for
pleasure, there is a natural tendency for the navigation to be a less continuous process
than in larger craft.

The equipment carried and the type of navigation employed depend primarily upon
the use of the craft and the preference of the user. If a rowboat, canoe, or small sailboat
is to be used only close to the shore in good weather, “seaman's eye" might be sufficient
for all navigational purposes. But if there is any possibility of the craft being out in a
fog, or proceeding to greater distances from shore, fog-signalling apparatus, a compass,
and some means of taking soundings should be carried.

A wide variety of equipment is available for yachts, and from this, suitable items
can be selected. A minimum list should include a compass, pelorus, charts, plotting
equipment (many types are available), means for determining speed or distance, log
book, tide and tidal current tables, light list, coast pilot or sailing directions, hand lead,
binoculars, flashlight, and fog-signal apparatus. A barometer and thermometer are
useful.

Several items of electronic equipment, some of which are relatively inexpensive,
are available for use in small craft, to aid in navigation and increase safety. The
principal item of radio equipment, from the standpoint of safety, is a marine radio-
telephone, which in addition to providing normal communication to other boats and
the shore, permits the boat carrying it to call for help in distress, and assists in the loca-
tion of the distressed vessel. The radio direction finder is a simple device requiring little
power, an important factor on small craft. A multiband direction finder may be used
as a second receiver in the broadcast and radiotelephone bands. Portable broadcast
receivers permit reception of weather information on even the smallest boats. For
larger craft, where ample power is available, radar and loran may be good investments.
In addition, every small craft should carry a corner reflector (art. 1209), so as more
readily to reflect radar signals. In an emergency a metal bucket might be of some
value as a reflector.

If the craft is to proceed out of sight of land for more than short intervals, celestial
navigation equipment should be carried. This includes a sextant, an accurate time-
piece, an almanac, sight reduction tables, and perhaps a star finder. If there is doubt
as to advisability of including some item of equipment, the safer decision is to include it.
It is better to have unused equipment than to risk danger of becoming lost because of
lack of needed equipment.

The practice of navigation in small craft varies even more widely than the equip-
ment carried. The variation extends from complete navigation similar to that of a
large ocean steamer to no navigation other than by eye. The completeness of the navi-
gation should fit the circumstances. There is an understandable tendency among small

606 THE PRACTICE OF MARINE NAVIGATION

craft navigators of limited experience to underestimate the need for thorough and
complete navigation. In general, it is good practice for the navigator of a small craft
to establish the routine of always following definite courses from buoy to buoy or from
landmark to landmark, so that the sudden onset of low visibility will not find him unable
to proceed to safety without delay. He should change course at established points,
maintain knowledge of his position at all times, and have reliable information on the
deviation of his compass. There is a place in small craft navigation for a complete,
accurate, neat plot. Where this is impractical because of heavy weather or limited
plotting space, a careful log and dead reckoning by table 3 should be substituted.

The accounts given in yachting magazines, and the large number of calls for assist-
ance received by the Coast Guard, indicate an inadequacy of the navigation of many
small craft. Part of this is due to a lack of appreciation of the need for careful naviga-
tion. Much of it is due to lack of knowledge on the part of the small craft owner.
The decision to omit some part of navigation should stem from knowledge, not ignorance.
To the adequately informed, navigation can be part of the pleasure of yachting.

CHAPTER XXIV
SUBMARINE NAVIGATION

2401. Introduction.—Submarines deserve special consideration, from a navigational
viewpoint, because of their inherent or self-imposed limitations. Somewhat different
techniques are used in each of four operating conditions, which will be considered
separately. These are: (1) surfaced, (2) submerged by day and surfaced by night,
(3) submerged at periscope depth, and (4) totally submerged.

2402. Surfaced.—The navigation of a submarine on the surface is essentially the
same as that of other vessels, but there are some special considerations. The amount
and type of equipment available is limited somewhat by space. Most of it is housed
inside the hull, where it can be available for use when the vessel is submerged.

Careful dead reckoning by hand plot is important because of the lesser accuracy of
mechanical equipment for this purpose. Speed or distance is measured as in other
vessels. Direction measurement is dependent largely upon the gyro compass, because
of the difficulty of adequately adjusting a magnetic compass heavily shielded by a steel
hull. The areas of weak horizontal intensity of the earth’s field, in which the magnetic
compass is unreliable (art. 2513), are larger for submarines than for other vessels.
Normally, leeway is negligible.

Piloting of submarines on the surface is carried on as in other vessels. However,
the amount of exposed equipment is somewhat limited, as is the space for plotting and
chart stowage. Because of the low height of eye, aids to navigation are not visible as
far away as in other vessels of like size. At ten feet above the surface the horizon is
only 3.6 miles away, while at 50 feet itis 8.1 miles distant. This may be an advantage
when picking up a dark buoy, which may be more conspicuous against the background
of a bright sky than against the darker water.

Electronic navigation is available to the submarines equipped to use it, but again
space limitations are a consideration. Most submarines are equipped with radar,
radio direction finders, and loran, as well as sonar and echo-sounding equipment. The
low antenna height restricts the range at which signals can be received in some cases,
particularly with radar.

With most of its hull under water, a submarine generally offers a steady platform
for making celestial observations. However, if there is much of a sea, difficulty may
be experienced in keeping the sextant mirrors dry, because the ship tends to go through
the waves instead of riding over them. Because of the low height of eye, the state of
the sea is an important consideration, and a correction for wave height (art. 1608) may
be justified. If the sea is calm, excessive and somewhat unpredictable refraction may
be encountered, particularly for heights of eye below about six feet.

2403. Submerged by day and surfaced by night.— This condition is not unusual
during war patrols. By day the ship proceeds largely by dead reckoning, which be-
comes of even greater importance than on the surface, where ample means of checking
its accuracy are usually available. Below the surface, where the ship is not buffeted
by waves and wind, a steady course can be steered. The steadiness increases the re-
liability of the gyro compass. Speed is determined by log or shaft revolutions. Tf the
latter is being used, it is well to remember that when the submarine is proceeding near
the bottom, its actual speed may be somewhat less than indicated. Dead reckoning

607

608 SUBMARINE NAVIGATION

should be kept up-to-date by a careful hand plot. The mechanical equipment for this
purpose provides a useful check, but is less accurate. Doppler or inertial navigation
(art. 809) may prove useful in submarines. The ship’s inertial navigation system
(SINS) is particularly promising.

Because of the very slow speeds normally used by submarines dependent upon
batteries, current is an important consideration. Its drift may equal or even exceed
the speed of the ship through the water. Pilot charts give helpful information on sur-
face currents, but both the set and drift of the current below the surface may differ
considerably. In relatively shallow water the drift may be greater for a short distance
below the surface, but generally the drift decreases with depth. Near the bottom,
the drift is noticeably reduced by friction. All available knowledge of subsurface
currents should be used, but information on the subject is far from complete. A device
called the geomagnetic electrokinetograph, or GEK, has been successfully used to
determine ocean currents by a surface vessel towing two electrodes. If this device can
be further perfected and adapted for use by submerged submarines, it will remove one
of the principal uncertainties of underwater navigation.

It may not be advisable to take echo soundings because of the danger of revealing
one's presence, but when they can be obtained, allowance should be made for the
depth of the submarine below the surface.

Determination of sunset and the end of evening twilight has added significance to
the crew of a submerged submarine in a war zone. In enemy waters it may not be
safe to surface until full darkness has set in. By this time the visible horizon is gone,
but if the sky is clear, there is no shortage of celestial bodies. If the moon is available,
it may provide enough illumination to permit reasonably accurate altitude observations.
However, false horizons frequently appear below a bright moon, and better results can
usually be obtained by making back sights (art. 1633) of bodies near the moon's azimuth.

Some experiments have been made with night vision and star observations on a
dark night. By thoroughly adapting their eyes to darkness and looking a little above
or below the image of the body on the horizon, some navigators have reported accept-
able results, using a relatively large number of observations. Most navigators using
the method prefer a six-power telescope, as from a pair of binoculars, but others use no
magnification and keep both eyes open.

When using this method, it is particularly desirable to observe stars all around the
horizon, so that any constant error in estimating the position of the horizon will have
minimum effect. When taking such observations, it is essential that nothing be done
to disturb the dark-adaptation of the eyes, which must operate at peak performance.
The observer and the assistant timing the observations should stand back to back.
The timer's flashlight should be shielded so as to give à minimum of light needed for
reading the watch. When the time has been noted and written down, the light should
be turned off. The observer then hands the sextant to the assistant, who again faces
away, turns cn his light, and reads and records the sextant altitude. He then turns
off the light, hands the sextant back to the observer, and the routine is repeated for the
next observation. A dim red or blue light is preferable, and safer in a war zone. It
is good practice to take and time several observations of each body, alternately in-
creasing and decreasing the altitude setting of the sextant. If the results are plotted
on cross-section paper, using altitude versus time, it should be possible to determine the
best shots for solution.

In fairing a line through the plotted points, it may be helpful to know the correct
direction of the line. One way of determining this direction is by means of H.O. Pub.
No. 214. Since At is the unit change in altitude (to two decimal places), 15 X At is the
change for 15 minutes of arc (one minute of time). However, this result is for a sta-

vita

SUBMARINE NAVIGATION 609

tionary observer. To correct for his motion, multiply the distance run in one minute
by the cosine of the relative azimuth of the body. If the body is forward of the beam,
add the correction to 15 X At if the body is rising, and subtract it if setting. Fora
body abaft the beam, reverse these signs. Having determined the change in altitude
in one minute, draw a line at the slope indicated and move it parallel to itself until it
best fits the plotted. points. In fitting the line to the points, it is usually good practice
to ignore the inconsistent shots. If At is changing rapidly, the change of altitude with
time is not satisfactorily represented by a straight line, and should be plotted as a curve.
This is most apparent for a body near the meridian, particularly one at a high altitude.
Once the line is located, any point on it can be taken as the observation, whether or not
it coincides with a plotted point, as long as the corresponding time is used. Thus, any
convenient time or altitude might be selected.

Bubble or pendulum sextants (art. 1513) usually do not produce satisfactory
results aboard ship because of the large acceleration errors produced by the motions
of the vessel. However, it is desirable for a submarine to be provided with an
artificial-horizon sextant, for there may be occasions when it affords the only available
method of determining position, and the results may be of usable accuracy. With a
reasonably smooth sea and a large number of observations, quite satisfactory results
can be obtained. Since this instrument does not depend upon a visible horizon, the
number of observations that can be obtained is limited only by the number of naviga-
tional bodies visible, and the time available to the observer. The assumed positions for
the various sights should all be advanced or retired to a common time before the lines
of positions are plotted, so that no confusion can result from the presence of the addi-
tional lines on the chart. For correction of artificial-horizon sextant altitudes, see
article 1625. In using an artificial-horizon sextant, it may be desirable to make a num-
ber of observations of each body and plot them as explained above. Since acceleration
error is due mostly to rolling, better observations can often be made over the bow or
stern. If conditions warrant, the ship should be headed directly toward or away from
each body as it is observed.

Whatever the method of observation, practice and some ingenuity are needed for
best results.

2404. Submerged at periscope depth.—At periscope depth the view is seriously
restricted, but not entirely lost. Reasonably accurate bearings of landmarks can be
obtained through the periscope. Electronic navigation is available if an antenna can
be surfaced, or, in some cases, kept submerged near the surface.

When the sun passes within a few degrees of the zenith, a number of azimuths can
sometimes be measured by periscope before and after meridian transit. In using this
information, it should be remembered that azimuth lines are great circles. Plot the
geographical position at the time of each observation, and advance or retire it for the
ship's run, so that all sights are for a common time. Apply the conversion angle cor-
rection from table 1 as for radio bearings, and plot the azimuth lines from the adjusted
positions. Reasonably accurate results have been reported with this method when
within about 400 miles of the geographical position of the sun. It can be used at
greater distances if accurate azimuths can be obtained. The method requires a good
level and cross-level of the periscope, and practice. For best results plot the azimuths
against time on cross-section paper. Fair a curve through the plotted points, ignoring
inconsistent observations. The points to use for plotting the azimuth lines on the
chart or plotting sheet are taken at uniform intervals along the curve. If plotting is
done on a gnomonic chart, conversion angle is not applied. However, because of
the very small scale of these charts, plotting must be done carefully if accurate results
are to be obtained. Lambert conformal charts can be used, but with some loss of

610 SUBMARINE NAVIGATION

accuracy. The method can be used for similar observations of the moon, planets, and
stars, if observations of these bodies can be made and the bodies identified. If a
single body is used, the best times are just before and just after meridian transit, when
the azimuth changes most rapidly and the ship is nearest the geographical position of
the body. The principal limitation of the method is the accuracy with which azimuths
can be observed. Unless the sea is almost a flat calm, the distance limitations are
severe, and considerable skill is needed for good results under any conditions.

Some success has been obtained with altitude observations by means of the per-
iscope, but this is difficult at best, and is limited to low altitudes. At low-power
magnification, altitudes as high as 25° can be measured, but at high power the method
is limited to about 7°. For good results the periscope should be accurately in the vertical,
and steady. One method of obtaining the altitude is by counting the graduations of
the vertical scale between the horizon and the body. Some navigators prefer the
use of the periscope stadimeter, which may give satisfactory results in either of two
ways. First, it may be offset so that the zero line of its vertical scale coincides with a
selected line (as at 5° or 6°) of the periscope field. This causes a false horizon to appear
at the selected periscope field line. As a body appears to cross this false horizon,
it is at the selected altitude. A variation of this method is to offset the stadimeter
zero line until the false horizon appears at the body, when the amount of the offset is
the altitude. The second way of using the stadimeter is to read the distance correspond-
ing to some arbitrarily chosen height. This height divided by the corresponding dis-
tance is the tangent of the altitude, which can be found in table 31. Better results
might be obtained by noting the moment at which the lower or upper limb of the sun
or moon is tangent to the horizon (or a planet or star crosses the horizon), and using
the altitude as 0?00:0, than by attempting to measure a low altitude through the
periscope. Correction of low-altitude observations is explained in article 1632.

Solution of low-altitude observations can be made by virtually any method,
including H.O. Pub. No 214. Low-altitude sight reduction is discussed in article
2010.

2405. Totally submerged.—The navigation of a totally submerged submarine is a
problem which has not been fully solved. Some of the methods being developed or in
use cannot be discussed because of security limitations. However, the following infor-
mation should serve as a useful guide.

Dead reckoning, the basic form of navigation under virtually any conditions, is
of increased importance to the totally submerged submarine. Submerged dead
reckoning is discussed in article 2403.

Soundings can be used to help establish position in an area where a reliable chart
of the bottom configuration is available, if allowance is made for the depth of the
submarine below the surface. Sonar (art. 1108) can sometimes be useful in avoiding
obstacles or even in locating position when there are identifiable, charted targets.
Both sofar and rafos (art. 1313) can be used when available.

Electronic navigation has limited application unless an antenna is above water.
However, very low frequency signals penetrate sea water to some extent, and if the
submerged antenna can be placed close to the surface, usable signals can sometimes be
obtained at great distances. These frequencies are little used for navigational informa-
tion, but increased requirements for navigation below the surface will undoubtedly
result in additional development in this part of the spectrum.

A useful method of submerged navigation might be based upon measurement of
any quantity that varies from place to place in a known pattern, such as gravity or
some element of the earth’s magnetism, some form of radiation, or even water temper-
ature or salinity. The use of such a method would require an instrument to provide

SUBMARINE NAVIGATION 611

sufficiently accurate measurements, and an accurate chart showing the pattern at the
time of observation. This would be similar to using bottom contours. Since a method
of this type might often provide lines of position only, two or more methods may be
needed to establish a fix.

Celestial navigation is not used by a totally submerged submarine.

The navigation of a submarine which remains below the surface for long periods,
with nothing extending above water, presents a challenge that is partly met by making

full use of every item of applicable information, and applying a generous amount of
judgment and common sense.

CHAPTER XXV
POLAR NAVIGATION

Polar Regions

2501. Introduction.—No single definition of the limits of the polar regions satisfies
the needs of all who are interested in these areas. Astronomically, the parallels of lati-
tude at which the sun becomes circumpolar (the arctic and antarctic circles at about
latitude 6725) are considered the lower limits. Meteorologically, the limits are irregular
lines which, in the arctic, coincides approximately with the tree line. For general
purposes, the navigator may consider polar regions as extending from the geographical
poles of the earth to latitude 70° (in the arctic coinciding approximately with the
northern coast of Alaska), with transitional sub-polar regions extending for an addi-
tional 10° (in the northern hemisphere extending to the southern tip of Greenland).

This chapter deals primarily with marine navigation in high latitudes. Information
relating to navigation ashore is given in chapter XXVII.

2502. Polar geography.—The north polar region, the arctic, consists of an elongated
central water area a little smaller than the United States, almost completely sur-
rounded by land (fig. 2502a). Some of this land is high and rugged with permanent
ice caps, but part of it is low and marshy when thawed. Underlying permafrost,
permanently frozen ground, prevents adequate drainage, resulting in large numbers
of lakes and ponds and extensive areas of muskeg, soft spongy ground with character-
istic growths of certain types of moss and tufts of grass or sedge. There are also large
areas of tundra, low treeless plains with vegetation consisting of mosses, lichens, shrubs,

FIGURE 2502a.— The north polar region, or arctic.

612

POLAR NAVIGATION 613

a 1409 1309 1209 1109 100° 90° 80° 70° 60° 50° 40°

` 1109 100°

FIGURE 2502b.—The south polar region, or antarctic.

willows, etc., and usually having an underlying layer of permafrost. The northernmost
point of land is Kap Morris Jesup, Greenland, about 380 nautical miles from the pole.

The central part of the Arctic Ocean, as the body of water is called, is a basin of
about 12,000 feet average depth. However, the bottom is not level, having a number of
seamounts and deeps. The greatest depth is probably a little more than 16,000
feet. At the north pole the depth is 14,150 feet. Surrounding the polar basin is an
extensive continental shelf, broken only in the area between Greenland and Svalbard
(Spitsbergen). The many islands of the Canadian archipelago are on this shelf. The
Greenland Sea, east of Greenland; Baffin Bay, west of Greenland; and the Bering Sea,
north of the Aleutians, each has its independent basin. In a sense, the Arctic Ocean
is an arm of the Atlantic, as shown in figure 2502a.

The south polar region, the antarctic, is in marked contrast to the arctic in physio-
graphical features. Here a high, mountainous land mass about twice the area of the
United States is surrounded by water (fig. 2502b). An extensive polar plateau covered
with snow and ice is about 10,000 feet high. There are several mountain ranges with
peaks rising to heights of more than 13,000 feet. The average height of Antarctica
is about 6,000 feet, which is higher than any other continent. The height at the south
pole is about 9,500 feet. The barrier presented by land and tremendous ice shelves
500 to 1,000 feet thick prevent ships from reaching very high latitudes. Much of
the coast of Antarctica is high and rugged, with few good harbors or anchorages.

2503. Navigation in polar regions.—Special techniques have been developed to
adapt navigation to the unique conditions of polar regions. These conditions are
largely the result of (1) high latitude, and (2) meteorological factors.

2504. High-latitude effects.—Much of the thinking of the marine navigator is
in terms of the “rectangular” world of the Mercator projection, on which the meridians
are equally spaced, vertical lines perpendicular to the horizontal parallels of latitude.
Directions are measured relative to the meridians, and are maintained by means of a

614 POLAR NAVIGATION

magnetic or gyro compass. A straight line on the chart is a rhumb line, the line used for
ordinary purposes of navigation. Celestial bodies rise above the eastern horizon, climb
to a maximum altitude often high in the sky as they cross the celestial meridian, and
set below the western horizon. By this motion the sun divides the day naturally into
two roughly equal periods of daylight and darkness, separated by relatively short
transitional periods of twilight. The hour of the day is associated with this daily
motion of the sun.

In polar regions conditions are different. Meridians all converge at the poles,
which are centers of series of concentric circles constituting the parallels of latitude.
The rapid convergence of the meridians renders the usual convention of direction in-
adequate for some purposes. A rhumb line is a curve which differs noticeably from a
great circle, even for short distances. Even visual bearings cannot adequately be
represented as rhumb lines. At the pole all directions are south or north, depending
upon the pole. Direction in the usual sense is replaced by longitude.

At the pole the zenith and celestial pole coincide. Hence, the celestial horizon
and celestial equator also coincide, and declination and computed altitude are the same.
Therefore, celestial bodies change computed altitude only by changing declination.
Stars circle the sky without noticeable change in altitude. Planets rise and set once
each sidereal period (12 years for Jupiter, 30 years for Saturn). At the north pole
the sun rises about March 21, slowly spirals to a maximum altitude of about 23°27’
near June 21, as slowly spirals downward to the horizon about September 23, and then
disappears for another six months. At the south pole a similar cycle takes place but
during the opposite time of year. It requires about 32 hours for the sun to cross the
horizon, during which time it circles the sky 1% times. The twilight periods following
sunset and preceding sunrise last for several weeks. The moon rises and sets about
once each month. Half the sky is always visible and the other half is never seen.

The long polar night is not wholly dark. "The full moon at this time rises relatively
high in the sky. Light from the aurora borealis in the arctic and the aurora australis
in the antarctic is often quite bright, occasionally exceeding that of the full moon.
Even the planets and stars contribute an appreciable amount of light in this area where
a snow cover provides an excellent reflecting surface.

All time zones, like all meridians, meet at the poles. Local time does not have its
usual significance, since the hour of the day bears no relation to periods of light and
darkness or to altitude of celestial bodies.

2505. Meteorological effects.—Polar regions are cold, but the temperature at sea
1s not as extreme as inland. The average winter temperature over the Arctic Ocean
is (—) 30°F to (—) 40°F, with an extreme low value near (—) 60°F. Colder tempera-
tures have been recorded in Yellowstone National Park. During the summer the
temperature remains above freezing over the ocean. Inland, extreme values are some-
times reached. At least one point on the arctic circle has experienced a temperature
of 100° F. Few points on the antarctic continent have recorded temperatures above
freezing, and the interior is probably the coldest part of the world.

Fog and clouds are common in polar regions, yet there is less precipitation than
in some desert regions, since the cold air has small capacity for holding moisture.
Very cold air over open water sometimes produces steaming of the surface, occasionally
to a height of several hundred feet. This is called frost smoke or sea smoke (fig.
2505). When there is no fog or frost smoke, the visibility is often excellent.
Sounds can sometimes be heard at great distances.

Sharp discontinuities or inversions in the temperature lapse rate sometimes produce
a variety of mirages and extreme values of refraction. The sun has been known to rise
several days before it was expected in the spring. False horizons are not uncommon.

POLAR NAVIGATION 615

Strong winds are common in the sub-arctic and in both the antarctic and sub-
antarctic. The belt of water surrounding Antarctica has been characterized as the
stormiest in the world, being an area of high winds and high seas. Strong winds are
not encountered over the Arctic Ocean.

In the polar and sub-polar regions the principal hazard to ships is ice, both that
formed at sea and land ice which has flowed into the sea in the form of glaciers. Many
low land areas are ice-free in summer. Ice is considered in more detail in chapter
XXXVI.

When snow obliterates surface features, and the sky is covered with a uniform
layer of cirrostratus or altostratus clouds, so that there are no shadows, the horizon

Figure 2505.—Frost smoke.

disappears and earth and sky blend together, forming an unbroken expanse of white,
without features. Landmarks cannot be distinguished, and with complete lack of
contrast, distance is virtually impossible to estimate. This is called arctic (or antarctic)
whiteout. It is particularly prevalent in northern Alaska during late winter and early
spring. l

2506. Miscellaneous.—The cold surface water of the Arctic Ocean flows outward
between Greenland and Svalbard and is replaced by warmer subsurface water
from the Atlantic. The surface currents depend largely upon the winds, and are
generally quite weak in the Arctic Ocean. However, there are a number of well-
established currents flowing with considerable consistency throughout the year. The

616 POLAR NAVIGATION

general circulation in the arctic is clockwise on the American side and around islands,
and counterclockwise on the Asian side. Tidal ranges in this area are generally small.
In the restricted waters of the upper Canadian-Greenland area both tides and currents
vary considerably from place to place. In the Baffin Bay-Davis Strait area the cur-
rents are strong and the tides are high, with a great difference between springs and
neaps. In the antarctic, currents are strong, and the general circulation offshore is
eastward or clockwise around the continent. Close to the shore, a weaker westerly or
counterclockwise current may be encountered, but there are many local variations.

Since both magnetic poles are situated within the polar regions, the horizontal
intensity of the earth’s magnetic field is so low that the magnetic compass is of reduced
value, and even useless in some areas. The magnetic storms centered in the auroral
zones (art. 2526) disrupt radio communications and alter magnetic compass errors.
The frozen ground in polar regions is a poor conductor of electricity, another factor
adversely affecting radio wave propagation.

APA IR

2507. Summary of conditions in polar regions.— The more prominent character- .

istic features associated with large portions of the polar regions may be summarized
as follows:
1. High latitude.
2. Rapid convergence of meridians.
3. Nearly horizontal diurnal motion of celestial bodies.
4. Long periods of daylight, twilight, and semidarkness.
5. Low mean temperatures.
6. Short, cool summers and long, cold winters.
7. High wind-chill factor.
8. Low evaporation rate.
9. Scant precipitation.
10. Dry air (low absolute humidity).
11. Excellent sound-transmitting conditions.
12. Periods of excellent visibility.
13. Extensive fog and clouds.
14. Large number and variety of mirages.
15. Extreme refraction and false horizons.
16. Winter freezing of rivers, lakes, and part of the sea.
17. Areas of permanent land and sea ice.
18. Areas of permanently frozen ground.
19. Large areas of tundra (arctic).
20. Large areas of poor drainage, with many lakes and ponds (arctic).
21. Large areas of muskeg (a grassy marsh when thawed) (arctic).
22. Extensive auroral activity.
23. Large areas of low horizontal intensity of earth's magnetic field.
24. Intense magnetic storms.
25. Uncertain radio wave propagation.
26. Strong winds (antarctic).
27. Frequent blizzards (antarctic).
28. Large quantities of blowing snow.

Charts

2508. Projections.—In polar regions, as elsewhere, the chart is an important item

of navigational equipment. The projections used for polar charts are considered in
articles 321 and 322.

POLAR NAVIGATION 617

For ordinary navigation the Mercator projection has long been the overwhelming
favorite of marine navigators, primarily because a rhumb line appears as a straight line
on this projection. Even in high latitudes the mariner has exhibited an understandable
partiality for Mercator charts, and these have been used virtually everywhere that ships
have gone.

However, as the latitude increases, the superiority of the Mercator projection
decreases, primarily because the value of the rhumb line becomes progressively less.
At latitudes greater than 60° the decrease in utility begins to be noticeable, and beyond
latitude 70° it becomes troublesome. In the clear polar atmosphere, visual bearings are
observed at great distances, sometimes 50 miles or more. The use of a rhumb line to
represent a bearing line introduces an error at any latitude, but at high latitudes this
error becomes excessive.

Another objection to Mercator charts at high latitudes is the increasing rate of
change of scale over a single chart. This results in distortion in the shape of land masses
and errors in measuring distances.

At some latitude the disadvantages of the Mercator projection outweigh its
advantages. The latitude at which this occurs depends upon the physical features of
the area, the configuration and orientation of land and water areas, the nature of the
operation, and, mostly, upon the previous experience and personal preference of the
mariner. Because of differences of opinion in this matter, a transitional zone exists
in which several projections may be encountered. The wise high-latitude navigator
is prepared to use any of them, since coverage of his operating area may not be adequate
on his favorite projection.

2509. Adequacy.—Charts of most polar areas are generally inferior to those of
other regions in at least three respects:

1. Lack of detail. Polar regions have not been surveyed with the thoroughness
needed to provide charts of the accustomed detail. Relatively few soundings are
available and many of the coastal features are shown by their general outlines only.
Large areas are perennially covered by ice, which presents a changing appearance as
the amount, position, and the character of the ice change. Heavy covers of ice and
snow prevent accurate determination of surface features of the earth beneath. Added
to this is the similarity between adjacent land features where the hundreds of points
and fiords in a rugged area or the extensive areas of treeless, flat coastal land in another
look strikingly alike. The thousands of shallow lakes and ponds along a flat coastal
plain lack distinctive features.

2. Inaccuracy. Polar charts are based upon incomplete surveys and reports of
those who have been in the areas. These reports are less reliable than in other areas
because icebergs are sometimes mistaken for islands, ice-covered islands are mistaken
for grounded icebergs, shore lines are not easy to detect when snow covers both land
and attached sea ice, inlets and sounds may be completely obscured by ice and snow,
and meteorological conditions may introduce inaccuracy in determination of position.
Consequently, many features are inaccurately shown in location, shape, and size, and
there are numerous omissions. Isogonic lines, too, are based upon incomplete informa-
tion, resulting in less than desired accuracy.

3. Coverage. Relatively few nautical charts of polar regions are available, and
the limits of some of these are not convenient for some operations. As in other areas,
charts have been made as the need has arisen. Hence, large-scale charts of some areas
are completely lacking. Aeronautical charts are sometimes quite helpful, as they often
show more detail of land areas than do the nautical charts. However, aeronautical
charts do not show soundings.

618 POLAR NAVIGATION

2510. Polar grid.—Because of the rapid convergence of the meridians in polar
regions, the true direction of an oblique line near the pole may vary considerably over
a relatively few miles. The meridians are radial lines meeting at the poles, instead of
being parallel, as they appear on the familiar Mercator chart.

Near the pole the convenience of parallel meridians is attained by means of a
polar grid. On the chart a number of lines are printed parallel to a selected reference
meridian, usually that of Greenwich. On transverse Mercator charts the fictitious
meridians may serve this purpose. Any straight line on the chart makes the same angle
with all grid lines. On the transverse Mercator projection it is therefore a fictitious
rhumb line. On any polar projection it is a close approximation to a great circle. If
north along the reference meridian is selected as the reference direction, all parallel
grid lines can be considered extending in the same direction. The constant direction
relative to the grid lines is called grid direction. North along the Greenwich meridian
is usually taken as grid north in both the northern and southern hemispheres.

The value of grid directions is indicated in figure 2510. In this figure A and B |
are 400 miles apart. The true bearing of B from A is 023°, yet at B this bearing line,
if continued, extends in true direction 163°, a change of 140° in 400 miles. The grid
direction at any point along the bearing line is 103°.

When north along the Greenwich meridian is used as grid north, interconversion
between grid and true directions is quite simple. Let G represent a grid direction and
T the corresponding true direction. Then for the arctic,

G= EEN

That is, in the western hemisphere, in the arctic, grid direction is found by adding
the longitude to the true direction. From this it follows that

T=G—1W,
and in the eastern hemisphere

G=T-—AE,

T=G+ dE.

In the southern hemisphere the signs (+ or —) of the longitude are reversed in all
formulas.

If a magnetic compass is used to follow a grid direction, variation and convergency
can be combined into a single correction called grid variation or grivation. It is cus-
tomary to show lines of equal grivation on polar charts rather than lines of equal varia-
tion. Hydrographic Office chart number 1706 GN shows the isogrivs (lines of equal
grivation) for the entire arctic.

With one modification the grid system of direction can be used in any latitude.
Meridians 1° apart make an angle of 1° with each other where they meet at the pole.
The convergency is one, and the 360° of longitude cover all 360° around the pole. At
the equator the meridians are parallel and the convergency is zero. Between these two
limits the convergency has some value between zero and one. Ona sphere it is equal to
the sine of the latitude. For practical navigation this relationship can be used on the
spheroidal earth. Onasimple conic or Lambert conformal chart a constant convergency
is used over the entire chart, and is known as the constant of the cone. On a simple
conic projection it is equal to the sine of the standard parallel. On a Lambert conformal
projection it is equal (approximately) to the sine of the latitude midway between the
two standard parallels. When convergency is printed on the chart, it is generally ad-
justed for ellipticity of the earth. If K is the constant of the cone,

K=sin 3 (L,+L»),

POLAR NAVIGATION 619

where L; and L, are the latitudes of the two standard parallels. On such a chart, grid

navigation is conducted as explained above, except that in each of the formulas the
longitude is multiplied by K:

G=T+K AW,
DA
G=T—KE,
De GA KAR.

Thus, a straight line on such a chart changes its true direction, not by 1° for each degree
of longitude, but by K”. As in higher latitudes, convergency and variation can be
combined.

In using grid navigation one should keep clearly in mind the fact that the grid lines
are parallel on the chart. Only on the transverse Mercator and polar gnomonic pro-
jections do the grid lines have geographical significance. On these projections, the
grid lines are great circles which meet at “poles” on the equator, 90° from the meridian
used as the fictitious equator. Since distortion varies on charts of different projections,
and on charts of conic projections having different standard parallels, the grid direction

=
pus
Sis
s|=
tee e]
DÐ
eļo
EM
E pz
Flo
el
o
e
ol 2
=

Popp 2510.—Polar grid navigation.

620 POLAR NAVIGATION

between any two given points is not the same on all charts. For operations which are to be
coordinated by means of grid directions, it is important that all charts showing the grid
be on a single graticule.

Except for nuclear powered submarines, ships seldom reach such high latitudes
that grid navigation with full convergency of one is used. In the sub-polar regions in
which most high-latitude surface ship navigation is conducted, a grid on a suitable
projection should be available.

2511. Plotting on polar charts, as on other charts, involves the measurement of
distance and direction. On a Mercator chart this is done as in lower latitudes. How-
ever, as latitude increases, expansion of the latitude scale increases at a more rapid
rate. For accurate results, it is essential that distances be measured in relatively short
steps and that an accurate mid latitude be used for each step, as shown in figure 2511a.
As latitude increases, the departure of a rhumb line from a great circle becomes greater,
and rhumb lines lose some of their value. If they are used to approximate a great circle,

85°N 85°N

84°N

30'

83 N

30’

82°N

30’
30'

FIGURE 2511a.— Measuring distance on a high-latitude Mercator chart.

em 8

POLAR NAVIGATION 621

as in great-circle sailing, shorter legs are needed to retain a good approximation. Even
visual bearing lines cannot accurately be represented by rhumb lines if the distance is
great, unless a Mercator correction (tab. 1) is applied as in the case of radio bearings.
Such reasons indicate using more suitable projections in high latitudes.

On a chart with converging meridians, as one on the Lambert conformal projection,
distance is measured by means of the latitude scale, as on a Mercator chart, but this
scale is so nearly constant that any part of it can be used without introducing a sig-
nificant error. A mile scale is sometimes shown in or near the margin of such a chart,
and can be used anywhere on that chart.

Since the meridians converge, a straight line makes a different angle with each
meridian, as shown in figure 2510. For this reason, compass roses are not customarily
shown on such a chart. If they do appear, each one applies only to the meridian on
which it is located. The navigator accustomed to using a Mercator chart can easily
forget this point, and hence will do well to ignore compass roses. If a drafting machine
is used, it should be aligned with the correct meridian each time a measurement is made.
Since this precaution can easily be overlooked, especially by a navigator accustomed to
resetting his drafting machine only when the chart is moved, and since the resulting
error may be too small to be apparent but too large to ignore, it is good practice to
discard this instrument when the Mercator chart is replaced by one with converging
meridians, unless positive steps are taken to prevent error.

The most nearly fool-proof and generally the most satisfactory method of measur-
ing directions on a chart with converging meridians is to use a protractor, or some kind
of plotter combining the features of a protractor and straightedge. One of the most
popular is the type B-2 aircraft plotter (fig. 2511b) available to U.S. naval activities
from the Aviation Supply Office at Philadelphia, or the AN plotter (or commercial
counterpart) shown in figure 2511c.

|

oB

|

ta PIVOT HOLE OVE
MID MERIDIAN

READ COURSE 050° ON INNER
SCALE AT MID MERIDIAN

FIGURE 2511b.— Measuring a course on a Lambert conformal chart, by B-2 aircraft
plotter. Note that measurement is made at the mid meridian.

622 POLAR NAVIGATION

If a course is to be meas-
ured, the mid meridian of each
leg should be used, as shown in
figure 2511b. If a bearing is
to be measured, the meridian
nearest the point at which the
bearing was determined should
be used, as shown in figure
2511c. Thus, in the usual case
of determining the bearing of a
landmark from a ship, the
meridian nearest the ship should
be used. In using either of the
plotters shown in figures 2511b
or 2511c, note that the center
hole is placed over the meridian
used, the straightedge part is
placed along the line to be
drawn or measured, and the
angle is read on the protractor at
the same meridian which passes
under the center hole. It is
sometimes more convenient to
invert the plotter, so that
the protractor part extends

FIGURE 2511c.—Measuring a bearing on a Lambert conformal ON the opposite side of the
chart, by AN plotter. Note that measurement is made at straightedge.

the meridian nearest the ship. For plo t ting eri d directions,
angles are measured from grid north, using any grid meridian. Any convenient
method can be used. If a protractor or plotter is being used for plotting grid
directions, it is usually desirable to use the same instrument for plotting true direc-
tions. The distance is the same whether grid or true directions are used.

READ BEARING 315° ON INNER
SCALE AT MERIDIAN NEAREST A

PIVOT HOLE OVER
MERIDIAN NEAREST A

Dead Reckoning

2512. Polar dead reckoning.—In polar regions, as elsewhere, dead reckoning
involves measurement of direction and distance traveled, and the use of this information
for determination of position.

Direction is normally determined by a compass, but in polar regions both magnetic
and gyro compasses are subject to certain limitations not encountered elsewhere.
However, the navigator who thoroughly understands the use of these instruments in
high latitudes can get much useful information from them. It is wise to carry, in
addition, some form of celestial compass, discussed in article 2515. The polar navigator
should not overlook the value of radar tracking or visual tracking for determining
direction of motion. This is discussed in article 2516.

Speed or distance is normally measured by log or engine revolution counter, but
these methods are not entirely suitable when the ship is operating in ice. The problem
of determining speed or distance in ice is discussed in article 2516.

2513. The magnetic compass depends for its directive force upon the horizontal
intensity of the magnetic field of the earth. As the magnetic poles are approached,
this force becomes progressively weaker until at some point the magnetic compass

POLAR NAVIGATION 623

becomes useless as a direction-measuring device. In a marginal area it is good practice
to keep the magnetic compass under almost constant scrutiny, as it is somewhat erratic
in dependability and its errors may change rapidly. Frequent compass checks by
celestial observation or any other method available are wise precautions. A log of
compass comparisons and observations is useful in predicting future reliability.

The magnetic poles themselves are somewhat elusive, since they participate in
the normal diurnal, annual, and secular changes in the earth’s field, as well as the more
erratic changes caused by magnetic storms. Measurements indicate that the north
magnetic pole moves within an elongated area of perhaps 100 miles in a generally
north-south direction and somewhat less in an east-west direction. Normally, it is at
the southern end of its area of movement at local noon and at the northern extremity
twelve hours later, but during a severe magnetic storm this motion is upset and becomes
highly erratic. Because of the motions of the poles, they are sometimes regarded as
areas rather than points. There is some evidence to support the belief that several
secondary poles exist, although such alleged poles may be anomalies (local attractions),
possibly of intermittent or temporary existence. Various severe anomalies have been
located in polar areas and others may exist.

The continual motion of the poles may account, at least in part, for the large
diurnal changes in variation encountered in high latitudes. Changes as large as 10°
have been reported.

Measurements of the earth’s magnetic field in polar regions are neither numerous
nor frequent. The isogonic lines in these areas are close together, resulting in rapid
change in short distances in some directions, and their locations are imperfectly known.
As a result, charted variation in polar regions is not of the same order of accuracy as
elsewhere.

The decrease in horizontal intensity encountered near the magnetic poles, as
well as magnetic storms, affects the deviation. Any deviating magnetic influence re-
maining after adjustment, which is seldom perfect, exerts a greater influence as the
directive force decreases. It is not uncommon for residual deviation determined in
moderate latitudes to increase 10- or 20-fold in marginal areas. Interactions between
correctors and compass magnets exert a deviating influence that may increase to a
troublesome degree in high latitudes. The heeling magnet, correcting for both per-
manent and induced magnetism, is accurately located only for one magnetic latitude.
Near the magnetic pole its position might be changed, but this may induce sufficient
magnetism in the Flinders bar to more than offset the change in deviation due to the
change in the position of the heeling magnet. The relatively strong vertical intensity
may render the Flinders bar a stronger influence than the horizontal field of the earth.
When this occurs, the compass reading remains nearly the same on any heading.

Another effect of the decrease in the directive force of the compass is a greater
influence of frictional errors. This, combined with an increase in the period of the
compass, results in greatly increased sluggishness in its return to the correct reading
after being disturbed. For this reason the compass performs better in a smooth sea
free from ice than in an ice-infested area where its equilibrium is frequently upset by
impact of the vessel against ice.

Magnetic storms affect the magnetism of a ship as well as that of the earth.
Changes in deviation of as much as 45° have been reported during severe magnetic
storms, although it is possible that such large changes may be a combination of
deviation and variation changes.

The area in which the magnetic compass is of reduced value cannot be stated in
specific terms. In general, a remote-reading Flux Gate compass performs as well or
better than a regular compass. A magnetic compass in an exposed position performs

624 | POLAR NAVIGATION

better than one in a steel pilot house. The performance of the compass varies consider-
ably with the type of compass, sensitiveness and period, thoroughness of adjustment,
location on the vessel, and magnetic properties of the vessel. It also varies with local
conditions.

` In a very general sense the magnetic compass can be considered of reduced re-
liability when the horizontal intensity is less than 0.09 oersted, erratic when the field
is less than 0.06 oersted, and useless when it is less than 0.03 oersted. The extent of these
areas in the northern hemisphere is indicated in figure 2513. Similar areas extend

120°E 105° E

FIGURE 2513.— Arctic areas in which the magnetic compass is of reduced value. Inside the
curves representing the 0.09, 0.06, and 0.03 oersted values of horizontal intensity the
compass can be considered of reduced reliability, erratic, and useless, respectively.

around the south magnetic pole, which is located at latitude 68°S, longitude 144° E
not far from the eastern shore of the Ross Sea. Hydrographic Office charts 1701 N ad
17018 show lines of equal horizontal intensity in the north and south polar regions
respectively. However, the effectiveness of the magnetic compass is influenced is
by local conditions. A compass on a vessel making a voyage through the islands of
the Canadian archipelago has been reported to give fair indication of direction in certain
small areas where the horizontal intensity is less than 0.02 oersted, yet to be useless
àt some places where the horizontal intensity is greater than 0.04 oersted.

nu

POLAR NAVIGATION 625

Despite its various limitations, the magnetic compass is a valuable instrument in
much of the polar regions, where the gyro compass is also of reduced reliability. With
careful adjustment, frequent checks, and a record of previous behavior, the, polar
navigator can get much useful service from his instrument.

When a compass is subjected to extremely low temperatures, there is danger of
the liquid freezing. Sufficient heat to prevent this can normally be obtained from the
compass light, which should not be turned off during severe weather.

2514. The gyro compass depends for its operation upon the rotation of the earth
about its axis. Its maximum directive force is at the equator, where the axis of the
compass is parallel to the axis of the earth. As the latitude increases, the angle between
these two axes increases. At the geographical poles the gyro compass has no directive
force.

The gyro compass is generally reliable to latitude 70°. At higher latitudes the
disturbing effect of imperfections in compass or adjustment is magnified. Latitude
adjustment becomes critical. Speed error increases as the speed of the vessel ap-
proaches the rotational speed of the earth. Ballistic deflection error becomes large
and the compass is slow to respond to correcting forces. Frequent changes of course
and speed, often necessary when proceeding through ice, introduce errors which are
slow to settle out. The impact of the vessel against ice deflects the gyro compass.
which does not return quickly to the correct reading.

The error increases and becomes more erratic as the vessel proceeds to higher
latitudes. Extreme errors as large as 27° have been reported at latitudes greater than
82°. The gyro compass probably becomes useless at about latitude 85°. At latitude
70° the gyro error should be determined frequently, perhaps every four hours, by means
of celestial bodies when these are available. As the error increases and becomes more
erratic, with higher latitude, it should be determined more frequently. In heavy ice
at extreme latitudes an almost constant check is desirable. The gyro and magnetic
compasses should be compared frequently and a log kept of the results of these com-
parisons and the gyro error determinations.

Most gyro compasses are not provided with a latitude correction setting above 70°.
Beyond this, correction can be made by either of two methods: (1) set the latitude
and speed correctors to zero and apply a correction from a table or diagram obtainable
from the manufacturer of the compass, or constructed as explained in article 640; or
(2) use an equivalent latitude and speed setting. Both of these methods have proved
generally satisfactory, although the second is considered superior to the first because
it at least partly corrects for errors introduced by a change in course. At least one
gyro compass has been made with provision for setting the latitude corrector to 80°.
As experience in high latitudes accumulates, improved gyro compass performance will
undoubtedly become available. In certain later types of gyro compasses, facilities for
their operation as directional gyros even to the poles is provided.

2515. Celestial compasses.—In some areas neither the magnetic nor gyro compass
provides adequate directional reference. In all areas of reduced compass reliability
frequent celestial checks are desirable. Several instruments are available for making
the celestial observations needed for determining heading in this manner.

A pelorus, alidade, or azimuth circle can be used for measuring the relative or
compass azimuth of a celestial body. Compass azimuth can then be compared with
a computed true azimuth to determine compass error. However, this can become
tedious and time-consuming when frequent heading checks are needed. Several in-
struments provide a quick mechanical solution.

626 POLAR NAVIGATION

A sun compass indicates direction by means of a shadow cast by a shadow pin
exposed to sunlight. The course on a horizontal, graduated azimuth dial is set opposite
a lubber’s line aligned with the fore-and-aft axis of the vessel. By means of another
dial adjusted by a latitude scale so as to be parallel to the plane of the equator, the
shadow pin, perpendicular to the plane of this dial and hence parallel to the polar
axis of the earth, is set to the local apparent time. When the vessel is on course, the
shadow of the pin falls across the center of the local apparent time dial. In some
models the local apparent time is maintained by clockwork; in others it is set frequently

DECLINATION SCALE

Dx LUMINOUS LINES
KA

T" SHADOW BAR
>

SIGHTING ASSEMBLY

TRANSLUCENT SCREEN ALIDADE

—LOCAL HOUR

ANGLE SETTING KNOB
E

WHIT
2 LOCAL HOUR ANGLE
ES (NORTH LATITUDES) AND
Ë TRUE BEARING

LATITUDE SCALE

SETTING KNOB

TRUE BEARING INDEX

LOCAL HOUR ANGLE INDEX
(SOUTH LATITUDES)

RED
LOCAL HOUR ANGLE SCALE
(SOUTH LATITUDES)

LUBBER'S LINE

LATITUDE
MICROMETER

SCALE 1 LEVELS

pu. K K uli
LATITUDE f

AZIMU
LEVELING SCREW SH TH SCALE

CLAMP LEVER

ASTRO-COMPASS
STANDARD

FIGURE 2515.—An astro compass.

by hand. The latitude and local apparent time (which varies with longitude) settings
are adjusted from time to time to agree with the changing position of the vessel. The
instrument is usable only when the sun is visible and when a knowledge of the position
is available.

An astro compass is similar in principle to a sun compass, but is usable with any
celestial body. When the device is set to the latitude of the observer and the local
hour angle and declination of the body, and rotated until the sighting assembly points

toward the body, the true heading is indicated at the lubber's line. This device is
illustrated in figure 2515.

ES

POLAR NAVIGATION 627

A sky compass indicates direction by means of the polarizing effect of the earth's
atmosphere on sunlight. Unpolarized sunlight, upon entering the earth’s atmosphere,
is scattered and becomes plane polarized, its vibrations being in a plane perpendicular
to the line from the sun to the observer. When the sun is on the horizon, this plane
is vertical. By means of a suitable analyzer of Polaroid material and Cellophane, the
sky compass detects this plane and the vertical plane which is perpendicular to it, or
in the direction of the sun. A possible 90° or 180° ambiguity exists, but this is not of
practical significance because the relative brightness of the sky indicates which of the
four possible directions is toward the sun. The instrument is set to local apparent
time, and a clock maintains this time. The analyzer is then rotated until dark and light
portions are of equal brightness, and the heading is indicated at the lubber’s line.
Unlike the sun and astro compasses, the sky compass is maintained with its face in a
level position, pointing at the zenith, which must be clear and unobstructed for an
accurate reading. The sun itself need not be visible, and can even be several degrees
below the horizon. Therefore, the compass can be used during twilight, when no
other celestial bodies may be visible. For this reason it is sometimes called a twilight
compass. It is most accurate when the zenith distance of the sun is 90°, and is seldom
used when the sun is more than a few degrees from the horizon. Its usefulness arises
principally from the fact that twilight periods in high latitudes are of several hours
duration, during which time no celestial body is visible unless the moon or a bright
planet is above the horizon.

Any celestial compass must be aligned with the fore-and-aft axis of the craft,
and is limited in its usefulness to periods when the celestial body being observed (the
zenith in the case of the sky compass) is visible. For accurate results certain parts
must be kept level. Despite their limitations, these are useful instruments in high
latitudes and a ship operating in these areas should be provided with one or more of
them.

2516. Distance and direction in ice.—In ice-free waters, distance or speed is
determined by some form of log or by engine revolution counter. In the presence of
ice, however, most logs are inoperative or inaccurate due to clogging by the ice. Engine
revolution counters are not accurate speed indicating devices when a ship is forcing
its way through ice. With experience, one can estimate the speed in relation to ice,
or a correction can be applied to speed by engine revolution counter. At best, however,
these methods are seldom of the desired accuracy.

If ranges and bearings of a land feature can be determined either visually or by
radar, course and speed of the vessel or distance traveled over the ground can be
determined by tracking the landmark and plotting the results. The feature used need
not be identified. Ice can be used if it is grounded or attached to the shore. Course
and speed or distance through the water can be determined by tracking a floating ice-
berg or other prominent floating ice feature. However, an error may be introduced
by this method if the effect of wind and current upon the floating feature is different
than upon the ship.

Example 1.—The radar operator of a ship proceeding through ice measures the
following bearings and ranges of a grounded iceberg:

Time Bearing Range

0835 028° 8,100 yds.
0840 037° 7,600 yds.
0845 047° 7,300 yds.
0850 057° 7,000 yds.

0855 066° 7,200 yds.

POLAR NAVIGATION

|
K EN x dë el
Ox 7 H
| X y i
< y 16 [—20
ES f § 4 Ð t
X $
pS y
«e Ý >
69 | K >
KEE daf i
| De A (3 |
“so AR
4

C dr

| qoo its; ve Ac?

ii

ui
PENES, = |
SE SE EE EE EE EE Ee)

e ET 1 y e w 2 A a MO e nana? x g SS R "' $ BoM E ES š

x
ies

SPEED in knots
Rete at actual

MANEUVERING BOARD

Be er PAG Wesisequon, D.C.

ew Poblicallon, èth. ES. Ape. 1930 Ath. Bären, April 1938 No. 2668 2

Figure 2516.— Determining course and speed by tracking an iceberg.

Required.—The course and speed of the ship.

Solution (fig. 2516).—The solution is conveniently made on a maneuvering board,
H.O. 2665-10, but ihis form is not essential. 9

(1) From K, representing the ship, plot points Mi, M, M3, M,, and M; repre-
senting successive positions of the iceberg relative to the ship.

(2) Fair a straight line through the points thus determined.

(3) Measure the direction of line M,M,, 147°. This is the direction of the ice-
berg relative to the ship. The direction of the ship's motion relative to the iceberg
is opposite, or 327?. Since the iceberg is stationary, this is the course of the ship.

(4) Measure the length of line M,M;, 5,000 yards or 2.5 miles. This is the dis-
tance of relative motion, and since the iceberg is stationary, the distance traveled by
the ship, in 20 minutes. The distance traveled in 60 minutes, or the speed, is 3X2.5=
7.5 knots. This solution is shown by nomogram at the bottom of the maneuvering
board. Vector er, represents the course and speed of the ship.

Answers. —C 327°, S 7.5 kn.

POLAR NAVIGATION 629

Example 2.—Solve example 1 assuming the iceberg is estimated to be moving
southwest at a speed of 1.5 knots.

í Solution (fig. 2516).—(1) Plot R, Mi, M», My, M,, and M; and fair a straight line

as in example 1.

(2) From e, plot em, the course and speed vector of the iceberg, locating point m.

(3) Determine the direction and speed of the ship relative to the iceberg as in
steps (3) and (4) of example 1. Lay this off from m, locating point r} The vector
ram is the relative movement of the iceberg with respect to the ship.

(4) Draw er», the course and speed vector of the ship.

Answers.—C 315°, S 7.3 kn.

If speed only is required, the method can be simplified. Elapsed time of tracking
and the relative distance covered can be determined by plot, as indicated above, or
possibly from the radar scope directly. Speed may then be determined by nomogram

Du : <
or by the formula se in which S is the speed in knots, D the distance in miles,

3D

and T the time in minutes. If distance is given in yards, the formula is S—100T

and if in feet, S— If a standard distance or time is used, the formula can be

abe
100T
further simplified because D or T becomes a constant. For instance, if a distance of

five miles or 10,000 yards is used, S= or if a time interval of ten minutes is used, S=

6D if D is in miles Ea if D is in yards, or x: if D is in feet )

This is the basis of the Dutchman's log, which can be used without tracking. A
ship traveling at one knot covers one mile or about 6076.1 feet in 60 minutes, or ap-
proximately 100 feet per minute. A length of 100 feet, or some fraction or multiple of
this, can be measured off in a fore-and-aft direction along the ship, and the ends of the
measured length marked. For maximum accuracy the longest possible line should be
used. A man is then stationed at each mark to note the time of passing some object
dead in the water, such as a prominent ice feature or an opening in pack ice. The

elapsed time between marks is measured and the speed calculated, using S= "m. if Dis

100T
measured in feet and T in minutes. In this application, T may be more conveniently
measured in seconds, when S= Mo UM For D —100 feet, Sam or speed is found by
í E . 60
dividing the number of seconds into 60. Thus, if T=15 seconds, the speed is 1574
60320012090: P | 30
knots. If D—200 feet, S— 100T T if D—50 feet, Sa ete.

Speed over the ground can be determined by two fixes. However, fixes relative
to land are not suitable for this purpose unless the land is accurately located on the
chart, or the same land features are used for both fixes. High-latitude electronic and
celestial fixes, too, are sometimes of less than usual accuracy (arts. 2526-2535).

2517. Tide, current, and wind.—Relatively little is known of tides and currents
in the polar regions. The tables do not extend to these areas, but some information
is given in the sailing directions. In general, tidal ranges are small, and the water
in most anchorages is relatively deep.

Currents in many coastal areas are strong and somewhat variable. When a vessel
is operating in ice, the current is often difficult to determine because of frequent changes

=

630 | * POLAR NAVIGATION

in course and speed of the vessel and inaccuracies in the measurement of direction and
distance traveled. | j

In the vicinity of land, and in the whole antarctic area, winds are variable in
direction, gusty, and often strong. Offshore, in the Arctic Ocean, the winds are not
strong and are steadier, but ships rarely operate in this area. The wind in polar
regions, as elsewhere, has two primary navigational effects upon vessels. First, its
direct effect is to produce leeway. When a vessel is operating in ice, the leeway may
be different from that in open water. It is well to determine this effect for one’s own
vessel. The second effect is to produce wind currents in the sea.

2518. Keeping the dead reckoning.—Because of the lack of facilities for fixing the
position of a vessel in polar regions, accurate dead reckoning is even more important
than elsewhere. The problem is complicated by the fact that the elements of dead
reckoning, direction and distance, are usually known with less certainty than in lower
latitudes. This only heightens the need for keeping the dead reckoning with all the
accuracy obtainable. This may usually be accomplished by careful hand plotting on
the available charts or plotting sheets.

Mechanical dead reckoning equipment is generally less accurate than a carefully-
kept hand plot. Older models of such equipment cannot be set to a higher latitude
than 70°. Newer equipment has provision for setting to latitude 80°. Dead reckoning
equipment has been used beyond its maximum range by setting to a lower latitude and
applying a correction, but this procedure is of questionable advisability because of the
error introduced by a gyro compass also operating beyond its range. This equipment
is intended for use with the Mercator projection. When a different projection is used,
better results are generally obtainable by setting the equipment to latitude 0°, and
letting its latitude indications represent change in latitude, and its difference of longi-
tude indications represent miles in an east-west direction.

Piloting

2519. Piloting in high latitudes is basically no different from that elsewhere. How-
ever, in polar regions piloting is the primary method of marine navigation. As pre-
viously indicated, dead reckoning is difficult and generally less accurate than in lower
latitudes. Celestial navigation has limited application. Electronic navigational aids
are almost nonexistent.

Piloting is associated with proximity to land and shoal water. A ship in polar
regions is seldom far from land, and the areas are not so accurately surveyed that the
navigator can be sure that uncharted shoals are not nearby.

Piloting is characterized by an alertness not required when a vessel is far from
danger of grounding. Nowhere is this alertness more necessary than in polar regions.
Added to the usual reasons for constant vigilance are the uncertainties of charted in-
formation and the lack of detail, as discussed in article 2509.

2520. Aids to navigation are virtually nonexistent in polar regions. There are no
lighthouses, few beacons, and very few buoys. Channels and shoals are not marked
and may not even be indicated on the chart. A few radiobeacons are available, notably
along the northern coast of Russia. Other radio transmitters are occasionally available
for use as beacons.

2521. Natural landmarks are plentiful in some areas, but their usefulness is re-
stricted by the difficulty in identifying them, or locating them on the chart. Along
many of the coasts the various points and inlets bear a marked resemblance to each
other. The appearance of a coast is often very different when many of its features are
obliterated by a heavy covering of snow or ice than when it is ice-free.

INS

POLAR NAVIGATION 631

i 2522. Bearings are useful, but have limitations. When bearings on more than two
objects are taken, they may fail to intersect at a point because the objects may not be
charted in their correct relation to each other. Even a point fix may be considerably
in error geographically if all of the objects used are shown in correct relation to each
other, but in the wrong position on the earth. However, in restricted waters it is
usually more important to know the position of the vessel relative to nearby land and
shoals than its latitude and longitude. The bearing and distance of even an unidentified
or uncharted point are valuable.

When a position is established relative to nearby landmarks, it is good practice to
use this to help establish the identity and location of some prominent feature a con-
siderable distance ahead, so that this feature, in turn, can be used to establish future
positions.

In high latitudes it is not unusual to make use of bearings on objects a considerable
distance from the vessel. Because of the rapid convergence of the meridians in these
areas, such bearings are not correctly represented by straight lines on a Mercator chart.
If this projection is used, the bearings should be corrected in the same manner that
radio bearings are corrected (using table 1), since both can be considered great circles.
Neither visual nor radio bearings are corrected when plotted on a Lambert conformal
chart.

2523. Soundings are so important in polar regions that echo sounders are custom-
arily operated continuously while the vessel is under way. It is good practice to have
at least two such instruments, preferably those of the recording type and having a
wide flexibility in the range of the recorder. In few parts of the polar regions have
enough soundings been obtained and made available to charting agencies to permit
adequate portrayal of the bottom configuration. However, since depth of water is a
primary consideration in avoiding an unwanted grounding, a constant watch should
be maintained to avoid unobserved shoaling.

Polar regions have relatively few shoals, but in some areas, notably along the
Labrador coast, a number of pinnacles and ledges rise abruptly from the bottom. These
constitute a real danger to vessels, since they are generally not surrounded by any ap-
parent shoaling. In such an area, or when entering an unknown harbor or any area of
questionable safety, it is good practice to send one or more small craft ahead with
portable sounding gear.

In very deep water, of the order of 1,000 fathoms or more, the echo returned from
the bottom is sometimes masked by the sound of ice coming in contact with the hull,
but this is generally not a problem when the bottom is close enough to be menacing.

The hand lead is of little value to a ship underway in ice, because the ice generally
prevents its effective use unless the vessel is stopped.

If a ship becomes beset by ice, so that steerage way is lost and the vessel drifts
with the ice, it may be in danger of grounding as the ice moves over a shoal. Hence,
it is important that soundings be continued even when beset. If necessary, a hole
should be made in the ice and a hand lead used. A vessel with limited means for
freeing itself may prudently save such means for use only when there is danger of
grounding.

Useful information on the depth of water in the vicinity of a ship can sometimes
be obtained by watching the ice. A stream of ice moving faster than surrounding ice,
or a stretch of open water in loose pack ice often marks the main channel through shoal
water. A patch of stationary ice in the midst of moving ice often marks a shoal.

Knowledge of earth formations may also prove helpful. The slope of land is often
an indication of the underwater gradient. Shoal water is often found off low islands,
spits, etc., but seldom near a steep shore. Where glaciation has occurred, the moraine

632 POLAR NAVIGATION

deposits are likely to have formed a bar some distance offshore. Submerged rocks and
pinnacles are more likely to be encountered off a rugged shore than near a low, sandy
beach. — IS R

2524. Anchorages.—Because good anchorages are not plentiful in high latitudes,
there is an understandable temptation to be less demanding in their selection. This
is dangerous practice, for in polar regions some of the requirements are accentuated.
The factors to be considered are:

1. Holding quality of the bottom. In polar regions a rocky bottom or one with only
fair to poor holding qualities is not uncommon. Sometimes the bottom is steep or
irregular. Since the nature of the bottom is seldom adequately shown on charts, a
wise precaution is to sample the bottom, and sound in the vicinity before anchoring.

2. Adequacy of room for swing. Because high winds are frequent along polar
shores, sometimes with little or no warning, long scopes of anchor chain are customarily
used. Some harbors are otherwise suitable, but allow inadéquate room for swing
of the vessel at anchor, or even for its yaw in a high wind. If a vessel is to anchor in
an unsurveyed area, the area should first be adequately covered by small boats with
portable sounding gear to detect any obstructions.

3. Protection from wind and sea. In polar regions protection from wind is probably
the most difficult requirement to meet. Generally, high land is accompanied by
strong wind blowing directly down the side of the mountains. Polar winds are extremely
variable, both in direction and speed. Shifts of 180° accompanied by an increase in
speed of more than 50 knots in a few minutes have been reported. It is important
that ground tackle be in good condition and that maximum-weight anchors be used.
All available weather reports should be obtained and a continuous watch kept on the
local weather. Whenever a heavy blow might reasonably be anticipated, the main
engines should be kept in an operating condition and on a standby status. Heavy
seas are seldom a problem.

4. Availability of suitable exit in event of extreme weather. In ice areas it is important
that a continuous watch be kept to prevent blocking of the entrance by ice, or actual
damage to the vessel by floating ice. However, in an unsurveyed area it may be
dangerous to shift anchorage without first sounding the area. It is a wise precaution
to do this in advance. Unless the vessel is immediately endangered by ice, it is gener-
ally safer to remain at anchor with optimum ground tackle and use of engines to assist
in preventing dragging, than to proceed to sea in a high wind, especially in the presence
of icebergs and growlers, and particularly during darkness.

5. Availability of objects for position determination. The familiar polar problem
of establishing a position by inaccurately charted or inadequately surveyed landmarks
is accentuated when an accurate position is desired to establish the position of an anchor.
Sometimes a trial and error method is needed, and it may be necessary to add land-
marks located by radar or visual observation. Because of chart inadequacy, the
suitability of an anchorage, from the standpoint of availability of suitable landmarks,
cannot always be adequately predicted before arrival.

An unsurveyed harbor should be entered with caution at slow speed, with both
the pilot house and engine room force alerted to possible radical changes in speed or
course with little or no warning. The anchor should be kept ready for letting go on
short notice and should be adequately attended. An engine combination providing
full backing power should be maintained.

2525. Sailing directions for high latitudes contain a wealth of valuable informa-
tion acquired by those who have previously visited the areas. However, since high
latitudes have not been visited with the frequency of other areas, and since they are
inadequately surveyed, the sailing directions for polar areas are neither as complete

POLAR NAVIGATION 633

nor as accurate as for other areas, and information on unvisited areas is completely
lacking. Until traffic in high latitudes increases and the sailing directions for these
areas incorporate the additional information obtained, unusual caution should accom-
pany their use. Each vessel that enters polar regions can help correct this condition
by recording accurate information and sending it to the U. S. Navy Hydrographic
Office or its counterpart in other countries.

Electronic Navigation

2526. Propagation.—In general, radio wave propagation in high latitudes follows
the same principles that apply elsewhere, as described in chapter X. However, certain
anomalous conditions occur, and although these are but imperfectly understood, and
experience to date has not always seemed consistent, there is much that has been
established. An understanding of
these conditions is important if maxi- NORTH AURORAL ZONE
mum effective use is to be made of
electronics in high latitudes.

Because of the influence of the
ionosphere (art.1008) upon radio wave
propagation, the most disruptive ef-
fects are associated with ionospheric
disturbances, one aspect of the fa-
miliar magnetic storms. These have
been found to be related to sunspot
activity, and this association provides
a basis for their prediction. Warn-
ings based upon such predictions are
broadcast by radio station WWV,
National Bureau of Standards, Wash-
ington, D. C., and by major U. S.
Navy radio stations. Such warn-
ings, usually broadcast several hours
before the start of a disturbance, are
confined i the expected ME UG. FIGURE 2526.— The auroral zone of the northern
Predictions of intensity or duration hemisphere.
have not been possible.

Severe ionospheric disturbances affect radio wave propagation throughout the
world, but the most erratic and persistent effects occur in the auroral zones. The
auroras (aurora borealis or “northern lights" in the northern hemisphere, and the
aurora australis or “southern lights" in the southern hemisphere) are believed to be
caused by emissions from the sun. When the emitted particles enter the earth's
magnetic field, they tend to follow the earth's lines of force downward toward the
geomagnetic poles (art. 706). When they encounter the ionosphere, they become
luminous, constituting the aurora familiar to the night observer in high latitudes. The
maximum auroral activity occurs in two belts, each about 600 miles wide and centered
at about 1,200 miles from one of the geomagnetic poles, as shown in figure 2526. In
the auroral zones, the aurora is a common occurrence, being visible on nearly any dark,
clear night. Frequency of occurrence decreases with increased distance from the
zones. During magnetic storms the auroral zones have a tendency to shift outward
from the geomagnetic poles.

When an ionospheric disturbance occurs, fading and ionospheric absorption in-
crease. The maximum usable frequency (art. 1008) decreases, and the minimum useful

North Geomagnetic Pole

634 POLAR NAVIGATION

high frequency increases. In extreme cases, the entire band of useful frequencies dis-
appears, resulting in a radio blackout which may continue for any period from a few
minutes to several days. In the auroral zones, higher frequencies used for communica-
tion have been known to be blacked out for as long as two weeks. The return to normal
usually occurs first on lower frequencies. k

During the early stages of an ionospheric disturbance, the path of propagation may
deviate erratically from normal, resulting in erroneous direction finder bearings and
consol readings. ,

Because of the shift of the auroral zones during a magnetic storm, radio propagation
within the usual positions of the belts may improve. Transmission is usually of greater
range along radial lines from the geomagnetic poles than across these lines.

Very low frequencies (10-30 ke) originating outside the auroral zone are not af-
fected appreciably by ionospheric disturbances, and propagation between 30 and 200
ke may even improve. This is believed to be due to a great increase in the density of
the lowest (D) layer of the ionosphere, which acts as a wave guide for lower frequencies,
while absorbing higher frequency transmissions.

In polar regions, long-range, high frequency propagation is sometimes erratic
even when conditions seem normal, and the usual procedure for selection of optimum
working frequencies for communication is not always valid. The shielding effect of
mountains seems to be greater than in lower latitudes.

2527. Radar.—In polar regions, where fog and long periods of continuous daylight
or darkness reduce the effectiveness of both celestial navigation and visual piloting, and
where other electronic aids are generally not available, radar is particularly valuable.
Its value is further enhanced by the fact that polar seas are generally smooth, re-
sulting in relatively little oscillation of the shipborne antenna. When ice is not present,
relatively little sea return is encountered from the calm sea.

However, certain limitations attend the use of radar in polar regions. Similarity
of detail along the polar shore is even more apparent by radar than by visual ob-
servation. Lack of accurate detail on charts adds to the difficulty of identification.
Identification is even more of a problem when the shore line is beyond the radar horizon
and accurate contours are not shown on the chart. When an extensive ice pack extends
out from shore, accurate location of the shore line is extremely difficult. :

Good training and extensive experience are needed to interpret accurately the
returns in polar regions where ice may cover both land and sea. A number of icebergs
close to a shore may be too close together to be resolved, giving an altered appearance
to a shore line, or they may be mistaken for off-lying islands. The shadow of an iceberg
or pressure ridge and the lack of return from an open lead in the ice may easily be
confused. Smooth ice may look like open water. In making rendezvous, one might
inadvertently close on an iceberg instead of a ship.

As with visual bearings, radar bearings need correction for convergency unless the
objects observed are quite close to the ship.

2528. Loran is usable in polar regions, but the coverage is greatly restricted.
As shown in the coverage diagram, figure 1302a, Loran-A groundwave coverage extends
into the edge of the arctic in several places. The skywave coverage extends some
distance beyond. Extensive areas in the arctic and all of the antarctic are without
coverage.

2529. Other electronic aids are virtually nonexistent in polar regions.

The radio direction finder is useful when the few transmitting stations are within
range. One of the principal uses of RDF in polar regions is to assist in locating other
vessels, for rendezvous or other purposes. This is particularly true in an area of many
icebergs, where radar may not distinguish between ships and icebergs.

POLAR NAVIGATION 635

Consol is available in the Norwegian Sea between Norway and Greenland.

The echo sounder is highly useful, as indicated in article 2523, and is operated
continuously in high latitudes.

Sonar is useful primarily for detecting ice, particularly growlers. Since about
72 to % of the ice is under water, its presence can sometimes be detected by sonar when
it is overlooked by radar or visual observation.

Celestial Navigation

2530. Celestial navigation in high latitudes.—Of the various types of navigation,
celestial is perhaps least changed in polar regions. However, certain special con-
siderations are applicable.

Because of the limitations of other forms of navigation, as-discussed earlier in this
chapter, celestial navigation provides the principal means of determining geographical
position. However, as indicated in article 2522, position relative to nearby dangers is
usually of more interest to the polar navigator than geographical position. Since
ships in high latitudes are seldom far from land, and since celestial navigation is at-
tended by several limitations, discussed in article 2531, its use in marine navigation
is generally confined to the following applications:

1. Navigation while proceeding to and from polar regions.

2. Checking the accuracy of dead reckoning.

3. Checking the accuracy of charted positions of landmarks, shoals, etc.

4. Providing a directional reference, either by means of a celestial compass (art.
2515) or by providing a means of checking the magnetic or gyro compass.

Although its applications are limited, celestial navigation is important in high
latitudes. Application 3 above, and application 4, even more so, can be of great value
to the polar navigator.

2531. Celestial observations.—The best celestial fixes are usually obtained by
star observations during twilight. As the latitude increases, these periods become
longer, providing additional time for observation. But with this increase comes longer
periods when the sun is just below the horizon and the stars have not yet appeared.
During this period, which in the extreme condition at the pole lasts for several days,
no celestial observations may be available. The moon is sometimes above the horizon
during this period and bright planets, notably Venus and Jupiter, may be visible. With
practice, the brighter stars can be observed when the sun is 2° to 3° below the horizon.

Beyond the polar circles the sun remains above the horizon without setting during
part of the summer. The length of this period increases with latitude. At Thule,
Greenland, about 10° inside the arctic circle, the sun remains above the horizon for four
months. During this period of continuous daylight the sun circles the sky, changing
azimuth about 15° each hour. A careful observation, or the average of several observa-
tions, each two hours provides a series of running fixes. An even better check on posi-
tion is provided by making hourly observations and establishing the most probable
position at each observation. Sometimes the moon is above the horizon, but within
several days of the new or full phase it provides lines of position nearly parallel to the
sun lines and hence of limited value in establishing fixes.

During the long polar night the sun is not available and the horizon is often in-
distinct. However, the long twilight, a bright aurora, and other sources of polar light
(art. 2504) shorten this period. By adapting their eyes to darkness, some navigators
can make reasonably accurate observations throughout the polar night. The full
moon in winter remains above the horizon more than half the time and attains higher

altitudes than at other seasons.

636 POLAR NAVIGATION

In addition to the long periods of darkness in high latitudes, other conditions are
sometimes present to complicate the problem of locating the horizon. During daylight
the horizon is frequently obscured by low fog, frost smoke, or blowing snow, yet the sun
may be clearly visible. Hummocked sea ice is sometimes a problem, particularly at
low heights of eye. Nearby land or an extensive ice foot can also be troublesome.
Extreme conditions of abnormal refraction are not uncommon in high latitudes, some-
times producing false horizons and always affecting the refraction and dip corrections.

Because of these conditions, it is advisable to be provided with an artificial-horizon
sextant (art. 1513). This instrument is generally not used aboard ship because of the
excessive acceleration error encountered as the ship rolls and pitches. However, in
polar regions there is generally little such motion and in the ice there may be virtually
none. Some practice is needed to obtain good results with an artificial-horizon sextant,
but these results are sometimes superior to those obtainable with a marine sextant, and
when some of the conditions mentioned above prevail, the artificial-horizon sextant may
provide the only means of making an observation. Better results with this instrument
can generally be obtained if the instrument is hung from some support, as it generally
is when used in aircraft.

An artificial horizon (art. 1512) can sometimes be used effectively, even an im-
provised one, as by placing heavy lubricating oil in a bucket.

It is sometimes possible to make better observations by artificial-horizon sextant
or artificial horizon from a nearby cake of ice than from the ship.

Clouds and high fog are frequent in high latitudes, but it is not uncommon,
particularly in the antarctic, for the fog to lift for brief periods, permitting an alert
navigator to obtain observations.

As the latitude increases, an error of time has less effect upon altitude. At the
equator an error of four seconds in time may result in an error in the location of the
position line of as much as one mile. At latitude 60° a position error of this
magnitude cannot occur unless the timing error is eight seconds. At 70° nearly 12
seconds are needed, and at 80° about 23 seconds are needed for such a position error.

Polaris is of diminished value in high northern latitudes because of its high altitude.
At high latitudes the second correction to observed altitude (a;) becomes greater. The
almanac makes no provision for applying this beyond latitude 68°. Bodies at high
altitudes are not desirable for azimuth determination, but if Polaris is used, the use of
the actual azimuth given at the bottom of the Polaris tables of the Nautical Almanac
is of increased importance because of its larger variation from 000° in high latitudes.
No azimuth is provided beyond latitude 65°.

In applying a sextant altitude correction for dip of the horizon, one should use
height of eye above the ice at the horizon, instead of height above water. The difference
between ice and water levels at the horizon can often be estimated by observing ice near
the vessel.

2532. Low-altitude observations.—Because of large and variable refraction at
low altitudes, navigators customarily avoid observations below some minimum, usually
5° to 15°, if higher bodies can be observed. In polar regions low-altitude observations
are often the only ones available. The sun, moon, and planets remain low in the sky
for relatively long periods, their diurnal motion being nearly horizontal. The only
lower limit is that imposed by the horizon itself. In fact, good observations can some-
times be made without a sextant by noting the time at which either the upper or lower
limb is tangent to the horizon. To such an observation sextant altitude corrections are
applied as for a marine sextant without an index correction.

Å Correction of low-altitude observations made by marine sextant is discussed in
article 1632. If a bubble or other artificial-horizon sextant is used, corrections are made

POLAR NAVIGATION 637

as for higher altitudes, being careful to use the refraction value corrected for tempera-
ture, or to make a separate correction for air temperature. In addition, a correction for
atmospheric pressure (tab. 24) is applied if of sufficient size to be of importance. `

Solution of low-altitude observations is discussed in article 2010. 4

2533. Abnormal refraction and dip.—Tables of refraction correction are based upon
a standard atmosphere. Variations in this atmosphere result in changes in the refrac-
tion, and since the atmosphere is seldom exactly standard, the mean refraction is seldom
the same as shown in the tables. Variations from standard conditions are usually not
great enough to be troublesome. i

In polar regions, however, it is normal for the atmosphere to differ considerably
from the standard, particularly near the surface. This affects both refraction and dip,
as indicated in article 1606. Outside polar regions, variations in refraction seldom
exceed 2’ or 3”, although extreme values of more than 30’ have been encountered
In polar regions refraction variations of several minutes are not uncommon and an
extreme value of about 5° has been reported. This would produce an error of 300
miles in a line of position. The sun has been known to rise as much as ten days before
it was expected.

Most celestial observations in polar regions produce satisfactory results, but the
high-latitude navigator should be on the alert for abnormal conditions, since they occur
more often than elsewhere, and have greater extreme values. A wise precaution is to
apply corrections for air temperature (tab. 23) and atmospheric pressure (tab. 24),
particularly for altitudes of less than 5°.

Abnormal dip affects the accuracy of celestial observations equally at any altitude,
if the visible horizon is used. Such errors may be avoided in any one of four ways:

1. The artificial-horizon sextant may be used, as indicated in article 2531.

2. When stars are available, three stars may be observed at azimuth intervals of
approximately 120°, (or four at 90° intervals, five at 72°, etc.). Any error in dip
or refraction will alter the size of the enclosed figure, but will not change the location
of its center unless the dip or refraction error varies in different directions. The stars
should preferably be at the same altitude.

3. The altitude of a single body may be observed twice, facing in opposite directions.
The sum of the two readings differs from 180° by twice the sum of the index and dip
corrections (also personal and instrument corrections, if present). This method assumes
that dip is the same in both directions, an assumption that is usually approximately cor-
rect. Also, the method requires that the arc of the sextant be sufficiently long and the
altitude of the body sufficiently great to permit observation of the back sight in the
opposite direction. In making such observations, it is necessary that allowance be
made for the change of altitude between readings. This may be done by taking a
direct sight, a back sight, and then another direct sight at equal intervals of time,
and using the average of the two direct sights.

4. A correction for the difference between air and sea temperatures (art. 1607)
may be applied to the sextant altitude. This will often provide reasonably good
results. However, there is considerable disagreement in the manner in which temper-
ature is to be measured, and in the factor to use for any given difference. Therefore,
the validity of this correction is not fully established.

There is still much to be learned regarding refraction and even with all known
precautions, results may occasionally be unsatisfactory.

2534. Sight reduction in polar regions is virtually the same as elsewhere. Compu-
tation can be made by nearly any method. In H.O. Pub. No. 214, tabulations are not
extended below an altitude of 5°, but this method can be used for lower altitudes, which
are not uncommon in polar regions, by selecting an assumed position some distance away,

638 POLAR NAVIGATION

|

in the general direction of the body. Thus, if the altitude is 2°, an assumed position 3° »

(180 miles) nearer the body (4? is a better choice to allow for possible error in the dead

reckoning and for adjustment for a convenient assumed position) should result in a `

computed altitude of 5? or more. This method will result in an unusually long altitude
difference, but the error introduced will be negligible if the assumed position is in the
direction of the body, and the chart used is one on which a straight line is a close approx-
imation to a great circle. A Lambert conformal chart is satisfactory for this purpose.
An example of such a solution is given in article 2010.

Some navigators prefer to use another method of sight reduction. Both H.O.
Pub. No. 208 and H.O. Pub. No. 211 are suitable for this purpose, but perhaps the
most satisfactory method is H.O. Pub. No. 249, which provides solutions down to the
visible horizon for any height of eye to be anticipated aboard ship and for any reasonable
altitude difference. However, except for certain specified stars, the method is limited
to celestial bodies having declinations not exceeding 30?. "This provides for the sun,
moon, planets, and a number of good navigational stars. Having been designed for

air navigation, H.O. Pub. No. 249 provides computed altitudes to the nearest whole `

minute, and azimuth to the nearest whole degree. For low altitudes this precision is
realistic.

From latitude 70? to the pole, hour angles in H.O. Pub. No. 249 are tabulated at
intervals of 2?. Near the pole this interval could be greatly increased because of the
small diameter of the parallels of latitude. Based upon this and the fact that azimuth
approaches LHA +180? near the north pole (360? —LHA near the south pole), various
special methods have been suggested for high latitudes, providing very short tables.
However, there is considerable advantage in using familiar methods and avoiding special
ones of limited application and often of little advantage.

One special method of considerable interest is conveniently applicable only within
about 5? of the pole, a higher latitude than is usually attainable by ships. This is the
method of using the pole as the assumed position. At this point the zenith and pole
coincide and hence the celestial equator and celestial horizon also coincide, and
the systems of coordinates based upon these two great circles of the celestial
sphere become identical. The declination is computed altitude, and GHA replaces
azimuth. A “toward” altitude difference is plotted along the upper branch of the
meridian over which the body is located, and an “away” difference is plotted in the
opposite direction, along the lower branch. Such a line or its AP is advanced or retired
in the usual manner. This method is a special application of the meridian altitude
sometimes used in lower latitudes. Beyond the limits of this method the meridian
altitude can be used in the usual manner (art. 2103) without complications and with
time of transit being less critical. However, table 29, for reduction to the meridian,
extends only to latitude 60?. Tables providing a correction to permit use of the
pole-assumed-position method with the polar stereographic projection at considerable
distance from the pole have been prepared, but are rarely used, and never by mariners.
These are known as the Ellsworth Tables.

2535. Plotting lines of position from celestial observations.—Lines of position
from celestial observations in polar regions are plotted as elsewhere, using an assumed
position, altitude difference, and azimuth. If a Mercator chart is used, the error in-
troduced by using rhumb lines for the azimuth line (a great circle) and line of position
(a small circle) is accentuated. This can be overcome by using a good dead reckoning
or estimated position as the assumed position or by using a chart on a more favorable
projection.

If a chart with nonparallel meridians, such as the Lambert conformal, is used, the
true azimuth should be plotted by protractor or plotter and measured at the meridian

POLAR NAVIGATION 639

of the assumed position. On a chart having a grid overprint the true azimuth can be
converted to grid azimuth, using the longitude of the assumed position, and the direction
measured from any grid line. This method involves an additional step, with no real
advantage.

Lines of position from high-altitude observations, to be plotted as circles with the
geographical position as the center (art. 2011), should not be plotted on a Mercator
chart because of the rapid change of scale, resulting in distortion of the circle as plotted
on the chart.

Lines of position are advanced or retired as in any latitude. However, the move-
ment of the line is no more accurate than the estimate of the direction and distance
traveled, and in polar regions this estimate may be of less than usual accuracy. In
addition to his problem of estimating direction of travel, the polar navigator may
encounter difficulty in accurately plotting the direction determined. If an accurate
gyro compass is used, the ship follows a rhumb line, which is accurately shown only on
a Mercator chart. If a magnetic compass is used, the rapid change in variation may
be a disturbing factor. If the ship is in ice, the course line may be far from straight.

Because of the various possible sources of error involved, it is good practice to avoid
advancing or retiring lines for a period longer than about two hours. When the sun
is the only body available, best results can sometimes be obtained by making an ob-
servation every hour, retiring the most recent line one hour and advancing for one hour
the line obtained two hours previously. The present position is then obtained by dead
reckoning from the running fix of an hour before. Another technique is to advance
the one or two previous lines to the present time for a running fix. A third method is
to drop a perpendicular from the dead reckoning or estimated position to the line of
position to obtain a new estimated position, from which a new dead reckoning plot
is carried forward to the time of the next observation. A variation of this method is
to evaluate the relative accuracy of the new line of position and the dead reckoning or
estimated position run up from the previous position and take some point between
them, halfway if no information is available on which to evaluate the relative ac-
curacies. None of these techniques is suitable for determining set and drift of the
current.

2536. Rising, setting, and twilight data are tabulated in the almanacs to latitude
72° N and 60° S. Within these limits the times of these phenomena are determined
as explained in chapter XVIII.

Beyond the northern limits of these tables the values can be obtained from a
series of graphs given near the back of the Air Almanac. These graphs are shown in
appendix W. For high latitudes, graphs are used instead of tables because graphs give
a clearer picture of conditions, which may change radically with relatively little change
in position or date. Under these conditions interpolation to practical precision is
simpler by graph than by table. In those parts of the graph which are difficult to read,
the times of the phenomena’s occurrence are themselves uncertain, being altered con-
siderably by a relatively small change in refraction or height of eye. |

On all of these graphs any given latitude is represented by a horizontal line, and
any given date by a vertical line. At the intersection of these two lines the duration
is read from the curves, interpolating by eye between curves.

The “Semiduration of Sunlight” graph gives the number of hours between sunrise
and meridian transit or between meridian transit and sunset. The dot scale near the
top of the graph indicates the LMT of meridian transit, the time represented by the
minute dot nearest the vertical date line being used. If the intersection occurs in the
area marked “sun above horizon," the sun does not set; and if in the area marked “sun
below horizon,” the sun does not rise.

640 POLAR NAVIGATION

Example 1.—Find the zone time of sunrise and sunset at lat. 71°30/0 N, long.

10%00/0 W near Jan Mayen Island, on August 25, 1958. THES:
Solution.— ;
August 25
LMT 1202 LAN, from top of graph
dà (—) 20

ZT 1142 LAN
semidur. 840 from graph

ZT 0802 sunrise (— semidur.)
ZT 2022 sunset (+ semidur.)

A vertical line through August 25 passes nearest the dot representing LAN 1202
on the scale near the top of the graph. This is LMT; at longitude 10%00/0 W the ZT
is 20™ earlier, or at 1142. The intersection of the vertical date line with the horizontal
latitude line occurs between the 8" and 9^ curves, at approximately 8^ 40™ Hence,
sunrise occurs at this interval before LAN and sunset at this interval after LAN.

The “Duration of Twilight” graph gives the number of hours between the beginning
of morning civil twilight (center of sun 6% below the horizon) and sunrise, or between
sunset and the end of evening civil twilight. If the sun does not rise, but twilight does
occur, the time taken from the graph is half the total length of the single twilight period,
or the number of hours from beginning of morning twilight to LAN, or from LAN to
end of evening twilight. If the intersection occurs in the area marked “continuous
twilight or sunlight,” the center of the sun does not get more than 6° below the horizon;
and if in the area marked “no twilight nor sunlight,” the sun remains more than 6°
below the horizon throughout the entire day.

Example 2.—Find the zone time of beginning of morning twilight and ending
of evening twilight at the place and date of example 1.

Solution. —
Twilight Twilight
ZT 0302 sunrise, from example 1 ZT 2022 sunset, from example 1
dur. 153 from graph dur. 153 from graph
ZT 0109 morning twilight ZT 2215 evening twilight

The intersection of the vertical date line and the horizontal latitude line occurs
approximately one-sixth of the distance from the 2^ line toward the 1^ 20™ line; or at
about 1” 53™. Morning twilight begins at this interval before sunrise, and evening
twilight ends at this interval after sunset.

The “Semiduration of Moonlight” graph gives the number of hours between
moonrise and meridian transit or between meridian transit and moonset. The dot
scale near the top of the graph indicates the LMT of meridian transit, each dot repre-
senting one hour. The phase symbols indicate the date on which the principal moon
phases occur, the open circle indicating full moon and the dark circle indicating new
moon. If the intersection of the vertical date line and the horizontal latitude line
falls in the “moon above horizon” or “moon below horizon” area, the moon remains
above or below the horizon, respectively, for the entire 24 hours DN UC day.

If approximations of the times of moonrise and moonset are sufficient, the values
of semiduration taken from the graph can be used without adjustment. For more
accurate results, the times on the required date and the adjacent date (the following
date in west longitude and the preceding date in east longitude) should be determined,

and an interpolation made for longitude, as in any lati : : :
1 atitude, since th
are for the Greenwich meridian. : y , e intervals given

POLAR NAVIGATION 641

Example 3.—Find the zone time of moonrise and moonset at lat. 74900/0 N ;
long. 108%00.0 W on May 16, 1958, and the phase of the moon on this date.

Solution.—
May 16 May 17
LMT 0952 LMT 1036 meridian transit, from graph
da (+) 12 INES AD
ZT 1004 ZT 1048 meridian transit
semidur. 8"48" semidur. ` 9155” from graph
ZT 0116 ZT 0053 (moonrise — semidur.)
dt biel 852 ZT 2043 (moonset + semidur.)
Moonrise Moonset
ZT 0116 May 16 ZT 1852 May 16
ZT 0053 May 17 ZT 2043 May 17
diff. (—) 23 diff. (+)111
23X108.0/360 (—)7 111X108.0/360 (+)33
ZT 0109 ZT 1925

The phase is crescent, about three days before new moon. The LMT of meridian
transits are found by noting the intersections of the vertical date lines with the dot
scale near the top of the graph, interpolating by eye. At longitude 108%00/0 W the
ZT is 12” later. The semiduration is found by noting the position, with respect to the
semiduration curves, of the intersection of the vertical date line with the horizontal
latitude line. "This interval is subtracted from the time of meridian transit to obtain
moonrise, and added to obtain moonset. These solutions are made for both May 16
and 17, and the difference determined in minutes. The adjustment to be applied to
the ZT on May 16 at Greenwich is determined by multiplying this difference by the
ratio 4/360. The phase is determined by noting the position of the vertical date
line with respect to the phase symbols. If the answer indicates that the phenomenon
occurs on a date differing from that desired, a new solution should be made, adjusting
the starting date accordingly. The phenomenon may occur twice on the same day,
or it may not occur at all. In high latitudes the effect on the time of moonrise and
moonset of a relatively small change in declination is considerably greater than in
lower latitudes, resulting in greater differences from day to day.

Sunlight, twilight, and moonlight graphs are not available for south latitudes.
Beyond latitude 65°S, the northern hemisphere graphs can be used for determining
the semiduration or duration, by using the vertical date line for a day when the declina-
tion has the same numerical value but opposite sign. The time of meridian transit
and the phase of the moon are determined as explained above, using the correct date.
Between latitudes 60?S and 658 solution is made by interpolation between the tables
and the graphs.

Several other methods of solution of these phenomena are available. The Tide
Tables tabulate sunrise and sunset from latitude 76°N to 60?S. A supplement
to the American Ephemeris of 1946, entitled Tables of Sunrise, Sunset, and Twilight,
provides tabulations from latitude 75? N to 75?S and graphs for semiduration of sun-
light and duration of twilight, with separate graphs for civil, nautical, and astronomical
twilights. Semiduration or duration can be determined graphically by means of a
diagram on the plane of the celestial meridian (art. 1432), or by computation. When
computation is used, solution is made for the meridian angle at which the required
negative altitude occurs. The meridian angle expressed in time units is the semi-
duration in the case of sunrise, sunset, moonrise, and moonset; and the semiduration

642 POLAR NAVIGATION

of the combined sunlight and twilight, or the time from meridian transit at which
morning twilight begins or evening twilight ends. For sunrise and sunset the altitude
used is (—) 50’. Allowance for height of eye can be made by algebraically subtracting
(numerically adding) the dip correction from this altitude. The altitude used for
twilight is (—) 6°, (—) 12°, or (—)18? for civil, nautical, or astronomical twilight,
respectively. The altitude used for moonrise and moonset is —34’—SD+ HP, where
SD is semidiameter and HP is horizontal parallax, from the daily pages of the Nautical
Almanac. The time sight formula can be used for making the computation:

hav t=sec L csc p cos s sin (s—h),

where t=meridian angle, s=%(h+L+p), h=altitude, L=latitude, and p=90°—d for
L and d (declination) same name and 90%+d for L and d contrary name. Another
formula which can be used is

cos t=sec L sec d (sin h—sin L sin d),

with the same notation as above.
General

2537. Ice.—Several references have been made to ice. The almost constant pres-
ence of large quantities of ice is one of the distinctive features of polar regions, and is
one of the primary considerations in any operations in these areas. The subject of
ice in the sea is covered in chapter XXXVI.

2538. Knowledge of polar regions.—Operations in polar regions are attended by
hazards and problems not encountered elsewhere. Lack of knowledge, sometimes
accompanied by fear of the unknown, has prevented navigation in these areas from
being conducted with the same confidence with which it is pursued in more familiar
areas. As experience in high latitudes has increased, much of the mystery surrounding
these areas has been dispelled, and operations there have become more predictable.

Before entering polar regions, the navigator will do well to acquaint himself with
the experience of those who have preceded him into the areas and under the conditions
he anticipates. This information can be found in a growing literature composed of
the accounts of explorers, reports of previous operations in high latitudes, articles in
professional journals, and several books on operations in polar regions. Some of it is
given in various volumes of sailing directions, particularly those for Antarctica (H.O.
Pub. No. 27). Additional information is available at the U.S. Navy Hydrographic
Office.

The search for knowledge should not be confined to navigation. The wise polar
navigator will seek information on living conditions, survival, geography, ice, climate
and weather, and operational experience of others who have been to the same area.
As elsewhere, knowledge and experience are valuable.

2539. Planning, important in any operation, is vital to the success of polar naviga-
tion. The first step to adequate planning is the acquisition of full knowledge, as dis-
cussed in article 2538. No item, however trivial, should escape attention. The ship
should be provided with all the needed charts, publications, and special navigational
material. All available data and information from previous operations in the area
should be studied. Key personnel should be adequately instructed in polar navigation
prior to departure or while en route to the polar regions. Forecasts on anticipated ice
and weather conditions should be obtained before departure and after getting under
way. All equipment should be put in top operating condition. All material should
be carefully inspected for completeness and condition. The navigator should make
certain that all items of equipment are familiar to those who will use them. Thisis par-

!
|

POLAR NAVIGATION 643

ticularly true of items not generally used at sea, such as charts on an unfamiliar projec-
tion, or a bubble sextant. Do not assume anything that can be known. On the
adequacy and thoroughness of the advanced planning and preparation, perhaps more
than anything else, will depend the success of polar navigation.

Problems

2510a. Convert the following true directions to grid directions using (1) a con-
vergency of one, (2) a convergency of 0.866. (Give answers to nearest whole degree.)

True Latitude Longitude
191^ N 279W
303° N 114%E
1183 S 63%E
042° S 147° W

Answers.—(1) 184°, 239°, 181°, 255%; (2) 180°, 254°, 173°, 275°.
2510b. Convert the following grid directions to true directions using (1) a con-
vergency of 0.629, (2) a convergency of one.

Grid Latitude Longitude
003° N 174° W
148° S 9° W
ST? N 64° E
2505 S 155%E

Answers.—(1) 254°, 154°, 357°, 159°; (2) 189°, 157°, 021°, 101°.
2516a. The radar operator of a ship proceeding through ice measures the following
bearings and ranges of an iceberg:

Time Bearing Range

1430 110° 4,000 yds.
1435 121° 3,300 yds.
1440 139° 2,600 yds.
1445 1632 2,300 yds.
1450 1882 2,500 yds.
1455 206° 3,100 yds.

Required.—(1) The course and speed of the ship if the iceberg is stationary.

(2) The course and speed of the ship if the iceberg is moving north at two knots.

Answers.—(1) C 075°, S 6.5 kn.; (2) C 059°, S 7.3 kn.

2516b. A navigator measures off a distance of 300 feet in a fore-and-aft direction
along the deck and stations a man at each end of this line. A stop watch is started
when a prominent ice feature is opposite the forward man. When the after man
reports that the same feature is opposite him, the watch is stopped, and the elapsed
time is found to be 34 seconds.

Required. —Speed.

Answer.—S 5.3 kn.

2536a. Find the zone time of sunrise and sunset at lat. 79%20'0 N, long. 332000
E, on August 31, 1958.

Answers.—Sunrise, ZT 0119; sunset, ZT 2219.

2536b. Find the zone time of beginning of morning civil twilight, sunrise, sunset,
and ending of evening civil twilight at lat. 67%30/0N, long. 167%00:0 W, on May 4, 1958.

Answers.—Morning twilight, ZT 0105; sunrise, ZT 0305; sunset, ZT 2105; evening
twilight, ZT 2305.

644 POLAR NAVIGATION

2536c. Find the zone time of moonrise and moonset at lat. 82230/0 N, long. 561510
W, on June 23, 1958, and the phase of the moon on this date.

Answers.—Moonrise, ZT 0904; moonset, ZT 0315; phase, crescent, about one day
before first quarter.

CHAPTER XXVI
LIFEBOAT NAVIGATION

Before Emergency Arises

2601. Introduction.—The methods and techniques used in lifeboat navigation are
those available at the time. With full equipment, lifeboat navigation differs little from
that aboard ship. More often, however, it is a matter of improvising equipment from
available materials, and developing procedures from a knowledge of basic principles.
Ingenuity is often essential. The officer who navigates by blindly “following the
steps” may be of little more value in a lifeboat devoid of familiar navigational equip-
ment than the man who has never set foot on the bridge of a ship. The wise officer
becomes thoroughly familiar with the theory of navigation: the celestial triangle, the
circle of equal altitude, and the other basic principles involved. He should be able
to identify the most useful stars, and know how to solve his sights by any widely used
method, because his favorite method may not be available. He should be able to
construct a plotting sheet with a protractor, and use distress signaling equipment.
Familiarity with the coordinates (latitude and longitude) of land points in the area
of operations, ability to interpret wind and weather signs, knowledge of the ocean
currents, and skill in handling a small boat are parts of the practical navigator's basic
education which assume their greatest importance in an emergency. For the navi-
gator prepared with such knowledge, and a determination to succeed, the situation is
never hopeless. Some method of navigation is always available.

2602. Emergency navigation kit.—In time of national emergency, the prudent
navigator will provide each lifeboat with a kit containing the equipment which it is
practical to carry for emergency navigational purposes (art. 2603). Even in peacetime
it is good practice to have one such kit permanently located in the chart house or the
wheel house so that it can be quickly transferred to a lifeboat when needed.

The least preparation made should be a check-off list of items to be assembled if
time permits, so that nothing will be overlooked. Such a list can be helpful even if
one or more emergency kits have been provided. The list should be kept in a prominent
place on the bridge or near the lifeboats, perhaps framed under glass. All officers
should be familiar with its location and should be acquainted with the location and
identity of each item listed.

Junior officers or reliable crew members should be assigned the duty of bringing
to their stations, during abandon ship drill, emergency navigational equipment not
permanently stowed in the boats. A senior officer should then check each item against
the equipment check-off list to ascertain that nothing has been overlooked.

2603. Equipment.—If practicable, full navigational equipment should be provided.
As many as possible of the items in the following list should be included. All of these
except a timepiece, and possibly a sextant and radio, can be kept in the emergency
navigation kit recommended in article 2602.

1. Notebook suitable for use as a deck log and for performing computations.
Several items of information should be written in this notebook in advance, so as to
be available when and if needed. Such items include the latitude and longitude of
various places in the area of operation; any desired information on currents and weather;

645

646 LIFEBOAT NAVIGATION

declination and SHA of several widely scattered stars, with any needed information `
on identifying them; desired notes and tables from this chapter and elsewhere ; any
desired general information, such as a list of poisonous fish and those items which may
prove useful for survival. This section of the notebook should be brief and the items
limited to those most essential in time of emergency.

2. Charts and other plotting materials. A pilot chart is most suitable for lifeboat
use, both for plotting and as a source of information on variation of the compass,
shipping lanes, currents, winds, and weather. Charts for both the summer and winter
seasons should be included. During World War II pilot charts were printed on water-
proof material suitable for use in a lifeboat. Plotting sheets (art. 323) are useful but
not essential if charts are available. The plotting sheets should cover the latitudes
in which the ship operates. Universal plotting sheets (art. 324) may be preferred,
particularly if the latitude coverage is large. Several maneuvering boards, H.O. 2665—
10, (art. 1212) and several sheets of cross-section paper (preferably with ten squares per
inch) should be included, as these have many uses.

3. Plotting equipment. Pencils, erasers, straightedge, protractor, dividers and
compasses (not essential, but useful), and a knife or pencil sharpener should be included.
Preferably, the straightedge and protractor should be combined in a single device
constituting some kind of plotter (art. 605). A ruler graduated in inches and fractions
may be useful.

4. Timepiece. A good watch is needed if longitude is to be determined astronom-
ically. This watch should be waterproof or kept in a waterproof container which permits
reading and winding of the watch without exposing it to the elements. The watch
should be wound regularly and a record kept of its error and rate of change. Even
if one or more such watches are available, the possibility of taking along the chro-
nometers should not be overlooked.

5. Sextant. A marine sextant should be taken along if possible. However, since
this may be impractical, a lifeboat sextant, or materials for constructing one, should
be provided. Several commercially manufactured lifeboat sextants have been made
available, particularly during wartime. A lifeboat sextant can be made of wood or
other rigid material, two small mirrors, and a pivot. The graduations of the arc
should be double those of a compass rose (an angle of 5° should be labeled 10°, etc.).
It is not necessary to provide a vernier, or means of adjusting the sextant, since
accuracy of 071 is satisfactory for lifeboat use.

6. Almanac. A Nautical Almanac for the current year is desirable. In an emer-
gency an almanac for another year can be used for stars and the sun without serious
error by lifeboat standards, if suitable adjustment is made (art. 2617). Some form of
long-term almanac, as that given in appendix X, might well be copied or pasted in
the notebook suggested as item 1, above.

7. Tables. Some form of table will be needed for reducing celestial observations.
The most suitable is one that does not require much space. If a table of trigonometric
functions (either logarithmic or natural) is provided, formulas should be included with
them. It is not wise to trust the memory for such vital information. A set of tables
similar to H.O. Pub. No. 214 can be made at 5° intervals of t, d, and L. Only one page
is needed for each latitude entry (5°) if declination is limited to about 30° (sufficient for
bodies of the solar system and many stars), entries are given to the nearest 0°1 for
altitudes and 1° for azimuth, and the delta (A) values are omitted. Traverse tables
and others given in this chapter are useful.

8. Compass. Each lifeboat is required to carry a magnetic compass. <A deviation
table for each compass should be made while in port, with magnetic material in its
normal place. It would be well to check the accuracy of each table periodically.

LIFEBOAT NAVIGATION 647

9. Flashlight. A flashlight is required to be carried in each lifeboat. The batteries
should be replaced from time to time, as necessary. Extra batteries and bulbs might
well be carried.

10. Portable radio. If a portable radio is available, be sure it is included. Whether
this is one of the transmitting-receiving sets approved by the Federal Communications
Commission for lifeboat use, or merely a small receiver of limited range owned by a
crew member, do not overlook it, as it may be used as a radio direction finder.

2604. Position of ship.—A knowledge of the position of the vessel at the time it is
abandoned is of great importance. The officer on watch on the bridge should never
permit himself to become careless in the matter of keeping a mental note of the ap-
proximate position of the vessel. During wartime, or whenever the possibility of
abandoning ship might reasonably be anticipated, the radio operator should be pro-
vided with a list of advance dead reckoning positions.

Abandoning Ship

2605. Before lowering boats.—The period between the decision to abandon ship
and the actual leaving of the vessel is a highly important one. It is also a period of
mental strain and possible confusion. The degree to which the crew can be prepared
for the ordeal ahead depends upon the amount of time available and the thoroughness
of the preparation that has been made. If there has been advance warning of the
possibility of the decision, certain preparations can be made before the decision is
reached. If time permits, after the decision to abandon ship has been made, the radio
operator should send a final distress message, giving the ship’s position and any other
pertinent information. It will be important later to know whether an acknowledgment
of receipt of the message was received. Any available time can be wisely used to check
the navigational equipment in each boat and assemble missing items. There may be
time to make a last minute check of position of the ship, position of any nearby land,
set and drift of current, present and forecast weather, watch error, and date. These
items should be written down. Perhaps the chart can be taken along. Equipment
should be properly secured before lowering the boats. In a rough sea it may be de-
sirable to lower the sextant, chronometer, and radio into the boat after it is afloat.

2606. Establishing command.—The identity of the person in command of each
boat, and the over-all commander, should be firmly established. Almost invariably
this will be the senior officer present. In a lifeboat, perhaps more than in any other
circumstances, strong leadership is required if the confidence of the crew is to be main-
tained. The officer whom the crew respects as a man, admires as a seaman, and rec-
ognizes as a gentleman will have little or no trouble with discipline and cooperation
of all on board.

Morale is a prime consideration, and it grows in importance with the passage of
time. The person in command should be recognized as the final authority in all
matters, but it is important that he give to each person an opportunity to be heard, and
that he keep all hands fully informed of the bad as well as of the good. Decisions will
be more acceptable if the crew has been informed of each consideration as it arises,
and so has been somewhat prepared. Complete fairness and impartiality are essential.

2607. Estimate of the situation.—Perhaps the first item which should engage the
attention of the person in command, after the lifeboat has cleared the stricken vessel,
is the questioning of each person aboard to collect all the useful information available.
It is well to determine what is known regarding the position of the ship, ocean currents,
weather, astronomy, navigation, seamanship, sailing, etc. Find out who owns watches
and what each owner knows about the error and rate of his watch. Establish a routine
for winding and comparing them. No useful skill or knowledge should be overlooked ;

648 LIFEBOAT NAVIGATION

all should be fully considered in making the important decision of whether to remain
in the vicinity of the disaster in the hope of rescue, or to attempt to reach land or a more
heavily traveled shipping lane. | |

This decision of whether to stay or leave may be the most important one of the
entire experience. Until comparatively recent times there was no problem. Because
there was virtually no hope of assistance, the lifeboat crew had to rely upon itself.
Since the development of modern communication and rescue facilities, however, it is
often wiser to remain than to complicate the rescue problem by increasing the area to
be searched. i )

The decision should not be made until careful consideration has been given to all
factors, nor should it be delayed longer than necessary. Considerations vary with the
circumstances, but certainly the following should be included:

Was a distress message sent before the ship was abandoned? Did it include the
position of the ship? How accurate was the position? Is there any reasonable doubt
that the message was received? If no message was sent, how soon will the ship be
missed? What rescue facilities are available? How far away are they and how long
will it be before help arrives? How conspicuous is the lifeboat? What facilities are
available for attracting attention, either visually or by radar? How proficient is the
crew in using such equipment? Is a radio transmitter available? What is the probable
running time to the nearest land in several directions, considering the prevailing winds
and currents, the motive power available, and the ability of the crew to use it? How
long will the fresh water and rations last, and will they be sufficient to sustain the crew
in the physical exertion required?

If the decision is to stay, how will the crew occupy its time, remembering the
increased morale problem with an idle crew? How will position be maintained, or
regained if the boat drifts? Would it be practical to wait two or three days, perhaps,
in the hope of rescue, and then to set out for land if help does not come?

If the decision is to leave, where should the boat head? How soon can a well-
traveled shipping lane be reached? In time of war, where is the enemy and where are
friends? How large and conspicuous is the land in each direction, considering the low
height of eye in a lifeboat? It may be better to head for conspicuous land 500 miles
away than for a small, low island 200 miles away, particularly if the latter is in a direc-
tion of unfavorable winds or currents, or takes the boat farther away from shipping
lanes.

Avoid, if possible, a hasty decision that will later be recognized as unwise. Dis-
cuss the matter thoroughly with the crew, and when the decision is made, inform them
of the reason for it. Do this in a manner that will invite their confidence and support.
Inform them of the best estimate of the situation.

2608. Selecting the route.—It is not always desirable to head directly for the
objective. A longer route with favorable winds and currents may be quicker. A
longer route by way of shipping lanes may enhance the possibility of rescue.

With clear skies, latitude can be found with relatively crude equipment. But
unless accurate Greenwich time is available, longitude cannot be found astronomically,
even with the best equipment; nor is a nonastronomical method likely to be available.
In the absence of reliable longitude information, it is better to head for a point at the
latitude of the destination but so far east or west of it that no reasonable doubt will exist
as to the direction of land when that latitude is reached. The distance of the point from
the destination depends upon the degree of uncertainty of the longitude, remembering
that this uncertainty is likely to increase with time. This method of “parallel sailing"

was used for centuries before a method of determining or “discovering” longitude at
sea was developed.

LIFEBOAT NAVIGATION 649

If the objective has a considerable extent in a north-south direction, the need for
a final east-west leg is less critical, and in attempting to reach a continent or very large
island, one need not consider it at all. In the absence of better information, an east
or west course should be selected from the outset, since most large land masses of the
earth are oriented in a general north-south direction.

2609. Keeping boats together.—If more than one boat is launched, every effort
should be made to keep them together. While the person in charge of each boat is
responsible for decisions regarding his boat, considerable advantage is to be gained by
keeping the boats together and recognizing one person, logically the senior officer
present, as the over-all commander. Since navigational equipment and skill probably
will differ widely from boat to boat, the benefits of any accurate navigation can be
shared by all if the boats are close together. Other knowledge can be exchanged,
equipment shared, and rations distributed equitably. It may be wise to shift some
personnel among the boats, perhaps on a periodic basis, either to effect a better balance
of skill and knowledge, or for morale purposes.

2610. Lookout.—Always there is the possibility of sighting another vessel. Hence,
a lookout should be posted at all times. This becomes of even greater importance
when approaching land, or if the location of all land along the route is not known. If
it is possible to rig a metal object high in the boat, this should be done to enhance the
possibility of detection by radar. :

Dead Reckoning

2611. Importance of dead reckoning.—Of the various kinds of navigation, dead
reckoning alone is always available in some form. It should never be neglected, but in
a lifeboat it is of more than average importance. A close check should be kept on the
direction and distance made good, and all disturbing elements such as wind and current
should be carefully evaluated. Long voyages have been successfully completed by
this method alone, and landfalls have been made with surprising accuracy. This is
not meant to minimize the importance of other methods of determining position, but
with the methods generally available in a lifeboat, one may well find that, during the
first few days, his dead reckoning positions are more accurate than those determined
by other methods. If the means of determining direction and distance—the elements
of dead reckoning—are accurate, it might be well to make an adjustment to the dead
reckoning only after consistent indication of the magnitude and direction of its error.
The dropping of the dead reckoning at each uncertain “fix” is at best a questionable
procedure. The conflicting information likely to be available calls for careful analysis
and good judgment on the part of the navigator.

2612. Deck log.—From the beginning a careful log should be kept. The date and
time of abandoning ship should be the first entry, followed by navigational information
available, and the various important decisions and the reasons for them. Since the
conservation of paper may be important, record only the essentials of the important
items, but do not overlook the recording in considerable detail of the selection of a
commanding officer, changes in command, deaths, missing persons, and navigational
information.

The best determination of the position of abandoning ship should be recorded,
followed by a full account of courses, distances, positions, winds, currents, and leeway.
No important navigational information should be left to memory if it can be recorded.

2613. Direction.—As one of the elements of dead reckoning, direction is an impor-
tant item. As indicated in article 2603, a deviation table for each lifeboat compass
should be determined in port, and checked periodically. At the first convenient oppor-

650 LIFEBOAT NAVIGATION

tunity after abandoning ship the accuracy should be checked on the course to be
followed.

If an almanac, accurate Greenwich time, and the necessary tables are available, `
the azimuth of any celestial body can be computed and this value compared with the
azimuth as measured by the compass. If it is difficult to observe the compass azimuth,
select a body dead ahead and note the compass heading. The difference between
computed and observed azimuths is compass error. This is of more immediate value
than deviation, but if the latter is desired, it can be determined by applying to the
compass error the variation, from the pilot chart.

- Several unique astronomical situations occur, permitting determination of azimuth
without computation:

Polaris is always within 2? of true north for observers between the equator and
latitude 60? N. When this star is directly above or below the celestial pole, its azimuth
is exactly north at any latitude. This occurs approximately when the trailing star of
either Cassiopeia (e Cassiopeiae) or the big dipper (Alkaid) is directly above or directly
below Polaris (fig. 2621). When a line through the trailing stars and Polaris is
horizontal, the maximum correction should be applied. Below latitude 50? this can
be considered 1%; and between 50° and 65%, 2%. If Cassiopeia is to the right of
Polaris, the azimuth is 001? (or 002°), and if to the left, 359? (or 358%). The south
celestial pole is located approximately at the intersection of a line through the longer
axis of the southern cross with a line from the northernmost star of Triangulum Aus-
trale perpendicular to the line joining the other two stars of the triangle. No conspic-
uous star marks this spot (figs. 2205-2208).

Meridian transit. Any celestial body bears due north or south at meridian transit,
either upper or lower. This is the moment of maximum (or minimum) altitude of the
body. However, since the altitude at this time is nearly constant during a considerable
change of azimuth, the instant of meridian transit may be difficult to determine. If
time and an almanac are available, and the longitude is known, the time of transit can
be computed.

Body on prime vertical. If any method is available for determining when a body
is on the prime vertical (due east or west), the compass azimuth at this time can be
observed. Table 25 provides this information. Any body on the celestial equator
(declination 0°) is on the prime vertical at the time of rising or setting. For the sun
this occurs at the time of the equinoxes (art. 1419). The star Mintaka (6 Orionis),
the leading star of Orion’s belt, has a declination of approximately 0°3 S and can be
considered on the celestial equator. For an observer near the equator, such a body is
always nearly east or west. Because of refraction and dip, the azimuth should be
noted when the center of the sun or a star is a little more than one sun diameter (half a
degree) above the horizon. The moon should be observed when its upper limb is on
the horizon.

Body at rising or setting. Except for the moon, the azimuth angle (art. 1428)
of a body is almost the same at rising as at setting, except that the former is toward the
east and the latter toward the west. If the azimuth is measured both at rising and set-
ting, true south (or north) is midway between the two observed values, and the differ-
ence between this value and 180° (or 000°) is the compass error. Thus, if the compass
Rae d a body is 073° at rising, and 277° at setting, true south (180°) is at
eere NA by compass, and the compass error is 5? E. This method may be
in error if the boat is moving rapidly in a north or south direction. If the declination
and latitude are known, the true azimuth of any body at rising or setting can be deter-

LIFEBOAT NAVIGATION 651

mined by means of a diagram on the plane of the celestial meridian (art. 1432) or by
computation (art. 2125). For this purpose the body (except the moon) should be con-
sidered as rising or setting when its center is a little more than one sun diameter (half a
degree) above the horizon, because of refraction and dip.
The direction of the sun in relation to the hands of a watch is sometimes advocated,
but the limitations of this method are too great to permit general application.
A simple nonastronomical method can be used for determining the deviation.
An object that will float but not drift rapidly before the wind is thrown overboard.
The boat is then steered as steadily as possible in the opposite direction to that desired.
At a distance of perhaps half a mile, or more if the floating object is still clearly in
view, the boat is turned around in the smallest practicable radius, and headed back
toward the floating object. The magnetic course is midway between the course
toward the object and the reciprocal of the course away from the object. Thus,
if the boat is on compass course 151° while heading away from the object,
and 337° while returning, the magnetic course is midway between 337° and

39/3381" :
151°+180°=331°, or aeei Since 334° magnetic is the same as 337°

by compass, the deviation on this heading is 3° W.

If a compass is not available, any celestial body can be used to steer by, if its
diurnal apparent motion is considered. A reasonably straight course can be steered
by noting the direction of the wind, the movement of the clouds, the direction of the
waves, or by watching the wake of the boat. A line can be secured to the side of the
boat at a point amidships or forward. The line should tend parallel to the center line
of the boat if on a straight course. The angle between the center line and the wake is
an indication of the amount of leeway. The accuracy of the towed-object or wake
method is affected adversely by a cross sea.

A body having a declination the same as the latitude of the destination is over
the destination once each day, at the time when its hour angle is the same as the longi-
tude, measured westward through 360°. At this time it should be dead ahead if the
boat is following the great circle leading directly through the destination.

2614. Motive power.—A lifeboat is equipped with one or more of the following
means of locomotion: oars, hand-operated propeller, motor, sail. Of these, only sail
offers a practical means of travel over an extended period of (ae. Men living in an
open boat, perhaps on reduced rations, should not attempt to expend their strength
on hand locomotion, except for short periods. Likewise, the comparatively small
fuel supply in a motorboat should be hoarded jealously. It may be desperately needed
later, as for landing through a surf, preventing the boat from drifting onto a rocky
coast, or making the land when a strong current is carrying the boat past an island.

A sail should be rigged, for in it lies the best hope of reaching distant land. If
the standard lifeboat sail is not available, a substitute can usually be devised, using the
boat cover, or even clothing, and oars.

2615. Distance can be determined directly between accurate fixes, but generally
it is found by means of speed and elapsed time. A loaded lifeboat will not travel fast,
under normal conditions. With fair wind and weather it may make good a speed of
about two knots through the water. Hence the importance of wind and current.
The navigator used to observing the sea from a high bridge usually overestimates
his speed in a lifeboat, where he is only a few feet from the water. With practice, his
ability should improve.

Speed may be determined by using a form of chip log. Attach a long line to a
heavy, floating object. Put one knot in the line twelve or fifteen fathoms from the

652 LIFEBOAT NAVIGATION

. .
object, and another just ten fathoms (or any convenient distance) from the first. |

Stream the device over the side and let the line run out freely, noting the elapsed time
between passage of the two knots through the hand. A variation of this is the Dutch-
man's log. A floating object is thrown overboard at the bow, and the elapsed time
required for a known length along the centerline to pass it is noted. If a line is attached
to the object, it may be used many times. With either variation, it is well to tie the
bitter end of the line to the boat, to minimize danger of losing the whole device
overboard.
With either the chip or Dutchman’s log, the speed is determined by the formula:

60 seconds per minute X60 minutes per hour Xfeet between marks,

= 6,000 feet per mileX seconds of elapsed time

This is equal to:

__3,600.Xfeet between marks 0.6 Xfeet between marks

RE 6/000 K seconds of elapsed time seconds of elapsed time `

Since the feet between marks is constant, a convenient number can be selected. Thus,
if the length is 16% feet, the formula becomes

SC? 10
~ seconds of elapsed time

If the elapsed time is ten seconds, the boat is traveling at one knot; if five seconds, at
two knots; if eight seconds, at 1% knots, etc.

If a watch is not available, a simple pendulum may be devised to time the interval.
A piece of string with a weight attached, of a length of 9.8 inches (to the center of gravity
of the weight), will, when suspended, make a complete swing (back and forth) once every
second. For a pendulum 39.1 inches long the period is two seconds. With practice,
time can be estimated with fair accuracy.

It is not always possible to head directly along the course to the destination,
because of adverse winds. It is better to make good progress in the general direction
desired than none at all, and much better on morale. However, at times conditions
may be so adverse that it will be best to drop sail until the wind shifts or abates. At
such a time a sea anchor should be streamed to minimize loss of precious mileage,
and, in severe conditions, to keep the boat headed into the sea.

2616. Position by dead reckoning.—Plotting can be done directly on a pilot
chart or plotting sheet. If this proves too difficult, or if an independent check is desired,
some form of mathematical reckoning may be useful. Table 2616,

Angle Factor a simplified traverse table, can be used for this purpose. This is a
z critical-type table, various factors being given for limiting values
dome of certain angles. To find the difference or change of latitude, in

ES 09 minutes, enter the table with course angle, reckoned from north or

41 " S south toward the east or west. Multiply the distance run, in miles,

P 0.6 by the factor. To find the departure, in miles, enter the table with

63 " i the complement of the course angle. Multiply the distance run, in

$ 0.3 miles, by the factor. To convert departure to difference of longi-

81 s tude, in minutes, enter the table with mid latitude. Divide the
0. 0

departure by the factor.
Example.—A lifeboat travels 26 miles on course 205?, from

Taste 2616.—Simpli- L 41°44 N, A 867217 W.
fied traverse table. Required.—Latitude and longitude of the point of arrival.

LIFEBOAT NAVIGATION 653

Solution.—The course angle is 205°—180°=S25°W, and the complement is
90°—25°=65°. The factors corresponding to these angles are 0.9 and 0.4, respectively.
The difference of latitude is 26X0.9=23' (to the nearest minute) and the departure is
26X0.4=10 mi. Since the course is in the southwestern quadrant, in the northern
hemisphere, the latitude of the point of arrival is 41°44’N—23’—41°21’N. The
factor corresponding to the mid latitude 41°32’ N is 0.7. The difference of longitude is
10+0.7=14’. The longitude of the point of arrival is 56°21’ W 4-14/ —56?35' W.

Answer.—L 41°21’ N, A 56°35’ W.

Celestial Navigation

2617. Celestial coordinates.—Almanac information, particularly declination and
Greenwich hour angle of bodies, is important to celestial navigation. If the current
Nautical Almanac is available, there is no problem. If the only copy available is for
a previous year, it can be used for the sun, Aries, and stars without serious error, by
lifeboat standards. However, for greater accuracy, proceed as follows: For de-
clination of the sun, enter the almanac with a time that is earlier than the correct time
by 5^49" times the number of years between the date of the almanac and the correct
date, adding 24^ for each February 29 that occurs between the dates. If the date is
February 29, use March 1 and reduce by one the number of 24" periods added. For
GHA of the sun or Aries determine the value for the correct time, adjusting the minutes
and tenths of arc to agree with that at the time for which the declination is determined.
Since the adjustment never exceeds half a degree, care should be used when the value is
near a whole degree, to prevent the value from being in error by 1%. Appendix X is a
long-term almanac giving values of GHAT, and GHA and declination of the sun.
Instructions for its use are included in the appendix. A reproduction of this almanac
might profitably be included in the navigational kit mentioned in article 2602.

If no almanac is available, a rough approximation of the declination of the sun
can be obtained as follows: Count the days from the given date to the nearer solstice
(June 21 or December 22). Divide this by the number of days from that solstice to
the equinox (March 21 or September 23), using the equinox that will result in the given
date being between it and the solstice. Multiply the result by 90°. Enter table 2616
with the angle so found, and extract the factor. Multiply this by 23°45 to find the
declination.

Example 1.—The date is August 24.

Required.—The approximate declination of the sun.

Solution.—The number of days from the given date to the nearer solstice (June
21) is 64. There are 94 days between June 21 and September 23. Dividing and
multiplying by 90°, Y

6 o o
947 90 = Oo:

The factor from table 2616 is 0.5. The declination is 23°45 X0.5=11°7. It is known
to be north because of the date.

Answer.—Dec. 11?7 N.

'The accuracy of this solution can be improved by considering the factor of table
2616 as the value for the mid angle beween the two limiting ones (except that 1.00
is correct for 0? and 0.00 is correct for 909), and interpolating to one additional decimal.
In this instance the interpolation would be between 0.50 at 59%5 and 0.40 at 66%.
The interpolated value is 0.47, giving a declination of 1170 N. Still greater accuracy
can be obtained by using a table of natural cosines instead of table 2616. By natural
cosine the value is 1123 N.

654 LIFEBOAT NAVIGATION

5 eg "PT 6

If the latitude is known, the declination of any body can be determined by observ- `
ing à meridian altitude. In a lifeboat it is usually best to make a number of observa-
tions shortly before and after transit, plot the values on cross-section paper, letting |

the ordinate (vertical scale) represent altitude, and the abscissa (horizontal scale) the
time. The altitude is found by fairing a curve or drawing an arc of a circle through
the points, and taking the highest value. A meridian altitude problem is then solved
in reverse.

Example 2.—The latitude of a lifeboat is 40°16’S. The sun is observed on the `

meridian, bearing north. The observed altitude is 36°29’.

Required.—Declination of the sun.

Solution.—The zenith distance is 90°—36°29’=53°31’. The sun is 53°31’ north
of the observer, or 13?15/ north of the equator. Hence, the declination is 13?15' N.

Answer.—Dec. 13?15' N.

The GHAT can be determined approximately by considering it equal to GMT
(in angular units) on September 23. To find GHA T on any other date, add 1° for
each day following September 23. The value is approximately 90% on December 22,
180? on March 21, and 270? on June 21. The values so found can be in error by as
much as several degrees, and so should not be used if better information is available.
An approximate check is provided by the great circle through Polaris, Caph (the leading
star of Cassiopeia), and the eastern side of the square of Pegasus. When this great
circle coincides with the meridian, LHA T is approximately 0°. The hour angle of a
body is equal to its SHA plus the hour angle of Aries.

If an error of as much as 4°, or a little more, is acceptable, the GHA of the sun
can be considered equal to GMT+180° (12"). For more accurate results, one can
make a table of the equation of time from the Nautical Almanac perhaps at five- or ten-
day intervals, and include this in the emergency navigation kit mentioned in article
2602. The equation of time is applied according to its sign to GMT+180° to find
GHA.

2618. Altitude measurement.—If a sextant is available, either one from the pilot
house or an emergency-type instrument, altitudes are measured in the usual manner.
The sextant should be shielded as much as possible from wind and spray. If the sea
is rough, the observer should brace himself against the mast and make his observation
when on the crest of a wave, when the horizon is least likely to be obscured by nearby
waves. It is usually good practice to make a number of observations and average
both the altitudes and times, or plot on cross-section paper the altitudes versus time,
using any convenient time and the corresponding altitude for solving the observation.

The improvisations which may be made in the absence of a sextant are so varied
that in virtually any circumstances the application of a little ingenuity and some effort
will produce a device for measuring altitude. The results obtained with any improvised
method will be approximate at best, but if a number of observations are averaged, the
accuracy should be improved. Almost always a measurement, however approximate,
is better than an estimate. Two general classes of improvisation are available:

1. By circle. Any circular scale, such as a maneuvering board (H.O. 2665-10),
compass rose, protractor, or plotter can be used to measure altitude or zenith distance
directly. This is the principle of the ancient astrolabe (art. 124). A maneuvering
board or compass rose is usually handled best by mounting it on a flat board. A pro-
tractor or plotter may be so mounted or used directly. There are a number of variations
of the technique of using such a device. Some of them are:
| A peg or nail is placed at the center of the circle and perpendicular toit. A weight
is hung from the 909 graduation, and a string for holding the device is attached at the
270° graduation. When it is held with the weight acting as a plumb bob, the 0°-180°

LIFEBOAT NAVIGATION 655

line is horizontal (fig. 2618a). In this posi-
tion the board is turned in azimuth until it
is in line with the sun. The intersection of
the shadow of the center peg with the arc of
the circle indicates the altitude of the center
of the sun.

The weight and loop can be omitted and
pegs placed at the 0° and 180° points of the
circle. While one observer sights along the
line of pegs to the horizon, an assistant notes
the altitude.

The weight can be attached to the center
pin, and the three pins (0°, center, 180°)
aligned with the celestial body. The reading
is made at the point where the string hold-
ing the weight crosses the scale. The reading
thus obtained is the zenith distance unless
the graduations are labeled to indicate alti-
tude. This method, illustrated in figure 2618b,
is used for bodies other than the sun.

Whatever the technique, it is good prac-
tice to reverse the device for half the readings
of a series, to minimize errors of construction.

LOOP OF STRING

yy

PEG |

y uL. QT
SU Y | / U7

v

"ny

dt

M,

yy,

FIGURE 2618a.—Improvised astrolabe; shad-

ow method. Pegs and board shown tilted
for clarity.

Generally, the circle method produces

more accurate results than the right triangle method, described below.

2. By right triangle.

The principle of the ancient cross-staff can be used to estab-

lish one or more right triangles, which can be solved by measurement of the angle

we
ann HEU ILU
R VERA / pm, ~ /
N 240 Ny, 5
`> N e “ny, Sg
7 SS ki y ^I E
LEON /

[yy
/ "ny,
7

0s!
/

pu

STRING

X T
su

Ņ
N
\ du R
Ww

gini

Figure 2618b.—Improvised astrolabe; S
method. Pegs and board shown tilted for clarity.

direct sighting

representing the altitude, either
directly or by reconstructing the
triangle. Another way of deter-
mining the altitude is to measure
two of the sides of the triangle
and divide one by the other to
determine one of the trigonomet-
ric functions. This procedure,
of course, requires a source of
information on the values of
trigonometric functions corre-
sponding to various angles. If
the cosine is found, table 2616
can be used. The tabulated
factors can be considered correct
to one additional decimal for the
value midway between the limit-
ing values (except that 1.00 is
the correct value for 0° and 0.00
is the correct value for 90°) with-
out serious error by lifeboat
standards. Interpolation can
then be made between such
values. By either protractor or

656 LIFEBOAT NAVIGATION

table, most devices can be graduated in advance so that angles can be read directly.
There are many variations of the right triangle method. Some of these are:

Two straight pieces of wood can be attached to each other in such a way that
the shorter one can be moved along the longer, the two always being perpendicular to
each other. The shorter piece is attached at its center. One end of the longer arm is
held to the eye. The shorter arm is moved until its top edge is in line with the celestial
body, and its bottom edge is in line with the horizon. Thus, two right triangles are
used (the third sides being the slant distances between the ends of the arms) each repre-
senting half the altitude (fig. 2618c). For low altitudes, only one of the triangles is used,
the long arm being held in line with the horizon. The length of half the short arm,
divided by the length of that part of the long arm between the eye and the intersection
with the short arm, is the tangent of half the altitude (the whole altitude if only one
right triangle is used). The cosine can be found by dividing that part of the long arm
between the eye and the intersection with the short arm by the slant distance from the
eye to one end of the short arm. Graduations consist of a series of marks along the

long arm indicating settings for

Y various angles. The device

Se should be inverted for alternate
readings of a series.

A rule or any stick can be
held at arm's length. The top
of the rule is placed in line with
the celestial body being ob-
served, and the top of the
thumb is placed in line with

qu om the horizon. The rule is held
TO HORIZON vertical. The length of rule
FIGURE 2618c.—Improvised cross-staff. above the thumb, divided by

the distance from the eye to the
top of the thumbis the tangent of the angle observed. The cosine can be found by divid-
ing the distance from the eye to the top of the thumb by the distance from the eye to
the top of the rule. If the rule is tilted toward the eye until the minimum of rule is
used, the distance from the eye to the middle of the rule is substituted for the distance
from the eye to the top of the thumb, half the length of the rule above the thumb is
used, and the angle found is multiplied by two. Graduations consist of marks cn the
rule or stick indicating various altitudes. For the average observer each inch of rule
will subtend an angle of about 2°3, assuming an eye-to-ruler distance of 25 inches. This
relationship is good to a maximum altitude of about 20°. The accuracy of this relation-
ship for a specific observer can be checked by comparing the measurement against
known angles in the sky. Angular distances between stars can be computed by sight
reduction methods, including H.O. Pub. No. 214, by using the declination of one star as
the latitude of the assumed position, and the difference between the hour angles (or
SHA’s) of the two bodies as the meridian angle. The angular distance is the complement
of the computed altitude. The angular distances between some well-known star pairs
are: end stars of Orion’s belt, 2°7; pointers of the big dipper, 5°4; Rigel to Orion’s belt,
970; eastern side of the great square of Pegasus, 1420; Dubhe (the pointer nearer Polaris)
and Mizar (the second star in the big dipper, counting from the end of the handle), 19°3.
The angle between the lines of sight from each eye is, at arm’s length, about 6°.
By holding a pencil or finger horizontal, and placing the head on its side, one can esti-
mate an angle of about 6° by closing first one eye and then the other, and noting how
much the pencil or finger appears to move in the sky.

LIFEBOAT NAVIGATION 657

The length of the shadow of a peg or nail mounted perpendicular to a horizontal
board can be used as one side of an altitude triangle. The other sides are the height
of the peg and the slant distance from the top of the peg to the end of the shadow. The
height of the peg, divided by the length of the shadow, is the tangent of the altitude of
the center of the sun. The length of the shadow divided by the slant distance is the
cosine. Graduations consist of a series of concentric circles indicating various altitudes,
the peg being at the common center. The device is kept horizontal by floating it in
a bucket of water. Half the readings of a series are taken with the board turned 180°
in azimuth.

Two pegs or nails can be mounted perpendicular to a board, with a weight hung
from the one farther from the eye. The board is held perpendicular and the two pegs
aligned with the body being observed. The finger is then placed over the string holding
the weight, to keep it in position as the board is turned on its side. A perpendicular
is dropped from the peg nearer the eye, to the string. The altitude is the acute angle
nearer the eye. For alternate readings of a series, the board should be inverted.
Graduations consist of a series of marks indicating the position of the string at various
altitudes.

As the altitude decreases, the triangle becomes smaller. At the celestial horizon
it becomes a straight line. No instrument is needed to measure the altitude when either
the upper or lower limb is tangent to the horizon, as the “sextant” altitude is then 0°.

2619. Sextant altitude corrections.—If altitudes are measured by a marine sextant,
the usual sextant altitude corrections apply (ch. XVI). If the center of the sun or
moon is observed, either by sighting at the center or by shadow, the lower-limb correc-
tions should be applied, as usual, and an additional correction of (—)16’ applied. If
the upper limb is observed, use (—) 32’. If a weight is used as a plumb bob, or if the
length of a shadow is measured, omit the dip (height of eye) correction.

If the almanac is not available for making corrections, each source of error can be
corrected separately, as follows:

Index correction. If a sextant is used, the index correction should be determined
and applied to all observations, or the sextant adjusted to eliminate index error.
Refraction is given to the nearest minute of arc in table
Alt. Refr. 2619. The value for a horizon observation is 34’. If the nearest
, 0%1 is sufficiently accurate, as with an improvised method of

root of the height of eye, in feet. The correction applies to all
observations in which the horizon is used as the horizontal ref-

Du observing altitude, a correction of 0?1 should be applied for
6 : 5 E
7 5 altitudes between 5? and 18?, and no correction applied for
e 6 greater altitudes. Refraction applies to all observations, and
12 5 is always a minus (—) correction.
ECK Dip, in minutes of arc, is approximately equal to the square
21 à p, ) DD y eq q

1

0

e erence. It is always a minus (—) correction. If 0°1 accuracy
TABLE 2619.—Re- is used, no dip correction is needed for lifeboat heights of eye.
fraction. Semidiameter. The semidiameter of either the sun or moon

does not differ greatly from 16’. The correction does not apply to other bodies or
to observations of the center of the sun and moon, by whatever method, including
shadow. The correction is plus (+) if the lower limb is observed, and minus (—) if
the upper limb is observed.

Parallax. For lifeboat accuracy, parallax is applied to observations of the moon
only. An approximate value, in minutes of arc, can be found by multiplying 57’
by the factor from table 2616, entering that table with altitude. For more accurate
results the factors can be considered correct to one additional decimal for the altitude

658 LIFEBOAT NAVIGATION

midway between the limiting values (except that 1.00 is correct for 0° and 0.00 is à
correct for 909), and the values for other altitudes can be found by interpolation. This |.
correction is always plus (+). |

For observations of celestial bodies on the horizon, the total correction for zero
height of eye is:

Sun. Lower limb: (—) 18’, upper limb: (—) 50’.
Moon. Lower limb: (+) 39’, upper limb: (+)7’.
Planet or star. (—) 34’.

Dip should be added algebraically to these values.

Since the “sextant” altitude is zero, the “observed” altitude is equal to the total `
correction.

2620. Sight reduction.—If any tables designed for sight reduction, such as H.O.
Pub. No. 214, are available, they should be safeguarded to prevent loss or damage. If
trigonometric tables and the necessary formulas are available, they will serve the `
purpose. Speed in solution is seldom a factor in a lifeboat. A slow method might
actually be an asset, from a morale standpoint, as it will provide occupation for a limited
time for at least one crew member. If tables but no formulas are available, carefully
determine the mathematical knowledge possessed by the crew. Someone may be able
to provide the missing information. If the formulas are available, but no tables,
approximate natural values of the various trigonometric functions can be obtained
graphically by the method explained in article O39. Graphical solution of the naviga-
tional triangle can be made by the orthographic method explained in article 1432. A
maneuvering board (H.O. 2665-10) might prove helpful in the. graphical solution for
either trigonometric functions or altitude and azimuth. Very careful work will be
needed for useful results by either method.

Unless full navigational equipment is available, better results might be obtained
by making separate determinations of latitude and longitude.

2621. Latitude determination.—Several methods are available for determining
latitude, and in none of them is accurate time needed.

Meridian altitude. Latitude can be determined by means of a meridian altitude
of any body, if its declination is known. The method is explained in article 2103.
If accurate time, knowledge of the longitude, and an almanac are available, the observa-
tion can be made at the correct moment, as determined in advance. However, if any
of these is lacking, or if an accurate altitude-measuring instrument is unavailable,
better procedure is to make a number of altitude observations before and after meridian
transit. A plot is then made of altitude versus time, if cross-section paper is available,
and the highest (or lowest, for lower transit) altitude is scaled from a curve faired
through the plotted points. At lifeboat speeds this procedure is not likely to introduce a
significant error. The time used for plotting the observations need not be accurate,
as elapsed time between observations is all that is needed, and this is not of critical
accuracy. Thus, even a watch that has run down and then been rewound can be used
without resetting. Any altitudes that are not consistent with others of the series
should be discarded.

Polaris. Latitude by Polaris is explained in article 2105. In a lifeboat, only
the first correction is of practical significance. If suitable tables are not available, this
correction can be estimated. The trailing star of Cassiopeia (e Cassiopetae) and Polaris
have almost exactly the same SHA. The trailing star of the big dipper (Alkaid) is
nearly opposite Polaris and e Cassiopeiae. These three stars, e Cassiopeiae, Polaris, and
Alkaid, form a line through the pole (approximately). When this line is horizontal,
there is no correction. When it is vertical, the maximum correction of 56’ applies.

LIFEBOAT NAVIGATION 659
4

It should be added to the observed altitude if Alkaid is at the top, and subtracted if
e Cassiopeiae is at the top. For any other position, estimate the angle this line makes
with the vertical (fig. 2621), and multiply the maximum correction (567) by the factor
from table 2616, adding if Alkaid is higher than e Cassiopeiae, and subtracting if it is
lower. For more accurate results, the factor from table 2616 can be considered accu-
rate to one additional decimal for the mid value between those tabulated (except that
1.00 is correct for 0° and 0.00 for 90°). Other values can be found by interpolation.
Length of day. The length of the day varies with latitude. Hence, latitude can
be determined if the elapsed time between sunrise and sunset can be observed. Correct
the observed length of day by adding 1” for each 15' of longitude traveled toward the
east and subtracting 1" for each 15' of longitude traveled toward the west. The latitude
determined by length of day is the value for the time of meridian transit. Since
meridian transit occurs approximately mid-
way between sunrise and sunset, half the |
interval may be observed and doubled. If E Cash 2 |
a sunrise and sunset table is not available, skalar ide |
the length of daylight can be determined han
graphically by means of a diagram on the A
plane of the celestial meridian (art. 1432).
A maneuvering board (H.O. 2665-10) is
useful for this purpose. This method can- Polaris
not be used near the time of the equinoxes,

N. CELESTIAL POLE
* *

accuracy, and allowance should be made for
the longitude correction.

Body in zenith. The declination of a ap e
body in the zenith is equal to the latitude et? 2621. Relative positions ot Cancio-
of the observer. If no means are available north celestial pole.
for measuring the altitude, the position
of the zenith may possibly be estimated in a calm sea by lying in the lifeboat and
looking skyward. The accuracy of the results depends upon the ability to estimate
the position of the zenith. Use of a plumb bob may help.

Variation of the compass can occasionally be used for determining latitude, as
explained in article 2622.

2622. Longitude determination.—Unlike latitude, longitude requires accurate
Greenwich time for its determination by astronomical means. All such methods
consist of noting the Greenwich time at which a phenomenon occurs locally. In
addition, a table indicating the time of occurrence of the same phenomenon at Green-
wich, or equivalent information, is needed.

Time of transit. When a body is on the local celestial meridian, its GHA is the
same as the longitude of the observer if in west longitude, or 360°—) in east longitude.
Thus, if the GMT of local transit is determined and a table of Greenwich hour angles
(or time of transit of the Greenwich meridian) is available, longitude can be computed.
If only the equation of time is available, the method can be used with the sun. This
is the reverse of the problem of finding the time of transit of a body (art. 2104). The
time of transit is not always apparent. If a curve is made of altitude versus time, as
suggested in article 2621, the time corresponding to the highest altitude is used in the
determination of longitude. Under some conditions it may be preferable to observe

|
and is of little value near the equator. The | x *
moon can be used if moonrise and moonset =] Jai
tables are available, but with the moon el
the half-interval method is of insufficient H *
>| Alkaid

660 LIFEBOAT NAVIGATION

an altitude before meridian transit and then again after meridian transit, when the
body has returned to the same altitude as at the first observation. Meridian transit
occurs midway between these two times. A body in the zenith is on the celestial
meridian. If accurate azimuth measurement is available, note the time when the
azimuth is 000° or 180°.

Sunrise and sunset. The difference between the observed GMT of sunrise or
sunset and the LMT tabulated in the almanac is the longitude in time units, which
can then be converted to angular measure. If the Nautical Almanac is used, this
information is tabulated for each third day only. Greater accuracy can be obtained if
interpolation is used for determining intermediate values. Moonrise or moonset can
be used if the tabulated LMT is corrected for longitude (art. 1812). Planets and
stars can be used if the means are available for determining the time of rising or setting.
This can be determined by computation (art. 2536) or, approximately, by means of a
diagram on the plane of the celestial meridian (art. 1432).

Either of these methods can be used in reverse to set a watch that has run down, `

or to check the accuracy of a watch, if the longitude is known. In the case of a meridian
transit the time need not be determined at the instant of transit. The watch is started
and the altitude is then measured several times before and after transit, or at equal
altitudes. The times of these observations are noted and from them the time of
meridian transit is determined. The difference between this time and the correct
time of transit can then be used as a correction to reset the watch. If a watch runs
down and cannot be reset from other timepieces, the correct time should be determined
at the first opportunity, if the longitude accuracy is likely to deteriorate.

Variation of the compass. If the deviation of the compass is known accurately
and an accurate azimuth can be observed, it is possible to determine the variation.
If this is compared with the variation shown on the pilot chart, an approximate line
of position can be determined. Since in many areas these lines run in a generally
north-south direction, this may be an indication of the longitude. However, if the line
has a large east-west component, it should be considered as any other such line of
position, rather than as a longitude line. In some areas it is more nearly a latitude
line. The accuracy of the method depends upon the accuracy with which the variation
can be determined, and the spacing between adjacent isogonic lines.

Time sight. If altitude of a celestial body is available, including zero “sextant”
altitude at rising or setting (art. 2619), longitude can be found by time sight (art. 2106).

Approaching Land

2623. Signs of land.—There are a number of signs which may indicate that the
lifeboat is approaching land.

The sky will sometimes indicate a break in the open sea. A small fixed cloud, when
surrounding ones are in motion or absent, will usually be over or close toland. At high
latitudes, a light-colored reflection in the sky might be over an ice area; a light green
reflection in the tropical sky might indicate a shallow lagoon. Such indications may be
even more apparent on the under side of a uniform cloud layer.

Birds most often fly away from land at dawn and toward it at dusk. A large
number of birds may indicate the nearness of land.

Swell, properly interpreted, may be used as a guide to land. Consecutive swells
travel parallel until they reach an island and then “bend” around it. Eddies are formed
where the distorted swell meets beyond the island. This eddy line may be used as a
bearing to land, sometimes at a considerable distance.

LIFEBOAT NAVIGATION 661

The color of the sea may act as a guide in finding land as the open sea generally
appears dark blue or dark green, and a lighter shade indicates shallow water, which
may be near land.

The sound of the surf is often heard while still a considerable distance from land.
Other sounds may also be heard at great distances.

Odors, as from burning wood, sometime carry a long way out to sea.

Sounds and odors may be particularly helpful in periods of reduced visibility.

2624. Distance off.—At sea in a lifeboat the navigator is handicapped by his
limited range of visibility. Distance to the horizon, in nautical miles, is given approxi-
mately by the formula 1.15/h, h being the height of eye in feet. Thus, distance in
miles is approximately 1% times the square root of the height in feet. At an eye height
of nine feet, the horizon is about 3% miles away. A loaded Victory ship, whose greatest
mast height is about 81 feet above the water line, could be seen 1.15-/81 or 10.35 miles
by an observer at zero height of eye. Ata height of eye of nine feet the top of the mast
should break the horizon when the ship is about 13.8 miles off.

If the height of an object above the horizon, or the distance between points on
it, is known, a simple proportion can be solved to determine the distance off by use of
the cross-staff (art. 2618) or a similar device. To do this, align the two ends of the
crosspiece with top and bottom, or two ends, of the object. The ratio of the length of
the crosspiece to the length from this piece to the eye is the same as the ratio of the

Figure 2624.—Using the cross-staff to measure distance.

height (or length) of the object to its distance from the observer (fig. 2624). Thus, if
the crosspiece is 18 inches and the intercepted length of the long piece is 31 inches, the
distance to an island 1% miles wide in the line of sight is found from the proportion

ST Do 518

In this proportion the two parts of either fraction must be expressed in the same units
if results are to be obtained without a conversion factor. Thus, both 18 and 31 are
expressed in inches, and both 1.5 and 2.6 are in miles. For small or distant objects
the crosspiece may be too long. In this case replace it with a shorter one, use half or
less of it, or substitute some other device such as a rule held at arm’s length. In the
case of a height, only the visible part of the object is used if the horizon is between the
observer and the object.

662 LIFEBOAT NAVIGATION

A variation of this method can produce approximate results rather quickly. Hold
a pencil, stick, or finger vertical at arm's length. Close one eye and align the vertical
member with one end of an object such as an island. Open the closed eye and close
the other one. Estimate the distance the vertical member appears to move against
the background. The distance of the background object is ten times the amount of
apparent movement, in the same units. The actual ratio varies somewhat among
individuals and can be determined by comparing the length of the outstretched arm with
the distance between eyes—or by practice on objects of known size at known distances.
For vertical objects hold the extended member horizontal and bend the head until it,
also, is horizontal.

2625. Beaching the boat.—The beaching of a lifeboat may be one of the most
dangerous parts of the entire experience. The approach to an island should be made
on the lee side, if possible, and every effort should be made to attract the attention of
any inhabitants so that advice on the best place to land, and perhaps assistance, might
be obtained. If no help is available, sail parallel to the coast to study the terrain and
determine the safest place to beach the boat. A lagoon or other sheltered area may be
available. It may be necessary to delay the landing overnight to make a complete study
of the terrain and to beach the boat by daylight. Surf appears less rough from the sea
than from land. High spray indicates.a rough surf.

If a steering oar is available, the rudder should be unshipped before the boat is
brought in, as the steering oar will provide better control in the surf zone. The sea
anchor should be used to lessen the possibility of broaching and capsizing. Storm oil
should be used, if available, to reduce the roughness of the surf. It is possible that the
course can be altered somewhat while heading in to the beach, to take advantage of a
better opening, but care should be taken to avoid broaching. Additional information
on handling a boat in a surf can be found in nearly any book on seamanship.

2626. Ashore.—Once the boat has been safely beached, the problem remains to
lead the survivors to civilization. Perhaps the land will be heavily populated and the
boat met by local people, or the way to safety may be indicated by a road or trail.
But the boat may be beached at a deserted place where there are no signs of life.

Chapter XXVII, "Land Navigation," deals with this problem in detail, but
remember that the choice of an initial course is almost as important in this case as it
is at sea. Generally, it is good practice to follow the coast, but if the shore is obviously
unsuitable for boat activity, a port is not likely to be nearby. The jungle should be
avoided for travel, but it may be a plentiful source of food if nonpoisonous plants can
be recognized. Often a stream can be followed to an inhabited place, for some source
of water is essential to the maintenance oflife. In an arid region, distant vegetation
may be an indication of habitation.

Many of the methods used to determine position at sea may also be used ashore,
and usually with greater accuracy due to the absence of motion. A distinctive method
of determining the meridian while ashore is by a variation of the equal altitude method.
Place a stick or rod upright on a level area, using a plumb bob to establish the per-
pendicularity of the stick. About an hour before noon mark the point where the tip
of the stick's shadow falls, and draw a circle through this point, with the base of the
stick as its center. Mark the point where the tip again falls exactly on the perimeter
of the circle. Midway between the two points lies the meridian of the observer.

Problems

2613a. The compass azimuth of the sun is 126? at rising and 252? at setting.
Required.—Compass error.

Answer.—CE 9? W.

qe
S

3

E

LIFEBOAT NAVIGATION 663

2613b. A life preserver is thrown overboard from a lifeboat and the boat headed
away on course 355%. Ata distance of half a mile the boat turns and heads back for
the life preserver. The return course is 169°. The variation is 5° W.

Required.—(1) True course back to the life preserver.

(2) Deviation on this heading.

Answers.—(1) TC 167°, (2) D 3°E.

2615. The two knots in the log line of an improvised chip log of a lifeboat
are 16% feet apart. The elapsed time between passage of the knots through the hands
of the observer is four seconds.

Required.—Speed of the lifeboat.

Answer.—S 2.5 kn.

2616. A lifeboat travels 18 miles on course 110°, from lat. 35°15’ S, long. 82°31’ W.

Required.—Latitude and longitude of the point of arrival.

Answer.—L 35°20’S, 82°11’ W.

2617a. The date is November 15.

Required.—The approximate declination of the sun, without reference to an
almanac.

Answer.—Dec. 18°88.

2617b. The latitude of a lifeboat is 22°47’N. A star is observed on the meridian,
bearing north. The observed altitude is 66°50’.

Required.—Declination of the star.

Answer.—Dec. 45°57’ N.

2617c. The GMT is 1000, October 15.

Required.—Approximate GHA T, without reference to an almanac.

Answer.—GHA Y 172°.

2624. Approaching land, the navigator wishes to determine his distance from a
lighthouse situated on the coast. He holds a rule at arm's length and finds that %
inch of the rule appears the same height as the top of the lighthouse above water. He
estimates the distance from his eye to the rule as 24 inches, and the height of the top
of the lighthouse as 150 feet above water.

Required.—Distance to the lighthouse.

Answer.—D 0.9 mi.

CHAPTER XXVII
LAND NAVIGATION

2701. Introduction.—Land navigation is the process of directing movement across
land or ice, from one point to another. When travel is along a well-marked system
of highways, trails, railways, etc., a good map and distance-measuring device are all
that are needed. But when travel is across unmarked areas, navigation may be more
difficult. When the track leads across an open expanse of desert, tundra, or ice, the
methods of navigation most nearly approach those used at sea or in the air.

The equipment used and the procedure followed should be suited to the circum-
stances. A high degree of common sense and adaptability is needed. It would be a
waste of effort to measure accurately every change of course if one were following a
stream whose general direction is known, but across an area without features, each
change of course might be of great importance. Sometimes a considerable amount of

ingenuity is needed to adapt available equipment or to improvise a suitable piece of |

equipment to meet a particular need. On land, as at sea or in the air, the navigator
should use all available means to further his end. Even odors can be utilized to
advantage in some instances. In any case, & preliminary estimate of the situation
and advance planning are important, as is constant vigilance en route.

Basically, navigation on land combines the same elements as navigation at sea.
Dead reckoning, piloting, electronic navigation, and celestial navigation all have their
use. In general, the equipment should be simple, reliable, rugged, and capable of
withstanding exposure to the weather. The mounting of equipment and the facilities
for plotting may leave much to be desired. Plotting in a vehicle crossing rough terrain
may be impossible while underway.

No trip across unfamiliar or desolate terrain should be attempted without provision
for adequate navigation, whether travel is by wheeled vehicle, tank, dog sledge, or
afoot. An adequately trained individual should have primary responsibility for navi-
gation, and should be provided with the necessary navigational aids to suit the cir-
cumstances. Assistants or alternates should be provided when appropriate, as when
a casualty is a reasonable possibility. During the trip the navigator should be given
opportunity to perform his assignment. Sometimes this may involve stops that would
not otherwise be scheduled.

2702. Charts The most useful charts for land navigation are topographic—those
showing elevations and various features of the topography. With a large-scale map
showing great detail, both the selecting and following of a route are relatively simple,
if there is a sufficient number of identifiable landmarks. Over flat, open country the
map is little more than a plotting sheet. The projection is not important, as long
as it 1s conformal (art. 302) so that angles and small shapes are correctly represented.
Since long, straight courses are rare, the form of representation of a great circle is
seldom important.

2703. Dead reckoning on land, as on the sea or in the air, consists of determining
position by means of the direction and distance traveled since leaving & known position.
A careful log should be kept. If the track is across an unsurveyed area, and if there
is a possibility of future passages over the same area, descriptions of the various land-
marks encountered should be included in the log.

Plotting may or may not be desirable. Along a well-marked route, the track can
be plotted in advance, and positions along the track can be marked as determined,
either by dead reckoning or otherwise. Since it is usually difficult to plot accurately

664

sw

LAND NAVIGATION 665

while riding or walking, the usual procedure is to keep a log and stop at intervals to
bring the plot up-to-date. Each item of the log should be recorded as it occurs, leaving
nothing to memory.

Over rugged terrain it is seldom practical to proceed directly toward the objective,
and the track selected is one which avoids the most difficult obstacles. Under these
conditions, the directions and distances used are averages. With practice, one can
become adept at estimating the course and distance made good along a track having
many changes of direction. When traversing an unfamiliar or poorly mapped area,
one may find it necessary to select the route as he proceeds, nearly always attempting
to work closer to the destination, but frequently departing from the direct path to
take advantage of features of the terrain.

Several types of mechanical dead reckoning equipment have been devised. One
type, known as a vehicle direction and position indicator, is designed for vehicle
installation and operates from the vehicle electrical system. With inputs from a gyro
compass and the odometer drive, it automatically computes and continuously displays
the vehicle position in map coordinates. It also computes and displays the distance
and direction to a preselected destination. It is designed for the addition of a map
plotter which can plot the course followed.

In any form of dead reckoning, it is well to keep in mind that if a heavy cross
wind is blowing, a certain amount of leeway can occur.

2704. Direction.—Over flat, open country, a steady course is relatively easy to
follow. In rugged or wooded country, many variations are needed. Under these
circumstances the direction made good is more important than individual directions of
motion. The determination of direction made good can often be accomplished by
measuring the bearing of a distant feature such as a mountain peak, prominent tree or
rock, a bend in a river or valley, etc., toward which one is steering. If the route follows
a river, mountain ridge, etc., the
general trend of the feature can
usually be determined. The fea-
tures which make necessary fre-
quent changes of course can them-
selves sometimes be used for estab-
lishing average directions. Celes-
tial bodies, too, can be used as a
steering guide if their changing
azimuth is considered. The sun
and moon are invaluable aids.
Polaris and bodies nearly east or
west are particularly useful be-
cause of their relatively slow
change of azimuth. Even a
steady wind, sastrugi (windrows
on snow), or clouds can be used,
if one is careful to interpret them
properly.

The type of compass used varies
with the circumstances. Mag- =
netic, gyro, and sun compasses Ficure 2704a.—Pocket compass.
are all used by land navigators.

666 LAND NAVIGATION

A magnetic compass used in land navigation is subject to the same errors as one
used at sea or in the air. Seldom is a vehicle an ideal location for a COMPASS. The
deviating forces are large, and in some cases erratic. If a compass designed for the
vehicle is not available, a boat compass might be used, but an aircraft-type compass may
be more suitable. If the vehicle is a dog sledge, the compass might best be lashed to a
convenient part. In a tank, truck, or jeep a permanent installation may be made.
Frequent changes of compass from one vehicle to another should be avoided, but where
this is necessary, some type of bracket or box should be provided to permit rapid
installation and alignment.

Careful magnetic adjustment (compensation) is essential if accurate results are
to be obtained. Usually, only permanent magnets are used, and in some compasses,

PIPE IDA

notably those of the aircraft type, these are permanently mounted in the compass —

case, being controlled by a screw driver. If a compass is to be moved from vehicle
to vehicle, the adjustment might be made in the vehicle itself. This is best done by
attaching magnets to the box in which the compass is placed. With any type o
adjustment, corrections may be needed if the magnetic latitude changes considerably

FIGURE 2704b.— Wrist compass.

Some experimentation may be necessary to establish the best location for the
compass. In general, a position should be found as remote as convenient from the motor
and electric wiring. A vertically graduated aircraft-type compass might be mounted
near the top of the windshield with satisfactory results. The dashboard is probably
the worst location in most instances.

Magnetic adjustment should be made with the motor running and with all magnetic
equipment in its regular place. The effect on the compass of various electrical equip-
ment, such as lights, windshield wiper, etc., should be noted. If needed, a deviation
table should be made up, separate tables being made for as many conditions as necessary.
In the determination of deviation, the vehicle can be pointed toward identifiable distant
objects, or a hand-held compass used at a sufficient distance from the vehicle to permit
accurate determination of direction and to preclude magnetic influence of the vehicle.
A compass rose located on the surface of an aerodrome can be used satisfactorily, if
available.

A portable compass has many uses, and if the party is proceeding on foot, it is the
only type suitable. It may be a hand-held compass weighing several pounds, or, more
often, a small pocket or wrist compass weighing but a few ounces. A pocket compass
is shown in figure 2704a, and a wrist compass in figure 2704b. In figure 2704a note the

LAND NAVIGATION | 667

lubber's line and the sighting vanes for measuring bearings. No provision is made for
adjusting a portable magnetic compass. When such an instrument is used, readings
should be made a sufficient distance from a vehicle or other magnetic material and
power lines to avoid any deviating influence. Magnetic material such as knives, keys
etc., should be removed from the observer's person during observation, unless it js
determined that they have no effect on the compass in the position used. Magnetic
material in the earth can cause deviation. The presence of such material is usually
indicated by erratic operation of the compass when moved a short distance.

A vehicle gyro compass has been developed and is used where the need warrants.
It is particularly useful in regions where the magnetic compass is not suitable, as near
the magnetic poles and in areas of extensive deposits of magnetic material. It is also

used in vehicles where satisfactory magnetic compass installations are difficult or im-
possible, as in some tanks.

SHADOW SCREEN

GNOMON RODS CLOCK DIAL N. HEMISPHERE

TIME CORRECTION
VERNIER & HAND

DECLINATION SCALE

LATITUDE SCALE LATITUDE MICROMETER

Á KNOB
WINDING KEY— — fl

: e : EE um, LATITUDE MICROMETER

E = H G M SCALE

CIRCULAR LEVEL
BUBBLE

PROTRACTOR
SCALE

24-HOUR MEAN TIME
CLOCK

SIGHTING DEVICE

FIGURE 2704c.—Sun compass.

A sun compass, figure 2704c, is a mechanical device for determining true directions
by means of celestial bodies, principally the sun. It is free from magnetic disturbances
and gyro errors, and needs no source of power. However, an almanac or other source
of celestial coordinates, accurate time, and a knowledge of the approximate position of
the observer are needed, and use of the instrument is limited to periods when a celestial
body is visible. This last limitation affects the choice of a mounting position for the
instrument.

Like the astro compass used in aircraft (art. 2515), the sun compass is not a compass
in the usual sense of seeking a reference direction. Both instruments consist of sighting

668 LAND NAVIGATION

devices which are oriented with respect to the axis and equator of the earth, and the
horizontal. When the device is so oriented and the sighting assembly or shadow is `
properly aligned with the celestial body, true directions are indicated on a circular scale.
Generally, the device is not used as a continuous indication of direction, but as a
means of checking direction at intervals. Each time an observation is made the
setting of the instrument is changed to agree with the coordinates of the celestial body
and observer at the time and place of observation. If the device is used for steering, `
it usually need not be reset oftener than every ten to 15 minutes.

Several emergency methods of establishing the approximate direction of north
are available. These are discussed in chapter XXVI. The method of double altitudes
is particularly applicable on land, where a plumb bob can be improvised and the length
of the shadow measured. At the time the first altitude is observed, perhaps an hour
before noon, an arc of a circle can be marked on the ground, with the center at the foot
of the plumb line, and of radius equal to the length of the shadow. The position of
the shadow tip on the circle is marked. The second altitude occurs when the end of
the shadow is again on the arc of the circle. From the plumb line, north (or south if the `
sun is north of the observer) is midway between the two equal-length shadows, if the
ground is level.

2705. Distance.—In land navigation, distance is usually determined directly,
rather than by means of speed and time. Speed may be used if constant enough, but
this is rarely the case.

For a vehicle with wheels, the obvious method is by odometer, the distance-meas-
uring device associated with a speedometer. For accurate results such a device should
be carefully calibrated. Size of tires, amount of tread left on tires, pressure, loading,
speed of the vehicle, and nature of the surface over which the vehicle travels all affect
the reading. However, except in extreme conditions, an average calibration should
produce good results. If the odometer is attached to the drive shaft, a certain amount
of slippage occurs, but allowance for this can be made in the calibration. Road slippage,
as when traveling on a slippery surface or one of loose material, results in too great a
reading. If the terrain is hilly, or if frequent minor changes in track are needed to
avoid obstacles, the distance indicated by odometer is greater than that shown on
the chart.

When one is traveling by sledge over snow or ice, a bicycle wheel can be attached
and a metering device connected to it. Most accurate results can be obtained if the
tire is used in a deflated condition, as it will then resist the tendency to increase in
diameter by accumulation of snow.

When traveling on foot, one can use a pedometer, a small, watch-size instrument,
usually attached to the belt, that records the number of steps taken. If this instrument
is calibrated in distance, it should be adjusted to the length of step of the wearer. If
such a device is not available, the number of steps or paces can be counted. If this is
done, it is well to have some method of preventing loss of the count. This might be done
by means of a counting device that registers each time a plunger is depressed. This
may be done at each pace (two steps), or at each multiple such as ten or 100 paces. If
no counting device is available, or if one of limited range is used, a small stone or other
object transferred from one pocket to another at intervals, as each 1,000 paces, may
prevent loss of count. With any method of counting steps or paces it is well to consider
the nature of the terrain, and other factors affecting the length of the pace. Over soft
ground, in high grass or weeds, and along inclined surfaces the length of the pace differs
from that on firm, level ground, generally becoming shorter. It may also shorten as

LAND NAVIGATION 669

the walker tires, and its effective length is reduced as he makes short detours to avoid
obstacles. A strong wind may either shorten or lengthen the pace. Variations in the
length of the pace can be handled by calibration over an area representative of the
conditions encountered, or by dropping (or adding) one pace out of a certain number,
as determined by measurement or estimate.

2706. Piloting.—In land navigation piloting is generally quite simple, consisting
merely of the recognition of landmarks, and notation of the time and distance at which
they are passed. It is somewhat similar to the passage of buoys as one proceeds along
a channel. In open country with distant mountains, bearings of identifiable features
can be plotted and ranges can be observed when two features are in line.

2707. Electronic navigation is seldom available on land, but should be used if one
has access to it. The most common electronic aid used is some form of radio direction
finder (directional characteristics of the loop antenna of a portable radio may be
utilized), usually used in connection with a transmitter at the destination. In this case
the direction finder is used as a homing device. ` If signals from other radio transmitters
at known locations can be received, position can be determined by plotting two or more
bearings. On land, radio reception is weak or nonexistent in certain “blind spots,”
and the accuracy of readings taken may be affected if the receiver is near man-made or
natural obstacles. Power or telephone lines, fences, railroad tracks, buildings, or cliffs
are particularly to be avoided if accurate bearings are required. Atmospheric and
magnetic conditions also affect radio transmission.

2708. Celestial navigation.—In areas with an abundance of landmarks, or where
an adequate method of homing is available, celestial navigation is not generally used,
except, possibly, in relation to a sun compass (art. 2704). However, in open country
without identifiable or stable features, as on the desert or in some parts of polar regions,
celestial navigation may provide the only means, other than dead reckoning, of deter-
mining position.

A marine sextant is not suitable with the type of horizon generally encountered
on land. However, if an artificial horizon (art. 1512) is available or can be improvised,
the instrument can provide satisfactory results. An aircraft-type sextant with a built-
in artificial horizon, such as a bubble (art. 1513), may be suitable. If greater precision
is desired, a surveying instrument such as a theodolite (art. 4004) or astrolabe (art.
4002) can be used. For any of these instruments, accurate results can be expected only
by stopping and making the observations from a stable position. Accurate timing of
the observation is essential unless the observation is of a meridian altitude or Polaris, or
unless the observer is near one of the geographic poles.

Sight reduction can be accomplished by any suitable method, several of which are
described in chapters XX and XXI.

When one is operating in an area where celestial navigation is needed, it is good
practice to obtain fixes twice daily, or oftener, if available. Celestial navigation may
also be useful when the continuity of dead reckoning has been broken and identifiable
landmarks are not available, as during a battle in time of war.

CHAPTER XXVIII
AIR NAVIGATION

2801. Introduction.—Air navigation is the navigation of all types of aircraft, -
including propeller-driven airplanes, jet airplanes, helicopters, dirigibles, blimps, bal- Å
loons, and airborne guided missiles. The term aircraft includes any craft designed for |
transportation through the air, except (1) safety contrivances such as a parachute
and (2) spacecraft designed for operation outside the earth's atmosphere.

The elements of air navigation are the same as those of marine and land navigation,
but with some differences in methods, practices, and emphasis. "These differences
result primarily from unique conditions encountered in air navigation, as follows:

1. Need for continued motion. A ship or land vehicle can stop, if necessary, and
resolve any uncertainty of position, awaiting more favorable conditions if necessary.
Except to a limited extent, most aircraft must keep going.

2. Limited endurance. Most aircraft can remain aloft for a relatively short time,
the period usually being a matter of hours.

3. Greater speed. The speed of propeller-driven aircraft is about 20 times that of
ships. Jet aircraft are even faster. The speed of lighter-than-air craft and helicopters
is about five to ten times that of ships. Quicker navigation methods are needed, even
if some accuracy is sacrificed.

4. Three-dimensional navigation. In air navigation the third dimension is of
considerably greater importance than in marine (even underwater) and Jand navigation.

5. Effect of weather. Except under extreme conditions, the weather element of
greatest concern to the marine and land navigator is the visibility. In air navigation
the visibility has a vital effect upon the ability to land and take-off, as well as the
availability of landmarks. In addition, wind has a more direct effect upon the position
of aircraft than upon that of ships or land vehicles. Changes of atmospheric pressure
and temperature affect the height measurement of aircraft using barometric altimeters.

The importance of weather is reflected in the designations of different flight con-
ditions, as follows:

Contact flight, when the surface of the earth is visible.

Visual flight, when the aircraft is more than a prescribed minimum distance
above, below, or laterally from clouds.

Instrument flight, when the conditions of contact and visual navigation are not met.

A closed aerodrome is one at which the visibility (horizontal or vertical) is below
certain prescribed minimums, rendering ordinary take-offs and landings unsafe.

Because of the conditions mentioned above, air navigation is closely regulated.
In the United States, regulations are prescribed by the Civil Aeronautics Board (CAB)
and the Federal Aviation Agency (FAA). Operating rules for military aircraft may
differ from those governing commercial and private aircraft.

2802. Charts and publications.—Aeronautical charts, like nautical charts, show
latitude and longitude scales, parallels, meridians, and aids to navigation. Unlike
their marine counterparts, however, aeronautical charts do not show soundings.
Contours and elevations are given more emphasis. Airways (art. 2805), control zones,
airports, and radio aids are given considerable prominence.

Except for local, approach, and. flight (strip) charts, many aeronautical charts are
arranged in coordinated series with no (or uniform) overlapping between charts. In
many cases this permits joining of adjacent charts to form a single large one (which

670

(THIS CHART SHOULD NOT BE USED FOR

NAVIGATIONAL PURPOSES.)

ELEVATIONS IN El

ANGER @(D-233)

Mill

Z A
PONY AREA

(6-243
á "n

Q

TE
CHEHALIS £A
Jryadr 7 4 — H 50 MÁ
A

Y ec No

Castle Rock
di
i

S

3 vi

10 120 130

140

A n
i R Towers and cab
XN

N
"n

qu N Sim,
V

€

V
(A

bs A

V SAND POINT RADIO
212 NE ES

E.
=

RANGER CRE!
Fairfax Y. E di

K

PACKWOOD
1053—+ 20

"ey

LĒTO! n
OLEDO RADIO
239 100.73 +

Spirit Lake
N = gift Lake

1
MOUNT i Cr

SAINTAHELENS: `
SETS X

o

ay

© Ap NN

"ei d N
77 Newhalem |
|

g)

ú
6954 —
PD

dk

TIETON

AC `
E .
A 2980-2!
Teton ,
// Reserualr.

2 ^ PEAK:
jessot
S z

ARE WENATCHEE

“EAST STEVENS-PASS QNIN

2170-21

M RW
ZW FELEENSBURE PT
875 EEN (=: M

ire

L——

ET

Ki

i

280
[227 ps ==:=]

keent A
Li COLYIULE =
SE AC WER =H 24
g AR

} ariklin D “>
Roosevelt, ake )
— y 3

SU IM
0
Gt :

f entry

dur

18 9 4 7L
a 3 £ d
WILBUR Ñ s
2175--30 VENPORT
| Vá 248 Sanoit
xg venpQ
Y

m Lio >
d 18 | i
£g) coute OU. en E». = m
b LAOS ==, À *
l DRAPER BROS
rok) : Qo mt. agngron
4 (ria) = 7 f d
Á 5 10 =s si =
A eK M
S i | SPOKANE, FA

OS

pa S
y
25

JANGER AREA
(D-245).

Z 2
P 9 Z7
GEA EE

EE
= 1438-4507
ms.
t
/ i
A

> PA c

: ‘ : NC O Marone
VISTA ð ¡e (RO |
Hoen, SIE 5 N ` ; : P cs ae ( AS “6379 d

à i Ë AR i X
| TEE». f da! a
å RT alla alla, A m Ronde
— «c 4 =

o db vet

VS 4
yy RANCH

FIGURE 2802.— Part of a typical aeronautical chart.

AIR NAVIGATION 671

may be wall mounted), or a strip chart for an individual flight. Because of the wider
use of radio aids and great-circle “sailing” in air navigation, the Mercator projection
is less commonly used in the air than aboard ship. Many aeronautical charts are on
the Lambert conformal projection (art. 314). The Mercator projection may be used near
the equator. Several projections are used in polar regions (arts. 321, 2508). Because
of the greater speed of aircraft, smaller scales are used for en route navigation. For
high-speed, high-altitude aircraft, charts are of even smaller scale, and show less detail.
Part of a typical aeronautical chart is shown in figure 2802.

In the United States, aeronautical charts are published chiefly by the U.S. Air
Force Aeronautical Chart and Information Center, St. Louis, Mo.; U.S. Coast and
Geodetic Survey, Department of Commerce, Washington, D.C., and the U.S. N avy
Hydrographic Office, Washington, D.C., Each of these three agencies publishes a
catalog of its products. The Federal Aviation Agency, Washington, D.C., publishes
regulatory material and other information.

Various publications are of assistance to the air navigator. Among these are the
following:

. The Airman's Information Manual (AIM), published by the FAA, provides
information necessary for the planning and conduct of civil flights in the National
Airspace System. The manual is divided into six sections each composed of a specific
category of information consistent with the operational needs of aviation.

The Alaska Airman’s Guide and Chart Supplement and the Pacific Airman’s
Guide and Chart Supplement provide civilian pilots with data required to supplement
the navigational information on aeronautical charts in the Alaska and Pacific Areas.

The International Flight Information Manual, published by the FAA, is designed
as a preflight and planning guide for use by U.S. non-scheduled operators, business,
and private aviators contemplating flights outside of the United States.

Flight Information Publications (FLIP), published by the Department of Defense,
contain textual and graphical information for military pilots. The series consists of
publications for (1) flight planning, (2) enroute operations, and (3) terminal opera-
tions. Each publication may contain charts, tables, and text material.

Notice to Aviators, published every two weeks by the U. S. Navy Hydrographic
Office, is the aviator’s counterpart of Notice to Mariners (art. 425).

Notice to Airmen (NOTAM) contains urgent information requiring immediate
dissemination. These notices are sent by teletype to airports throughout the United
States.

Federal Aviation Regulations (FAR), published by the FAA.

A comprehensive book giving complete text and reference material on the prin-
ciples and practices of air navigation is published by the U.S. Navy Hydrographic
Office under the title Air Navigation (H.O. Pub. No. 216). A book, in three volumes,
giving somewhat similar information on air navigation as practiced in the United
States Air Force is published by the USAF under the title Air Navigation (Air Force
Manual 51-40).

2803. Dead reckoning in the air, as aboard ship, comprises the elements of direction
and distance. Several terms related to direction are used:

Heading, the horizontal direction in which an aircraft is pointed. This may be a
momentary direction, an average, or the intended direction.

Heading line, a line extending in the direction of a heading.

Course, the intended horizontal direction of travel.

Course line, a line extending in the direction of a course.

Course made good, the direction from one established position to a later one.

672 ` AIR NAVIGATION

Track, the horizontal component of the path followed or intended to be followed,
and sometimes the direction of this path.

Drift angle, the angle between the heading line and the track, labeled “right” or
“left” depending upon the direction of drift.

Drift correction angle, the angle between the heading line and the course line, or the
anticipated drift angle.

As in marine navigation, the various directions can be stated relative to any of
several reference directions, true, magnetic, compass, and grid being the usual ones.
True directions are usually used for plotting, but magnetic directions are more widely
used than in marine navigation because some form of magnetic compass is commonly
used for measuring direction. With the development of better directional gyro com-
passes, grid directions are coming into wider use. |

The effect of wind on aircraft is similar to that of current on ships. There is nearly
always some wind, which varies from place to place and from time to time. The air
navigator is alert to indications of changes, and has frequent occasion to solve the |
wird triangle, solutions similar to those for current (art. 807). The usual solution
determines the heading to fly to make good the selected course. Because of the fre-
quent, and often urgent, need for solution of the wind triangle, aviators customarily
use some form of mechanical computer. If direction and speed of the wind are known,
both heading (or track) and ground speed can be determined. If only drift angle
is known, a quantity which usually can be measured in flight, the approximate head-
ing (or track) can be determined without plot, but not the ground speed. With
observed drift on two or more headings of considerable difference in direction, one can
solve for wind speed and direction. Such observations might be made before and after
a turn.

An air plot of heading and air speed (rate of motion relative to the air) provides
a series of no-wind positions, sometimes called air positions. These are the successive
positions an aircraft would occupy if there were no wind. A dead reckoning plot of
course and ground speed (rate of motion relative to the surface of the earth) provides
a series of dead reckoning positions.

Most aircraft compasses are magnetic, but those more commonly used are remote
indicating. The active element is placed at a location relatively free from magnetic
disturbances from the aircraft, such as in a wing or the tail, and provided with indicators
at various locations, as needed. Because of the large errors introduced when a mag-
netic compass tilts, the better aircraft compasses are gyro stabilized. The most widely
used aircraft compass is known as the Gyro Flux Gate compass. In general, aircraft
magnetic compasses are compensated (adjusted) by means of flexible cams mounted
within the case and controlled by a screw driver. No adjustment is made for vertical
soft iron, for quadrantal deviation, or for heeling. Swinging for residual deviation may
be done on the ground, by means of a hand-held compass or a compass rose located on
the hard surface of an aerodrome; or in the air by means of celestial bodies or straight
roads, power lines, etc. The compass correction card (deviation table) is usually
made up on the basis of the compass direction to steer for a desired magnetic heading,
the value of deviation not being given.

The north-seeking gyro compass commonly used aboard ship has not been practical
in the air because of its weight and the fact that it would not work satisfactorily at
modern aircraft speeds, which are comparable to or greater than the rotational speed
of the earth. However, efforts have been made to overcome these obstacles, and it is
possible that a suitable north-seeking gyro compass will be developed for use in aircraft.
The directional gyro compass is used widely. Such an instrument is essentially a
gyroscope pointed in a desired direction which it maintains over a period of several
minutes. This instrument was devised primarily to provide directional guidance

AIR NAVIGATION 673

during a turn of the aircraft, when the older magnetic compasses are erratic. More
recent directional gyros require less frequent resetting, provide greater accuracy, and
compensate for rotation of the earth (the gyroscope tends to maintain the same direction
in space), and they may be monitored by a remote-indicating magnetic compass. With
the best modern directional gyros an aircraft is able to follow a great circle with about
the same accuracy that it can follow a rhumb line (using a magnetic compass). A
directional gyro is checked from time to time by means of a magnetic compass or an
astro compass (art. 2515).

Air speed is usually determined by measurement of the difference between static
air pressure and the pressure exerted by the apparent wind, which, in the air, is always
from dead ahead and equal to the speed of the aircraft through the air. This pressure
difference is measured by a device called a “Pitot tube," and transmitted by tubes to the
air speed indicator. Corrections are applied for nonstandard air temperature at the
pressure altitude, compressibility, and heating effect. Higher speeds are sometimes
stated in terms of a percentage of the speed of sound at the aircraft. On this basis the
speed is called the Mach (mdk) number. A Mach number of one is the speed of sound,
which varies with the density of the air; Mach number 0.9 is 90 percent of the speed of
sound, etc. A Mach meter is an instrument which measures Mach number directly.

Height is usually measured by means of a barometric altimeter, which is essentially
an aneroid barometer graduated in feet above sea level. If the atmospheric pressure is
not standard, the altimeter will not read the correct value at sea level unless adjusted
to the existing pressure. A knob is provided for this purpose. If the decrease of pres-
sure with height is not standard, additional error is introduced. Altitude separation of
aircraft along airways is based upon indications of an accurate barometric altimeter set
to standard conditions, so that all instruments at the same height should have the same
reading. For landing and take-off the instrument is usually adjusted so that it will
read the correct altitude when the aircraft is on the surface. For landings, the necessary
information is supplied by radio from the control tower. An instrument which measures
height above the surface (absolute altitude) is called an absolute altimeter. The usual
absolute altimeter is a form of radar beamed vertically downward. It measures height
in a manner similar to the measurement of water depth by an echo sounder (art. 619).

As in marine and land navigation, dead reckoning is the basis of navigation in the
air, all other forms serving to correct positions so determined. However, because of
the nature of air navigation and the aids available, dead reckoning in the air, particularly
along airways, is often a mental process, or one in which the dead reckoning for the entire
flight is plotted in advance, with DR position at frequent intervals, as every ten minutes,
being marked on the plot. The problem is then one of maintaining the schedule or
keeping a record of deviation from it.

Various automatic dead reckoning systems show promise of providing accurate
means for determining position over long stretches of water or over terrain lacking in
distinctive features as aids to navigation. Such systems are based upon accurate
means of measuring direction and distance. These, in turn, require accurate directional
and horizontal references. Examples of such systems are those based upon measure-
ment of accelerations (inertial systems) and those based upon measurement of the
Doppler shift (change of frequency) of echoes from radio or radar beams transmitted
obliquely from the aircraft to the ground (Doppler systems). Additional information
on this subject is given in article 809. Systems under development combine one or
both of these principles with some other principle, such as automatic celestial navigation.

2804. Piloting, often called pilotage in air navigation, is similar in principle to that
performed aboard ship. In practice it more nearly resembles land navigation. Lines
of position from observed bearings or distances are rarely plotted by air navigators.

674 AIR NAVIGATION

The more common practice is to compare observed features with the chart, keeping a
record of one’s progress as he proceeds. If this is not a continuous process, combined
with mental or plotted dead reckoning, one can soon become lost, particularly in an
area where many features are similar in appearance. One can learn to watch for distinc-
tive features. Two towns may look very much alike, but the pattern of roads, rail-
roads, and streams in the vicinity may be quite different. A race track, mine, or other
distinctive feature may help one distinguish between otherwise similar areas. However,
it is essential that the air navigator not be hasty in identification, for mistakes can easily
be made. A position established by identifying a feature directly below the aircraft
is called a pinpoint. FAME

Over well-traveled areas, extensive use is made of various radio aids to navigation.
These are discussed in article 2805. So complete is coverage across the United States
that an experienced aviator with suitable publications can travel from coast to coast
without an aeronautical chart, whether or not the surface is visible. Over such areas,
navigational duties are customarily performed by the pilot and copilot, a separate
navigator being carried only on flights requiring his services, as on long over-water
flights or in polar regions.

2805. Electronic navigation is more widely used in the air than on land or sea, for
several reasons. Because of the greater height of aircraft, there is less obstruction of
radio signals, and higher frequency “line of sight" systems are available over greater
ranges. Over land, aids can be placed at suitable intervals to provide essentially con-
tinuous, short-range guidance over long distances. The difficulty of observing bearings,
celestial bodies, etc., from aircraft renders electronic methods more attractive. De-
creased accuracy of other methods when used in the air enhance the value of electronics.
The greater speed and adaptability of electronic methods are of higher value aboard a
fast-moving aircraft. The electronic navigational equipment carried in aircraft is
compact and especially adapted to use in the air. Airborne computers are being
developed for use with advanced navigation systems.

The automatic radio direction finder commonly used in the air provides a continu-
ous indication of direction toward the transmitter by means of a needle pivoted at the
center of a compass rose. The navigator has only to tune to the correct frequency and
watch the needle. Its steadiness is some indication of the reliability of. the reading.

The first nationwide system of electronic navigational aids was composed of several
hundred low frequency ‘four-course ranges." At each range station the international
Morse code letter for N (== e) is transmitted in two opposite sectors called “quadrants.”
In the other two “quadrants” the letter A (+ =m) is transmitted. These signals are so
related that along the boundaries between sectors, where the two signals are of equal
strength, the dots and dashes interlock to form a continuous monotone. It is possible
to control the direction of these monotones or “beams” so that they indicate desirable
directions of travel. Along these “beams” a series of airways are established, somewhat
resembling highways. The magnetic directions of these beams are indicated on the
chart, as shown in figure 2802. To use these ranges the navigator has only to follow
one leg to the station and another leg out until he picks up the next beam.

These ranges are being supplemented by a series of very high frequency vortac
stations. Each vortac station provides two methods of establishing direction,
and means for determining distance. The two direction systems are tacan (tactical
air navigation) for military aircraft, and omnirange (VOR) for commercial and private
Se The suitably equipped aircraft is thus provided an infinite number of

radials” (in practice 360 at 1° intervals around each station) by means of which an
aviator can receive guidance along any radial line from the station. With direction
and distance available at all times, a continuous fix is provided, whether or not the

»

AIR NAVIGATION 675

aircraft is following a radial. If the aviator selects the radial he wishes to follow, a
dial indicates when he is off the radial, and which direction he should turn to get back
on it. A “To-FROM” indicator tells the aviator whether the selected radial is to be
measured toward or away from the station. If the aircraft is equipped with a course
computer, he can fly toward or away from an offset way point with the same indications
as though it were the range station. Thus, multilane airways are available.

Longer range aids used by aircraft, particularly over ocean areas, include loran
(art. 1302), Decca (art. 1309), and consol (art. 1312). A number of other systems
have been suggested, and the future will undoubtedly see an increase in the use of
electronics in air navigation, particularly in dead reckoning and celestial systems.

Airborne radar is a valuable navigational aid. With practice one can learn to
identify the echoes from different features of the terrain, and often to locate his position
by piloting methods when the surface is obscured by an undercast.

Various beacons are designed primarily for use by aviators. A racon is a radar
beacon which returns a coded signal when triggered by a signal from the aircraft’s
radar, thus providing identification as well as bearing and range. Fan markers trans-
mit vertical fan- or bone-shaped patterns at selected points along an airway to indicate
passage of those points. Nondirectional markers are placed at other points. Above
each station of a four-course range an inverted cone of silence occurs, where little or
no signal from the ranges is received. At some of these stations Z markers are installed
to transmit distinctive signals upward to indicate location of the stations.

2806. Celestial navigation.—In the air, celestial navigation is used in polar regions
and on long over-water flights. Observations are invariably made with some form of
artificial-horizon sextant (art. 1513), usually one having a bubble or pendulum reference.
In air navigation, positions are needed more often than on land or sea. An entire
flight across the Atlantic may be made between evening twilight and dawn. A common
practice over the oceans is to obtain fixes at intervals of one hour. Another reason
for using an artificial-horizon sextant is that the natural horizon is often obscured by
clouds or haze, while celestial bodies are clearly visible. If a periscopic sextant (fig.
1513a) is not available, observations are usually made through an astrodome.

Because of the speed of aircraft, time zones may be crossed at frequent intervals.
It is customary to keep navigational timepieces set to GMT. For celestial navigation,
a high-grade watch is carried. It may have a 24-hour dial, and in most instances it
has a sweep second hand.

Rapid sight reduction is important at aircraft speeds. In ten minutes a modern
plane may travel 100 miles. The method most commonly used is H.O. Pub. No. 249
(art. 2113), with the Air Almanac. By precomputation, a navigator can obtain a fix
within two or three minutes after the observations. Observation at a selected time is
not a problem, because the sight continues over a period, usually two minutes, during
which an averaging device is in operation. This eliminates large acceleration errors
that might arise from motions of the aircraft. Thus, ten minutes may be required for
observation of three stars at four-minute intervals between the mid times of observation.
Celestial observations in the air are inherently less accurate than good observations
with a marine sextant aboard ship. In the air an error of five to ten miles is considered
normal for favorable conditions.

As speeds increase, the need for faster observation and reduction becomes more
urgent. This has lead to development of automatic celestial navigation (art. 2124).

2807. Pressure pattern navigation.—On a long over-water flight, the great circle
is a good approximation of the shortest distance between point of departure and desti-
nation. However, it may not be the least-time route, because of unfavorable winds.
At more than one or two thousand feet above the surface of the earth, winds tend to

676 AIR NAVIGATION

blow along the isobars (except near the equator). If the pattern of isobars (the ‘‘pres-

sure pattern”) at flight altitude is known, an experienced air navigator can often select `

a route that may add miles to the flight but increase ground speed to such an extent
that time is reduced. This is one form of pressure pattern navigation.

A pressure pattern flight is customarily made at a constant pressure altitude (for
instance the 500-millibar level at a standard altitude of 18,281 feet). By means of
barometric and absolute altimeters, the navigator is able to determine any increase or
decrease in height of the constant pressure surface over a time interval. With this
information, he is able to compute the cross component of the wind, or the lateral drift.
This is of assistance in dead reckoning, and it serves as a check on predicted pressure and
wind. It is the basis for alterations that may be needed in the original plan.

2808. Flight planning.— Before take-off, a careful study is made of weather con-
ditions expected to be encountered en route and at the terminal. If a choice of route
and altitude is available, the most favorable are selected. Wind triangles for various
parts of the flight are solved, and heading and ground speed determined. From this,
the flight time and the amount of fuel needed for the flight can be computed. A suit-
able alternate aerodrome is selected for use if weather makes landing at the scheduled
destination hazardous. Fuel deemed sufficient for the flight to-the destination and then
to the alternate, plus the amount needed for warm-up and take-off, and an adequate
reserve, is taken aboard.

During the flight a close check is kept upon the actual rate of fuel consumption,
and if this exceeds the predicted rate to such an extent that there is danger of ex-
hausting the fuel supply before reaching the destination, the aircraft returns or is
diverted to another aerodrome.

An adequate flight plan, properly used, is vital to safe flight over long distances.
The plan is filed at the aerodrome of departure or other designated place, which notifies
the destination of the estimated time of arrival (ETA). During the flight, periodic
reports by radio provide information on progress and deviations from the plan. "These
serve as the basis for search and rescue operations, should they become necessary.

2809. Space navigation.—Navigation of a spacecraft through the atmosphere of
the earth and beyond left the realm of science fiction and became a reality with the
first successful launching of an artificial earth satellite in 1957. The same basic
principles that govern terrestrial navigation are involved in space navigation, but
with some differences of technique and emphasis.

Space navigation is four-dimensional, in contrast to the essentially two-dimensional
navigation on or near the surface of the earth. In addition to the obvious third dimen-
sion of space, time has increased significance. Progress toward a final point is, by itself,
inadequate. One must arrive at the point at the right instant to effect satisfactory
rendezvous with another moving object. Neither direction of motion nor speed is
directly measurable to satisfactory accuracy for navigation, and both motion and speed
are likely to be varying continually. With the tremendous speeds involved and serious
power limitations, only minor corrections to either speed or direction are likely to be
available. There is little probability of recovering from a serious mistake.

Because of the fantastic distances and the propulsion systems now considered
feasible, flight times to the nearest stars will be measured in life spans. Consequently,
meaningful space navigation in this century is likely to be limited to the solar system.
The techniques expected to be used during this period differ somewhat in each of four
phases of space flight: (1) escape, (2) in the near vicinity of a celestial body, (3) mid-
course, and (4) terminal.

During escape, whether from the surface of the earth or an orbit around it, a carefully
precalculated trajectory is followed. Tracking is performed from the earth. Acceler-

AIR NAVIGATION 677

ometers control the cutoff at the desired speed. All space missions are so carefully
planned in advance that the need for later corrections is dependent directly upon the
accuracy with which the escape phase navigation is performed.

In the vicinity of a celestial body, as in the escape phase, position is determined
with respect to the body involved. The coordinate system used is (1) distance from
the body, and (2) latitude and longitude on the sphere thus identified. This might be
determined from the celestial body, as is commonly done with artificial earth satellites
and space probes from the earth, or it might be determined from aboard the spacecraft.
Distance from the celestial body might be determined by radar or by measurement of the
apparent diameter of the body. Position on the sphere can be established by observa-

tion of the position of the body among the background of stars, thus establishing
celestial lines of position. i

During the midcourse phase of a flight to another planet, navigation is primarily a
matter of determining position and comparing it with the scheduled position at the time
of fix. Thus, dead reckoning and position fixing serve the same functions as on earth.
Position determined relative to other bodies of the solar system is a form of piloting.
Celestial navigation involves use of the background of stars. Position is identified as
distance from the sun and some form of “latitude” and “longitude'”on the sphere thus
identified. Distance from the sun can be determined directly by measurement of its
apparent diameter. Optical measurement of the angle between lines of sight to a planet
and star establishes position on a cone having its apex at the planet. Two such cones
each with its apex at the same planet intersect in two lines, and a third cone will remove
the ambiguity. Three-dimensional position can also be determined by means of cones
referred to three bodies of the solar system or by means of celestial lines of position on
two such bodies, noting their positions relative to the background of stars. A discrep-
ancy in scheduled position might be corrected by (1) returning to the original schedule
at a specific time, (2) establishing a new path to intercept the destination planet at the
original time and place, or (3) determining a new optimum path to intercept the planet.

During the terminal phase, thrust is applied to place the spacecraft in an orbit
around the destination planet or guide the craft to & soft landing. Position is deter-
mined with respect to the body being approached. It is important that the dead
reckoning be advanced far enough ahead to allow timely alteration of path, if needed,
to place the spacecraft in an appropriate position for carrying out terminal phase
maneuvers.

When continuous thrust of relatively small power becomes available, a procedure
which will greatly simplify the navigation will be to proceed first to the line connecting
the sun and destination planet and then to apply continuous thrust to stay on this line,
reaching the destination by homing techniques.

Use of some kind of physical phenomena has been suggested for either establishing
lines or surfaces of position, or measuring either speed or direction of motion. This
approach has not been promising.

The present state of the art seems adequate to develop a fully automatic system for
navigation during any space mission possible. However, a considerable amount of
engineering will be needed before a reliable system is available.

References

U.S. Department of the Air Force. Air Navigation. AFM 51-40. Washington, 1962.

U.S. Navy Hydrographic Office. Air Navigation. H.O. Pub. No. 216. Washington.
U. S. Govt. Print. Off., 1955.

Moody, Alton B., “Space Navigation." Proceedings of the IRE, Vol. 50, No. 5 (May

1962).
Weems, P. V. H. Air Navigation. 4th ed. Annapolis, Weems, 1955.

CHAPTER XXIX
NAVIGATIONAL ERRORS

2901. Introduction.—As commonly practiced, navigation is not an exact science.
A number of approximations which would be unacceptable in careful scientific work are
used by the navigator, because greater accuracy may not be consistent with the re-
quirements or time available, or because there is no alternative.

Thus, when the navigator uses his latitude graduations as a mile scale, or computes
a great-circle course and distance, he neglects the flattening of the earth at the poles,

e

a practice that is not acceptable to the geodetic surveyor. When the navigator plots -

a visual bearing, or an azimuth line for a celestial line of position, on a Mercator chart, ,

he uses a rhumb line to represent a great circle. When he plots the celestial line of
position, he substitutes a rhumb line for a small circle. When he interpolates in tables
of logarithms or in loran tables, he assumes a linear (constant-rate) change between
tabulated values. When he measures distance by radar, or depth by sonic depth finder,
he assumes that the radio- or sound-wave has constant speed under all conditions.
When he applies dip and refraction corrections to his sextant altitude, he generally
assumes standard atmospheric conditions.

These are only a few of the approximations commonly applied by a navigator.
There are so many that there is a natural tendency for some of them to cancel others.
Thus, under favorable conditions, a position at sea, determined from celestial observa-
tion by an experienced observer, should seldom be in error by more than two miles.
However, if the various small errors in a particular observation all have the same sign
(all plus or all minus), the error might be several times this amount, without any mis-
take having been made by the navigator.

Greater accuracy could be attained, but at a price. The navigator is a practical
individual. In the course of ordinary navigation, he would rather spend ten minutes
determining a position having a probable error of plus or minus two miles, than to
spend several hours learning where he was to an accuracy of a few yards. But if he
can determine a recent or present position to greater accuracy, the decrease in error is
attractive to him. The various navigational aids have been designed with this in
mind. Greater accuracy in plotting could be achieved by increasing the scale of the
chart or plotting sheet. This has been done for confined waters where a higher degree
of accuracy is needed, but a large-scale plotting sheet would be a nuisance at sea.
The hand-held marine sextant is not sufficiently accurate for use in determining an
astronomical position in a geodetic survey. But it is much more satisfactory at sea
than the surveyor's astrolabe or theodolite (arts. 4002, 4004), which require stable
platforms if their potential accuracy is to be realized.

An understanding of the kinds of errors involved in navigation, and of the ele-
end principles of probability, should be of assistance to a navigator in interpreting

1s results.

2902. Definitions.—The following definitions apply to the discussions of this
chapter:

Error is the difference between a specific value and the correct or standard value.
As here used, it does not include mistakes, but is related to lack of perfection. Thus, an

altitude determined by marine sextant is corrected for a standard amount of refraction,
678 |

NAVIGATIONAL ERRORS 679

but if the actual refraction at the time of observation varies from the standard, the
` value taken from the table is in error by the difference between standard and actual
refraction. This error will be compounded with others in the observed altitude. Simi-
larly, depth determined by echo sounder is in error, among other things, by the difference
between the actual speed of sound waves in the water and the speed used for calibration
of the instrument. It will also be in error if an echo is returned from a phantom bottom
(art. 3504) instead of from the actual bottom. This chapter is concerned primarily
with the deviation from standards. Thus, while variation of the compass is an error
when referred to true directions, the difference between the assumed variation and that
actually existing is an error with reference to magnetic direction. Corrections can be
applied for standard values of error. It is the deviation from standard, as well as
mistakes, that produce inaccurate results in navigation. Various kinds of error are
discussed in the following articles.

Mistake is a blunder, such as an incorrect reading of an instrument, the taking
of a wrong value from a table, or the plotting of a reciprocal bearing.

Standard is something established by custom, agreement, or authority as a basis

for comparison. It is customary to use nautical miles for measuring distances between
ports. By international agreement the nautical mile is defined as a certain number of
meters. By authority of various countries which are parties to the agreement, this
length is translated to the linear units adopted by that country. It is the fact of
establishment or general acceptance that determines whether a given quantity or
condition has become a standard of measure or quality. Thus, in 1960, the standard
unit of length agreed upon at the Eleventh General (International) Conference on
Weights and Measures to redefine the meter was 1,650,763.73 wavelengths of the
orange-red radiation in vacuum of krypton 86 corresponding to the unperturbed transi-
tion between the 2p, and 5d, levels. Where accepted, this established standard of
length now serves as a basis for measurement of any physical magnitude, as the length
of the meridian, rather than the reverse, which was originally proposed. Multiples
and submultiples of a standard are exact. In 1959, the U.S. adopted the exact relation-
ships of one yard as equal to 0.9144 meter and one inch as equal to 2.54 centimeters.
Hence, 39.37 U. S. inches are approximately equal to one meter. Because one foot
equals 12 inches by definition, and the international nautical mile has been defined as
1852 meters, the international nautical mile is equal to 6,076.11549 U. S. feet (approxi-
mately). The previous U. S. foot (6,076.10333 . . . feet equals one nautical mile)
has been redesignated as the U. S. survey foot. „It will still be encountered frequently
during the transitional period. The values and tables in this 1962 edition are based on
those adopted by the United States in 1959.
Frequently, a standard is so chosen that it serves as a model which approximates a
mean or average condition. However, the distinction between the standard value and
the actual value at any time should not be forgotten. Thus, a standard atmosphere
has been established in which the temperature, pressure, density, etc., are precisely
specified for each altitude. Actual conditions, however, are generally different from
those defined by the standard atmosphere. Similarly, the values for dip given in the
almanacs are considered standard by those who use them, but actual dip may be
appreciably different from that tabulated.

Accuracy is the degree of conformance with the correct value, while precision
is the degree of refinement of a value. Thus, an altitude determined by marine sextant
might be stated to the nearest 0/1, and yet be accurate only to the nearest 1’ if the
horizon is indistinct. Accuracy and precision are further discussed in article O3.

2903. Systematic errors are those which follow some law by which they can be
predicted. The accuracy with which a systematic error can be predicted depends

680 NAVIGATIONAL ERRORS

upon the accuracy with which the governing law is understood. An error which can `

be predicted can be eliminated, or compensation can be made for it.

The simplest form of systematic error is one of unchanging magnitude and sign. `

This is called a constant error. Examples are the index error of a marine sextant,
watch error, or the error resulting from a lubber's line not being accurately aligned with
the longitudinal axis of the craft. In each of these cases, all readings are in error by a
constant amount as long as the adjustment remains unchanged, and can be removed by
applying a correction of equal magnitude and opposite sign. Index error and watch
error can be removed by adjustment of the instrument. Lubber’s line error can be
removed by aligning the lubber's line with the longitudinal axis of the craft.

Another type of systematic error results from a nonstandard rate. If a watch is
gaining four seconds per day, its readings will be in error by one second after an interval
of six hours, eight seconds at the end of two days, etc. This principle is used in estab-
lishing a chronometer rate (art. 1908) for determination of chronometer error between
comparisons of the chronometer with time signals. It can be eliminated by adjusting
the rate. Tf a current is running and no allowance for it is made in the dead reckoning,
the DR position is in error by an amount proportional to elapsed time. The error
introduced by maintaining heading by means of an inaccurate compass is proportional
to distanee, as is the lateral error in a position line plotted from an inaccurate bearing.

One of the causes of equation of time (art. 1912) is the fact that the ecliptic,
around which annual motion occurs, is not parallel to the celestial equator, around or
parallel to which apparent daily motion takes place. The same type systematic error
is involved in other measurements. Consider the measurement of bearing with a tilted
compass card. Bearing is measured by a system of uniform graduations (degrees) of a
circle (such as a compass card) in the horizontal plane. If the card is tilted, and its
graduations are projected onto the horizontal plane, the circle becomes an ellipse with
the graduations unequally spaced. Along the axis of tilt and a line perpendicular to it,
directions are correct. But near the axis of tilt the graduations are too close together,
and near the perpendicular they are too widely spaced. The error thus introduced is
similar to that:which would arise if a watch face were tilted but the motion of the hands
remained horizontal. If it were tilted around the “3-9” line, it would appear to run slow
near the hour and half hour, and fast near the quarter and three-quarter hours. If the
direction to be observed is of an object above or below the horizontal, as the azimuth of
a celestial body, measurement is made to the foot of the perpendicular through the
object. The sight vanes of a compass move in a plane perpendicular to the compass
card. Hence, if the card is tilted, measurement is made to the foot of a perpendicular
to the card, rather than to the foot of a perpendicular to the horizontal, introducing an
error which increases with the angle of tilt and also with the angle of elevation (or
depression) of the object. This error is greatest along the axis of tilt, and zero along
the perpendicular to it. Both of these tilt errors can be corrected by leveling the
compass card.

A different type of tilt error occurs when a reflection takes place from a tilted
surface, such as the ionosphere (art. 1007), the error being proportional to the angle
of tilt. In some respects, this error is similar to coastal refraction of a radio wave
(art. 1006).

Additional examples of systematic error are uncorrected deviation of the compass
(art. 709), polarization error (art. 1203), error due to a position in a pattern of hyper-
bolas (art. 1109), error due to incorrect location of a loran transmitter (art. 1306),
uncorrected parallax (art. 1620), and uncorrected personal error (art. 1507).

2904. Random errors are chance errors, unpredictable in magnitude or sign.
They are governed by the laws of probability. If the altitude of a celestial body is

ana

SAT

NAVIGATIONAL ERRORS 681

Ka SEO HIT Aa observed, the reading may be (1) too great, (2)
AR o Í correct; or'(3) too small: Tf a number of observa
= 10" 0 0.0 tions are made, and there is no systematic error,
aid i a d the probability of a positive error is exactly equal
-7 3 0.8 to the probability of a negative error. This does
" S t i 3 not mean that every second observation having
— 4 28 5.6 an error will be too great. However, the greater
A a En Ae the number of observations, the greater is the
e: 63 19. 6 probability that the number of positive errors
A o + He å will equal the number of negative ones, and that
+ 2% 53 10. 6 their magnitudes will correspond.
i 3) 29 T0 Suppose that 500 observations are made,
aos 17 3.4 with the results shown in table 2904. A close
m 2 1 i å approximation of the plot of these errors is shown
43 gt 2 0.4 in figure 2904a. The plot has been modified
ea 1 ae slightly to constitute the normal curve of
i random errors, which is the same as the actual
0 500 100. 0 curve except that the normal curve approaches

zero as the error increases, while the actual

TABLE 2904.— Normal distribution of curve reaches zero at (+)10’ and (—)10’. The
random errors. : >

height of the curve at any point represents the

percentage of observations that can be expected to have the error indicated at that

point. The probability of any similar observation having any given error is the

proportion of the number of observations having this error to the total number of

observations, or the percentage expressed as a decimal. Thus, the probability of an

: | 0) Nola ifo
observation having an error of (—)3’ is 500 125 9.08 (8%).

If the area under the curve represents 100 percent of the observations, half the
area (the shaded portion of figure 2904a) represents 50 percent of the observations.
The value of the error at the limits of this shaded portion is often called the “50 percent
error,” or probable error, meaning that 50 percent of the observations can be expected
to have less error, and 50 percent greater error. Similarly, the limits which contain
the central 95 percent of the area denote the 95 percent error. The percentage of
error is found mathematically. For a normal curve, each error is squared, the sum of
the squares is divided by one less than the number of observations, and the square
root of the quotient is determined. This value is called the standard deviation (s) or
root mean square. In the illustration, the standard deviation is the square root of
0xX(=)102+1Xx(2)9+2X (—)8?-+4X (—)7?-9 X (—)6*, etc., divided by 499 or

don = 18.966 =2.99 (about 3). The standard deviation is the 68 percent error. The
probability of the occurrence of an error of or less than a specific magnitude may be
determined by the following relationship (with the answers for the illustration given):

50% error— %Xs= 2’ (approx.)
68% error=1 Xs= 3 (approx.)
95% error=2 Xs= 6’ (approx.)
99% error=2%Xs= 8” (approx.)
99.9% error=3%4Xs=10" (approx.)

Many of the errors of navigation are not of the “normal” type. In H.O. Pub. No.
214 (art. 2003) values of altitude can be taken only to the nearest 0/1. The error might

682 NAVIGATIONAL ERRORS

have any value from (+) 0:05 to (—) 0:05, and any value within these limits is as likely i
to occur as any other of the same precision. The same is true of a sextant that cannot `
be read closer than 0/1, and of a loran receiver that cannot be read closer than lus. `

These values refer to the single errors indicated, and not to the total error that might be
involved. Thisis a rectangular error, so called because of the shape of its plot, as shown
in figure 2904b. The 100 percent error is half the dif-
ference between readings. The 50 percent error is half
this amount, the 95 percent error is 0.95 times this
amount, etc.

Still another type random error is encountered in
navigation. If a compass is fluctuating periodically
due to yaw of a ship, its motion slows as the end of a
swing is approached, when the error approaches
maximum value. Tf readings were taken continuously

NM CE m E or at equal intervals of time, the interval being a small

ERROR percentage of the total period of oscillation, the curve

of errors would have a characteristic U-shape, as

Erunt Er pM shown in figure 2904c. The same type error is involved

of area shaded. Limits of in measurement of altitude of a celestial body from a

placed ares indicate probable ing of the bridge of a heavily rolling vessel, when

the roll causes large changes in the height of eye. This

type of error is called a periodic error. The effect is accentuated by the tendency of

the observer to make readings near one of the extreme values because the instrument

appears steadiest at this time. If it is impractical to make a reading at the center

of the period, the error can be eliminated or reduced by averaging readings taken con-

tinuously or at short intervals, as indicated above. This is the method used in averag-

ing type artificial-horizon sextants (art. 1513).

Generally, better results can be obtained by taking

maximum positive and maximum negative readings,
and averaging the results.

The curve of any type of random error is sym-
metrical about the line representing zero error. This
means that in the ideal plot every point on one side ` Gronn 2904b.—Rectangular error,
of the curve is exactly matched by one on the other with 50 percent area shaded.
side, or for every positive error there is a negative
error of the same magnitude. The average of all
readings, considering signs, is zero. The larger the
number of readings, the greater the probability of
the errors fitting the ideal curve.. Another way of
stating this is that as the number of readings in-
creases, the error of the average can be expected to
decrease.

2905. Combinations of errors.—Many of the
results obtained in navigation are subject to more
than one error. Chapter XVI lists 19 errors appli-
cable to sextant altitudes. Some of these have several components. A number of
possible errors are involved in the determination of computed altitude and azimuth.
A rectangular error is possible in finding the altitude difference. Several additional
errors may affect the accuracy of plotting. Thus, the line of position as finally
plotted may include 30 errors or more. Corrections are applied for some of the
larger ones, so that in each of these cases the applicable error is the difference

PROBABILITY

Probability

Probability

FIGURE 2904c.—Periodic error, with
50 percent area shaded.

AR U

WT E ESAS AE AAA

NAVIGATIONAL ERRORS 683

between the applied correction and the actual error. Thus, a dip correction may
be applied for a height of eye of 30 feet, while the actual height at the moment
of observation may be 31 feet 6 inches. Even if the height of eye is exactly 30 feet,
a rectangular error may be involved in taking the dip correction from the table.

Corrections which might be random as far as an individual observation is con-
cerned may be systematic for a series of observations. Thus, if the average or standard
conditions upon which a correction is based do not exist at the time of observation
the value at any given time is as likely to be greater as it is to be less than the standard
amount. But if a number of observations are taken in quick succession, the error
will be about the same for each.

If two or more errors are applicable to a given result, the total error is equal to
the algebraic sum of all errors. Thus, if a given number is subject to errors of (+) 4,
(—) 2, (—) 1, (+) 3, (+) 2, 0, and (—) 2, the total error is (+) 4. Systematic errors
can be combined by adding the curves of individual errors. Thus, a magnetic compass
may have a quadrantal error as shown
by the top curve of figure 2905, and a
semicircular error as shown by the second
curve. The sum of these two errors is
shown in the bottom curve. If, in addi-
tion, the compass has a constant error, QUADRANTAL ERROR
the bottom curve is moved vertically up-
ward or downward by the amount of the
constant error, without undergoing a
change of form. If the constant error is
greater than the maximum value of the
combined curves, all errors are positive
or all are negative, but of varying mag-
nitude.

If a number of random errors are
combined, the result tends to follow a
normal curve regardless of the shape of
the individual errors, and the greater the COMBINED QUADRANTAL ERROR AND SEMICIRCULAR ERROR
number, the more nearly the result can be FIGURE 2905.—Combining systematic errors.
expected to approach the normal curve
(fig. 2904a). If a given result is subject to errors of plus or minus 3, 2, 1, 2, 4,
2, 1, 8, 1, and 2, the total error could be as much as 26 if all errors had the
same sign. However, if these are truly random, the probability of them all
having the same sign is only one in 1024. This is so because the chance of any
one being positive (or negative) is X. That is, of a large number of results,
approximately half will have any one particular correction positive (or negative).
By the same reasoning, approximately half of the positive (or negative) results
will have any one particular additional correction positive (or negative). Thus,
the probability of any two particular corrections having the same sign is 4X 4= (14)”= A.

SEMICIRCULAR ERROR

; e il
The probability of all ten corrections having the same sign 1s (04) "=10294 If there

were 20 corrections, the probability of all having the same sign would be
il
720. —— ^
(2) ~ 1,048,576
The standard deviation of the sum of such errors is found by squaring each error
individually, adding the results and taking the square root of the sum. Thus, in the
example, the following results are obtained:

684 . NAVIGATIONAL ERRORS

Error Error Squared

NH D ta bo BW N æ
p=
R BROR

sum 108
square root +10.4

Thus, the standard deviation is +10.4. Signs need not be considered because the
sguare of either a positive or negative number is positive.

The individual errors have been treated as if they were fixed in amount. If they
are 50 percent normal errors, the result is the standard deviations of the 50 percent
errors; if 99 percent, the result is the standard deviations of the 99 percent errors, etc.,
if the individual errors are normal and independent. If they are of a different type,
an adjustment is needed. Thus, the square of each rectangular error should be multi-
plied by the following factors:

50% error %

95% error 1%

99% error 2%
99.9% error 4.

The information required to determine the standard deviation is usually not
available to a navigator, because the probable magnitude of many of the individual
errors has never been determined. However, the example given above reveals at least
one interesting point which is highly practical. In the tabulation of errors, the largest
has a value of eight. This single error accounts for less than one-third the total possible
error, but its square is more than half the sum of squares. If this error could be
eliminated, the standard deviation would be only 6.6.. If it could be reduced vo 5,
a 37.5 percent reduction, the standard deviation would be reduced to 8.3. In con-
trast, if the next largest error, four, were reduced by three, a reduction of 75 percent,
the standard deviation would be reduced by only 0.8, to 9.6. If the three errors of one
each could be completely eliminated, the standard deviation would be reduced by only
0.2, to 10.2. In the reduction of total error, therefore, a relatively small reduction in
a large error has a much greater effect upon the standard deviation than the same
numerical reduction (larger percentage reduction) in a small error, because the result
of a random error is proportional to its square.

Therefore, the perfection of one part of a process, sometimes at great expense or
by the introduction of considerable inconvenience, may not be justified until larger
errors are corrected. Thus, it would hardly be worth the effort and expense to build
a loran receiver capable of making a reading to 0.1 us (present receivers can be read
to about 1 us) as long as synchronization of signals may be in error as much as 2 us OT
more. Conversely, the introduction of an additional small error may add considerably
to the convenience of a process without materially affecting the accuracy. Thus, the

use of some of the "short" methods of sight reduction (ch. XXI) without interpolation
is justified if the interval of tabulation is small.

Hp e a

NAVIGATIONAL ERRORS 685

When both systematic and random errors are present in a process, both effects
are present. An increase in the number of readings decreases the residual random error,
but regardless of the number of readings, a systematic error is present in its entirety.
Thus, if a number of Decca readings are made at a fixed point, the average should be
a good approximation of the true value if there is no systematic error. But if the
equipment is out of adjustment to the extent that the lane is incorrectly identified,
no number of readings will correct this error. In this illustration, a constant error is
combined with a normal random error. The normal curve has the correct shape, but
is offset from the zero value.

Under some conditions, systematic errors can be eliminated from the results even
when the magnitude is not determined. Thus, if two celestial bodies differ in azimuth
by 180°, and the altitude of each is observed, the line midway between the lines of posi-
tion resulting from these observations is free from any constant error in the altitude
(such as abnormal refraction or dip, or incorrect IC). It would not be free from such a
constant error as one in time (unless the bodies were on the celestial meridian). Simi-
larly, a fix obtained by observations of three stars differing in azimuth by 120°, or
four stars differing by 90° is free from constant error in the altitude, if the center of the
figure made by the lines of position is used. The center of the figure formed by circles
of position from distances of objects equally spaced in azimuth is free from a constant
error in range. A constant error in bearing lines does not introduce an error in the
fix if the objects are equally spaced in azimuth. In all of these examples, the correct
position is outside the figure formed by the lines of position if all objects observed are
on the same side of the observer (that is, if they lie within an arc of less than 180°).

2906. Most probable position.—Some navigators, particularly those of little ex-
perience, have been encouraged by the oversimplified definitions and explanations us-
ually given in texts to conclude that the line of position is infallible, and that a fix is
without error, overlooking the frequent incompatibility of these two notions. Too
often the idea has prevailed that information is either all right or all wrong. An ex-
ample is the practice of establishing an estimated position at the foot of the perpendicular
from a dead reckoning position, or previous estimated position, to a line of position.
The assumption is that the vessel must be somewhere on the line of position, and that
the only value of the DR position is to locate which point on the line to use as the EP.

A more realistic concept is that of the most probable position (MPP), which recog-
nizes the probability of error in all navigational information, and determines position
by an evaluation of all available information, using the principles of errors.

Suppose a vessel were to start from a completely accurate position and proceed
on dead reckoning. If course and speed over the bottom were of equal accuracy, the
uncertainty of dead reckoning positions would increase equally in all directions with
either distance or elapsed time (for any one speed these would be directly proportional
and therefore either could be used). Therefore, a circle of uncertainty would grow
around the dead reckoning position as the vessel proceeded. If the navigator had full
knowledge of the distribution and nature of the errors of course and speed, and the neces-
sary knowledge of statistical analysis, he could compute the radius of the circle of un-
certainty, using the 50 percent, 95 percent, or other value of individual errors.

In ordinary navigation, this is not practicable, but based upon his experience and
judgment, the navigator might estimate at any time the probable error of his dead
reckoning or estimated position. With practice, he might acquire considerable skill
in making this estimate. He would take into account, too, the fact that the area cf
uncertainty might better be represented by an ellipse than a circle, the major axis
being along the course line if the probable error of the speed were greater than that of
the course, and the minor axis being along the course line if the probable error of the

686 NAVIGATIONAL ERRORS

course were greater. He would recognize, too, that the size of the area of uncertainty ?
would not grow in direct proportion to the distance or elapsed time, because disturbing `

PORTU

ZA á

ey y

+

factors such as wind and current could not be expected to remain of constant magnitude E
and direction. Also, he would know that the starting point of the dead reckoning `

would not be completely free from error.

At some future time additional positional information would be obtained. This S

might be a line of position from a celestial observation or by loran. This, too, would
be accompanied by a probable error which might be computed if the necessary informa-
tion and knowledge were available, but which in
practice would be estimated. If the dead reckon-
ing had started from a good position obtained by
means of landmarks, the probable error of the initial
position would be very small. At first the dead
reckoning or estimated position would probably be `
more reliable than a line of position obtained by celes-
um ud —. tial observation or loran. But at some distance the
Ficure 2906a.—A most probable two would be equal, and beyond this the line of

position based upon a dead reckon- position might be more accurate.

ing position and line of position 3 :

having equal probable errors. However, the determination of most probable

position does not depend upon determination of

which information is most accurate. In figure 2906a a dead reckoning position is
shown surrounded by a circle of uncertainty. A line of position is also shown, with
its area of uncertainty. The most probable position is within the overlapping area,
and if the uncertainty of the dead reckoning position and that of the line of posi-
tion are about equal, it might be taken at the center of the area. If the overall
errors are considered normal, and they are probably approximately so, the effect of each
is proportional to its square (art. 2905). Thus, if the probable error of a dead reckoning
position is three miles, and that of a line of position is two miles, the most probable

position is nearer the line of position, being at a distance equal to ==> that from the

dead reckoning position (or %; of the
perpendicular distance from the dead
reckoning position to the line of position).

If a fix is obtained from two lines of
position, the area of uncertainty is a circle
if the lines are perpendicular, have equal
probable errors, and these errors can be
considered normal. If one is considered
more accurate than the other, the area is
an ellipse, the two axes being proportional
to the squares of the two errors. Asshown Fieune 2906b.—Ellipse of uncertainty with lines
in figure 2906b, it is also an ellipse if the > Det EE probable errors crossing at
probable error of each is equal and the

lines cross at an oblique angle. If the errors are unequal, the major axis of the ellipse
is more nearly in line with the line of position having the smaller probable error. If
the angle between lines is very small, they are better considered a single line of position
in the direction of the major axis of the ellipse.

| If a fix is obtained from three or more lines of position, and the error of each line
is normal and equal to that of the others, the most probable position is the center of
the figure. By "center" is meant that point within the figure which is equidistant
from the sides. If the lines are of unequal probable error, the distance of the most

NAVIGATIONAL ERRORS 687

probable position from each line of position is proportional to the square of the probable
error of that line. Thus, if three lines have probable errors of one, two, and three miles,
respectively, the distances of the most probable position from the lines are in the ratio
of one, four, and nine, respectively.

In the discussion of most probable position from lines of position, it has been as-
sumed that no other positional information is available. Usually, this is an incorrect
assumption, for there is nearly always a dead reckoning or estimated position. "This
can be considered in any of several ways. The square of its probable error can be used
in the same manner as the square of the probable error of each line of position. A most
probable position based upon the dead reckoning or estimated position and the most
reliable line of position might be determined as explained above, and that line of
position replaced with a new one parallel to it but passing through the most probable
position just determined. This adjusted line of position can then be assigned a smaller
probable error and used with the other lines of position to determine the overall most
probable position. A third way is to establish a probable error for the fix, and consider
the most probable position as that point along the straight line joining the fix and the
dead reckoning or estimated position, the relative distances being equal to the square
of the probable error of each position.

The value of the most probable position determined as suggested above depends
upon the degree to which the various errors are in fact normal, and the accuracy with
which the probable error of each is established. From a practical standpoint, the second
factor is largely a matter of judgment based upon experience. It might seem that inter-
pretation of results and establishment of most probable position is a matter of judgment
anyway, and that the procedure outlined above is not needed. If a person will follow
this procedure while gaining experience, and evaluate his results, the judgment he
develops should be more reliable than if developed without benefit of a knowledge of
the principles involved. The important point to remember is that the relative effects
of normal random errors are proportional to their squares.

Systematic errors are treated differently. Generally, an attempt is made to dis-
cover the errors and eliminate them or compensate for them. In the case of a position
determined by three or more lines of position resulting from readings with constant
error, the error might be eliminated by finding and applying that correction (including
sign) which will bring all lines through à common point.

2907. Mistakes.— The recognition of a mistake, as contrasted with an error (art.
2902), is not always easy, since a mistake may have any magnitude, and may be either
positive or negative. A large mistake should be readily apparent if the navigator is
alert and has an understanding of the size of error to be reasonably expected. A
small mistake is usually not detected unless the work is checked.

If results by two methods are compared, as a dead reckoning position and a line
of position, exact agreement is not to be expected. But if the discrepancy is unreason-
ably large, a mistake is logically suspected. The definition of “unreasonably large"
is a matter of opinion. If the 99.9 percent areas of the two results just touch, it is
possible that no mistake has been made. However, the probability of either one having
so great an error is remote if the errors are normal. The probability of both having
99.9 percent error of opposite sign at the same instant is very small indeed. Perhaps
a reasonable standard is that unless the most accurate result lies within the 95 percent
area of the least accurate result, the possibility of a mistake should be investigated.
Thus, if the areas of uncertainty shown in figure 2906a represent the 95 percent areas,
it is probable that a mistake has been made.

As in other matters pertaining to navigation, judgment is important. The use
to be made of the results is certainly a consideration. In the middle of an ocean pas-

688 NAVIGATIONAL ERRORS

sage a mistake is usually not serious, and will undoubtedly be corrected before it jeopard-
izes the safety of the vessel. But if landfall is soon to be made, or if search and rescue
operations are to be based upon the position, almost any mistake is intolerable.

2908. Miscellaneous.—The correct identification of the nature of an error is
important if the error is to be handled intelligently. Thus, the statement is some-
times made that a radio bearing need not be corrected if the receiver is within 50 miles
of the transmitter. The need for a correction arises from the fact that radio waves
are assumed to follow great circles, and if radio bearings are to be plotted on a Mercator
chart, the equivalent rhumb line is needed. The statement regarding 50 miles implies
that the size of the correction is proportional to distance only. It overlooks the fact
that latitude and direction of the bearing line are also important factors, and is therefore
a dangerous statement unless its limitations are understood.

The recognition of the type of error is also important. A systematic error has

L a a

quite a different effect than a random error, and cannot be reduced by additional

readings unless some method or procedure is instituted which will cause the errors to
cancel each other. If a position is subject to a rectangular error only, its 100 percent
circle has twice the radius and four times the area of the 50 percent circle. But if the
error is normal, the 95 percent circle has approximately three times the radius and nine
times the area of the 50 percent circle. It is not correct to suppose that a craft is as
likely to be at one point within a circle of uncertainty as at any other point. If the
error is normal, the probability might be represented by a three-dimensional figure
formed by rotating the normal curve (fig. 2904a) around its axis of symmetry.

The probable error is usually of greater interest than the “average” value. The
average of a large number of normal errors approaches zero, but the probable error
might be quite large. An average or mean value determined by a number of observa-
tions is sometimes given with its probable error. Thus, a person might make a number
of measurements of the speed of light and state his results as 299,792+2 kilometers
per second.

A person who understands the nature of errors avoids many pitfalls. Thus, the
magnitude of the errors of individual lines of position is not a reliable indication of the
size of the error of the fix obtained from them. The size of the triangle formed by
three lines of position has often been used as a guide to the accuracy of the fix, although
a large triangle might be the result of a large constant error if the objects observed are
equally spaced in azimuth. On the other hand, two lines of position with small errors
might produce a fix having a much larger error if the lines cross at a small angle.

The size of a triangle of position might be deceptive for another reason. A con-
stant error in time shifts all lines of position from celestial observation an approximately
equal amount (in minutes of arc) toward the east or toward the west. If all objects
observed for a fix are on the same side of the observer, a constant error in measurement
shifts all objects and the fix, so that if the constant error is larger than the random error,
the actual position is outside the figure formed by the lines of position.

References

Croxton, F. E., and Cowden, D. J. Applied General Statistics. New York, Prentice-
Hall, 1939.

Deming, W. E. Statistical Adjustment of Data. New York, Wiley, 1943.

Mills, F. C. Statistical Methods. New York, Holt, 1929.

PART SIX
OCEANOGRAPHY

PART SIX
OCEANOGRAPHY

Page
CHAPTER XXX. The Oceans. LA. AE At tee snes IE MD 691
CHAPTER XX XL Tides and Lidal Currenis 260 S 703
CHAPTER XXXII Ocean: Currents SE ee S 718
CHAPTER XA ATID Ocean Waves Se S S 227
CHAPTER XXXIV. Amphibious Operations. -mma 737
CHAPTER XX XV Sound in the Sea arco. NN 742

CHAPTER XXXVI “Ice in the Sea... "oec 746

CHAPTER XXX
THE OCEANS

3001. Introduction.—Oceanography is the application of the sciences to the
phenomena of the oceans. It includes a study of their forms; physical, chemical, and
biological features; and phenomena. Thus, it embraces the widely separated fields of
geography, geology, chemistry, physics, and biology. Many subdivisions of these
sciences, such as sedimentation, ecology (biological relationship between organisms
and their environment), bacteriology, biochemistry, hydrodynamics, acoustics, and
optics, have been extensively studied in the oceans.

The oceans cover 70.8 percent of the surface of the earth. The Atlantic covers 16.2
percent, the Pacific 32.4 percent (3.2 percent more than the land area of the entire earth),
the Indian Ocean 14.4 percent, and marginal and adjacent areas (of which the largest is
the Arctic Ocean) 7.8 percent. Their extent alone makes them an important subject
for study. However, greater incentive lies in their use for transportation, their influence
upon weather and climate, and their potentiality as a source of power, food, fresh water,
and mineral and organic substances.

3002. History of oceanography.—The earliest studies of the oceans were concerned
principally with problems of navigation. Information concerning tides, currents, sound-
ings, ice, and distances between ports was needed as ocean commerce increased. Ac-
cording to Posidonius, a depth of 1,000 fathoms had been measured in the Sea of
Sardinia as early as the second century BC. About the middle of the 19th century,
the Darwinian theories of evolution gave a great impetus to the collection of marine
organisms, since it is believed by some that all terrestrial forms have evolved from
oceanic ancestors. Later, the serious depletion of many fisheries called for investigation
of the relation of the economically valuable organisms to the physical characteristics
of their environment, especially in northwestern Europe and off Japan. Still later, the
growing use of the oceans in warfare, particularly after the development of the submarine,
required that much effort be expended in problems of detection and attack, resulting
in the study of many previously neglected scientific aspects of the sea.

Oceanographic exploration. Exploration of the seas was primarily geographical
until the 19th century, although the accumulated observations of seafarers, as recorded
in the early charts and sailing directions, often included data on tides, currents, and
other oceanographic phenomena. The great voyages of discovery, particularly those
beginning in 1768 with Captain Cook, and continued by such commanders as La
Pérouse, Bellingshausen, and Wilkes, included scientists in their complements. However,
scientific work on the oceans at this period was severely limited by lack of suitable in-
struments for probing conditions below the surface. Meanwhile, Lieutenant Matthew
Fontaine Maury, USN, working in the forerunner of the U. S. Navy Hydrographic
Office in Washington, developed to a high degree of perfection the analysis of log-book
observations. His first results, published in 1848, were of great importance to ship
operations in the recommendation of favorable sailing routes, and they stimulated inter-
national cooperation in the fields of oceanography and marine meteorology.

In the rapid advances in technology after 1850, oceanographic instrumentation
problems were not neglected, with the result that the British Navy in 1872-76 was
able to send HMS Challenger around the world on the first purely deep-sea oceano-

691

692 THE OCEANS

graphic expedition ever attempted. Her bottom samples, as analyzed by Sir John
Murray, laid the foundation of geological oceanography, and 77 of her sea water
samples, analyzed by C. R. Dittmar, proved for the first time that various constituents
of the salts in sea water are everywhere in virtually the same proportions.

Since that time, the coastal waters and fishing banks of many nations have been
extensively studied, and numerous vessels of various nationalities have conducted work
on the high seas. Notable among these have been the American Albatross from 1882
to 1920; the Austrian Pola in the Mediterranean and Red Seas between 1890 and 1896;
the Danish Dana, which during its voyages of 1920-22 discovered the breeding place
of the European eels in the Sargasso Sea; the American Carnegie in 1927-29; the German
Meteor in the Atlantic from 1928 to 1938; and the British Discovery II in the antarctic
between 1930 and 1939. Notable also were the drifts of the Norwegian vessels Fram
and Maud in the arctic ice pack from 1893 to 1896 and 1918 to 1925, respectively;
the attempt by Sir George Hubert Wilkins to operate under the ice in the British sub-
marine Nautilus in 1931; and the Russian station set up at the north pole in 1937, which
made observations from the drifting pack ice.

At the same time, investigations pursued ashore provided the theoretical basis
for the explanation of ocean currents, under the leadership of Helland-Hansen in
Norway and Ekman and the Bjerknes in Sweden, while Martin Knudsen in Denmark
worked out the precise details of the relationship between chlorinity, salinity, and
density, enabling the theories to be verified by field observations.

During World War II, basic investigations were interrupted while work on purely
military applications of oceanography was carried out. Deep-sea expeditions were
renewed by the Swedish Albatross after the war, followed by the Danish Galathea,
the second British Challenger (built in 1931) and Discovery IT in the antarctic, and vessels
of the American Scripps Institution in the Pacific. Oceanographic work was carried out
by Americans and Russians in the arctic. By 1961, a total of ten Russian and three
United States drifting ice stations had been established. Two United States stations
were also established aboard floating ice islands.

Institutions. Among the leading oceanographic institutions in Europe are the
Geophysical Institute of the University of Bergen in Norway; the Oceanographic
Institute at Góteborg, Sweden; the National Institute of Oceanography in Great
Britain; the German Hydrographic Institute in Hamburg; and the Museum of Oceanog-
raphy at Monaco. The Marine Biological Station at Naples, Italy, has served as a
model for others throughout the world.

In the Far East, the Hydrographic Division of the Maritime Safety Agency is
perhaps the most prominent of a number of Japanese oceanographic activities. The
Institute of Oceanology at Vladivostok is the foremost oceanographic establishment
on the Asiatic mainland.

Canada maintains the Pacific Oceanographic Group at Nanaimo, B. C., and the
Atlantic Oceanographic Group at St. Andrews, N. B. In the United States, the
leading nongovernmental oceanographic institutions include the Scripps Institution
of Oceanography of the University of California, La Jolla, Calif.; the Department of
Oceanography of the University of Washington, Seattle, Wash.; Woods Hole Oceano-
graphic Institution, Woods Hole, Mass.; the Marine Laboratory of the University of
Miami, Coral Gables, Fla.; and the Department of Oceanography of Texas A. & M.
College, College Station, Tex.

There exist also various international organizations in the field of oceanography,
which coordinate and promote international cooperation. The International Council
for the Exploration of the Sea, with headquarters in Copenhagen, which was established

— Yt

THE OCEANS 693

to exchange data on fisheries problems in the waters of northwestern Europe, has been
notably successful, and similar organizations have been established in other areas.

3003. Origin of the oceans.—Although many leading geologists still disagree with
the conclusion that the structure of the continents is fundamentally different from
that of the oceans, there is a growing body of evidence in support of the theory that
the rocks underlying the ocean floors are more dense than those underlying the con-
tinents. According to this theory, all the earth’s crust floats on a central liquid core,
and the portions that make up the continents, being lighter, float with a higher free-
board. Thus, the thinner areas, composed of heavier rock, form natural basins where
water has collected.

The origin of the water in the oceans is also controversial. Although some geol-
ogists have postulated that all the water existed as vapor in the atmosphere of the
primeval earth, and that it fell in great torrents of rain as soon as the earth cooled
sufficiently, another school holds that the atmosphere of the original hot earth was
lost, and that the water gradually accumulated as it was given off in steam by volcanoes
or worked to the surface in hot springs.

Most of the water on the earth’s crust is now in the oceans—about 328,000,000
cubic statute miles, or about 85 percent of the total. The mean depth of the ocean
is 2,075 fathoms, and the total area is 139,000,000 square statute miles.

3004. Oceanographic chemistry may be divided into three main parts: the
chemistry of (1) sea water, (2) marine sediments, and (3) organisms living in the sea.
The first is of particular interest to the navigator.

Chemical properties of sea water are determined by analyzing samples of water
obtained at various places and depths. Samples from below the surface are obtained
by means of metal bottles designed for this purpose. The open bottles are attached
at suitable intervals to a wire lowered into the sea. When they reach the desired
depths, a metal ring or messenger is dropped down the wire. When the messenger
arrives at the first bottle, it causes the bottle to close, trapping a sample of the water
at that depth, and releasing a second messenger which travels on down the wire. The
process is repeated at each bottle until all are closed, when they are hauled up and each
bottle detached as it comes within reach. Of the various types devised, the Nansen
bottle is the most widely used. It is equipped with a removable frame for attaching
a thermometer.

For centuries table salt has been produced from sea water by natural evaporation
in countries with a suitable climate. More recently, practical industrial processes
have been developed for recovering bromine and magnesium from the sea. Calcium
carbonate, in the form of oyster shells or coral rock, is obtained after precipitation by
living organisms.

Three elements in the sea, silicon, nitrogen, and phosphorus, are most significant
in the growth of living organisms.

Certain of the elements, notably chlorine, bromine, sulfur, and boron, are much
more abundant in the ocean than in the rest of the earth’s crust. These elements are
among the more volatile ones, and their abundance in the sea tends to confirm the
hypothesis that volcanic action is largely responsible for the present oceans.

In many cases, chemical relationships influence the abundance of elements in the
sea. Barium, for example, forms a sulfate of very limited solubility, and thus the
high concentration of sulfate in sea water limits the possible amount of dissolved
barium. Thus, the concentration of many elements is limited by the solubility of their
most insoluble compounds. Table 3004 indicates the amounts of the various elements
found in solution in the oceans.

694 THE OCEANS

In addition to dissolved solids, sea water contains in solution all of the gases

found in the atmosphere (art. 1410), but not in the same proportions. The most
abundant is nitrogen, which, however, because of its chemical inertness, does not
enter into biological processes. Oxygen, produced in the surface layers by plant
photosynthesis (art. 3024) or dissolved directly from the atmosphere, is of major
importance for all forms of life. By biological activity, the oxygen concentration at
depths below the surface is usually reduced to a fraction of the surface values, and
under certain conditions, owing either to the presence of abundant oxidizable material,
or a stagnant condition, or both, it may become completely exhausted. Under these
conditions, sulfate-reducing bacteria produce hydrogen sulfide gas from the abundant
sulfate in sea water. The existence of such conditions is often indicated to the mariner
by the blackening of white lead paint, a well-known phenomenon in badly polluted
estuaries.

V

Hydrogen sulfide may also be encountered at great depths in the ocean. The `

fiords of Norway, deep channels cut by former glaciers, are characterized in general
by shallow sills at the entrances, where the terminal moraines of the glaciers were
deposited. These sills serve as barriers to the mixing and renewing of the deeper waters
within the fiords, and, as a result, conditions producing hydrogen sulfide are frequently
encountered.

Element Parts per million Element Parts per million |
Aluminum 0. 01 Manganese 0. 001-0. 01
Arsenic 0. 003 Mercury 0. 00003
Barium 0. 006 Molybdenum 0. 01
Boron 4.7 Nickel 0. 0005
Bromine 66 Nitrogen 0. 01-0. 7
Cadmium 0. 00006 Phosphorus 0. 001-0. 1
Calcium 408 Potassium 387
Carbon 28093 Radium 0. 00000000003
Cerium 0. 0004 Rubidium 0.3
Cesium 0. 001 Scandium 0. 00004
Chlorine 19, 353 Selenium 0. 004
Chromium 0. 00005 Silicon 0. 02-4. 0
Cobalt 0. 0005 Silver 0. 0003
Copper 0. 001-0. 01 Sodium 10, 769
Fluorine 1.4 Strontium 10
Gallium 0. 0005 Sulfur 901
Gold 0. 000004 Thorium 0. 0007
Iodine 0. 05 Tin 0. 003
Tron 0. 002-0. 02 Titanium 0. 001
Lanthanum 0. 0003 Uranium 0. 0083
Lead 0. 003 Vanadium 0. 001
Lithium 0. 2 Yttrium 0. 0003
Magnesium 1, 297 Zine 0. 01

TABLE 3004.— Elements found in solution in the ocean. The amounts are for a Salinity of 35 parts

per thousand. These values are based upon a tabulation by Professor E. D. Goldberg of the Scripps
Institution of Oceanography.

A similar situation exists in the Black Sea. Here the Bosporus and Dardanelles
act as sills, and all the deeper water of the Black Sea is cut off from contact with the
surface waters, which, diluted by the runoff from the Danube and Don Rivers, have a
salinity (art. 3006) of about 17.5 parts per thousand. The deeper water, renewed only
by the bottom current through the Bosporus, has a salinity of 22 parts per thousand,
and the great density difference between the surface layers and the deeper water effec-
tively prevents mixing and the transfer of dissolved oxygen from the surface layers to
greater depths. Below about 100 fathoms, therefore, the waters of the Black Sea are

THE OCEANS 695

completely devoid of dissolved oxygen, containing instead large concentrations of
hydrogen sulfide.

No living creatures exist under these conditions except anaerobic bacteria, which
comprise the only form of life in five-sixths of the waters of the Black Sea.

3005. Physical properties of sea water are dependent primarily upon salinity,
temperature, and pressure. However, factors like motion of the water and the amount
of suspended matter affect such properties as color and transparency, conduction of
heat, absorption of radiation, etc.

3006. Salinity is the amount of dissolved solid material in the water, usually
expressed as parts per thousand (by weight), under certain standard conditions. This
is not the same as chlorinity, which is equal approximately to the amount of chlorine
in the water. (Actually the chlorine content is about 1.00045 times the chlorinity as
determined by standard procedures.) The two have been found to be related
empirically by the formula

salinity —0.03 4-1.805 X chlorinity.

Since the determination of salinity is a slow and difficult process, while chlorinity can
be determined easily and accurately by titration with silver nitrate, it is customary to
determine chlorinity and compute salinity by the formula given above. By this
process, salinity can be determined with an error not exceeding 0.02 parts per thousand.
It generally varies between about 33 and 37 parts per thousand, the average being
about 35 parts per thousand. However, when the water has been diluted, as near the
mouth of a river or after a heavy rainfall, the salinity is somewhat less; and in areas of
excessive evaporation, the salinity may be as high as 40 parts per thousand. In certain
confined bodies of water, notably the Great Salt Lake in Utah, and the Dead Sea in
Asia Minor, the salinity is several times this maximum. Chlorinity accounts for about
55 percent of salinity, the average being about 19 parts per thousand.

3007. Temperature in the ocean varies widely, both horizontally and with depth.
Maximum values of about 90? F are encountered in the Persian Gulf in summer, and
the lowest possible values of about 28? F (the usual minimum freezing point of sea
water) occur in polar regions. H.O. Pub. No. 225, World Atlas of Sea Surface Tem-
peratures, shows in detail the average sea surface temperatures for each month. "The
following tabulation gives the percentage distribution of temperatures for the world
for the months of February and August, as derived from this source:

Surface temperature Percentage of area of ocean
eE February August
<35 12.0 JA]

35-40 6.5 3.3
40-45 4.0 3.0
45-50 4.5 5.0
50-55 4.0 6.5
55—60 5.0 6.0
60—65 5.5 6.3
65-70 8.0 7.0
70-75 10. 0 10. 4
75-80 RES 16.5
80-85 23.0 AA
85-90 0.0 0. 2

The vertical distribution of temperature in the sea nearly everywhere shows a
decrease of temperature with depth. Since colder water is denser, it sinks below warmer

696 THE OCEANS

water. This results in a temperature distribution just opposite to that in the earth’s
crust, where temperature increases with depth below the surface of the ground.

In general, in the sea there is usually a mixed layer of isothermal water below the
surface, where the temperature is the same as that of the surface. This layer is best
developed in the trade-wind belts, where it may extend to a depth of 100 fathoms;
in temperate latitudes in the spring, it may disappear entirely. Below this layer is a
zone of rapid temperature decrease, called the thermocline, to the temperature of the
deep oceans. At a depth greater than 200 fathoms, the temperature everywhere is
below 60°F, and in the deeper layers, fed by cooled waters that have sunk from the
surface in the arctic and antarctic, temperatures as low as 33°F exist.

In the deepest ocean basins, the temperature increases slightly with depth, the
increase being about 1°F at 3,000 fathoms. The warming is believed to be caused
more by the slight compression of sea water than by heat from the earth’s crust.

A typical curve of temperature at various depths is shown in figure 3503a. Tem- .

perature at any desired depth is determined by means of a reversing thermometer at-
tached to a Nansen bottle (art.3004). When the bottle closes, the thermometer measures
the temperature to within 0°04F, thus providing a reading for a particular time and
point. Within about 75 fathoms of the surface, where the principal changes occur, a
continuous record of temperature can be obtained by an instrument called a
bathythermograph, invented by Spilhaus in 1938.

3008. Pressure.—In oceanographic work, pressure is generally expressed in units
of the centimeter-gram-second system. The basic unit of this system is one dyne per
square centimeter. This is a very small unit, one million constituting a practical unit
called a bar, which is nearly equal to one atmosphere. Atmospheric pressure is often
expressed in terms of millibars, 1,000 of these being equal to one bar. In oceanographic
work, water pressure is commonly expressed in terms of decibars, ten of these being
equal to one bar. One decibar is equal to nearly 1% pounds per square inch. This
unit is convenient because it is very nearly the pressure exerted by one meter of water.
Thus, the pressure in decibars is approximately the same as the depth in meters, the
unit of depth customarily used in oceanographic research. In terms more familiar
to the mariner, the pressure at various depths is as follows:

Depth in Pressure in pounds per
fathoms square inch

1, 000 2, 680

2, 000 5, 390

3, 000 8, 100

4, 000 10, 810

5, 000 13, 520

The increase in pressure with depth is nearly constant because water is only slightly
compressible.

Although virtually all of the physical properties of sea water are affected to a
measurable extent by pressure, the effect is not as great as those of salinity and tem-
perature. Pressure is of particular importance to submarines, directly because of the
stress it induces in the materials of the craft, and indirectly because of its effect upon
buoyancy.

3009. Density is mass per unit volume. Oceanographers use the centimeter-
gram-second system, in which density is expressed as grams per cubic centimeter.
The ratio of the density of a substance to that of a standard substance under stated
conditions is called specific gravity. By definition, the density of distilled water at
4°C (39?2F) is one gram per milliliter (approximately one gram per cubic centimeter).

i Á A

THE OCEANS 697

Therefore, if this is used as the standard, as it is in oceanographic work, density and
specific gravity are virtually identical numerically.

The density of sea water depends upon salinity, temperature, and pressure. At
constant temperature and pressure, density varies with salinity or, because of the
relationship between this and chlorinity, with the chlorinity. A temperature of 32° F
and atmospheric pressure are considered standard for density determination. The
effects of thermal expansion and compressibility are used to determine the density
at other temperatures and pressures. The density at a particular pressure affects
the buoyancy of submarines. It is also important in its relation to ocean currents.

The greatest changes in density of sea water occur at the surface, where the water
is subject to influences not present at depths. Here density is decreased by precipita-
tion, run-off from land, melting of ice, or heating. When the surface water becomes
less dense, it tends to float on top of the more dense water below. There is little
tendency for the water to mix, and so the condition is one of stability. The density
of surface water is increased by evaporation, formation of sea ice, and by cooling.
If the surface water becomes more dense than that below, it sinks to the level at which
other water has the same density. Here it tends to spread out to form a layer, or to
increase the thickness of the layer below it. The less dense water rises to make room
for it, and the surface water moves in to replace that which has descended. Thus, a
convective circulation is established. It continues until the density becomes uniform
from the surface to the depth at which a greater density occurs. If the surface water
becomes sufficiently dense, it sinks all the way to the bottom. If this occurs in an
area where horizontal flow is unobstructed, the water which has descended spreads to
other regions, creating a dense bottom layer. Since the greatest increase in density
occurs in polar regions, where the air is cold and great quantities of ice form, the cold,
dense polar water sinks to the bottom and then spreads to lower latitudes. This
process has continued for a sufficiently long period of time that the entire ocean floor
is covered with this dense polar water, thus explaining the layer of cold water at great
depths in all the oceans.

In some respects, oceanographic processes are similar to those occurring in the
atmosphere (ch. XXXVIII). The convective circulation in the ocean is somewhat
similar to that in the atmosphere. Water masses having nearly uniform characteristics
are analogous to air masses.

3010. Compressibility.—Sea water is nearly incompressible, its coefficient of
compressibility being only 0.000046 per bar under standard conditions. This value
changes slightly with changes of temperature or salinity. The effect of compression is
to force the molecules of the substance closer together, causing it to become more dense.
Even though the compressibility is low, its total effect is considerable because of the
amount of water involved. If the compressibility of sea water were zero, sea level
would be about 90 feet higher than it now is.

3011. Viscosity is resistance to flow. Sea water is slightly more viscous than
fresh water. Its viscosity increases with greater salinity, but the effect is not nearly
as marked as that occurring with decreasing temperature. The rate is not uniform,
becoming greater as the temperature decreases. Because of the effect of temperature
upon viscosity, an incompressible object might sink at a faster rate in warm surface
water than in colder water below. However, for most objects, this effect may be more
than offset by the compressibility of the object. ;

The actual relationships existing in the ocean are considerably more complicated
than indicated by the simple explanation given above, because of turbulent motion
within the sea. The disturbing effect is called eddy viscosity.

698 THE OCEANS

3012. Specific heat is the amount of heat required to raise the temperature of a
unit mass of a substance a stated amount. In oceanographic work, specific heat is
stated, in centimeter-gram-second units, as the number of calories needed to raise one
gram of the substance 1°C. Specific heat at constant pressure is usually the quantity
desired when liquids are involved, but occasionally the specific heat at constant volume
is required. The ratio of these two quantities has a direct relationship to the speed of
sound in sea water.

The specific heat of sea water decreases slightly as salinity increases. However,
it is much greater than that of land. This accounts, in part, for the greater tempera-
ture range of land and the atmosphere above it, resulting in monsoons (art. 3810) and
the familiar land and sea breezes of tropical and temperate regions (art. 3814).

3013. Thermal expansion.—The rate of expansion with increased temperature is
greater in sea water than in fresh water. Thus, at temperature 15°C (59°F), and
atmospheric pressure, the coefficient of thermal expansion is 0.000151 per degree
Celsius for fresh water and 0.000214 per degree Celsius for water of 35 parts per thousand
salinity. The coefficient of thermal expansion increases not only with greater salinity,
but also with increased temperature and pressure. At 35 parts per thousand, the
coefficient of surface water increases from 0.000051 per degree Celsius at 0°C (32°F)
to 0.000334 per degree Celsius at 30°C (86°F). Ata constant temperature of 0°C
(32°F) and a salinity of 34.85 parts per thousand, the coefficient increases to 0.000276
per degree Celsius at a pressure of 10,000 decibars (at a depth of approximately 10,000
meters).

3014. Thermal conductivity.—In water, as in other substances, one method of
heat transfer is by conduction. Fresh water is a poor conductor of heat, having a
coefficient of thermal conductivity of 0.00139 calories per second per centimeter per
degree Celsius. For sea water it is slightly less but increases with greater temperature
or pressure.

However, if turbulence is present, which it nearly always is to some extent in the
ocean, the processes of heat transfer are altered. The effect of turbulence is to increase
greatly the rate of heat transfer. The “eddy” coefficient used in place of the still-water
coefficient is so many times larger, and so dependent upon the degree of turbulence that
the effects of temperature and pressure are not important.

3015. Electrical conductivity.—Water without impurities is a very poor conductor
of electricity. However, when salt is in solution in water, the salt molecules are ionized
(art. 1007) and therefore are carriers of electricity. Hence, the electrical conductivity
of sea water is directly proportional to the number of salt molecules in the water. For
any given salinity, the conductivity increases with an increase in temperature.

3016. Radioactivity Although the amount of radioactive material in sea water
(tab. 3004) is very small, this material is present in marine sediments. to a greater
extent than in the rocks of the earth’s crust. This is probably due to precipitation
of radium or other radioactive material from the water. The radioactivity of the top
layers of sediment is less than that of deeper layers. This may be due to absorption
of radioactive material in the soft tissues of marine organisms.

3017. Refractive index (art. 1613) of sea water increases as salinity becomes
greater, or as temperature decreases. Since it varies with frequency of the radiant
energy, the “D line” of sodium is usually used as the standard for comparison.

3018. Surface tension of water in dynes per square centimeter is approximately
equal to 75.64—0.144 T 4-0.0399 Cl, where T is temperature in degrees Celsius (centi-
grade) and Cl is the chlorinity of the water in parts per thousand. As indicated by
the last term, the surface tension increases with chlorinity, and is therefore a little

e Pee re ssk

THE OCEANS 699

more for sea water than for fresh water. However, the presence of impurities causes
it to be somewhat less than indicated by the formula.

3019. Transparency of sea water varies with the number, size, and nature of
particles suspended in the water, as well as with the nature and intensity of illumina-
tion. The rate of decrease of light energy with depth is called the “extinction coeffi-
cient." The earliest method of measuring transparency was by means of a Secchi disk,
a white disk 30 centimeters (a little less than one foot) in diameter. This was lowered
into the sea, and the depth at which it disappeared was recorded. In coastal waters
the depth varies from about 5 to 25 meters (16 to 82 feet). Offshore, the depth is
usually about 45 to 60 meters (148 to 197 feet). The greatest recorded depth at which
the disk has disappeared is 66 meters (217 feet), in the Sargasso Sea.

Although the Secchi disk still affords a simple method of measuring transparency,
more exact methods have been devised.

3020. Color.—The color of sea water varies considerably. Water of the Gulf
Stream is a deep indigo blue, while a similar current off Japan was named Kuroshio
(Black Stream) because of the dark color of its water. Along many coasts the water
is green. In certain localities a brown or brownish-red water has been observed.

Offshore, some shade of blue is common, particularly in tropical or sub-tropical
regions. It is due to scattering of sunlight by minute particles suspended in the water,
or by molecules of the water itself. Because of its short wave length, blue light is
more effectively scattered than light of longer waves. Thus, the ocean appears blue
for the same reason that the sky does (art. 3817). The green color often seen near
the coast is a mixture of the blue due to scattering of light and a stable soluble yellow
pigment associated with phytoplankton (art. 3024). Brown or brownish-red water
receives its color from large quantities of certain types of algae, microscopic plants in
the sea.

3021. Marine geology is a branch of oceanography dealing with bottom relief,
particularly the characteristics of ocean basins and the geological processes that brought
them into being and tend to alter them, as well as with marine sediments.

3022. Bottom relief. —Compared to land, relatively little is known of relief below
the surface of the sea. It would be difficult to withhold knowledge of a major land
feature in an area often visited by man, but the sea has until recent years proved an
effective barrier to acquisition of knowledge of features below its surface. Although
soundings of 1,000 fathoms were probably made as early as the second century BC
(art. 3002), the number of deep sea soundings by means of a weight lowered to the
bottom has been relatively few. The process is a time-consuming one requiring special
equipment. Several hours are needed for a single sounding. Since the development
of an effective echo sounder (art. 619) in 1922, the number of deep sea soundings has
greatly increased. Later, a recording echo sounder was developed to permit the con-
tinuous tracing of a bottom profile. This has assisted materially in the acquisition of
knowledge of bottom relief. By this means, many flat-topped seamounts (called
guyots), mountain ranges, and other features have been discovered. Although the
main features are becoming known, a great many details are yet to be learned.

Along most of the coasts of the continents, the bottom slopes gradually downward
to a depth of about 100 fathoms or somewhat less, where it falls away more rapidly
to greater depths. This continental shelf averages about 30 miles in width, but varies
from nothing to about 800 miles, the widest part being off the Siberian arctic coast.
A similar shelf extending outward from an island or group of islands is called an insular
shelf. At the outer edge of the shelf, the steeper slope of 2° to 4° is called the conti-

700 THE OCEANS

nental talus or continental slope, or the insular talus or insular slope, according to
whether it surrounds a continent or group of islands. The shelf itself is not uniform,
but has numerous hills, ridges, terraces, and canyons, the largest being comparable in
size to the Grand Canyon.

As a general rule, the slope of the deep sea bottom is gradual, averaging between
20’ and 40’, but there are many exceptions to this. Off a volcanic island it may be as
much as 45°. The relief of the ocean floor is comparable to that of land. Both have
steep, rugged mountains, deep canyons, rolling hills, plains, etc. Most of the ocean
floor is considered to be made up of a number of more-or-less circular or oval depressions
called basins, surrounded by walls of lesser depth.

The average depth of water in the oceans is 2,075 fathoms (12,450 feet), as com-
pared to an average height of land above the sea of about 2,750 feet. The greatest
known depth is 35,640 feet, in the Marianas Trench in the Pacific. The highest known
land is Mount Everest, 29,002 feet. About 23 percent of the ocean is shallower than
10,000 feet, about 76 percent is between 10,000 and 20,000 feet, and a little more than
one percent is deeper than 20,000 feet. A very deep part, generally that below 3,000
fathoms, is called a deep. A long, narrow depression with steep sides is called a trench.

3023. Marine sediments.—The ocean floor is composed of material deposited
there through the years. This material consists principally of (1) earth and rocks
washed into the sea by streams and waves, (2) volcanic ashes and lava, and (3) the
remains of marine organisms. Lesser amounts of land material are carried into the
sea by glaciers, or blown out to sea by wind. In the ocean, the material is transported
by ocean currents, waves, and ice. Near shore the material is deposited at the rate of
about three inches in 1,000 years, while in the deep water offshore the rate is only about
half an inch in 1,000 years. Marine deposits in water deep enough to be relatively
free from wave action are subject to little erosion. Because of this and the slow rate
of deposit, marine sediments provide a better geological record than does the land.

Marine sediments are composed of individual particles of all sizes from the finest
clay to large boulders. In general, the inorganic deposits near shore are relatively
coarse (sand, gravel, shingle, etc.), while those in deep water are much finer (clay).
In some areas the siliceous remains of marine organisms or the calcareous deposits
(of either organic or inorganic origin) are sufficient to predominate on the ocean floor.

A wide range of colors is found in marine sediments. The lighter colors (white
or a pale tint) are usually associated with coarse-grained quartz or limestone deposits.
Darker colors (red, blue, green, etc.) are usually found in mud having a predominance
of some mineral substance, such as an oxide of iron or manganese. Black mud is often
found in an area that is little disturbed, such as at the bottom of an inlet or in a de-
pression without free access to other areas.

Marine sediments are studied primarily by means of bottom samples. Samples
of surface deposits are obtained by means of a snapper (for mud, sand, etc.) or
“dredge” (usually for rocky material). If a sample of material below the bottom
surface is desired, a “coring” device is used. This device consists essentially of a
tube driven into the bottom by weights or explosives. A sample obtained in this way
preserves the natural order of the various layers. Samples of more than 100 feet in
depth have been obtained by means of coring devices. The bottom sample obtained
by the mariner, by arming his lead with tallow or soap (art. 617), is an incomplete
indication of bottom surface conditions.

3024. Marine biology.—Sea water has all of the chemical elements needed to
sustain plant and animal life. Because of this, and the fact that the oceans contain
about 300 times as much space for the existence of life as is available on land and in
fresh water, organic material is present in vast quantities.

iii

THE OCEANS 701

| Marine life may be divided into three major groups: (1) nekton (strong-swimming
animals such as fish), (2) plankton (tiny floating plants or feebly swimming or floating
animals), and (3) benthos (plants and animals living on the bottom, such as seaweed,
barnacles, and crabs). Plankton may be divided into: (a) the phytoplankton, consisting
of microscopic floating plants; and (b) the zooplankton, consisting of feebly swimming
or floating animals. Most plankton vary in size from microscopic units to those a small
fraction of an inch in length.

Most organic material in the sea is in the form of plankton, which is carried by the
ocean currents, not having sufficient strength to choose its environment. Either directly
or indirectly, nearly all marine life depends upon these organisms. By means of
photosynthesis, a process using sunlight, phytoplankton changes chemical nutrients
(silicates, nitrates, phosphates) in the sea into primary food which is used by the
zooplankton and, to some extent, by larger animals. However, most of the larger
animals feed upon the zooplankton. The chemical nutrients are replaced by the
excretion of animals and bacterial action in the decomposition of dead plants and
animals. Thus, a food cycle is continually going on from chemical nutrient to phyto-
plankton to zooplankton to nekton and benthos to chemical nutrients.

As indicated above, growth of phytoplankton requires both sunlight and a supply
of chemical nutrients. Sunlight in sufficient strength to permit photosynthesis pene-
trates to a maximum depth of about 500 feet or less. This upper layer in which the
process occurs is called the euphotic zone. Within this zone, photosynthesis is limited
primarily by the supply of chemical nutrients. Under favorable conditions, phyto-
plankton may increase by as much as 300 percent in a single day.

The abundance of marine life is directly related to the supply of phytoplankton.
In shallow water, the chemical nutrients on the bottom are stirred up by motion of the
water, and carried into the euphotic zone. This is why an area such as the Grand Banks
is a good fishing ground. In polar regions the chemical nutrients are relatively abun-
dant, being brought to the surface by convective currents as the cold surface water
sinks and is replaced by the warmer water from the bottom. In the tropics, on the
other hand, the sea is relatively stable, and the chemical nutrients have a tendency to
sink below the euphotic zone. Even though the clear, blue water has the deepest
euphotic zone, photosynthesis proceeds at a slow rate. For this reason blue is sometimes
called the “desert color of the sea."

Ocean currents and marine life are so interrelated that currents can sometimes
be traced by their supply of plankton. In general, the oceanic circulation helps
sustain marine life by stirring up the chemical nutrients and carrying them, or the
plankton formed from them, into regions which have an inadequate supply. However,
the reverse effect can occur. A notable example occurs from time to time off the west
coast of South America. At varying intervals averaging about 12 years, a well-
developed stream of tropical water having a relatively small supply of chemical nu-
trients and plankton flows southward, close to the shore. This water replaces the
colder water which is rich in chemical nutrients and plankton. The result is a whole-
sale destruction of fish which cannot obtain a sufficient supply of food. In some
areas the dead fish are washed ashore in such quantities as to constitute a serious
problem. With the destruction of so many fish, the supply of guano also decreases
because of the death of large numbers of the birds which depend upon the fish for their
food supply. Since it commonly occurs near Christmas, this phenomenon is called
“El Niño.” A strong current such as the Gulf Stream annually carries many fish to
their deaths by transporting them from their normally warm habitat to areas where
they encounter water which is too cold for them to endure.

702 THE OCEANS

References

Crease, J. “The Origin of Ocean Currents.” Journal of the Institute of Navigation
(British), vol. 5, no. 3 (July 1952).

Day, A., Rear Admiral. “Navigation and Hydrography.” Journal of the Institute of
Navigation (British), vol. 6, no. 1 (January 1953).

Deacon, G. E. R. “Oceanographical Research and Navigation.” Journal of the
Institute of Navigation (British), vol. 4, no. 3 (July 1951).

Defant, A. Physical Oceanography. (2 vols.) New York, Pergamon, 1961.

Marmer, H. A. The Scope of Oceanography. James Johnstone Memorial Volume.
Liverpool, University Press of Liverpool, 1934.

National Research Council. Physics of the Earth—Oceanography. Bulletin no. 85,
Chapter V. Washington, The National Academy of Sciences, 1932.

Satow, P. G. “Some Problems of Underwater Navigation.” Journal of the Institute
of Navigation (British), vol. 4, no. 3 (July 1951).

Shepard, F. P. Submarine Geology. New York, Harper, 1948.

Sverdrup, H. U., Johnson, M. W., and Fleming, R. H. The Oceans, Their Physics,
Chemistry and General Biology. New York, Prentice-Hall, 1942.

CHAPTER XXXI
TIDES AND TIDAL CURRENTS

General

3101. The tidal phenomenon is the periodic motion of the waters of the sea due
to differences in the attractive forces of various celestial bodies, principally the moon
and sun, upon different parts of the rotating earth. It can be either a help or hindrance
to the mariner—the water's rise and fall may at certain times provide enough depth
to clear a bar and at others may prevent him from entering or leaving a harbor. The
flow of the current may help his progress or hinder it, may set him toward dangers or
away from them. By understanding this phenomenon and by making intelligent use
of predictions published in tide and tidal current tables and of descriptions in sailing
directions, the mariner can set his course and schedule his passage to make the tide
serve him, or at least to avoid its dangers.

3102. Tide and current.—In its rise and fall, the tide is accompanied by a periodic
horizontal movement of the water called tidal current. The two movements, tide and
tidal current, are intimately related, forming parts of the same phenomenon brought
about by the tide-producing forces of the sun and moon, principally.

It is necessary, however, to distinguish clearly between tide and tidal current,
for the relation between them is not a simple one nor is it everywhere the same. For
the sake of clearness and to avoid misunderstanding, it is desirable that the mariner
adopt the technical usage: tide for the vertical rise and fall of the water, and current
for the horizontal flow. The tide rises and falls, the tidal current floods and ebbs. In
British usage, tidal current is called tidal stream.

3103. Cause.—Tides result from differences in the gravitational attraction of
various celestial bodies, principally the moon and sun, upon different parts of the rotat-
ing earth. The gravity of the earth acts approximately toward the earth’s center,
and tends to hold the earth in the shape of a sphere. But the moon and sun provide
disturbing, or tide-producing, forces. Consider the earth and moon. The moon
appears to revolve about the earth, but actually the moon and earth revolve about
their common center of mass. They are held together by gravitational attraction
and kept apart by an equal and opposite centrifugal force. In this earth-moon system,
the tide-producing force on the earth’s hemisphere nearer the moon is in the direction
of the moon’s attraction, or toward the moon. On the hemisphere opposite the moon
the tide-producing force is in the direction of the centrifugal force, or away from the
moon.

At the sublunar point, and its antipode, the moon’s attractive force is vertical, in
the opposite direction to gravity. Along the great circle midway between these points,
the force is horizontal, parallel to the earth’s surface. At any other point, the moon’s
tide-producing force can be resolved into horizontal and vertical components. Both
are very small compared to the earth’s gravity. Since the horizontal component 1s
not operating against gravity and can draw particles of water over the surface of the
earth, it is the more effective in generating tides.

The tide-producing forces, then, tend to create high tides on the sides of the earth
nearest to and farthest from the moon, with a low tide belt between them. As the

703

704 TIDES AND TIDAL CURRENTS
earth rotates, a point on earth passes through two high and two low areas each day if
the moon is over the equator (fig. 3103, A). When the moon is north or south of the
equator, the force pattern is as shown in figure 3103, B, and a point on the equator
passes through two equal highs, but a point in higher latitudes passes through two
unequal highs or only one high. Thus, due to changes in the moon’s declination, there
is introduced a diurnal inequality in the pattern of the tidal forces at a particular place.
There are similar forces due to the sun, and the total tide producing force is the resultant
of the two. Minute tidal effects are caused by other celestial bodies.

The mathematician develops his formulas by considering the difference in attrac-
tion between a point on the earth’s surface and a point at the earth’s center. In
accordance with Newton’s law, gravitational attraction of an astronomical body varies
directly as its mass and inversely as the square of its distance. But the tide-producing
(differential) force varies directly as the mass and inversely as the cube of the distance.
As a consequence, only the moon and sun produce any appreciable tidal effect upon
the earth. Further, although the moon’s mass is but a fraction of the sun’s, dividing
such masses by the cube of their respective distances— (238,862)? statute miles and
(92,900,000)? statute miles, respectively—reduces the sun’s tide-producing force to
only 0.46 that of the moon. It is because of this that the timing of the tides is identified
so closely with the motions of the moon.

Though the tide-producing forces are distributed over the earth in a regular
manner, the sizes and shapes of the ocean basins and the interference of the land masses
prevent the tides of the oceans from assuming a
simple, regular pattern. The way in which the
waters in different parts of the oceans, as well as in
the smaller waterways, respond to these known regu-
lar forces is dependent in large part upon the size,
depth, and configuration of the basin or waterway.

Tide

3104. General features.—Tide is the periodic
rise and fall of the water accompanying the
tidal phenomenon. At most places it occurs twice
daily. The tide rises until it reaches a maximum
height, called high tide or high water, and then falls
to a minimum level called low tide or low water.

The rate of rise and fall is not uniform. From
low water, the tide begins to rise slowly at first but
at an increasing rate until it is about halfway to high
water. The rate of rise then decreases until high
water is reached and the rise ceases. The falling tide
behaves in a similar manner. The period at high or

Toward the Moon
————

Figure 3103.—Tide-producing
forces. The arrows represent the

magnitude and direction of the
horizontal component of the tide-
producing force on the earth’s
surface. (A) When the moon is
in the plane of the equator, the
forces are equal in magnitude at
the two points on the same parallel
of latitude and 180° apart in
longitude. (B) When the moon is
at north (or south) declination, the
forces are unequal at such points
and tend to cause an inequality in
the two high waters and the two
low waters of a day.

low water during which there is no sensible change
of level is called stand. The difference in height be-
tween consecutive high and low waters is the range.

Figure 3104 is a graphical representation of the
rise and fall of the tide at New York during a 24-
hour period. The tide curve has the general form
of a sine curve (fig. O40b).

3105. Types of tide.—A body of water has a
natural period of oscillation that is dependent upon
its dimensions. None of the oceans appears to be a

TIDES AND TIDAL CURRENTS 705

3 6 es e e 1-21 single oscillating body, but rather each

d one is made up of a number of oscillat-

ing basins. As such basins are acted

E upon by the tide-producing forces, some

13 respond more readily to daily or diurnal

M forces, others to semidiurnal forces, and

others almost equally to both. Hence,

| tides at a place are classified as one of three

0 types—semidiurnal, diurnal, or mixed—

pis Neto according to the characteristics of the
tidal pattern occurring at the place.

Figure 3104.— The rise and fall of the tid e Je :
New Yok showd EE Vaks In the semidiurnal type of tide, there

are two high and two low waters each tidal
day, with relatively small inequality in the high and low water heights. Tides on the
Atlantic coast of the United States are representative of the semidiurnal type, which
is illustrated in figure 3105a by the tide curve for Boston Harbor.

In the diurnal type of tide, only a single high and single low water occur each
tidal day. Tides of the diurnal type occur along the northern shore of the Gulf of
Mexico, in the Java Sea, the Gulf of Tonkin (off the Vietnam-China coast), and in a few
other localities. The tide curve for Pakhoi, China, illustrated in figure 3105b, is an
example of the diurnal type.

In the mixed type of tide, the diurnal and semidiurnal oscillations are both im-
portant factors and the tide is characterized by a large inequality in the high water
heights, low water heights, or in both. There are usually two high and two low waters
each day, but occasionally the tide may become diurnal. Such tides are prevalent
along the Pacific coast of the United States and in many other parts of the world.
Examples of mixed types of tide are shown in figure 3105c. At Los Angeles, it is typical
that the inequalities in the high and low waters are about the same. At Seattle the
greater inequalities are typically in the low waters, while at Honolulu it is the
high waters that have the greater inequalities.

3106. Solar tide.—The natural period of oscil- 6 9 121518210 3 6 9 12151821
lation of a body of water may accentuate either the
solar or the lunar tidal oscillations. Though it is
a general rule that the tides follow the moon, the
relative importance of the solar effect varies in
different areas. There are a few places, primarily
in the South Pacific and the Indonesian areas, where
the solar oscillation is the more important, and
at those places the high and low waters occur at Fieure 3105a.—Semidiurnal type of
about the same time each day. At Port Adelaide, tide.

Australia (fig. 3106), the solar and lunar semi-
diurnal oscillations are equal and nullify one another
at neaps (art. 3108).

3107. Special effects.—As a progressive wave
enters shallow water, its speed is decreased. Since
the trough is shallower than the crest, its retarda-
tion is greater, resulting in a steepening of the wave
front. Therefore, in many rivers, the duration of
rise is considerably less than the duration of fall.
In a few estuaries, the advance of the low water
trough is so much retarded that the crest of the Frevre 3105b.—Diurnal type of tide.

BOSTON

706 TIDES AND TIDAL CURRENTS

rising tide overtakes the low, and advances upstream as a churning, foaming wall of
water called a bore. Bores that are large and dangerous at times of large tidal ranges
may be mere ripples at those times of the month when the range is small. Examples
occur in the Petitcodiac River in the Bay of Fundy and at Haining, China, in the

Tsientang Kiang. The tide tables indicate where bores occur.
Other special features are the double low water (as at Hoek Van Holland) and the
double high water (as at Southampton, England). At such places there is often a
slight fall or rise in the middle of the high or low

water period. The practical effect is to create a
63 6 9 12151821 0 3 6 9 1215 1821 E Ë

HOURS HOURS longer period of stand at high or low tide. The tide
5 tables direct attention to these and other peculiari-
4 ties where they occur.

3108. Variations in range.—Though the tide
at a particular place can be classified as to type,
it exhibits many variations during the month (fig.
3106). The range of the tide varies in accordance

[^]

FEET

=

LOS ANGELES

0 with the intensity of the tide-producing force,
às though there may be a lag of a day or two (age
9 of tide) between a particular astronomic cause and
3 the tidal effect.

6 Thus, when the moon is at the point in its
5 orbit nearest the earth (at perigee), the lunar semi-
AU diurnal range is increased and perigean tides occur;
2 when the moon is farthest from the earth (at apogee),
l SEATTLE the smaller apogean tides occur. When the moon
2 and sun are in line and pulling together, as at new

and full moon, spring tides occur (the term spring
has nothing to do with the season of year); when
the moon and sun oppose each other, as at the
quadratures, the smaller neap tides occur.

I When certain of these phenomena coincide,
the great perigean spring tides, the small apogean
neap tides, etc., occur.

These are variations in the semidiurnal por-

FrcunE 3105c.—Mixed types of tide. tion of the tide. Variations in the diurnal portion

occur as the moon and sun change declination.

When the moon is at its maximum semi-monthly declination (either north or south),

tropic tides occur in which the diurnal effect is at a maximum; when it crosses the

equator, the diurnal effect is a minimum and equatorial tides occur.

It should be noted that when the range of tide is increased, as at spring tides,
there is more water available only at high tide; at low tide there is less, for the high
waters rise higher and the low waters fall lower at these times. There is more water
at neap low water than at spring low water. With tropic tides, there is usually more
depth at one low water during the day than at the other. While it is desirable to know
the meanings of these terms, the best way of determining the height of the tide at any
place and time is to examine the tide predictions for the place as given in the tide
tables. Figure 3108 illustrates variations in the ranges and heights of tides in a locality
where the water level always exceeds the charted depth.

-1 HONOLULU

TIDES AND TIDAL CURRENTS 707

N € ^ ) E O
E S P Kb?
SEPTEMBER O, 3
1.2 3 4/8 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 i 25 26 27 28 29 30 "
IE [ M
M

FATA | BH V

O w ^ O FEET

RUPEE n ii IA RUE nm VIRTU
BICI II JANI
| BA LAVADO AN NNNNA PRA

: MLLW *
SEATTLE
B | Je be
$ MHHW
4 MHW
2
MLW

0 MLLW *

LOS ANGELES

18 iF + TcHHW
16 + MHHW
14
12

10

8 5

: MLLW
e PAKHOI F TcLLW

|
2
0 *

@ new moon; J, first quarter; O, full moon; C, last quarter; E, moon on the Equator; N,S, moon
farthest north or south of the Equator; A,P, moon in apogee or perigee; O, sun at autumnal equinox.

* chart datum.

FIGURE 3106—Tidal variations at various places during a month.

708 TIDES AND TIDAL CURRENTS

MEAN HIGH WATER SPRINGS

MEAN HIGH WATER

MEAN HIGH WATER NEAPS

HALF -TIDE LEVEL

MEAN LOW WATER NEAPS

MEAN LOW WATER

MEAN LOW WATER SPRINGS

LEVEL OF DATUM

/CHARTED SS |

Figure 3108.— Variations in the ranges and heights of tide in a locality where the water level
always exceeds the charted depth.

3109. Tidal cycles.— Tidal oscillations go through a number of cycles. The
shortest cycle, completed in about 12 hours and 25 minutes for a semidiurnal tide,
extends from any phase of the tide to the next recurrence of the same phase. During a
lunar day (averaging 24 hours and 50 minutes) there are two highs and two lows (two of
the shorter cycles) for a semidiurnaltide. The effect of the phase variation is completed
in about two weeks as the moon varies from new to full or full to new. The effect of
the moon's declination is also repeated about each two weeks. "The cycle involving the
moon's distance requires approximately a lunar month (a synodical month of about 29%
days). The sun's declination and distance cycles are respectively a half year and a year
in length. An important lunar cycle, called the nodal period, is 18.6 years (usually
expressed in round figures as 19 years). For a tidal value, particularly a range, to be
considered à true mean, it must be either based upon observations extended over this
period of time or adjusted to take account of variations known to occur during the cycle.

3110. Time of tide.—Since the lunar tide-producing force has the greater effect
in producing tides at most places, the tides “follow the moon." Because of the rotation
of the earth, high water lags behind meridian passage (upper and lower) of the moon.
The tidal day, which is also the lunar day, is the time between consecutive transits

TIDES AND TIDAL CURRENTS 709

of the moon, or 24 hours and 50 minutes on the average. Where the tide is largely
semidiurnal in type, the lunitidal interval—the interval between the moon's meridian
transit and a particular phase of tide—is fairly constant throughout the month, varying
somewhat with the tidal cycles. There are many places, however, where solar or
diurnal oscillations are effective in upsetting this relationship, and the newer editions
of charts of many countries now omit intervals because of the tendency to use them
for prediction even though accurate predictions are available in tide tables. However,
the lunitidal interval may be encountered. The interval generally given is the average
elapsed time from the meridian transit (upper or lower) of the moon until the next
high tide. This may may be called mean high water lunitidal interval or establishment
of the port. The high water full and change (HWF&C) or vulgar establishment,
sometimes given, is the average interval on days of full or new moon, and approximates
the mean high water lunitidal interval.

In the ocean, the tide may be of the nature of a progressive wave with the crest
moving forward, a stationary or standing wave which oscillates in a seesaw fashion,
or a combination of the two. Consequently, caution should be used in inferring the
time of tide at a place from tidal data for nearby places. In a river or estuary, the tide
enters from the sea and is usually sent upstream as a progressive wave, so that the
tide occurs progressively later at various places upstream.

3111. Tidal datums.—A tidal datum is a level from which heights and depths
are measured. There are a number of such levels of reference that are important
to the mariner. The relation of the tide each day during a month to these datums is
shown, for certain places, in figure 3106.

The most important level of reference to the mariner is the datum of soundings
on charts. Since the tide rises and falls continually while soundings are being taken
during & hydrographic survey, the tide should be observed during the survey so that
soundings taken at all stages of the tide can be reduced to a common datum. Soundings
on charts show depths below a selected low water datum (occasionally mean sea level),
and tide predictions in tide tables show heights above the same level. 'The depth
of water available at any time is obtained by adding the height of the tide at the time
in question to the charted depth, or by subtracting the predicted height if it is negative.

By international agreement, the level used as chart datum should be just low
enough so that low waters do not go far below it. At most places, however, the level
used is one determined from a mean of a number of low waters (usually over a 19-year
period); therefore some low waters can be expected to fall below it. The following are
some of the datums in general use.

The highest low water datum in considerable use is mean low water (MLW), which
is the average height of all low waters at a place. About half of the low waters fall
below it. Mean low water springs (MLWS), usually shortened to low water springs, is
the average level of the low waters that occur at the times of spring tides. Mean lower
low water (MLLW) is the average height of the lower low waters at a place. Tropic
lower low water (TcLLW) is the average height of the lower low waters (or of the single
daily low waters if the tide becomes diurnal) that occur when the moon is near maximum
declination and the diurnal effect is most pronounced. "This datum is not in common
use as a tidal reference. Indian spring low water (ISLW) sometimes called Indian tide
plane or harmonic tide plane, is a low datum that includes the spring effect of the semi-
diurnal portion of the tide and the tropic effect of the diurnal portion. It is about the
level of lower low water of mixed tides at the time that the moon's maximum declination
coincides with the time of new or full moon. Mean lower low water springs is the aver-

710 TIDES AND TIDAL CURRENTS

age level of the lower of the two low waters on the days of spring tides. Some still
lower datums used on charts are determined from tide observations and some are
determined arbitrarily and later referred to the tide. Most of them fall close to one or
the other of the following two datums. Lowest normal low water is a datum that
approximates the average height of monthly lowest low waters, discarding any tides
disturbed by storms. Lowest low water is an extremely low datum. It conforms
generally to the lowest tide observed, or even somewhat lower. Once a tidal
datum is established, it is generally retained for an indefinite period, even though it
might differ slightly from a better determination from later observations. When this
occurs, the established datum may be called low water datum, lower low water datum, etc.

In some areas where there is little or no tide, such as the Baltic Sea, mean sea
level (MSL) is used as chart datum. This is the average height of the surface of the
sea for all stages of the tide over a 19-year period. This may differ slightly from
half-tide level, which is the level midway between mean high water and mean low water.

Inconsistencies of terminology are found among charts of different countries
and between charts issued at different times. For example, the spring effect as defined
here is a feature of only the semidiurnal tide, yet it is sometimes used synonymously
with tropic effect to refer to times of increased range of a diurnal tide. Such incon-
sistencies are being reduced through increased international cooperation.

Large-scale charts usually specify the datum of soundings and may contain a
tide note giving mean heights of the tide at one or more places on the chart. These
heights are intended merely as a rough guide to the change in depth to be expected
under the specified conditions. They should not be used for the prediction of heights
on any particular day. Such predictions should be obtained from tide tables (arts.
921-924). The tidal datums used in various areas are listed in appendix M.

3112. High water datums.—Heights of land features are usually referred on nautical
charts to a high water datum. The one used on charts of the United States, its ter-
ritories, and possessions, and widely used elsewhere, is mean high water (MHW),
which is the average height of all high waters over a 19-year period. Any other high
water datum in use on charts is likely to be higher than this. Other high water datums
are mean high water springs (MHWS), which is the average level of the high waters
that occur at the time of spring tides; mean higher high water (MHHW), which is the
average height of the higher high waters of each day; and tropic higher high water
(TcHHW), which is the average height of the higher high waters (or the single daily
high waters if the tide becomes diurnal) that occur when the moon is near maximum
declination and the diurnal effect is most pronounced. A reference merely to “high
water" leaves some doubt as to the specific level referred to, for the height of high water
varies from day to day. Where the range is large, the variation during a two-week
period may be considerable.

3113. Observations and predictions.—Since the tide at different places responds
differently to the tide-producing forces, the nature of the tide at any place can be
determined most accurately by actual observation. The predictions in tide tables
and the tidal data on nautical charts are based upon such observations.

Tides are usually observed by means of a continuously recording gage. A year
of observations is the minimum length desirable for determining the harmonic constants
used in prediction. For establishing mean sea level and the long-time changes in the
relative elevations of land and sea, as well as for other special uses, observations have
been made over periods of 20, 30, and even 50 years at important locations. Observa-
tions for a month or less will establish the type of tide and suffice for comparison with a
longer series of a similar type to determine tidal differences and constants.

TIDES AND TIDAL CURRENTS 711

Mathematically, the variations in the lunar and solar tide-producing forces, such
as those due to changing phase, distance, and declination, are considered as separate
constituent forces, and the harmonic analysis of observations reveals the response of
each constituent of the tide to its corresponding force. At any one place this response
remains constant and is shown for each constituent by harmonic constants which are
in the form of a phase angle for the time relation and an amplitude for the height.
Harmonic constants are used in making technical studies of the tide and predictions on
the tide predicting machine. Most published tide predictions are made by machine.

3114. Tide tables are published annually by most of the maritime nations of the
world. They consist primarily of two parts. One contains predictions of the time and
height of each high and low water for every day of the year for many important ports
called reference stations. The other part contains tidal differences for thousands of
other places, called subordinate stations, and specifies the reference station to which
the differences are to be applied in order to obtain time and height of tide for any day
at the subordinate station. The type of tide at a subordinate station is the same as
at its reference station. The use of tide tables is explained in articles 921-924.

3115. Meteorological effects.—The foregoing discussion of tide behavior assumes
normal weather conditions. The level of the sea is affected by wind and atmospheric
pressure. In general, onshore winds raise the level and offshore winds lower it, but the
amount of change varies at different places. During periods of low atmospheric
pressure, the water level tends to be higher than normal. For a stationary low, the
increase in elevation can be found by the formula

.=0.0325 (1010— P),

in which R, is the increase in elevation in feet, and P is the atmospheric pressure in
millibars. This is equal approximately to one centimeter per millibar depression, or
one foot (13.6 inches) per inch depression. For a moving low, the increase in elevation
is given by the formula

in which R is the increase in elevation in feet, Ro is the increase in feet for a stationary
low, C is the rate cf motion of the low in feet per second, g is the acceleration due to
gravity (32.2 feet per second per second), and h is the depth of water in feet.

Where the range of tide is very small, the meteorological effect may sometimes be

greater than the normal tide.
Tidal Current

3116. Tidal and nontidal currents.—Horizontal movement of the water is current.
It may beclassified as “tidal” and “nontidal.” Tidal current is the periodic horizontal flow
of water accompanying the rise and fall of the tide, and results from the same cause.
Nontidal current is any current not due to the tidal movement. Nontidal currents in-
clude the permanent currents in the general circulatory system of the oceans as well
as temporary currents arising from meteorological conditions. The current experienced
at any time is usually a combination of tidal and nontidal currents.

In navigation, the effect of the tidal current is often of more importance than the
changing depth due to the tide, and many mariners speak of “the tide," when they
have in mind the flow of the tidal current.

3117. General features.—Offshore, where the direction of flow is not restricted
by any barriers, the tidal current is rotary; that is, it flows continuously, with the direc-
tion changing through all points of the compass during the tidal period. The tendency

412 TIDES AND TIDAL CURRENTS

NORT a, pylinga for the rotation in direction has its origin in the de-
7 H—2 flecting force of the earth's rotation, and unless

| Yo ` modified by local conditions, the change 1s clockwise
"i H-l in the northern hemisphere aud counterclockwise in
eed | the southern hemisphere. The speed usually varies

/ H throughout the tidal cycle, passing through two

ri e ab st? maximums in approximately opposite directions, and

| wate a two minimums about halfway between the maxi-
Geh mums in time and direction. Rotary currents can be

p* N / depicted as in figure 3117a, by a series of arrows rep-
Lat Gei ege resenting the direction and speed of the current at
PR 7 LIGHTSHIP each hour. This is sometimes called a current rose.

1 KNOT Because of the elliptical pattern formed by the ends

IT abe e d Sca 208. of the arrows, it is also referred to as a current ellipse.
rent. Times are hours before and In rivers or straits, or where the direction of flow

after high and low tide at Nan- js more or less restricted to certain channels, the tidal

tucket Shoals Lightship. The : A pea e

bearing and length of each arrow current is reversing; that is, it flows alternately in

represents the hourly direction and approximately opposite directions with an instant or

speed of the current. See figure f :

3120a. short period. of little or no current, called slack

water, at each reversal of the current. During the

flow in each direction, the speed varies from zero at the time of slack water to a
maximum, called strength of flood or ebb, about midway between the slacks. Re-
versing currents can be indicated graphically, as in figure 3117b, by arrows that
represent the speed of the current at each hour. The flood is usually depicted above
the slack water line and the ebb belowit. The tidal current curve formed by the ends of
the arrows has the same characteristic sine form as the tide curve. (In illustrations
for certain purposes, as in figures 3118b and 3120b, it is convenient to omit the arrows
and show only the curve.)

A slight departure from the sine form is exhibited by the reversing current in a
strait, such as East River, New York, that connects two tidal bodies of water. The
tides at the two ends of a strait are seldom in phase or equal in range, and the current,
called hydraulic current, is generated largely by the continuously changing difference
in height of water at the two ends. The speed of a hydraulic current varies nearly
as the square root of the difference in height. The speed reaches a maximum more
quickly and remains at strength for a longer period than shown in figure 3117b, and
the period of weak current near the time of slack is considerably shortened.

The current direction or set is the direction
toward which the current flows. The speed is some-
times called the drift. The term “velocity” is often
used as the equivalent of “speed” when referring to
current, although strictly “velocity” implies direction
as well as speed. The term “strength” is also used
to refer to speed, but more often to greatest speed
between consecutive slack waters. The movement
toward shore or upstream is the flood, the move-
ment away from shore or downstream is the ebb.
In a purely semidiurnal type of current unaffected -
by nontidal flow, the flood and ebb each last about

ZA 6 SP 1OMI2 N14 16182022
HOURS

EBB STRENGTH Xý
ADMIRALTY INLET, PUGET SOUND

Ë . i ape à FIGURE 3117b.—Reversing tidal cur-
six hours and 13 minutes. But if there is either diur- rent. (Such graphs may show only
nal inequality or nontidal flow, the durations of flood the Our A Dorna

à arrows, as in figures 3118b and
and ebb may be quite unequal. 3120b.) See Aire 3120b.

TIDES AND TIDAL CURRENTS

713

3118. Types of tidal current.—Tidal currents may be of the semidiurnal, diurnal,
or mixed type; corresponding to a considerable degree to the type of tide at the place,
but often with a stronger semidiurnal tendency.

The tidal currents in tidal estuaries along the Atlantic coast of the United States
are examples of the semidiurnal type of reversing current. At Mobile Bay entrance

EBB] FLOOD

zx WATER

1 N
N / \

ch THE NARROWS, V

NEW YORK HARBOR >

V

Q
1 ^ o
TIN ^, fo)
N E
0 ll x3 4 ` u-
^^ SLACK “CI WATER T
Ñ ao
1 w
TAMPA BAY ENTRANCE 7
S ~
a
1 = 2
=3
o SLACK WATER ES
N ~ a
Lë a
w
1 ` y
Y

2 JUAN DE FUCA STRAIT ENTRANCE

FLOOD

EBB

`

UNIMAK PASS, ALEUTIAN IS.

ka

~

N
1 Z S

N
WATER

EBB] FLOOD

Hn
Æ
ee
N

N

MOBILE BAY ENTRANCE

FIGURE 3118a.— Several types of revers-

ing current. The pattern changes
gradually from day to day, particu-
larly for mixed types, passing through
cycles somewhat similar to that
shown for tides in figure 3106.

Islands.

Figure 3118a shows several types of reversing current.

they are almost purely diurnal. At most places,
however, the type is mixed to a greater or lesser
degree. At Tampa and Galveston entrances there
is only one flood and one ebb each day when the
moon is near its maximum declination, and two
floods and two ebbs each day when the moon is
near the equator. Along the Pacific coast of the
United States there are generally two floods and
two ebbs every day, but one of the floods or ebbs
has a greater speed and longer duration than the
other, the inequality varying with the declination
of the moon. The inequalities in the current often
differ considerably from place to place even within
limited areas, such as adjacent passages in Puget
Sound and various passages between the Aleutian

=P. N
SN FLOOD=-

0

s
o
z
x

ADMIRALTY INLET,
PUGET SOUND

Ficure 3118b.—Changes in a current of the mixed
type. Note that each day as the inequality increases,
the morning slacks draw together in time until on the
17th the morning flood disappears. On that day the
current ebbs throughout the morning.

Figure 3118b shows

how the flood disappears as the diurnal inequality increases at one station.

Offshore rotary currents that are purely semidiurnal repeat the elliptical pattern
(fig. 31172) each tidal cycle of 12 hours and 25 minutes. If there is considerable diurnal
inequality, the plotted hourly current arrows describe a set of two ellipses of different
sizes during a period of 24 hours and 50 minutes, as shown in figure 3118c, and the greater
the diurnal inequality, the greater the difference between the sizes of the two ellipses.
In a completely diurnal rotary current, the smaller ellipse disappears and only one
ellipse is produced in 24 hours and 50 minutes.

SWIFTSURE
BANK

NORTH HL—14" ——

h
N LH+1
N
HL-2 S LH+2h
LH+3h
earch 1 KNOT E

FicvRE 3118c.—Rotary tidal current with di-
urnal inequality. Times are in hours referred
to tides (higher high, lower low, lower high, and
higher low) at Swiftsure Bank.

TIDES AND TIDAL CURRENTS

3119. Variations and cycles.— Tidal
currents have periods and cycles similar
to those of the tides (art. 3109), and are
subject to similar variations, but flood and
ebb of the current do not necessarily occur
at the same times as the rise and fall of
the tide. The relationship is explained
further in article 3121.

The speed at strength increases and
decreases during the two-week period,
month, and year with the variations in
the range of tide. Thus, the stronger
spring and perigean currents occur near
the times of new and full moon and near
the times of the moon's perigee, or at times

of spring and perigean tides (art. 3108);
the weaker neap and apogean currents occur at the times of neap and apogean
tides; tropic currents with increased diurnal speeds or with larger diurnal inequali-
ties in speed occur at times of tropic tides; and equatorial currents with a minimum
diurnal effect occur at times of equatorial tides; etc.

As with the tide, a mean value represents an average obtained from a 19-year
series. Since a series of current observations is usually limited to a day or two, and
seldom covers more than a month or two, it is necessary to adjust the observed values,
usually by comparison with tides at a nearby place, to obtain such a mean.

3120. Effect of nontidal flow.—The current existing at any time is seldom purely
tidal, but usually includes also a nontidal current that is due to drainage, oceanic circu-
lation, wind, or other cause. The method in which tidal and nontidal currents combine
is best explained graphically, as in figures 31208 and 3120b. The pattern of the tidal
current remains unchanged, but the curve is shifted from the point or line from which the
currents are measured in the direction of the nontidal NORTH L+3
current and by an amount equal to it. It is some-
times more convenient graphically merely to move
the line or point of origin in the opposite direction.

Thus, the speed of the current flowing in the
direction of the nontidal current is increased by an
amount equal to the magnitude of the nontidal cur-
rent, and the speed of the current flowing in the op-
posite direction is decreased by an equal amount.
In figure 3120a a nontidal current is represented
both in direction and speed by the vector 40. Since
this is greater than the speed of the tidal current
in the opposite direction, the point A is outside the
ellipse. The direction and speed of the combined

— —
H+3

I 1 KNOT j
Figure 3120a.—Effect of nontidal

tidal and nontidal currents at any time is represented
by a vector from A to that point on the curve repre-
senting the given time, and can be scaled from the
graph. The strongest and weakest currents may no
longer be in the directions of the maximum and min-
imum of the tidal current. In a reversing current
(fig. 3120b), the effect is to advance the time of one
. slack and to retard the following one. If the speed of

current on the rotary tidal current
of figure 3117a. If the nontidal
current is northwest at 0.3 knot, it
may be represented by BO, and all
hourly directions and speeds will
then be measured from B. If it is
1.0 knot, it will be represented by
AO and the actual resultant hourly
directions and speeds will be meas-
ured from <A, as shown by the
arrows.

TIDES AND TIDAL CURRENTS 715

the nontidal current exceeds that of the reversing
tidal current, the resultant current flows continu-
ously in one direction without coming to a slack. In
this case, the speed varies from a maximum to a min-
imum and back to a maximum in each tidal cycle.
In figure 3120b the horizontal line 4 represents slack
water if only tidal currents are present. Line B
represents the effect of a 0.5-knot nontidal ebb, and
line C the effect of a 1.0-knot nontidal ebb. With
the condition shown at C there is only one flood each
tidal day. If the nontidal ebb were to increase to
approximately two knots, there would be no flood,
two maximum ebbs and two minimum ebbs occur-
ring during a tidal day.

3121. Relation between time of tidal current
and time of tide.—At many places where current
and tide are both semidiurnal, there is a definite re-
lation between times of current and times of high
and low water in the locality. Current atlases and
notes on nautical charts often make use of this rela-
tionship by presenting for particular locations the
direction and speed of the current at each succeeding

ADMIRALTY INLET,
PUGET SOUND

Figure 3120b.—Effect of nontidal

current on the reversing tidal
current of figure 3117b. If the
nontidal current is 0.5 knot in the
ebb direction, the ebb is increased
by moving the slack water line
from position A up 0.5 knot to
position B. Speeds will then be
measured from this broken line as
shown by the scale on the right,
and times of slack are changed.
If the nontidal current is 1.0 knot
in the ebb direction, as shown by
line C, the speeds are as shown on
the left, and the current will not
reverse to a flood in the afternoon;
it will merely slacken at about

hour after high and low water at a place for which 1500.
tide predictions are available.

In localities where there is considerable diurnal inequality in tide or current, or
where the type of current differs from the type of tide, the relationship is not constant,
and it may be hazardous to try to predict the times of current from times of tide.
Note the current curve for Unimak Pass in the Aleutians in figure 3118a. It shows
the current as predicted in the tidal current tables. Predictions of high and low waters
in the tide tables might have led one to expect the current to change from flood to ebb
in the late morning, whereas actually the current continued to run flood with some
strength at that time.

Since the relationship between times of tidal current and tide is not everywhere
the same, and may be variable at the same place, one should exercise extreme caution
in using general rules. The belief that slacks occur at local high and low tides and that
the maximum flood and ebb occur when the tide is rising or falling most rapidly may be
approximately true at the seaward entrance to, and in the upper reaches of, an inland
tidal waterway. But generally this is not true in other parts of inland waterways.
When an inland waterway is extensive or its entrance constricted, the slacks in some
parts of the waterway often occur midway between the times of high and low tide.
Usually in such waterways the relationship changes from place to place as one pro-
gresses upstream, slack water getting progressively later with respect to the local tide
until at the head of tidewater (the inland limit of water affected by a tide) the slacks
occur at the times of high and low tide.

3122. Relation between speed of current and range of tide.—The variation in
the speed of the tidal current from place to place is not necessarily consistent with the
range of tide. It may be the reverse. For example, currents are weak in the Gulf of
Maine where the tides are large, and strong near Nantucket Island and in Nantucket
Sound where the tides are small.

At any one place, however, the speed of the current at strength of flood and
ebb varies during the month in about the same proportion as the range of tide, and

716 TIDES AND TIDAL CURRENTS

one can use this relationship to determine the relative strength of currents on
any day. R :

3123. Variation across an estuary.—In inland tidal waterways the time of tidal
current varies across the channel from shore to shore. On the average, the current
turns earlier near shore than in midstream, where the speed is greater. Differences of
half an hour to an hour are not uncommon, but the difference varies and the relationship
may be nullified by the effect of nontidal flow.

The speed of the current also varies across the channel, usually being greater in
midstream or midchannel than near shore, but in a winding river or channel the
strongest currents occur near the concave shore. Near the opposite (convex) shore
the currents are weak or may eddy.

3124. Variation with depth.—In tidal rivers the subsurface current acting on the
lower portion of the hull may differ considerably from the surface current. An ap-
preciable subsurface current may be present when the surface movement appears to be
practically slack, and the subsurface current may even be flowing with appreciable
speed in the opposite direction to the surface current.

In a tidal estuary, particularly in the lower reaches where there is considerable
difference in density from top to bottom, flood usually begins earlier near the bottom
than at the surface. The differences may be an hour or two or as little as a few minutes,
depending upon the estuary, the location in the estuary, and freshet conditions. Even
when the fresh water runoff becomes so great as to prevent the surface current from
flooding, it may still flood below the surface. The difference in time of ebb from
surface to bottom is normally small but subject to variation with time and location.

The ebb speed at strength usually decreases gradually from top to bottom, but
the speed of flood at strength often is stronger at subsurface depths than at the surface.

3125. Observations.—Observations of the current are made by means of a current
meter or current pole and log line. In the past, most successful meters required a vessel
and observers in continual attendance, as is necessary with the pole and line. Because
of the difficulty and expense of such observations, they usually covered only a period
of a day or two at a place. Observations of a month are the exception, and longer
series were obtained only where ship and observers were available because of other
duties, such as at lightships, where observations have been continued over a number of
years.

Newer meters have been and are being developed that are suspended from a buoy
and that record either in the buoy or send speed and direction impulses by radio to a
base station on ship or land. With them, the period of observation has been increased
so that in some recent surveys of United States harbors, the minimum period of ob-
servation was four days, with observations at several stations being continued over a
period of 15 to 29 days.

3126. Tidal current tables and other sources of information.—The navigator
should not attempt to predict currents without specific information for the locality in
which he is interested. Such information is contained in various forms in many navi-
gational publications.

Tidal current tables, issued annually, list daily predictions of the times and strengths
of flood and ebb currents, and of the times of intervening slacks. Due to lack of
observational data, coverage is considerably more limited than for the tides. The
tidal current tables do include supplemental data by which tidal current predictions can
be determined for many places in addition to those for which daily predictions
are given. The predictions are made by the tide-predicting machine, using cur-
rent harmonic constants that are obtained by analyzing current observations in

the same manner as for tides (art. 3113). The use of tidal current tables is explained in
articles 925-929.

TIDES AND TIDAL CURRENTS 717

Sailing directions and coast pilots issued by maritime nations include general
descriptions of current behavior in various localities throughout the world.

Tidal current charts. A number of important harbors and waterways are covered
by sets of tidal current charts showing graphically the hourly current movement.

References

Doodson, A. T., and Warburg, H. D. Admiralty Manual of Tides. London, H. M.
Stationery Office, 1941.

Marmer, H. A. The Tide. New York, Appleton, 1926.

Schureman, Paul. Manual of the Harmonic Analysis and Prediction of Tides. Rev.
ed. U.S. Coast and Geodetic Survey Special Publication No. 98. Washington,
U.S. Govt. Print. Off., 1940.

Schureman, Paul. Tide and Current Glossary. Rev. ed. U.S. Coast and Geodetic
Survey Special Publication No. 228. Washington, U. S. Govt. Print. Off., 1949.

U. S. Coast and Geodetic Survey. Manual of Current Observations. Special Publica-
tion No. 215. Rev. ed. Washington, U. S. Govt. Print. Off., 1950.

U.S. Coast and Geodetic Survey. Manual of Tide Observations. Special Publication
No. 196. Rev. ed. Washington, U. S. Govt. Print. Off., 1941.

U.S. Coast and Geodetic Survey. Tidal Current Charts. Washington, several published
periodically.

U.S. Coast and Geodetic Survey. Tide Tables and Tidal Current Tables. Washington,
U. S. Govt. Print. Off., several volumes of each published annually.

ø

CHAPTER XXXII
OCEAN CURRENTS

3201. Introduction.—The movement of water comprising the oceans is one of the
principal sources of discrepancy between dead reckoning and actual positions of vessels.
Water in essentially horizontal motion is called a current, the direction toward which it
moves being the set, and its speed the drift. A well-defined current extending over a
considerable region of the ocean is called an ocean current.

A periodic current is one the speed or direction of which changes cyclically at
somewhat regular intervals, as a tidal current. A seasonal current is one which has
large changes in speed or direction due to seasonal winds. A permanent current is one
which experiences relatively little periodic or seasonal change.

A coastal current flows roughly parallel to a coast, outside the surf zone, while a
longshore current is one parallel to a shore, inside the surf zone, and generated by waves
striking the beach at an angle. Any current some distance from the shore may be
called an offshore current, and one close to the shore an inshore current.

A surface current is one present at the surface, particularly one that does not ex-
tend more than a relatively few feet below the surface. A subsurface current is one
which is present below the surface only.

There is evidence to indicate that the strongest ocean currents consist of relatively
narrow, high-speed streams that follow winding, shifting courses. Often associated
with these currents are secondary countercurrents flowing adjacent to them but in the
opposite direction, and somewhat local, roughly circular, eddy currents. A relatively
narrow, deep, fast-moving current is sometimes called a stream current, and a broad,
shallow, slow-moving one a drift current.

3202. Causes of ocean currents.—Although man’s knowledge of the processes
which produce and maintain ocean currents is far from complete, he does have a
general understanding of the principal factors involved. The primary generating force
is wind, and the chief secondary force is the density differences in the water. In addi-
tion, such factors as depth of water, underwater topography, shape of the basin in
which the current is running, extent and location of land, and deflection by the rotation
of the earth all affect the oceanic circulation.

3203. Wind currents.—The stress of wind blowing across the sea causes the surface
layer of water to move. This motion is transmitted to each succeeding layer below
the surface, but due to internal friction within the water, the rate of motion decreases
with depth. The current thus set up is called a wind current. Although there are
many variables, it is generally true that a steady wind for about 12 hours is needed
to establish such a current.

A wind current does not flow in the direction of the wind, being deflected by
Coriolis force (art. 1611), due to rotation of the earth. This deflection is toward the
right in the northern hemisphere, and toward the left in the southern hemisphere. The
Coriolis force is greater in higher latitudes, and is more effective in deep water. In gen-
eral, the difference between wind direction and surface wind-current direction varies
from about 15° along shallow coastal areas to a maximum of 45° in the deep oceans.

The angle increases with depth. At several hundred fathoms the current may flow in
the opposite direction to the surface current.

718

OCEAN CURRENTS 719

The speed of the current depends upon the speed of the wind, its constancy, the
length of time it has blown, and other factors. In general, however, about two percent
of the wind speed, or a little less, is a good average for deep water where the wind
has been blowing steadily for at least 12 hours.

3204. Currents related to density differences.—As indicated in article 3009, the
density of water varies with salinity, temperature, and pressure. At any given depth,
the differences in density are due to differences in temperature and salinity. When
suitable information is available, a map showing geographical density distribution at
a certain depth could be drawn, with lines connecting points of equal density. These
isopycnic lines, or lines connecting points at which a given density occurs at the same
depth, would be similar to isobars on a weather map (art. 3827), and would serve
an analogous purpose, showing areas of high density and those of low density. In
an area of high density, the water surface is lower than in an area of low density, the max-
imum difference in height being of the order of one to two feet in 40 miles. Because
of this difference, water tends to flow from an area of higher water (low density) to
one of lower water (high density), but due to rotation of the earth, it is deflected
toward the right in the northern hemisphere, and toward the left in the southern
hemisphere. Thus, a circulation is set up similar to the cyclonic and anticyclonic
circulation in the atmosphere. The greater the density gradient (rate of change with
distance), the faster the related current.

3205. Oceanic circulation.—A number of ocean currents flow with great persist-
ence, setting up a circulation that continues with relatively little change throughout
the year. Because of the influence of wind in creating current (art. 3203), there is a
relationship between this oceanic circulation and the general circulation of the atmos-
phere (art. 3804). The oceanic circulation is shown in figure 3205, with the names of
the major ocean currents. Some differences in opinion exist regarding the names and
limits of some of the currents, but those shown are representative. The spacing of
the lines is a general indication of speed, but conditions vary somewhat with the
season. This is particularly noticeable in the Indian Ocean and along the South
China coast, where currents are influenced to a marked degree by the monsoons (art.
3810).

3206. Atlantic Ocean currents.—The trade winds (art. 3806), which blow with
great persistence, set up a system of equatorial currents which at times extends over
as much as 50° of latitude, or even more. There are two westerly flowing currents
conforming generally with the areas of trade winds, separated by a weaker, easterly
flowing countercurrent.

The north equatorial current originates to the northward of the Cape Verde Islands
and flows almost due west at an average speed of about 0.7 knot.

The south equatorial current is more extensive. It starts off the west coast of
Africa, south of the Gulf of Guinea, and flows in a generally westerly direction at an
average speed of about 0.6 knot. However, the speed gradually increases until it may
reach a value of 2.5 knots or more off the east coast of South America. As the current
approaches Cabo de Sáo Roque, the eastern extremity of South America, it divides, the
southern part curving toward the south along the coast of Brazil, and the northern
part being deflected by the continent of South America toward the north.

Between the north and south equatorial currents a weaker equatorial counter-
current sets toward the east in the general vicinity of the doldrums (art. 3805). This
is fed by water from the two westerly flowing equatorial currents, particularly the
south equatorial current. The extent and strength of the equatorial countercurrent
changes with the seasonal variations of the wind. It reaches a maximum during July
and August, when it extends from about 50% west longitude to the Gulf of Guinea.

OCEAN CURRENTS

720

"(I19gur M 919YASTUIY UL9YJIOU) P[IOM 94 JO SĻU91INO oovjgms IOÍSJA —'S0OC8 YNDI A

Borat „GET 20ST

lex cae

«T
en Pinos

|
A REE all M

4

D 2uiDvd HIMON|

NA

OCEAN CURRENTS 721

During its minimum, in December and January, it is of very limited extent, the western
portion disappearing altogether.

That part of the south equatorial current flowing along the northern coast of
South America which does not feed the equatorial countercurrent unites with the north
equatorial current at a point west of the equatorial countercurrent. A large part of
the combined current flows through various passages between the Windward Islands,
into the Caribbean Sea. It sets toward the west, and then somewhat north of west,
finally arriving off the Yucatan peninsula. From here, some of the water curves
toward the right, flowing some distance off the shore of the Gulf of Mexico, and part
of it curves more sharply toward the east and flows directly toward the north coast
of Cuba. These two parts reunite in the Straits of Florida to form the most remarkable
of all ocean currents, the Gulf Stream. Off the southeast coast of Florida this current
is augmented by a current flowing along the northern coasts of Puerto Rico, Hispaniola,
and Cuba. Another current flowing eastward of the Bahamas joins the stream north
of these islands.

The Gulf Stream follows generally along the east coast of North America, flowing
around Florida, northward and then northeastward toward Cape Hatteras, and then
curving toward the east and becoming broader and slower. After passing the Grand
Banks, it turns more toward the north and becomes a broad drift current flowing across
the North Atlantic. That part in the Straits of Florida is sometimes called the Florida
current.

A tremendous volume of water flows northward in the Gulf Stream. It can be
distinguished by its deep indigo-blue color, which contrasts sharply with the dull
green of the surrounding water. It is accompanied by frequent squalls. When the
Gulf Stream encounters the cold water of the Labrador current, principally in the
vicinity of the Grand Banks, there is little mixing of the waters. Instead, the junction
is marked by a sharp change in temperature. The line or surface along which this
occurs is called the cold wall. When the warm Gulf Stream water encounters cold air,
evaporation is so rapid that the rising vapor may be visible as frost smoke (art. 3815).
The stream carries large quantities of gulfweed from the tropics to higher latitudes.

Recent investigations have shown that the current itself is much narrower and
faster than previously supposed, and considerably more variable in its position and
speed. The maximum current off Florida ranges from about two to four knots. To
the northward the speed is generally less, and decreases further after the current passes
Cape Hatteras. As the stream meanders and shifts position, eddies sometimes break
off and continue as separate, circular flows until they dissipate. Boats in the Bermuda
Race have been known to be within sight of each other and be carried in opposite
directions by different parts of the same current. As the current shifts position, its
extent does not always coincide with the area of warm, blue water. When the sea is
relatively smooth, the edges of the current are marked by ripples.

Information is not yet available to permit prediction of the position and speed of
the current at any future time, but it has been found that tidal forces apparently
influence the current, which reaches its daily maximum speed about three hours after
transit of the moon. The current generally is faster at the time of neap tides than at
spring tides. When the moon is over the equator, the stream is narrower and faster
than at maximum northerly or southerly declination. Variations in the trade winds
(art. 3806) also affect the current.

As the Gulf Stream continues eastward and northeastward beyond the Grand
Banks, it gradually widens and decreases speed until it becomes a vast, slow-moving
drift current known as the North Atlantic current, in the general vicinity of the pre-

122 OCEAN CURRENTS

vailing westerlies (art. 3808). In the eastern part of the Atlantic it divides into the
northeast drift current and the southeast drift current.

The northeast drift current continues in a generally northeasterly direction toward
the Norwegian Sea. As it does so, it continues to widen and decrease speed. South
of Iceland it branches to form the Irminger current and the Norway current. The
Irminger current curves toward the north and northwest to join the East Greenland
current southwest of Iceland. The Norway current continues in a northeasterly
direction along the coast of Norway. Part of it, the North Cape current, rounds North
Cape into the Barents Sea. The other part curves toward the north and becomes
known as the Spitzbergen current. Before reaching Svalbard (Spitzbergen), it curves
toward the west and joins the cold east Greenland current flowing southward in the
Greenland Sea. As this current flows past Iceland, it is further augmented by the
Irminger current.

Off Kap Farvel, at the southern tip of Greenland, the east Greenland current
curves sharply to the northwest, following the coast line. As it does so, it becomes
known as the west Greenland current. This current continues along the west coast
of Greenland, through Davis Strait, and into Baffin Bay. Both east and west Green-
land currents are sometimes known by the single name Greenland current.

In Baffin Bay the Greenland current follows generally the coast, curving west-
ward off Kap York to form the southerly flowing Labrador current. This cold current
flows southward off the coast of Baffin Island, through Davis Strait, along the coast
of Labrador and Newfoundland, to the Grand Banks, carrying with it large quantities
of ice (ch. XXXVI). Here it encounters the warm water of the Gulf Stream, creating
the “cold wall.” Some of the cold water flows southward along the east coast of
North America, inshore of the Gulf Stream, as far as Cape Hatteras. The remainder
curves toward the east and flows along the northern edge of the North Atlantic and
northeast drift currents, gradually merging with them.

The southeast drift current curves toward the east, southeast, and then south
as it is deflected by the coast of Europe. It flows past the Bay of Biscay, toward
southeastern Europe and the Canary Islands, where it continues as the Canary current.
In the vicinity of the Cape Verde Islands, this current divides, part of it curving toward
the west to help form the north equatorial current, and part of it curving toward the
east to follow the coast of Africa into the Gulf of Guinea, where it is known as the
Guinea current. This current is augmented by the equatorial countercurrent and, in
summer, it is strengthened by monsoon winds. It flows in close proximity to the
south equatorial current, but in the opposite direction. As it curves toward the south,
still following the African coast, it merges with the south equatorial current.

The clockwise circulation of the North Atlantic leaves a large central area having
no well-defined currents. This area is known as the Sargasso Sea, from the large
quantities of sargasso or gulfweed encountered there. j

That branch of the south equatorial current which curves toward the south off
the east coast of South America follows the coast as the warm, highly-saline Brazil
current, which in some respects resembles the Gulf Stream. Off Uruguay, it encounters
the colder, less-salty Falkland current and the two curve toward the east to form the
broad, slow-moving South Atlantic current, in the general vicinity of the prevailing
westerlies (art. 3808). This current flows eastward to a point west of the Cape of
Good Hope, where it curves northward to follow the west coast of Africa as the strong
Benguela current, augmented somewhat by part of the Agulhas current flowing around
the southern part of Africa from the Indian Ocean. As it continues northward, the
current gradually widens and slows. At a point east of St. Helena Island it curves
westward to continue as part of the south equatorial current, thus completing the

OCEAN CURRENTS 7239

counterclockwise circulation of the South Atlantic. The Benguela current is augmented
somewhat by the west wind drift, a current which flows easterly around Antarctica.
As the west wind drift flows past Cape Horn, that part in the immediate vicinity
of the cape is called the Cape Horn current. This current rounds the cape and flows
in & northerly and northeasterly direction along the coast of South America as the
Falkland current.

3207. Pacific Ocean currents follow the general pattern of those in the Atlantic.
The north equatorial current flows westward in the general area of the northeast
trades, and the south equatorial current follows a similar path in the region of the
southeast trades. Between these two, the weaker equatorial countercurrent sets
toward the east, just north of the equator.

After passing the Mariana Islands, the major part of the north equatorial current
curves somewhat toward the northwest, past the Philippines and Formosa. Here it is
deflected further toward the north, where it becomes known as the Kuroshio, and then
toward the northeast past the Nansei Shoto and Japan, and on in a more easterly
direction. Part of the Kuroshio, called the Tsushima current, flows through Tsushima
Strait, between Japan and Korea, and the Sea of Japan, following generally the north-
west coast of Japan. North of Japan it curves eastward and then southeastward to
rejoin the main part of the Kuroshio. The limits and volume of the Kuroshio are in-
fluenced by the monsoons (art. 3810), being augmented during the season of southwest-
erly winds, and diminished when the northeasterly winds are prevalent.

The Kuroshio (Japanese for “Black Stream") is so named because of the dark
color of its water. It is sometimes called the Japan Stream. In many respects it is
similar to the Gulf Stream of the Atlantic. Like that current, it carries large quantities
of warm tropical water to higher latitudes, and then curves toward the east as a major
part of the general clockwise circulation in the northern hemisphere. As it does so,
it widens and slows. A small part of it curves to the right to form a weak clockwise
circulation west of the Hawaiian Islands. The major portion continues on between
the Aleutians and the Hawaiian Islands, where it becomes known as the North Pacific
current.

As this current approaches the North American continent, most of it is deflected
toward the right to form a clockwise circulation between the west coast of North
America and the Hawaiian Islands. This part of the current has become so broad that
the circulation is generally weak. A small part near the coast, however, joins the
southern branch of the Aleutian current, and flows southeastward as the California
current. The average speed of this current is about 0.8 knot. It is strongest near
land. Near the southern end of Baja (Lower) California, this current curves sharply
to the west and broadens to form the major portion of the north equatorial current.

During the winter, a weak countercurrent flows northwestward along the west
coast of North America from Southern California to Vancouver Island, inshore of the
southeasterly-flowing California current. This is called the Davidson current.

Off the west coast of Mexico, south of Baja California, the current flows south-
eastward, as a continuation of part of the California current, during the winter. During
the summer, the current in this area is northwestward, as a continuation of the equatorial
countercurrent, before it turns westward to help form the north equatorial current.

As in the Atlantic, there is in the Pacific a counterclockwise circulation to the
north of the clockwise circulation. Cold water flowing southward through the western
part of Bering Strait between Alaska and Siberia is joined by water circulating counter-
clockwise in the Bering Sea to form the Oyashio. As the current leaves the strait, it
curves toward the right and flows southwesterly along the coast of Siberia and the
Kuril Islands. This current brings quantities of sea ice, but no icebergs. When it

724 OCEAN CURRENTS

encounters the Kuroshio, the Oyashio curves southward and then eastward, the
greater portion joining the Kuroshio and North Pacific current. The northern portion
continues eastward to join the curving Aleutian current.

As this current approaches the west coast of North America, west of Vancouver
Island, part of it curves toward the right and is joined by water from the North Pacific
current, to form the California current. The northern branch of the Aleutian current
curves in a counterclockwise direction to form the Alaska current, which generally
follows the coast of Canada and Alaska. When it arrives off the Aleutian Islands, it
becomes known as the Aleutian current. Part of it flows along the southern side of
these islands to about the 180th meridian, where it curves in a counterclockwise
direction and becomes an easterly flowing current, being augmented by the northern
part of the Oyashio. The other part of the Aleutian current flows through various
openings between the Aleutian Islands, into the Bering Sea. Here it flows in a general
counterclockwise direction, most of it finally joining the southerly flowing Oyashio,
and a small part of it flowing northward through the eastern side of the Bering Strait,
into the Arctic Ocean.

The south equatorial current, extending in width between about 4? N latitude and
10°S, flows westward from South America to the western Pacific. After this current
crosses the 180th meridian, the major part curves in & counterclockwise direction,
entering the Coral Sea, and then curving more sharply toward the south along the
east coast of Australia, where it is known as the east Australia current. In the Tasman
Sea, northeast of Tasmania, it is augmented by water from the west wind drift, flowing
eastward south of Australia. It curves toward the southeast and then the east, grad-
ually merging with the easterly flowing west wind drift, a broad, slow-moving current
that circles Antarctica.

Near the southern extremity of South America, most of this current flows east-
ward into the Atlantic, but part of it curves toward the left and flows generally north-
ward along the west coast of South America as the Peru current. Occasionally a set
directly toward land is encountered. At about Cabo Blanco, where the coast falls
away to the right, the current curves toward the left, past the Galapagos Islands, where
it takes a westerly set and constitutes the major portion of the south equatorial current,
thus completing the counterclockwise circulation of the South Pacific.

During the northern hemisphere summer, a weak northern branch of the south
equatorial current, known as the Rossel current, continues on toward the west and
northwest along both the southern and northeastern coasts of New Guinea. The
southern part flows through Torres Strait, between New Guinea and Australia, into
the Arafura Sea. Here, it gradually loses its identity, part of it flowing on toward the
west as part of the south equatorial current of the Indian Ocean, and part of it fol-
lowing the coast of Australia and finally joining the easterly flowing west wind
drift. The northern part of the Rossel current curves in a clockwise direction to
help form the Pacific equatorial countercurrent. During the northern hemisphere
winter, the Rossel current is replaced by an easterly flowing current from the Indian
Ocean.

3208. Indian Ocean currents follow generally the pattern of the Atlantic and Pacific,
but with differences caused principally by the monsoons (art. 3810) and the more
limited extent of water in the northern hemisphere. During the northern hemisphere
winter, the north equatorial current and south equatorial current flow toward the west,
with the weaker, easterly flowing equatorial countercurrent flowing between them, as
in the Atlantic and Pacific (but somewhat south of the equator). But during the
northern hemisphere summer, both the north equatorial current and the equatorial

OCEAN CURRENTS 725

countercurrent are replaced by the monsoon current, which flows eastward and south-
eastward across the Arabian Sea and the Bay of Bengal. Near Sumatra, this current
curves in a clockwise direction and flows westward, augmenting the south equatorial
current and setting up a clockwise circulation in the northern part of the Indian Ocean.

As the south equatorial current approaches the coast of Africa, it curves toward
the southwest, part of it flowing through the Mozambique Channel between M adagascar
and the mainland, and part flowing along the east coast of Madagascar. At the
southern end of this island the two join to form the strong Agulhas current, which is
analogous to the Gulf Stream.

A small part of the Agulhas current rounds the southern end of Africa and helps
form the Benguela current. The major portion, however, curves sharply southward
and then eastward to join the west wind drift. This junction is often marked by a
broken and confused sea. During the northern hemisphere winter the northern
part of this current curves in a counterclockwise direction to form the west Australia
current, which flows northward along the west coast of Australia. As it passes North-
west Cape, it curves northwestward to help form the south equatorial current. During
the northern hemisphere summer, the west Australia current is replaced by a weak
current flowing around the western part of Australia as an extension of the southern
branch of the Rossel current.

3209. Polar currents.—The waters of the North Atlantic enter the Arctic Ocean
between Norway and Svalbard. The currents flow easterly north of Siberia to the
region of the Novosibirskiye Ostrova, where they turn northerly across the north pole
and continue down the Greenland coast to form the east Greenland current. On the
American side of the arctic basin, there is a weak, continuous clockwise flow centered
in the vicinity of 80? N, 150°W. A current north through Bering Strait along the
American coast is balanced by an outward southerly flow along the Siberian coast,
which eventually becomes part of the Oyashio. Each of the main islands or island
groups in the arctic, as far as is known, seems to have a clockwise nearshore circulation
around it. The Barents Sea, Kara Sea, and Laptev Sea each have a weak counter-
clockwise circulation. A similar but weaker counterclockwise current system appears
to exist in the East Siberian Sea.

In the antarctic, the circulation is generally from west to east in a broad, slow-
moving current extending completely around Antarctica. This is called the west wind
drift, although it is formed partly by the strong westerly wind in this area and partly
by density differences. This current is augmented by the Brazil and Falkland cur-
rents in the Atlantic, the east Australia current in the Pacific, and the Agulhas cur-
rent in the Indian Ocean. In return, part of it curves northward to form the Cape Horn,
Falkland, and most of the Benguela currents in the Atlantic, the Peru current in the .
Pacific, and west Australia current in the Indian Ocean.

3210. Ocean currents and climate.—Many of the ocean currents exert a marked
influence upon the climate of the coastal regions along which they flow. Thus, warm
water from the Gulf Stream, continuing as the North Atlantic, northeast drift, and
Irminger currents, arrives off the southwest coast of Iceland, warming it to the extent
that Reykjavik has a higher average winter temperature than New York City, far to the
south. Great Britain and Labrador are at about the same latitude, but the climate of
Great Britain is much milder because of the difference of temperature of currents. The
West Coast of the United States is cooled in the summer by the California current, and
warmed in the winter by the Davidson current. As a result of this condition, partly,
the range of monthly average temperature is comparatively small.

Currents exercise other influences besides those on temperature. The pressure
pattern is affected materially, as air over a cold current contracts as it is cooled, and

726 OCEAN CURRENTS

that over a warm current expands. As air cools above a cold ocean current, fog is
likely to form. Frost smoke (art. 3815) is most prevalent over a warm current which
flows into a colder region. Evaporation is greater from warm water than from cold
water.

In these and other ways, the climate of the earth is closely associated with the
ocean currents, although other factors, such as topography and prevailing winds, are
also important.

References

Stream Drift Chart of the World—January. U.S. Navy Hydrographic Office Pilot
Charts (various editions).

Stream Drift Chart of the World—July. U.S. Navy Hydrographic Office Pilot Charts
(various editions).

Sverdrup, H. U., Johnson, M. W., and Fleming, R. H. The Oceans, Their Physics,
Ohemástry and General Biology. New York, Prentice-Hall, 1942.

CHAPTER XXXIII
OCEAN WAVES

3301. Introduction.—Undulations of the surface of the water, called waves, are
perhaps the most widely observed phenomenon at sea, and possibly the least under-
stood by the average seaman. The mariner equipped with a knowledge of the basic
facts concerning waves is able to use them to his advantage, and either avoid hazardous
conditions or operate with a minimum of danger if such conditions cannot be avoided.

3302. Causes of waves.—Waves on the surface of the sea are caused principally
by wind, but other factors, such as submarine earthquakes, volcanic eruptions, and the
tide, also cause waves. If a breeze of less than two knots starts to blow across smooth
water, small wavelets called ripples form almost instantaneously. When the breeze
dies, the ripples disappear as suddenly as they formed, the level surface being restored
by surface tension of the water. If the wind speed exceeds two knots, more stable
gravity waves gradually form, and progress with the wind.

While the generating wind blows, the resulting waves may be referred to as sea.
When the wind stops or changes direction, the waves that continue on without relation
to local winds are called swell.

Unlike wind and current, waves are not deflected appreciably by the rotation of
the earth, but move in the direction in which the generating wind blows. When this
wind ceases, friction and spreading cause the waves to be reduced in height, or at-
tenuated, as they move across the surface. However, the reduction takes place so
slowly that swell continues until it reaches some obstruction, such as a shore.

When sufficient data on wind conditions are available, the swell and state of the
sea a day or more in advance can be predicted. Such forecasts have been found
useful in wartime offshore unloading operations. The U. S. Navy Hydrographic Office
forecasts sea and swell conditions.

3303. Wave characteristics.—Ocean waves are very nearly in the shape of an
inverted cycloid, the figure formed by a point inside the rim of a wheel rolling along
a level surface. This shape is shown in figure 33032. The highest parts of waves are
called crests, and the interven-

ing lowest parts, troughs. Since HA +]

the crests are steeper and nar- A STILL WATER LEVEL —. 7 SS H
rower than the troughs, the

mean or still water level is a FIGURE 3303a.—A typical sea wave.

little lower than halfway be-

tween the crests and troughs. The vertical distance between trough and crest is
called wave height, labeled H in figure 3303a. The horizontal distance between
successive crests, measured in the direction of travel, is called wave length, labeled L.
The time interval between passage of successive crests at a stationary point is called
wave period (P). Wave height, length, and period depend upon a number of factors, such
as the wind speed, the length of time it has blown, and its fetch (the straight distance
it has traveled over the surface). Table 3303 indicates the relationship between wind
speed, fetch, length of time the wind blows, wave height, and wave period in deep

water.
TPH

728

p
A
m
A
5
Z
E
e
o
E
5
4
E
m

OCEAN WAVES

WACO c»
ÁÓBABSS
rr

(O 00 mo
EEN
ana

19 O 1910 O
SIS
GO HH tH

ooo
Noom
SIA

EE
down
rd rd rd rd mA
- 00 41 00
Una

nanon
SESS

no O19 ©
SISOS
65 c6 C0 65 YA

OD OD» rA e
Nod 15 cB o6
rr
omo+-oa
0600005

KEE? | onwnoo

reco
NAS

sirds
C C9 C0 OD OD

ooo
«d dodo

monroe | BOVOM

HHS OS
Hmm

mo oma
te 06 od o6

SANS
DON +
BIS

OMRON
BARS
rr

Seene
GEELEN

A C C wi

CERE

omoco
SEET
ANANN

eene
GS is ss
NANNN

t-O ooo
Banda
rd rd rA

ioc cou
Moo
mom A O

DOSORO

SASR

NDONS
Sra
65 c9 63 a

59.2 | 27.5

Based upon the relation-

Fetch in nautical miles.

feet) and P period (in seconds).

in

ficant height (i

igni

ships given in H.O. Pub. No. 604, Techniques for Forecasting Wind Waves and Swell. See also H.O. Pub. No. 603, Observing and Forecasting Ocean Waves.

TABLE 3303.—Minimum Time (T) in hours that wind must blow to form waves of H s

OCEAN WAVES 729

If the water is deeper than one-half the wave length (L), this length in feet is
theoretically related to period (P) in seconds by the formula

L=5.12P?,

The actual value has been found to be a little less than this for swell, and about two-
thirds the length determined by this formula for sea. When the waves leave the
generating area and continue as free waves, the wave length and period continue to
increase, while the height decreases. The rate of change gradually decreases.

The speed (S) of a free wave in deep water is nearly independent of its height or
steepness. For swell, its relationship in knots to the period (P) in seconds is given
by the formula

S=3.03P.

The relationship for sea is not known.

The theoretical relationship between speed, wave length, and period is shown in
figure 3303b. Thus, as waves continue on beyond the generating area, the period,
length, and speed all increase, providing some indication of the distance of the gener-

a
En

Sa T—
j]

i- AE ————— 1
o

60 —

50

SPEED (S), KNOTS
wW
o

20

ü

zb
— dis
"m

0 200 400 600 800 1000 1200 1400 1600 1800

LENGTH (L), FEET

FicGurE 3303b.— Relationship between speed, length, and period of waves in deep water,
based upon the theoretical relationship between period and length.

ating area. However, the time needed for a wave system to travel some distance is
double that which would be indicated by the speed of individual waves. This is because
the front wave gradually disappears and transfers its energy to succeeding waves. The
process is followed by each front wave in succession, at such a rate that the wave
system advances at a speed which is just half that of individual waves. This process
can be seen in the bow wave of a vessel. The speed at which the wave system advances
is called group velocity.

Because of the existence of many independent wave systems at the same time,
the sea surface acquires a complex and irregular pattern. Also, since the longer waves
outrun the shorter ones, the resulting interference adds to the complexity of the pattern.

730 OCEAN WAVES

The process of interference, il-
lustrated in figure 3303c, is du-
plicated many times in the sea,
being the principal reason that
successive waves are not of the
same height. The irregularity
of the surface may be further
accentuated by the presence of
wave systems crossing at an
angle to each other, producing
peak-like rises.

FIGURE 3303c.—Interference. The upper part of A shows two :
waves of equal height and nearly equal length traveling in 4 In reporting average wave
the same direction. The lower part of A shows the resulting heights, the mariner has a tend-

e alae R poe information is shown for short ency to neglect the it St x

It has been found that the
reported value is about the average for the highest one-third. This is sometimes
called the “significant” wave height. The approximate relationship between this
height and others, is as follows:

Wave Relative height
Average 0. 64
Significant 1.00
Highest 10 percent 1.29
Highest 1.87

3304. Path of water particles in a wave.—As shown in figure 3304, a particle of
water on the surface of the ocean follows a somewhat circular orbit as a wave passes,
but moves very little in the direction of motion of the

wave. The common wave producing this action is m p
called an oscillatory wave. As the crest passes, the S
particle moves forward, giving the water the appear- Im E

ance of moving with the wave. As the trough passes,
the motion is in the opposite direction. The radius of
the circular orbit decreases with depth, approaching zero
at a depth equal to about half the wave length. In
shallower water the orbits become more elliptical, and in
very shallow water, as at a beach, the vertical motion
disappears almost completely.

Since the speed is greater at the top of the orbit than
at the bottom, the particle is not at exactly its original
point following passage of a wave, but has moved slightly

in the direction of motion of the wave. However, since pygure 3304.—Orbital motion

this advance is small in relation to the vertical displace- and MR: 8, Ry a

. : : : particle on the surface of deep
ment, a floating object is raised and lowered by passage water during two wave bos
of & wave, but moved little from its original position. riods.

If this were not so, a slow moving vessel might experi-
ence considerable difficulty in making way against a wave train. In figure 3304
the forward displacement is greatly exaggerated.

3305. Effects of currents on waves.—A following current increases wave lengths
and decreases wave heights. An opposing current has the opposite effect, decreasing
the length and increasing the height. A strong opposing current may cause the waves

OCEAN WAVES 731

to break. The extent of wave alteration is dependent upon the ratio of the still-water
wave speed to the speed of the current.

Moderate ocean currents running at oblique angles to wave directions appear to
have little effect, but strong tidal currents perpendicular to a system of waves have
been observed to completely destroy them in a short period of time.

3306. The effect of ice on waves.—When ice crystals form in sea water, internal
friction is greatly increased. This results in smoothing of the sea surface. The effect
of pack ice is even more pronounced. A vessel following a lead through such ice may
be in smooth water even when a gale is blowing and heavy seas are beating against the
outer edge of the pack. Hail is also effective in flattening the sea, even in a high wind.

3307. Waves and shallow water.—When a wave encounters shallow water, the
movement of the individual particles of water is restricted by the bottom, resulting
in reduced wave speed. If the wave approaches the shoal at an angle, each part is

v E ==, T L ] i 15

14

0.8

ZRT

0.4

o
hN

SPEED RELATIVE TO SPEED IN DEEP WATER
LENGTH RELATIVE TO LENGTH IN DEEP WATER
o
a
HEIGHT RELATIVE TO HEIGHT IN DEEP WATER

0 | 0.9
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
DEPTH, RELATIVE TO LENGTH OF WAVE IN DEEP WATER

FIGURE 3307.—Alteration of the characteristics of waves as they cross a shoal.

slowed successively as the depth decreases. This causes a change in direction of motion
or refraction, the wave tending to become parallel to the depth curves. The effect
is similar to the refraction of light and other forms of radiant energy (art. 1613).

As each wave slows, the next wave behind it, in deeper water, tends to catch up.
As the wave length decreases, the height generally becomes greater. The lower part of
a wave, being nearest the bottom, is slowed more than the top. This may cause the
wave to become unstable, the faster-moving top falling or breaking. Such a wave is
called a breaker, and a series of breakers, surf. This subject is covered in greater
detail in chapter XXXIV.

Swell passing over a shoal but not breaking undergoes a decrease in wave length
and speed, and an increase in height. Such ground swell may cause heavy rolling if
it is on the beam and its period is the same as the period of roll of a vessel, even though
the sea may appear relatively calm. Figure 3307 illustrates the approximate alteration
of the characteristics of waves as they cross a shoal.

3308. Energy of waves.—The potential energy of a wave is related to the vertical
distance of each particle from its still-water position, and therefore moves with the

732 OCEAN WAVES

wave. In contrast, the kinetic energy of a wave is related to the speed of the particles,
being distributed evenly along the entire wave.

The amount of kinetic energy in even a moderate wave is tremendous. A four-
foot, ten-second wave striking a coast expends more than 35,000 horsepower per mile
of beach. For each 56 miles of coast, the energy expended equals the power generated
at Hoover Dam. An increase in temperature of the water in the relatively narrow
surf zone in which this energy is expended would seem to be indicated, but no pro-
nounced increase has been measured. Apparently, any heat that may be generated is
dissipated to the deeper water beyond the surf zone.

3309. Wave measurement aboard ship.—With suitable equipment and adequate
training, one can make reasonably reliable measurements of the height, length, period,
and speed of waves. However, the mariner’s estimates of height and length usually
contain relatively large errors. There is a tendency to underestimate the heights of
low waves, and overestimate the heights of high ones. There are numerous accounts
of waves 75 to 80 feet high, or even higher, although waves more than 55 feet high are
very rare. Wave length is usually underestimated. The motions of the vessel from
which measurements are made perhaps contribute to such errors.

Height. Measurement of wave height is particularly difficult. A microbarograph
(art. 3705) can be used if the wave is long enough to permit the vessel to ride up and
down with it. If the waves are approaching from dead ahead or dead astern, this
requires a wave length at least twice the length of the vessel. For most accurate
results the instrument should be placed at the center of roll and pitch, to minimize
the effects of these motions. Wave height can often be estimated with reasonable
accuracy by comparing it with freeboard of the vessel. This is less accurate as wave
height and vessel motion increase. If a point of observation can be found at which the
top of a wave is in line with the horizon when the observer is in the trough, the wave
height is equal to height of eye. However, if the vessel is rolling or pitching, this height
at the moment of observation may be difficult to determine.

Length. The dimensions of the vessel can be used to determine wave length.
Errors are introduced by perspective and disturbance of the wave pattern by the
vessel. These errors are minimized if observations are made from maximum height.
Best results are obtained if the sea is from dead ahead or dead astern.

Period. If allowance is made for the motion of the vessel, wave period can be
determined by measuring the interval between passages of wave crests past the ob-
server. The correction for the motion of the vessel can be eliminated by timing the
passage of successive wave crests past a patch of foam or a floating object at some
distance from the vessel. Accuracy of results can be improved by averaging several
observations.

Speed can be determined by timing the passage of the wave between measured points
along the side of the ship, if corrections are applied for the direction of travel of the
wave and the speed of the ship.

More detailed instructions on making wave observations are given in H.O. Pub.
No. 606-e, Sea and Swell Observations, and H.O. Spec. Pub. 44, Visual Wave Observations.

The length, period, and speed of waves in deep waters are interrelated by the
relationships indicated in article 3303. However, these should be used as a general
guide only, because exact mathematical relationships have not been established, as
indicated. In the case of speed and period, there is evidence to indicate that for sea
the relationship may be more nearly expressed by the formula L=SP than by that given
in article 3303, although there is considerable doubt as to the exact relationship. There

is no definite mathematical relationship between wave height and length, period, or
speed.

OCEAN WAVES 733

j 3310. Tsunamis are ocean waves produced by sudden, large-scale motion of a por-
tion of the ocean floor or the shore, as by volcanic eruption, earthquake (sometimes called
seaquake if it occurs at sea), or landslide. If they are caused by a submarine earth-
quake, they are usually called seismic sea waves. The point directly above the dis-
turbance, at which the waves originate, is called the epicenter. Either a tsunami or a
storm wave (art. 3311) that overflows the land is popularly called a tidal wave, although
it bears no relation to the tide.

If a volcanic eruption occurs below the surface of the sea, the escaping gases cause
a quantity of water to be pushed upward in the shape of a dome or mound. The same
effect is caused by the sudden rising of a portion of the bottom. As this water settles
back, it creates a wave which travels at high speed across the surface of the ocean.

Tsunamis usually occur in series, gradually increasing in height until a maximum
is reached between about the third and eighth wave. Following the maximum, they
again become smaller. Waves may continue to form for several hours, or even for days.

In deep water the wave height of a tsunami is probably never greater than two or
three feet. Since the wave length is usually considerably more than 100 miles, the
wave is not conspicuous at sea. In the Pacific, where most tsunamis occur, the wave
period varies between about 15 and 60 minutes, and the speed in deep water is more
than 400 knots. The approximate speed can be computed by the formula

S=0.6 Jgd —3.4 4/4,

where S is the speed in knots, g is the acceleration due to gravity (32.2 feet per second
per second), and d is the depth of water in feet. This formula is applicable to any
wave in water having a depth of less than half the wave length. For most ocean waves
it applies only in shallow water, because of the relatively short wave length.

When a tsunami enters shoal water, it undergoes the same changes as other waves.
The formula indicates that speed is proportional to depth of water. Because of the
great speed of a tsunami when it is in relatively deep water, the slowing is relatively
much greater than that of an ordinary wave crested by wind. Therefore, the increase
in height is also much greater. Tsunamis 50 feet in height or higher have reached the
shore, inflicting widespread damage. On April 1, 1946, seismic sea waves originating
at an epicenter near the Aleutians spread over the entire Pacific. Scotch Cap Light
on Unimak Island, 57 feet above sea level, was completely destroyed. Traveling at
an average speed of 490 miles per hour, the waves reached the Hawaiian Islands in four
hours and 34 minutes, where they arrived as waves 50 feet above the high water level,
and flooded a strip of coast more than 1,000 feet wide at some places. They left a
death toll of 173, and property damage of $25,000,000. Less destructive waves reached
the shores of North and South America, and Australia, 6,700 miles from the epicenter.

After this disaster, a tsunami warning system was set up in the Pacific, even though
destructive waves are relatively rare (averaging about one in 20 years in the Hawaiian
Islands). The system consists of three sections. First, a number of seismograph
stations to provide information for establishing the time and epicenter of quakes.
Second, a group of tide stations to report any evidence of a tsunami. These stations
are alerted when a quake is recorded at the seismograph stations. Third, a communi-
cation system which gives tsunami warnings high priority because of their speed and
possible destructiveness. A travel time chart centered upon the Hawaiian Islands is
used to estimate time of arrival of the waves.

Fortunately, relatively few earthquakes produce seismic sea waves. The size of
the waves that do form depends upon the nature and intensity of the disturbance.
The height and destructiveness of the waves arriving at any place depend upon its
distance from the epicenter, topography of the ocean floor, and the coast line itself.

734 OCEAN WAVES

The angle at which the wave arrives, the shape of the coast line, and the topography
along the coast and offshore all have their effect. The position of the shore is also a
factor, as it may be sheltered by intervening land, or be in a position where waves
have a tendency to converge, either because of refraction or reflection, or both.

In addition to seismic sea waves, earthquakes below the surface of the sea may
produce a longitudinal wave that travels upward toward the surface, at the speed of
sound. When a ship encounters such a wave, it is felt as a sudden shock which may
be of such severity that the crew thinks the vessel has struck bottom. Because of
such reports, some older charts indicated shoal areas at places where the depth is now
known to be a thousand fathoms or more.

3311. Storm waves.—In relatively tideless seas like the Baltic and Mediterranean,
winds cause the chief fluctuations in sea level. Elsewhere, the astronomical tide
usually masks these variations. However, under exceptional conditions, either
severe extratropical storms or tropical cyclones can produce changes in sea level
that exceed the normal range of tide. Low sea level is of little concern except to
shipping, but a rise above ordinary high-water mark, particularly when it is accom-
panied by high waves, can result in a catastrophe.

Although, like tsunamis, these storm waves or storm surges are popularly called
tidal waves, they are not associated with the tide. They consist of a single wave
crest and hence have no period or wave length.

Three effects in a storm induce a rise in sea level. The first is wind stress on the
sea surface, which results in a piling-up of water (sometimes called “wind set-up”).
The second effect is the convergence of wind-driven currents, which elevates the sea
surface along the convergence line. In shallow water, bottom friction and the effects
of local topography cause this elevation to persist and may even intensify it. The low
atmospheric pressure that accompanies severe storms causes the third effect, which is
sometimes referred to as the “inverted barometer." An inch of mercury is equivalent
to about 13.6 inches of water (art. 3115) and the adjustment of the sea surface to the
reduced pressure can amount to several feet at equilibrium (art. 3911).

All three of these causes act independently, and if they happen to occur simul-
taneously, their effects are additive. In addition, the wave can be intensified or ampli-
fied by the effects of local topography. Storm waves may reach heights of 20 feet or
more, and it is estimated that they cause three-fourths of the deaths attributed to
hurricanes.

3312. Standing waves and microseisms.— Previous articles in this chapter have
dealt with progressive waves which appear to move regularly with time. When two
systems of progressive waves having the same period travel in opposite directions
across the same area, a series of standing waves may form. "These appear to remain
stationary. Recent investigation has indicated that when this condition occurs, a
pressure variation is exerted on the ocean bottom proportional to the product of the
wave heights of the two wave systems. The period of these pressure variations is
half that of the progressive waves. The magnitude and period of these variations are
of the right order to cause a series of minute earth shocks of the magnitude of those
recorded by very sensitive seismographs and known as microseisms. It is probable,
therefore, that microseisms are generated by standing waves established in any manner,
as by waves from independent sources, those in the wake of a moving circulation,
waves at the center of a stationary circulation, or by reflection of waves striking &
steep shore.

Another type of standing wave, called a seiche (sásh), sometimes occurs in a
confined body of water. It is a long wave, usually having its crest at one end of the
confined space, and its trough at the other. Its period may be anything from a few

OCEAN WAVES 735

minutes to an hour or more, but somewhat less than the tidal period. Seiches are
usually attributed to strong winds or differences in atmospheric pressure.

i 3313. Tide waves.—As indicated in chapter XXXI, there are, in general, two
regions of high tide separated by two regions of low tide, and these regions move pro-
gressively westward around the earth as the moon revolves in its orbit. The high tides
are the crests of these tide waves, and the low tides are the troughs. The wave is not
noticeable at sea, but becomes apparent along the coasts, particularly in funnel-shaped
estuaries. In certain river mouths or estuaries of particular configuration, the incom-
ing wave of high water overtakes the preceding low tide, resulting in a high-crested,
roaring wave which progresses upstream in one mighty surge called a bore.

3314. Internal waves.—Thus far, the discussion has been confined to waves on
the surface of the sea, the boundary between air and water. Internal waves, or
boundary waves, are created below the surface, at the boundaries between water
strata of different densities. The density differences between adjacent water strata
in the sea are considerably less than that between sea and air. Consequently, internal
waves are much more easily formed than surface waves, and they are often much larger.
The maximum height of wind waves on the surface is about 60 feet, but internal wave
heights as great as 300 feet have been encountered.

Internal waves are detected by a number of observations of the vertical temperature
distribution, using recording devices such as the bathythermograph (art. 3007). They
have periods as short as a few minutes, and as long as 12 or 24 hours, these greater
periods being associated with the tides.

A slow-moving ship operating in a fresh water layer having a depth approximating
the draft of the vessel may produce short-period internal waves. This may occur off
rivers emptying into the sea or in polar regions in the vicinity of melting ice. Under
suitable conditions, the normal propulsion energy of the ship is expended in generating
and maintaining these internal waves and the ship appears to “stick” in the water,
becoming sluggish and making little headway. The phenomenon, known as dead
water, disappears when speed is increased by a few knots.

The full significance of internal waves has not been determined, but it is known
that they may cause submarines to rise and fall like a ship at the surface, and they
may also affect sound transmission in the sea.

3315. Waves and ships.—The effects of waves on a ship vary considerably with
the type ship, its course and speed, and the condition of the sea. A short vessel has a
tendency to ride up one side of a wave and down the other side, while a larger vessel
may tend to ride through the waves on an even keel. If the waves are of such length
that the bow and stern of a vessel are alternately in successive crests and successive
troughs, the vessel is subject to heavy sagging and hogging stresses, and under extreme
conditions may break in two. A change of heading may reduce the danger. Because
of the danger from sagging and hogging, a small vessel is sometimes better able to ride
out a storm than a large one.

If successive waves strike the side of a vessel at the same phase of successive rolls,
relatively small waves can cause heavy rolling. The effect is similar to that of swinging
a child, where the strength of the push is not as important as its timing. The same
effect, if applied to the bow or stern in time with the pitch, can cause heavy pitching.
A change of either heading or speed can reduce the effect.

A wave having a length twice that of a ship places that ship in danger of falling
off into the trough of the sea, particularly if it is a slow-moving vessel. The effect is
especially pronounced if the sea is broad on the bow or broad on the quarter. An
increase of speed reduces the hazard.

736 OCEAN WAVES

3316. Use of oil for modifying the effects of breaking waves.—Oil has proved
effective in modifying the effects of breaking waves, and has proved useful to vessels
at sea, whether making way or stopped, particularly when lowering or hoisting boats.
Its effect is greatest in deep water, where a small quantity suffices if the oil can be made
to spread to windward. In shallow water where the water is in motion over the bottom,
oil is less effective but of some value.

The heaviest oils, notably animal and vegetable oils, are the most effective. Crude
petroleum is useful, but its effectiveness can be improved by mixing it with animal and
vegetable oils. Gasoline or kerosene are of little value. Oil spreads slowly. In cold
weather it may need some thinning with petroleum to hasten the process and produce
the desired spread before the vessel is too far away for the effect to be useful.

At sea, best results can be expected if the vessel drifts or runs slowly before the
wind, with the oil being discharged on both sides from waste pipes or by other con-
venient method. If a sea anchor is used, oil can be distributed from a container inserted
within it for this purpose. If such a container is not available, an oil bag can be
fastened to an endless line rove through a block on the sea anchor. This permits
distribution of oil to windward, and provides a means for hauling the bag aboard for
refilling. If another vessel is being towed, the oil should be distributed from the
towing vessel, forward and on both sides, so that both vessels will be benefited. If a
drifting vessel is to be approached, the oil might be distributed from both sides of the
dritting vessel or by the approaching vessel, which should distribute it to leeward of
the drifting vessel so that that vessel will drift into it. If the vessel being approached
is aground, the procedure best suiting the circumstances should be used.

If oil is needed in crossing a bar to enter a harbor, it can be floated in ahead of
the vessel if a flood current is running. A considerable amount may be needed. Dur-
ing slack water a hose might be trailed over the bow and oil poured freely through it
if no more convenient method is available. With an ebb current oil is of little use,
unless it can be distributed from another vessel or in some other manner from the op-
posite side of the bar.

CHAPTER XXXIV
AMPHIBIOUS OPERATIONS

3401. Amphibious operations and the navigator.—Among the major problems in
amphibious operations are the safe navigation of landing craft through the surf zone to
the beach, trafficability of the beach, and movement inland. The purpose of this chapter
is to acquaint the navigator with the first two of these and the oceanographic factors
affecting them. The navigational aspects of the third problem are discussed in chapter
XXVII, “Land Navigation.”

3402. Refraction.—As explained in article 3307, wave speed is slowed in shallow
water, causing refraction if the waves approach the beach at an angle. Along a per-
fectly straight beach, with uniform shoaling, the wave fronts tend to become parallel to
the shore. Any irregularities in the coast line or bottom contours, however, affect the
refraction, causing irregularity. In the case of a ridge perpendicular to the beach, for
instance, the shoaling is more rapid, causing greater refraction. The waves tend to
align themselves with the bottom contours. Waves on both sides of the ridge have a
component of motion toward the ridge. This convergence of water toward the ridge
causes an increase in wave or breaker height. A submarine canyon or valley perpen-
dicular to the beach, on the other hand, produces divergence, with a decrease in wave
or breaker height. These effects are illustrated in figure 3402. Bends in the coast
line have a similar effect, convergence occuring at a point, and divergence if the coast
is concave to the sea.

Under suitable conditions, currents also cause refraction. This is of particular
importance at entrances of tidal estuaries. When waves encounter a current running
in the opposite direction, they become higher and shorter. This results in a choppy

SS

S?
m
Wi

Courtesy of Robert L. Wiegel, Council on Wave Research, University of California.

Figure 3402.—The effect of bottom topography in causing wave convergence and
wave divergence.

DIVERGENCE OF
| OMTMOGOMALS
PRODUCES LOW
WAVES IN THIS
AREA

ARENA
COVE
CONVERGENCE OF ORTHOGONALS

PRODUCES HIGH WAVES IN THIS
AREA

——-DEPTH CONTOURS,
IN FATHOMS

12 SECOND PERIOD

7 D
scare

737

738 AMPHIBIOUS OPERATIONS

sea, often with breakers. When waves move in the same direction as current, they
decrease in height, and become longer. Refraction occurs when waves encounter a
current at an angle.

Refraction diagrams, useful in planning amphibious operations, can be prepared
with the aid of nautical charts or aerial photographs. The method of doing so is
explained in H.O. Pub. No. 605, Graphical Construction of Wave Refraction Diagrams.

3403. Breakers and surf.—In deep water, swell generally moves across the surface
as somewhat regular, smooth undulations (ch. XXXIII). When shoal water is reached,
the wave period remains the same, but the speed decreases. The amount of decrease
is negligible until the depth of water becomes about one-half the wave length, when the
waves begin to “feel” bottom. There is a slight decrease in wave height, followed by
a rapid increase, if the waves are traveling perpendicular to a straight coast with a
uniformly sloping bottom. As the waves become higher and shorter, they also become
steeper, and the crest becomes narrower. When the speed of individual particles at
the crest becomes greater than that of the wave, the front face of the wave becomes
steeper than the rear face. This process continues at an accelerating rate as the depth
of water decreases. At some point the wave may become unstable, toppling forward
to form a breaker.

There are three general classes of breakers. A spilling breaker breaks gradually
over a considerable distance. A plunging breaker tends to curl over and break with a
single crash. A surging breaker peaks up, but surges up the beach without spilling or
plunging. It is classed as a breaker even though it does not actually break. The
type of breaker is determined by the steepness of the beach and the steepness of the
wave before it reaches shallow water, as illustrated in figure 3403.

Longer waves break in deeper water, and have a greater breaker height. The
effect of a steeper beach is also to increase breaker height. The height of breakers is
less if the waves approach the beach at an acute angle. With a steeper beach slope
there is greater tendency of the breakers to plunge or surge. Following the uprush
of water onto a beach after the breaking of a wave, the seaward backrush occurs. The
returning water is called backwash. It tends to further slow the bottom of a wave,
thus increasing its tendency to break. This effect is greater as either the speed or
depth of the backwash increases. The still water depth at the point of breaking is
approximately 1.3 times the average breaker height.

Surf varies with both position along the beach and time. A change in position
often means a change in bottom contour, with the refraction effects discussed in article
3402. At the same point, the height and period of waves vary considerably from wave
to wave. A group of high waves is usually followed by several lower ones. Therefore,
passage through surf can usually be made most easily immediately following a series of
higher waves.

Since surf conditions are directly related to height of the waves approaching a beach,
and the configuration of the bottom, the state of the surf at any time can be predicted
if one has the necessary information and knowledge of the principles involved. Height
of the sea and swell can be predicted from wind data, and information on bottom con-
figuration can generally be obtained from the nautical chart. In addition, the area
of lightest surf along a beach can be predicted if details of the bottom configuration are
available. Detailed information on prediction of surf conditions is given in H.O. Pub.
No. 234, Breakers and Surf; Principles in Forecasting.

3404. Currents in the surf zone.—In and adjacent to the surf zone, currents are

generated by waves approaching the bottom contours at an angle, and by irregularities
in the bottom.

AMPHIBIOUS OPERATIONS 739

BREAKING
POINT

BEACH BOTTOM

BEACH IS USUALLY VERY FLAT

SKETCH SHOWING THE GENERAL CHARACTER
OF SPILLING BREAKERS

BREAKING

BEACH IS USUALLY STEEP

PLUNGING BREAKER SKETCH SHOWING THE GENERAL CHARACTER
F ` r a OF PLUNGING BREAKERS

FOAM LINE FOAM LINE FOAM LINE

BEACH IS USUALLY VERY STEEP

SKETCH SHOWING THE GENERAL CHARACTER
OF SURGING BREAKERS

Courtesy of Robert L. Weigel, Council on Wave Research, University of California.

FiGURE 3403.—The three types of breakers.

Waves approaching at an angle produce a longshore current parallel to the beach,
within the surf zone. Longshore currents are most common along straight beaches.
Their speeds increase with increasing breaker height, decreasing wave period, increasing
angle of breaker line with the beach, and increasing beach slope. Speed seldom exceeds
one knot, but sustained speeds as high as three knots have been recorded. Longshore
currents are usually constant in direction. They increase the danger of landing craft
broaching to.

As explained in article 3402, wave fronts advancing over nonparallel bottom
contours are refracted to cause convergence or divergence of the energy of the waves.
Energy concentrations, in areas of convergence, form barriers to the returning back-

740 AMPHIBIOUS OPERATIONS

wash, which is deflected along the beach to areas of less resistance. Backwash ac-
cumulates at weak points, and returns seaward in concentrations, forming rip currents
through the surf. At these points the large volume of returning water has a retarding
effect upon the incoming waves, thus adding to the condition causing the rip current.
The waves on one or both sides of the rip, having greater energy and not being retarded
by the concentration of backwash, advance faster and farther up the beach. From
here, they move along the beach as feeder currents. At some point of low resistance,
the water flows seaward through the surf, forming the neck of the rip current. Outside
the breaker line the current widens and slackens, forming the head. The various
parts of a rip current are shown in figure 3404.

Rip currents may also be caused by irregularities in the beach face. If a beach
indentation causes an uprush to advance farther than the average, the backrush is

FEEDER CURRENT

BEACH

IDEALIZED RIP CURRENT
Courtesy of Robert L. Weigel, Council on Wave Research, University of California.

FIGURE 3404.—A rip current (left) and a diagram of its parts (right).

delayed and this in turn retards the next incoming foam line (the front of a wave as
it advances shoreward after breaking) at that point. The foam line on each side of
the retarded point continues in its advance, however, and tends to fill in the retarded
area, producing a rip current.
| 3405. Beach trafficability.—The trafficability of an area depends upon character-
istics of both the area itself and the vehicles to be used in traversing the area. |
In amphibious operations, landing craft must successively negotiate the sub-
merged section of the beach between landing craft and shore, the moist “beach face"
which is covered by water at high tide, the dry section which is never submerged, and
the backshore. Several types and conditions of soils may be encountered in oe
the four sections. l 3
! Bearing capacity, traction capacity, and rolling resistance are the main factors in
soil trafficability. Bearing capacity concerns the ability of the soil to support the
vehicle; traction capacity deals with its ability to give the vehicle a forward thrust;
rolling resistance refers to the tendency of the soil to oppose the forward thrist
These main factors are themselves dependent upon vehicle characteristics trafo
density, slope of the ground, nature of the soil, and certain soil clinractoristica hich
depend chiefly upon the water content of the soil. | e?

_ Trafficability investigations have led to the following general conclusions: (1)
Serious trafficability problems arise with mud. (2) The trafficability of sandy beach
composed of coarse-grained soils increases with increased flatness. _ The bearin a id
traction capacities of such soils are satisfactory if the soil is REC) as by tā uso
large low-pressure tires or wide tracks. (3) Wet sand offers less E than dry

AMPHIBIOUS OPERATIONS 741

sand. Therefore, vehicles are best discharged at low tide, onto the moist part of the
beach face thus exposed. Vehicles landed after a heavy rain will encounter better
trafficability than those landed when the beach is dry. (4) The landing of tracked
vehicles on all but the flattest beaches disturbs the soil to such an extent that wheeled
vehicles have great difficulty in operating. However, tracked vehicles can operate on
many beaches where wheeled vehicles cannot be used under any circumstances.

When a beach is insufficiently stable to support sustained traffic from landing
craft to backshore, artificial means may be used to increase the stability. The three
general methods are (1) densification of the soil, (2) addition of cementing agents, and
(3) elimination of excess moisture and the prevention of moisture accumulation.
Another approach is to bring vehicles ashore by means of pontoon causeways, landing
mats, or other types of temporary roadways.

CHAPTER XXXV
SOUND IN THE SEA

3501. Underwater sound and the navigator.—The clarity with which the noises
associated with weighing anchor, propelling a ship, and other underwater motions are
heard below the water line and near the skin of a vessel is an indication of the high
sound-transmitting qualities of sea water. Water is a better conductor of sound than
is air because it absorbs less energy from the sound. There are several ways in which
underwater sound can be used in navigation.

The direction of travel of sound waves can be measured either by means of binaural
hearing (hearing with two “ears”), or by equipment which has directional character-
istics similar to those of a directional antenna used in radio (art. 1012). Either method
can be used for determining the direction from which general noise is coming, but
only the latter is used in sonar equipment (art. 1108) for determining direction and dis-
tance by reception of an echo from a directional signal, in a manner similar to radar
(art. 1208).

Distance can be determined by (1) measuring the elapsed time between trans-
mission of a signal and return of its echo, (2) measuring the elapsed time between
transmission of a signal and its receipt at a second station, (3) measuring the time
difference between reception of a signal transmitted through water and one transmitted
through air, (4) measuring the difference in phase between two signals or change of
phase of a signal when it returns as an echo, or (5) measuring the angle at which an
echo is received from a signal produced at another place. The first method, used in
sonar (art. 1108) and echo sounding equipment (art. 619), is similar in principle to
radar (art. 1208). The second method is used primarily in RAR (art. 1205), in which
underwater sound signals trigger a “sonobuoy,”” which transmits a radio signal to indi-
cate the time of reception of the sound signal. The third method is used at distance
finding stations (art. 1205). The fourth and fifth methods were used in early forms of
echo sounders.

The difference in time of reception of the same signal at two or more points is
used in sofar (art. 1313) in a manner which is similar but reversed to that of loran
(art. 1302).

3502. Sources of sound in the ocean.—Underwater sounds intended for navigational
use are produced in one of three basic ways: (1) by percussion, as the striking of a
bell, gong, or the bottom of the vessel; (2) by oscillator, as the vibration of a diaphragm;
(3) by explosion, as by small bomb or depth charge. Certain man-made noises ordi-
narily produced in water, such as those due to operation of the main engines of a vessel,
can be detected by an appropriate listening device.

In addition, many noises are made by animals living in the ocean. Certain
shrimp, great numbers of which inhabit some areas, make a snapping noise with their
claws. Some fish make a noise by stridulating (scraping). When shellfish are being
eaten, a sound is emitted as the shells are broken by the teeth of the fish which are
feeding. Grunting noises are made by many kinds of fish, usually by means of their
swim bladders. Porpoises produce sounds of a high pitch. Sounds of various fre-
quency and amplitude are produced by other forms of marine life. Where sound-
producing marine life is very abundant, it interferes with detection of man-made

742

SOUND IN THE SEA 743

sounds, requiring a high signal-to-noise ratio. The effect is similar to that of a high
atmospheric noise level in radio.

3503. Speed of sound in sea water.—Three variables govern the speed (S) of sound
in a fluid. They are density (p), compressibility (8), and the ratio between the specific
heats of the fluid at constant pressure and at constant volume (y). The following
formula is sufficiently accurate for most navigational purposes:

Y

à Vas
Density and specific heat are discussed in articles 3009 and 3012, respectively. Com-
pressibility refers to the relative change in volume for a given change in pressure.
The compressibility of water is low, and consequently the speed of sound in water is
high. "The specific heat ratio enters the formula because the energy of a sound impulse
is briefly transformed into heat, and then reconverted (with slight loss) into kinetic
energy. The ratio rarely exceeds 1.02 in sea water and is commonly taken as unity.
For atmospheric pressure 29.92 inches of mercury, temperature 60? F, and salinity
34.85 parts per thousand, the density of sea water is 64 pounds per cubic foot and the
compressibility approximately 0.0000435 per atmosphere (one atmosphere equals
14.696 pounds per square inch). Using these values and 32.174 feet per second per

second (the acceleration of gravity at latitude 45?) and 144 square inches per square
foot, and taking y equal to unity, one obtains:

ae O ft./sec.

64 X0.0000435

The same formula can be used to determine the speed of sound in air. For
atmospheric pressure 29.92 and temperature 60° F, the density of air is 0.0764 pound
per cubic foot and, since air is a gas, the compressibility is the reciprocal of the pressure.
Taking y equal to 1.4, one obtains:

Se ES EOXI 17 eee

0.0764X1

The speed of sound in water is approximately 4.5 times its speed in air.

An increase in temperature decreases both density and compressibility, resulting
in an increase in the speed of sound. In sea water, an increase in pressure or salinity
produces a slight increase in density and a larger decrease in compressibility, resulting
in a net increase in the speed of sound. Thus, in sea water, an increase in temperature,
pressure, or salinity results in greater speed of sound. Of the three, temperature has
the greatest influence on the speed of sound in sea water in the upper layers. At depth,
pressure, and in coastal areas, changes in salinity, may have the greatest effect.

Normally, the change of these three elements is much more rapid in a vertical
direction than in a horizontal direction. The change with depth varies with location.
With respect to temperature, much of the ocean is considered to consist of three layers,
a surface layer influenced greatly by the temperature of the air above it, a thermocline
of rapidly decreasing temperature, and a nearly uniform deep-water layer. Typical
curves showing change of temperature and salinity with depth are shown in figure 3503a.
The increase of pressure with depth is almost uniform, the pressure at 10,000 feet
being approximately twice that at 5,000 feet, and ten times that at 1,000 feet. A typical
curve of speed of sound with depth is shown in figure 3503b. The speeds for all tem-
perature, pressure, and salinity conditions encountered in the sea are given in Tables of

744 SOUND IN THE SEA

o SPEED OF SOUND,
ESE
TEMPERATURE, FT. / SEC.
^ 60* 4850 | 4900 4950 5000
2000 2000
4000 7 wai
=
W E
e ry
U
= =
2 6000 Q& 6000
a ul
Q
8000 - 8000
10,000 ———
1000033 34 35
SALINITY, PARTS PER THOUSAND
FIGURE 3503a.—Variation of tem- FIGURE 3503b.—Typical variation of
perature and salinity with depth speed of sound with depth in the
at one locality. ocean.

Sound Speed in Sea Water, SP 58, published by the U.S. Navy Hydrographic Office.

Study of transmission of sound from underwater explosions indicates that near
the explosion the speed of sound may be somewhat higher than expected, probably due
to increased pressure caused by the disturbance. This effect extends over such a short
distance that it is insignificant in ordinary underwater sound transmission.

3504. Reflection of underwater sound waves.—In water, as in air, sound is re-
flected by obstructions in the form of solid objects or sharp discontinuities. Thus,
sound is reflected from the bottom, the shore, hulls of ships, the surface of the water,
etc. It is this reflecting energy that is used in echo sounders (art. 619) to determine
depth, and in sonar equipment (art. 1108) used for echo ranging.

Reflecting properties of various substances differ markedly. Rock reflects almost
all of the sound that strikes its surface, while soft mud absorbs or is penetrated by
sound. Thus, in echo sounding, a layer of soft mud over rock may result in two echoes,
indicating two depths.

Fish and even tiny sea animals also reflect sound. As a result, echo sounders are
widely used among fishermen to locate schools of fish. In deep water it is not unusual
for an echo sounder to receive an echo from a depth of about 200 fathoms, although the
depth decreases somewhat at night. This phantom bottom or deep scattering layer,
which is undoubtedly the source of many erroneous shoal sounding reports, is believed
to be due to large numbers of tiny marine animals, or other marine life.

A sharp discontinuity within the water causes reflection of sound. Thus, an echo
sounder may detect the boundary between a layer of fresh water overlying salt water,
a condition which might occur near the mouth of a river.

SOUND IN THE SEA 745

Sharp, distinct echoes denoting precise depths are difficult to obtain over rough-
surfaced bottoms. Therefore, considerable discretion should be exercised in evaluating
soundings taken over bottoms possessing a high degree of relief.

3505. Refraction of underwater sound waves.—The laws of refraction as applied
to light (art. 1613) and radio waves (art. 1006) apply also to sound. Because of dif-
ferences of speed of sound in sea water, an advancing sound wave is refracted toward
the area of slower speed. If sound is traveling vertically downward, as in echo sounding,
the effect of refraction is relatively slight because the layers of water in which speed
differs are approximately horizontal, and when the direction of travel of the sound is
normal to the refracting surface or layer, there is no refraction.

When a beam of sound is directed in a horizontal direction, however, refraction is
greatest. If the speed decreases with depth, the usual situation, the upper part of the
beam travels faster than the lower part, and the beam is diverted downward, leaving
a shadow zone near the surface in which the sound does not enter, except for a weak
signal due to scattering. If the speed increases with depth, the lower part moves faster,
and the beam is deflected upward toward the surface, where part of it is reflected, part
moves along the surface with some scattering if the surface is not smooth, and part (less
than 1%) is lost to the air.

With typical distribution of speed with depth, as shown in figure 3503b, speed
decreases with depth until a minimum is reached at some level below the surface, and
below this the speed increases. In figure 3503b minimum speed occurs at about 2,400
feet. In the tropics this level of minimum speed may be as deep at 6,000 feet, and in
polar regions it may be at the surface. Sound produced at any level tends to be re-
fracted to the level of minimum
speed, and to remain there, for
as it attempts to leave this level,
it is refracted back toward it, as
shown in figure 3505. This, of
course, does not refer to sound
traveling vertically. Ifa sound
is produced at this level, as by
Soop osiomob amor) or depth FIGURE 3505.— Transmission of sound rays along the
charge, the sound waves start minimum sound level.
to move outward as expand-
ing spheres, but most of the rays are refracted back toward the minimum speed level.
Because of this effect, such a sound may travel great distances with relatively little
decrease in intensity. Listening gear placed at this level has detected sounds produced
thousands of miles away. This is the principle used in sofar (art. 1313).

SOUND RAYs

CHAPTER XXXVI
ICE IN THE SEA

3601. Ice and the navigator.—The perpetually frozen Arctic Ocean and the solid
sheet of ice beneath which Antarctica is buried offer evidence that the earth has not yet
completely emerged from its most recent Ice Age. Each winter this polar ice increases
and spreads toward more temperate latitudes, and each summer it contracts again
as part of the ice melts. Some of the fragments are carried by ocean currents into
shipping lanes, forming a major hazard to shipping. There is evidence to indicate
that the polar regions are becoming warmer. Nearly all glaciers are receding;
the ice shelves off northern Canada and Greenland are breaking up; shipping off
the Siberian coast has become possible; cod are found ever farther north along the
Greenland coast.

Ice is of direct concern to the navigator because it restricts and sometimes controls
his movements, it affects his dead reckoning by forcing frequent and sometimes inac-
curately determined changes of course and speed, it affects his piloting by altering the
appearance or obliterating the features of landmarks and by rendering difficult the
establishment and maintenance of aids to navigation, it affects his electronic navigation
by its effect upon propagation of radio waves and the changes it produces both in sur-
face features and radar returns from such features, it affects his celestial navigation by
altering the refraction and obscuring his horizon and celestial bodies either directly or
by the weather it influences, and it affects his charts by introducing various difficulties
to the hydrographic surveyor.

Because of his direct concern with ice, the prospective polar navigator will do well
to acquaint himself with its nature and extent in the area he expects to navigate. To
this end he should consult the sailing directions for the area, and whatever other
literature may be available to him, including reports of previous operations in the same
area.

3602. Formation of ice.—As it cools, water contracts until the temperature of max-
imum density is reached. Further cooling results in expansion. The maximum
density of fresh water occurs at a temperature of 39°2F, and freezing takes place at
32°F. The addition of salt lowers both the temperature of maximum density and, to
a lesser extent, that of freezing. The relationships are shown in figure 3602. The two -
lines meet at a salinity of 24.7 parts per thousand, at which maximum density occurs
at the freezing temperature of 29°61F. At this and greater salinities, the density
increases right down to the freezing point. At a salinity of 35 parts per thousand, the
approximate average for the oceans, the freezing point is 28°6 F.

Generally, ice forms first at the water surface. As it does, most of the dissolved
solids remain in the water, beneath the ice, increasing the density of the water there.
This lowers the freezing point, thus tending to retard the freezing process. It is further
retarded by the fact that ice is a poor conductor of heat and therefore serves as an
insulator to protect the water from colder air above.

In shoal water and streams, particularly where motion is sufficient to cause thorough
mixing, the freezing temperature may extend from the surface to the bottom. When
this occurs, ice crystals may form at any depth. Because of their decreased density,
they tend to rise to the surface, unless they form at the bottom and attach themselves

746

ICE IN THE SEA 747

TEMPERATURE (F)

SALINITY PARTS PER THOUSAND

FIGURE 3602.—Relationship between temperature of maximum density and
freezing point for water of varying salinity.

there. This bottom ice, sometimes called anchor ice, continues to grow as additional
ice freezes to that already formed.

Ice may also be formed by the compacting of fallen snow, or by the freezing of a
mixture of snow and sea water.

3603. Land ice is formed on land by the freezing of fresh water or the compacting
of snow as layer upon layer adds to the pressure on that beneath. As snow becomes
hardened by wind, temperature, and pressure, it reaches an intermediate stage when
it is known as névé (nå và).

Under great pressure ice becomes slightly plastic and is forced outward and down-
ward along an inclined surface. If a large area is relatively flat, as on the antarctic
plateau, or if the outward flow is obstructed, as on Greenland, an ice cap forms and
remains winter and summer, in some places reaching depths of several thousand feet.
Where ravines or mountain passes permit flow of the ice, a glacier is formed. This is
a slow-moving river of ice that flows to lower levels, exhibiting many of the character-
istics of rivers of water. The flow may be more than 100 feet per day, but is generally
much less. When a glacier reaches a comparatively level area, it spreads out. When
a glacier flows into the sea, the buoyant force of the water breaks off pieces from time
to time, and these float away as icebergs.

An iceberg seldom melts uniformly because of lack of uniformity in the ice itself,
differences in the temperature above and below the water line, exposure of one side to

748 ICE IN THE SEA

the sun, strains, cracks, mechanical erosion, etc. The inclusion of rocks, silt, and
other foreign matter further accentuates the differences. As a result, changes in
equilibrium take place, which may cause the berg to tilt or capsize. Parts of it may
break off or calve, forming separate, smaller bergs. A small berg about the size of a
house is called a bergy bit, and one still smaller but large enough to inflict serious
damage to a vessel is called a growler because of the noise it sometimes makes as it
bobs up and down in the sea. Bergy bits and growlers are usually pieces calved from
icebergs, but they may be formed by consolidation of sea ice or by the melting of an
iceberg. The principal danger from icebergs is their tendency to break or shift position,
and possible underwater extensions, called rams.

3604. Sea ice forms by the freezing of sea water. The first indication is a greasy
or oily appearance of the surface, with a peculiar gray or leaden tint. The small
individual particles of ice, called spicules, then become visible. As the number in-
creases, the mixture of water and ice is soupy or mushy, having about the consistency
of wetsnow. At this stage itis called slush. The height of waves is noticeably reduced.
As the individual particles freeze together, a thin layer of highly plastic ice forms.
This bends easily and moves up and down with the waves. A layer of two inches of
fresh-water ice is brittle but strong enough to support the weight of a heavy man.
In contrast, the same thickness of newly formed sea ice will support not more than about
ten percent of this weight, although its strength varies with the temperature at which
it is formed, very cold ice supporting a greater weight than warmer ice. When snow
falls into sea water which is near its freezing point, but colder than the melting point of
snow, it does not melt, but floats on the surface, drifting with the wind into beds which
may become several feet thick. If the temperature drops below the freezing point of
the sea water, the mixture of snow and water freezes quickly into a soft ice similar to
that formed when snow is not present. As it ages, sea ice becomes harder and more
brittle.

Close to land the ice may be attached to the shore as an ice foot. The width of
this fast ice varies considerably, but in an area with many irregularities in the coast
line, especially if there are offshore islands or shoals, and relatively shallow water, it
may extend for several miles to seaward. Although the width generally varies from
two to 20 miles, a maximum of about 270 miles has been observed in the vicinity of
Novosibirskiye Ostrova (New Siberian Islands). On an exposed, abrupt coast bordered
by deep water there may be no ice foot at all.

In a bay or other sheltered area, ice formed on the surface of the sea, often augmented
by snow and land ice, may build up a shelf which remains attached to the land for many
years. In the Ross Sea in Antarctica this shelf ice attains a thickness of 500 to 1,000
feet. At the outer edge, large pieces eventually break away, forming tabular icebergs
(fig. 3604a), with dimensions measured in miles. In 1854 and 1855 several ships in the
South Atlantic reported a crescent-shaped iceberg with one horn 40 miles long, the
other 60 miles long, and with an embayment 40 miles wide between the tips. In 1927
a berg 100 miles long, 100 miles wide, and 130 feet high above water was reported.
The largest iceberg ever reported was sighted in 1956 by the USS Glacier, a U. S. Navy
icebreaker, about 150 miles west of Scott Island. This berg was 60 miles wide and 208
miles long, more than twice the size of Connecticut. Icebergs ten miles or more in
length have been seen on many occasions in the antarctic. In contrast, the largest
iceberg reported in the northern hemisphere was seven miles long and three and a half
miles wide. This berg was sighted off Baffin Island in 1882. In 1928 an iceberg
four miles long was reported seen in the North Atlantic. The expression “tabular
iceberg” is not applied to northern hemisphere bergs, but similar formations there
are called ice islands. These are believed to originate when shelf ice breaks up north

ICE IN THE SEA 749

FIGURE 3604a.—A tabular iceberg.

of Canada and Greenland. Most of them remain in the Arctic Ocean and have not
been encountered by ships, although the large icebergs sighted in 1882 and 1928
were possibly ice islands. For several years the United States maintained a weather
station on one of the arctic ice islands.

Sea ice is exposed to several forces, including currents, wave motion, tides, wind,
and temperature differences. In its early stages, its plasticity permits it to conform
readily to virtually any shape required by the forces acting upon it. As it becomes
older, thicker, and more brittle, exposed sea ice cracks and breaks under the strain.
Under the influence of wind and current, the broken pieces may shift position relative
to pieces around them.

A single piece of relatively flat sea ice is called an ice cake. When ice is formed
in the presence of considerable wave motion, circular cakes several feet in diameter
are formed, rather than a single large sheet. "These circular cakes are called pancakes,
and a collection of pancakes is called pancake ice (fig. 3604b). Wave motion may
cause the pancakes to break into smaller pieces. With continued freezing, individual
pieces unite into floes, and floes into ice fields which extend over many miles.

FiGvRE 3604b.—Pancake ice, with an iceberg in the background.

750 ICE IN THE SEA

When one floe encounters another, or the shore, the individual pieces may be forced
closer together into a thickly compacted mass. If the force is sufficient, and the ice
is sufficiently plastic, bending takes place, or tenting if the contacting edges of individual
cakes force each other to rise above their surroundings. More frequently, however,
rafting occurs as one cake overrides another. Sea ice having any readily observed
roughness of the surface is called pressure ice. A line of ice piled haphazardly along
the edge of two floes which have collided is called a pressure ridge. Pressure ice with
numerous mounds or hillocks which have become somewhat rounded and smooth by
weathering or the accumulation of snow is called hummocked ice, each mound being
called a hummock.

The motion of adjacent floes is seldom equal. The rougher the surface, the greater
the effect of wind, since each piece extending above the surface acts as a sail. Some
floes are in rotary motion as they tend to trim themselves into the wind. Since ridges
extend below as well as above the surface, the deeper ones are influenced more by
deep-water currents. When a strong wind blows in the same direction for a considerable
period, each floe exerts pressure on the next one, and as the distance increases, the pres-
sure becomes tremendous. Near land the result is an almost unbelievably chaotic
piling of ice. Individual ridges near the shore may extend as much as 60 or 70 feet
above surrounding ice and have a total thickness of 150 to 200 feet in extreme cases.
Far from land, the height and thickness seldom exceed half these figures.

The continual motion of various floes results in separation as well as consolidation.
A long, narrow, jagged crack may appear and widen enough to permit passage of a
ship, when it is called a lead (léd). In winter, a thin coating of newly formed ice
usually covers the water, but in summer the water remains ice-free until a shift in the
movement forces the two sides together again. Before this occurs, lateral motion
usually takes place between the floes, so that they no longer fit, and unless the pressure
is extreme, numerous patches of open water remain. A large one is called a polynya.

A large mass of sea ice, consisting of various floes, pressure ridges, and openings,
is called a pack (fig. 3604c). In the arctic the main pack extends over the entire
Arctic Ocean and for a varying distance outward from it, the limits receding con-
siderably during summer. Each year a large portion of the ice from the Arctic Ocean
moves outward between Greenland and Norway, into the North Atlantic, and is
replaced by new ice. Relatively little of the pack ice is more than ten years old.
The ice pole, the approximate center of the arctic pack, is at latitude 83°5
N, longitude 160° W, north of western Alaska and about 390 miles from the north pole.
In the antarctic the pack exists as a relatively narrow strip between the continent of
Antarctica and the notoriously stormy seas which hasten the pack’s destruction.

The alternate melting and refreezing of the surface of the pack, producing weathered
ice, combined with the various motions to which the pack is subjected, result in widely
varying conditions within the pack itself. The extent to which it can be penetrated
by a ship varies from place to place and with changing weather conditions. In some
areas the limit of navigable water is abrupt and complete, as at the edge of shelf ice.
Such ice is called a barrier.

3605. Thickness of sea ice.—The seasonal thickness of fast ice in two harbors of
the northern hemisphere is shown in figure 3605, at the latitudes indicated. Pack ice
in these latitudes undergoes a similar change. As ice thickens, it provides increased
insulation to protect the sea water beneath from the colder air above, and the rate of
freezing decreases. Sea ice rarely exceeds six feet in thickness during its first year.
In a coastal area where the melting rate is less than the freezing rate, the thickness
increases during succeeding winters, being augmented by compacted and frozen snow,
until a maximum thickness of about 12 to 15 feet may eventually be reached. These

ICE IN THE SEA 751

100

90

THICKNESS OF ICE — INCHES

HEBHSC
BER...

x
N

30

20

10

Sept Oct Nov Dec Jan Feb Mar Apr May June July

Figure 3605.—Thickness of ice in two typical sheltered harbors in the northern
hemisphere, at the latitudes indicated.

752 ICE IN THE SEA

values refer to single, unbroken pieces of floating ice. Shelf ice and pressure ice may
be much thicker, as indicated previously (art. 3604).

During the summer, the sea ice insulates the sea water from warmer air above, so
that melting is confined almost entirely to the upper portion. As the fresher melt
water runs off into the sea, it tends to float on top of the heavier and colder salt water
of the ocean. The temperature of the sea water may be lower than the freezing point
of the fresher melt water, resulting in some refreezing as the melt water runs under the
ice.

3606. Salinity of sea ice.—Sea ice forms first as salt-free crystals near the surface
of the sea. As the process continues, these crystals are joined together and, as they
do so, small quantities of brine are trapped within the ice. On the average, new ice
six inches thick contains five to ten parts of salt per thousand. With lower temperature,
freezing takes place faster. With faster freezing, a greater amount of salt is trapped
in the ice.

Depending upon the temperature, the trapped brine may either freeze or remain
liquid, but because its density is greater than that of the pure ice, it tends to settle
down through the pure ice. As it does so, the ice gradually freshens, becoming clearer,
stronger, and more brittle. At an age of one year sea ice is sufficiently fresh that its
melt water, if found in puddles of sufficient size, and not contaminated by spray from
the sea, can be used to replenish the fresh water supply of a ship. However, ponds of
sufficient size to water ships are seldom found except in ice of great age, and then much
of the melt water is from snow which has accumulated on the surface of the ice. When
sea ice reaches an age of about two years, virtually all of the salt has been eliminated.
Icebergs contain no salt, and uncontaminated melt water obtained from them is
fresh.

The settling out of the brine gives sea ice a honeycomb structure which greatly
hastens its disintegration when the temperature rises above freezing. In this state,
when it is called rotten ice, much more surface is exposed to warm air and water, and
the rate of melting is increased. In a day’s time, a floe of apparently solid ice several
inches thick may disappear completely.

3607. Density of ice.—The density of fresh-water ice at its freezing point is 0.917.
Newly formed sea ice, due to its salt content, is more dense, 0.925 being a representative
value. The density decreases as the ice freshens (art. 3606). By the time it has shed
most of its salt, sea ice is less dense than fresh-water ice, because ice formed in the sea
contains more air bubbles. Ice having no salt but containing air to the extent of eight
percent by volume (an approximately maximum value for sea ice) has a density of
0.845.

The density of land ice varies over even wider limits. That formed by freezing
of fresh water has a density of 0.917, as stated above. Much of the land ice, however,
is formed by compacting of snow. This results in the entrapping of relatively large
quantities of air. Névé, in the transitional stage between snow and ice, may have an
air content of as much as 50 percent by volume. By the time the ice of a glacier reaches
the sea, its density approaches that of fresh-water ice. A sample taken from an iceberg
on the Grand Banks had a density of 0.899.

When ice floats, part of it is above water and part is below the surface. The per-
centage of the mass below the surface can be found by dividing the average density of
the ice by the density of the water in which it floats. Thus, if an iceberg of density
0.920 floats in water of density 1.028 (corresponding to a salinity of 35 parts per thousand
and a temperature of 30? F), 89.5 percent of its mass will be below the surface. That is,
about nine-tenths of the mass will be below the surface, and only about one-tenth
will be above the surface. If the ice is a perfectly uniform block, which some tabular

ICE IN THE SEA 753

icebergs approach, the depth below the surface is about seven times the height above
water, under the conditions stated above. However, most of the icebergs of the northern
hemisphere are irregular in shape, the depth probably averaging about five times the
height. Icebergs have been estimated to be as high as 1,000 feet above water, but
the highest measured in the northern hemisphere was 447 feet. The largest tabular
icebergs of the antarctic extend about 300 feet above the water.

3608. Drift of ice.—Although surface currents have some effect upon the drift of
pack ice, the principal factor is wind. Due to Coriolis force (art. 1611), ice does not drift
in the direction of the wind, but about 30° from this direction. In the northern hemi-
sphere, this drift is to the right of the direction toward which the wind blows, and in
the southern hemisphere it is toward the left. Since the surface wind is deflected about
twice this amount from the direction of the pressure gradient, the total deflection of the
ice is about 90° from the pressure gradient, or along the isobars, with the atmospheric
low toward the left and the high toward the right in the northern hemisphere. In the
southern hemisphere, these directions are reversed. The rate of drift is about one to
seven percent of the wind speed, depending upon the roughness of the surface and the
concentration of the ice.

Icebergs, which extend a considerable distance below the surface, and have a rela-
tively small “sail area,” are influenced more by surface currents than by wind. How-
ever, if a strong wind blows for a number of hours in a steady direction, the drift of ice-
bergs will be materially affected. In this case the effect is two-fold. The wind acts
directly against the iceberg, and also generates a surface current in about the same
direction. Because of inertia, an iceberg may continue to move from the influence of
wind for some time after the wind stops or changes direction.

3609. Extent of ice in the sea.—Several Hydrographic Office publications contain
monthly charts showing average extent of various degrees of navigability in the northern
and southern hemispheres throughout the year. A sample of the type of information
given is shown in figure 3609. Similar information is shown on the various pilot charts
(art. 414). Useful information on ice conditions in different localities is given in the
sailing directions for those areas. The information given in H.O. Pub. No. 27, Sailing
Directions, Antarctica, is particularly complete and of somewhat general application.

However, since formation of ice, in common with other meteorological and ocean-
ographic phenomena, varies considerably from year to year, wide deviations from aver-
age conditions are not unusual. Most countries having vessels operating in ice main-
tain ice information services. Details of these services are given in the appropriate
volumes of sailing directions. The ice bulletins broadcast by the U. S. Navy Hydro-
graphic-Office are discussed in article 3615. The latest bulletins, as well as information
on average conditions, should be consulted when operating in ice.

3610. Ice in the North Atlantic.—Sea-level glaciers exist on a number of land
masses bordering the northern seas, including Alaska, Greenland, Svalbard (Spitz-
bergen), Zemlya Frantsa-Iosifa (Franz Josef Land), Novaya Zemlya, and Severnaya
Zemlya (Nicholas II Land). Except in Greenland, the rate of calving is relatively slow,
and the few icebergs produced melt near their points of formation. Many of those
produced along the coasts of Greenland, however, are eventually carried into the ship-
ping lanes of the North Atlantic, where they constitute a major menace to ships. It is for
this reason that more southerly lanes (art. 3611) are specified when icebergs are prevalent.

The icebergs produced along the east coast of Greenland are carried by the east
Greenland current around Kap Farvel and northward by the west Greenland cur-
rent toward Davis Strait. Relatively few of these icebergs menace shipping, but they
have been encountered as far as 200 miles southeast of Kap Farvel.

754 ICE IN THE SEA

ICE CHART
NORTHERN HEMISPHERE

JANUARY

TYPES OF ICE

Permanent polar pack, inaccessible
to navigation. `

| Unnavigable sea and land-fast ice, occasion "A

ally penetrable by powerful icebreakers. M
Generally unnavigable sea and land-fast ice. Icebreaker >

H assistance normally required, although at tímes pen- DET
etrable by heavily built vessels,

Sea and land-fast ice generally navigable by heavily-
SS built vessels. g S » y

2 MU 2 i y

FIGURE 3609.—Average limits of various degrees of navigability of ice in the northern hemisphere in
January.

The most prolific source of icebergs is the west coast of Greenland. In this area
there are about 100 tidewater glaciers, 20 of them being the principal producers of
icebergs. About 7,500 icebergs are formed here each year. The west Greenland
current carries them northward and then westward until they encounter the south-
flowing Labrador current. West Greenland icebergs generally spend their first winter
in Baffin Bay. During the next summer they are carried southward by the Labrador
current. In many cases, their second winter is spent in Davis Strait. When they are
freed by the break-up of the pack ice, they drift southward. An average of about
400 per year reach latitude 48? N, and about 35 are carried south of the Grand Banks
(latitude 43? N) before they melt. Icebergs have been encountered south of Bermuda,
off the Azores, and within a few hundred miles of Great Britain.

The variation from average is considerable. More than 1,350 icebergs have been
sighted south of latitude 48°N in a single year (1929), while in 1940 only two were
encountered in this area. Although this variation has not been fully explained, it is

ICE IN THE SEA 755

er of irehergs and

Dd e pverage numb
for| the [month eer on the Basi
E reported positiong witHin one-dagreela gle

the! 30-year period, 1911

D

FIGURE 3610a.— Average iceberg conditions in the vicinity of the Grand Banks in April.

apparently related to wind conditions, the distribution of pack ice in Davis Strait, and
to the amount of pack ice off Labrador. It has been suggested that the distribution of
the Davis Strait-Labrador Sea pack ice influences the effectiveness of this ice in holding
back the icebergs. According to this theory, when pack ice is heavy along the Labrador
coast, the icebergs are forced well offshore, where warmer water causes them to melt
before they reach the North Atlantic shipping lanes; but when the pack ice is not suffi-
cient for this, the icebergs drift closer to shore, where there is colder water which
prolongs their existence.

Icebergs may be encountered during any part of the year, but in the Grand Banks
area they are most numerous during the spring. Average iceberg and pack ice condi-
tions in this area during April, May, and June are shown in figures 3610a, 3610b, and
3610c. Off Newfoundland, part of the pack ice is brought south by the Labrador
current, and part of it comes through Cabot Strait, having originated in the Gulf of
St. Lawrence.

3611. The North Atlantic lane routes.—In his 1855 sailing directions, Matthew
Fontaine Maury included a section on “Steam Lanes Across the Atlantic.” Maury
was inspired by the collision and sinking the previous year of the French Vesta and
American Arctic, in which about 300 lives were lost, and he recommended separate

756 ICE IN THE SEA

go
e

Figure 3610b.— Average iceberg conditions in the vicinity of the Grand Banks in May.

routes for eastbound and westbound vessels to avoid the risks due to fog. "The U. S.
Navy Hydrographic Office continued to advocate the use of lane routes during the
next 35 years, ultimately designating different routes for different times of the year
to avoid ice dangers. In 1889 representatives of 26 maritime nations, meeting at the
International Marine Conference in Washington, ruled against establishing steamer `
lanes by international agreement of the governments involved, but recommended that
companies engaged in the North Atlantic trade establish such routes for their own
vessels. Two years later a group of steamship companies operating passenger liners in
the North Atlantic, led by the Cunard Line, agreed to follow designated tracks which
were essentially the ones proposed by the U. S. Navy Hydrographic Office. The lanes
have been altered somewhat from time to time. "The principal ones now in use are
shown in figure 3611. Each lane is composed of two tracks separated by a safe distance,
the southern track being used by eastbound vessels, and the northern one by westbound
vessels.

Routes A, B, and C connect the United States and Europe, while routes D, E, F,
and G run between Canada and Europe. Normally, route B is used between April 11
and June 30, and route C during the remainder of the year. However, when icebergs
are numerous south of the Grand Banks, the use of lane A is specified. "This route

ICE IN THE SEA 757 <

o

FIGURE 3610c.— Average iceberg conditions in the vicinity of the Grand Banks in June.

adds 150 to 200 miles to the great-circle track, but the increased distance is acceptable
because it improves the safety and reduces the possibility of delays due to pack ice.
Normally, route D is used between February 15 and April 10; route E from April 11
through May 15, and from December 1 through February 14; route F from May 16
until route G is clear, about July 1, or through November 30 if route G is not used;
and route G from the opening of Belle Isle Strait, about July 1, through November 14.
Specified lanes are shown on pilot charts for the North Atlantic (H.O. Chart No. 1400).

Variations in this schedule are specified by a designated official of the Cunard
Line, acting upon advice from the Hydrographer of the U. S. Navy. The Hydrog-
rapher makes his recommendation after consultation with the Commandant of the
U. S. Coast Guard, taking into account the information provided by the International
Ice Patrol (art. 3612). Virtually all passenger liners and most freight vessels use these
routes.

3612. The International Ice Patrol was established in 1913 by the International
Convention for the Safety of Life at Sea held that year as a result of the sinking of
the SS Titanic the previous year. On its maiden voyage this vessel struck an iceberg
and sank with the loss of 1,513 lives. In accordance with the agreement reached at
the convention, this patrol is conducted by the U. S. Coast Guard, which each year

758 ICE IN THE SEA

40° 30° 20°

FIGURE 3611.—Principal North Atlantic steamer lanes.

assigns vessels to remain in the vicinity of the Grand Banks during the ice season to
observe and report ice conditions.

During the war years of 1916-18 and 1941-45 the patrol was suspended. Follow-
ing World War II, aircraft were added to the patrol force, and Argentia, Newfoundland,
was established as the base of operations. Aircraft have played an increasing role in
ice reconnaissance each year since then, and today they perform most of the
work. Twice each day during the iceberg season an ice bulletin is broadcast from
Argentia and printed in the Daily Memorandum of the U. S. Navy Hydrographic Office.
Ice patrol vessels copy the broadcasts when on station and make them available to other
ships upon request. In return for this service, all vessels in the area are requested to
report to the patrol vessels any ice observed, and to send weather data and surface sea
water temperature every four hours.

When engaged in patrolling ice areas, the vessels conduct oceanographic surveys
and maintain an up-to-date map of the currents, for use in predicting future drift of
icebergs. Recommendations for changes in the use of lane routes (art. 3611) are based
upon information gathered by the International Ice Patrol.

As used by the U. S. Coast Guard, the expression “ice observation service" means
that a continuous surface vessel patrol is not in effect, ice reconnaissance being accom-
plished chiefly by aircraft. When a continuous surface patrol is used to augment the
ice observation service, the expression “ice patrol service” is used,

3613. Ice detection.—As a ship proceeds into higher latitudes, the first ice it
encounters is likely to be in the form of icebergs, because such large pieces require a
longer time to disintegrate. Icebergs can easily be avoided if detected soon enough.

ICE IN THE SEA 759

The distance at which an iceberg can be seen depends upon the visibility, height of
the berg, source and condition of lighting, and the observer. On a clear day with
excellent visibility a large berg might be sighted at a distance of 18 miles. With a
low-lying haze around the horizon this may be reduced to ten miles. In light fog or
drizzling rain this is further reduced to one to three miles. There is a tendency to over-
estimate the distance.

In a dense fog a berg may not be visible until it is close aboard, when it appears
as a luminous, white mass if the sun is shining; or as a dark, sombre mass if the sun is
not shining. If the layer of fog is not thick, an iceberg may be sighted from aloft sooner
than from a point lower in the vessel, but this fact should not be considered justification
for omitting a bow lookout.

On a clear, dark night an iceberg will seldom be picked up visually at a distance
greater than one-fourth of a mile, but if its bearing is known, an observer with bin-
oculars can occasionally observe a light spot where a wave breaks against it at a distance
of a mile.

A moon may either help or hinder, depending upon its phase and position relative
to ship and berg. A full moon in the direction of the berg interferes with its
detection, while light from one in the opposite direction produces a “blink” which
renders the iceberg visible for a greater distance, possibly as much as three miles.
Clouds, particularly broken clouds, with intermittent moonlight, add to the difficulty
of detecting ice.

If an iceberg is in the process of disintegration, its presence may be detected by
the cracking sound as a piece breaks off, or by the thunderous roar as a large piece
falls into the water. The appearance of smaller pieces of ice in the water often indicates
the presence of an iceberg nearby. In calm weather such pieces may form a curved
line with the parent iceberg on the concave side. Some of the pieces broken from an
iceberg are themselves large enough to be a menace to ships.

As the ship proceeds to higher latitudes, it eventually encounters pack ice. If the
ice is approached from leeward, it is likely to be loose and somewhat scattered, often in
long, narrow arms. If it is approached from windward, it is usually compact and the
edge is sharply defined.

One of the most reliable signs of the approach to pack ice, especially from leeward,
is the somewhat abrupt smoothing of the sea in a fresh breeze, and the more gradual
lessening of the swell. Abrupt changes in air or sea temperature or sea-water salinity
are not reliable signs of the approach to either icebergs or pack ice, but if the sea
temperature gradually drops below 32° F, the ship may be nearing an ice field.

Another reliable sign of the approach to pack ice is the appearance of the horizon
orsky. A yellowish glare or ice blink appears in the sky above an ice field. If clouds
are present, the blink is whiter. Reflection of light from snow, whether on land or
sea ice, is white and is called snow blink. In contrast, the sky above open water is
dark. This is called water sky. Somewhat similar land sky above ice- and snow-free
land is grayer. The combination of these various effects in the sky is called a sky map.
One experienced in reading the sky map finds it very useful in avoiding ice or searching
out openings which may permit his vessel to make progress while proceeding through
an ice field.

The presence of seals or certain types of birds may indicate the presence of ice
nearby. It is well to observe the habits of the various species encountered.

If aircraft or other vessels can be contacted by radio, much useful information can
sometimes be obtained from them. Some ships, particularly icebreakers, proceeding
into high latitudes carry helicopters, which are invaluable in locating ice and determining
the relative navigability of different portions of it.

760 . ICE IN THE SEA

Echoes from the ship’s whistle or horn will sometimes reveal the presence of ice-
bergs, but are useless against pack ice. Such echoes can give an indication of direction,
and if the time interval between the sound and its echo is measured, the distance in
feet can be determined by multiplying the number of seconds by 550. However,
echoes are not a reliable indication because only those pieces of ice with large vertical

"areas facing the ship return enough echo to be heard, and also because echoes might be
received from land or a fog bank.

At relatively short ranges, sonar is sometimes helpful in locating ice. The first
contact with icebergs may be when as much as three miles or more off, but is usually
considerably less. Growlers may be picked up at one-half to one mile and even smaller
pieces may be detected in time to avoid them. Since one-half to seven-eighths of the
mass of ice is below the surface, the underwater portion presents a better target than
the portion above water.

Radar is highly useful in detecting ice, but is by no means infallible. Ice is a
relatively poor radar target, and much depends upon the nature of the exposed surface.
Icebergs with sides sloping gently toward the vessel can be seen visually long before
they are picked up by radar, if the day is clear. One iceberg 700 feet long and 200
feet high was reported to have been approached to within three miles before it appeared
on the radar screen. However, the average berg is picked up at a range of eight to ten
miles, and the large vertical-sided tabular icebergs of the antarctic are usually detected
at ranges of 15 to 30 miles, with an extreme range of 37 miles having been reported.
Growlers are the chief concern. While a large iceberg is almost always detected in time
to be avoided, a growler large enough to be a serious menace may be lost in the sea
return and escape detection altogether. If an iceberg or growler is detected, tracking is
sometimes necessary to distinguish it from a rock, islet, or ship.

Against sea ice, radar can be of great assistance to one experienced in interpreting
the scope picture. Smooth sea ice, like smooth water, returns little or no echo, but
rough, hummocky sea ice can be detected at a range of two to three miles. The re-
turn is similar to sea return, but the same echoes appear at each sweep. A lead in
smooth ice broken by a preceding vessel is clearly visible, even though a thin coating of
new ice has formed in the opening. A light covering of snow obliterating many of the
features to the eye has little effect upon a radar return.

The ranges at which ice can be detected by radar are somewhat dependent upon
refraction, which is sometimes quite abnormal in polar regions. Adequate training
and experience are essential if full benefit is to be realized from radar.

No method yet devised to detect the presence of ice is infallible, and all should be
regarded with suspicion, although none should be overlooked. In ice, as elsewhere,
there is no substitute for constant vigilance. |

3614. Operations in ice.—For operations in ice it is preferable to.have a vessel
designed for this purpose. Such a vessel has a heavily reinforced bow, reinforced plat-
ing along the water line, absence of vertical sides, deep screws, blunt bow, and other
desirable features. The full list depends upon the area of operations, kinds of ice to
be encountered, length of stay in the vicinity of ice, anticipated assistance by icebreakers,
and possibly other factors. Any vessel expecting to penetrate the pack ice should as

„a minimum have reinforcement along the water line, particularly at the bow, which
should be strengthened both inside and outside.

Whatever the nature of the vessel, it will be subjected to various hazards which
may cause damage. Its safety depends largely upon the thoroughness of advance
preparations, the alertness and skill of its crew, and their ability to make repairs if
damage is sustained. Before the ice is entered, the ship should be trimmed so as to be
down by the stern slightly (not more than two or three feet).

ICE IN THE SEA 761

In the vicinity of icebergs, a sharp lookout should be kept and all bergs given a
wide berth. It is dangerous to approach close to them because of the possibility of
encountering underwater extensions and because bergs that are disintegrating may sud-
denly capsize or readjust their masses to new positions of equilibrium. In periods of low
visibility the utmost caution is needed. The speed should be reduced and the watch
prepared for quick maneuvering.

Upon the approach to pack ice, a careful decision is needed to determine the best
action. Often it is possible to go around the ice, rather than through it. Unless the
pack is quite loose, this action usually gains rather than loses time. When skirting a
field of ice or an iceberg, do so to windward, if a choice is available, to avoid
projecting tongues of ice or individual pieces that have been blown away from the
main body of ice.

When it is considered necessary to enter pack ice, select the point of entry with
great care. Get all available information on the nature and extent of ice and open water.
Seek the weakest part of the ice and particularly avoid ice under pressure. If an off-
shore wind is blowing, a relatively ice-free shore lead may be available. Enter ice from
leeward if possible, at slow speed. Enter on a course perpendicular to the ice edge,
avoiding projecting tongues of ice.

Having entered the pack, always work with the ice, not against it, and keep moving,
but do not rush the work of negotiating the pack. Patience may pay big dividends.
Respect the ice but do not fear it. Stay in open water or areas of weak ice if possible,
remembering that it is better to make good progress in the general direction desired
than to fight heavy floes in the exact direction to be made good. However, avoid the
temptation to proceed far to one side of the course. It is sometimes better to back out
and seek a more penetrable area, being careful not to damage the screws while backing.
Keep clear of corners and projecting points of ice. Never hit a large piece of ice if it
can be avoided, but if it cannot be avoided, hit it head-on. Keep a sharp watch on the
screws and rudder, fending off pieces of ice which might damage these vital parts, or
stopping the propellers if the ice cannot be avoided. Back with extreme caution.
Aircraft, particularly helicopters, are of great value in determining the nature and
distribution of ice ahead. Since ice is continually shifting its position, the changing
situation should be kept under observation and all forms of pressure avoided if possible.
The windward side of icebergs within pack ice should be avoided because the pack ice
usually moves with the wind, while the berg does not do so to the same extent, resulting
in pressure on the windward side and open water to leeward. Because of its poor
maneuverability in ice, a vessel may even be set down upon the iceberg.

If a narrow strait or a bay is entered, an alert watch should be maintained, because
if the wind blows directly into the confined space, drifting ice may be forced down
upon the vessel. An increase in wind on the windward side of a prominent point,
grounded iceberg, or land ice tongue extending into the sea may similarly endanger
a vessel.

While a ship is in pack ice, it is always in danger of being beset, or so closely sur-
rounded by ice that steering control is lost. It may then be carried into shallow water
or heavy ice with dangerous underwater projections. If pressure is exerted against
the hull, the vessel is said to be nipped. When this occurs, it is in danger of being crushed.
A ship in the ice is in constant danger of colliding with sharp pieces of ice, and while
in the ice sharp turns to avoid such collisions may throw the stern against the ice,
resulting in a bent or broken screw blade or propeller shaft. If a ship cannot free it-
self by maneuvering, an explosive charge or ice saws may have to be used. Dynamite
is the explosive usually used. If detonated while the engines are going full astern and
a strain is taken on an ice anchor (a stockless, single-fluked hook imbedded in the ice),

762 ICE IN THE SEA

a 2% pound charge placed in a hole cut nearly to the bottom of the ice about 35-40
feet off the beam may help to free a beset ship.

Attempts to clear ice jams in navigable channels by use of explosives and with the
heat generated by thermite charges have met with some success, but the same tactics
used against icebergs at sea have proven of little value. Icebergs in the southern
Grand Banks area have disintegrated more rapidly when depth charges have been
detonated against their underwater portions, but destruction by this method, as well
as by other types of ordnance attempted, has been resisted by icebergs in higher
latitudes.

If an icebreaker is in the vicinity, its instructions should be followed carefully in
all ice operations.

Underice submarine operations require information on the thickness of ice below
the surface as well as the extent of water openings between ice floes. While icebergs
are believed to extend to depths of nearly 1,000 feet, ice hummocks between floes of
polar ice may extend 150 feet below sea level. Submarine navigation thus involves
vertical positioning as well as dead reckoning considerations, plus the necessity of
finding open water or thin ice for surfacing purposes.

Only the basic principles of operating in ice have been given. Before entering
areas of ice, those responsible for the maneuvering of a ship should become well ac-
quainted with the experience of others who have operated in ice, especially those who
have been in the same area. Some of this information is to be found in various volumes
of sailing directions, particularly those for Antarctica (H.O. Pub. No. 27), and ad-
ditional information is available at the U.S. Navy Hydrographic Office.

3615. Ice observing and forecasting.—Advance knowledge of ice conditions to
be encountered is valuable in both planning and operational phases of any program to
be conducted in high latitudes. Through the cooperation of observers aboard ship,
in the air, and on land, the U. S. Navy Hydrographic Office collects and analyzes ice
data in the arctic, and distributes ice information in the form of ice bulletins as part of
regularly scheduled broadcasts.

For this program to be fully effective, it is essential that all vessels and air units
operating in ice areas cooperate by submitting reports. To assist in this program, and
to provide uniformity in reporting procedure, the U. S. Navy Hydrographic Office has
published an observer's manual, H.O. Pub. No. 606-d, Jee Observations; H.O. Pub.
No. 609, A Functional Glossary of Ice Terminology; and convenient ice log forms for
recording the observations. When filled in, the log sheets are mailed to the U. S.
a Hydrographic Office, Washington, D. C., and certain reports are sent by radio.
ie kas who regularly sends complete reports can contribute to an increase in

ge of ice conditions and to the accuracy and completeness of ice bulletins.

In addition to its ice bulletins, the U. S. Navy Hydrographic Office is developing

techniques for forecasting ice growth and thickness, movement and concentration, and
melting and break-up. j

a daa M uci Spi d i Or? ]
l wu Asian, is provi Wa m Y

(0 PART SEVEN m bi emo Tes NV mpl A

eo vé mast 1 hs th. ant e ti e" m4) r d f.
R ` r x T! Di `

ti , A E
4 cr DOE TRE) us i PR AITAN
E A f Ý ` fy
cl k eim VSO TOL (n í DY A 3 Hu
is d Io Y - 18

PART SEVEN

WEATHER =
age
CHAPTER XXXVII! Weather Observations tee 765
CHAPTER XX XVIII. Weather and Weather Forecasts____________-__-_---_-_- 793

CHAPTER XXXIX Tropical Cyclone. SemS 819

CHAPTER XXXVII
WEATHER OBSERVATIONS

3701. Introduction.—Weather forecasts are generally based upon information
acquired by observations made at a large number of stations. Ashore, these stations
are located so as to provide adequate coverage of the area of interest. Most ob-
servations at sea are made by mariners, wherever they happen to be. Since the number
of observations at sea is small compared to the number ashore, marine observations
are of importance in areas where little or no information is available from other sources.
Results of these observations are recorded in the deck log (art. 3726), or other appro-
priate form. Data recorded by designated vessels are sent by radio to centers ashore,
where they are plotted, along with other observations, to provide data for drawing
synoptic charts (art. 3827). These charts are used to make forecasts. Complete
weather information gathered at sea is mailed to the appropriate meteorological serv-
ices for use in the preparation of weather atlases and in marine climatological studies.

The analysis of the weather map can be no better than the weather reports used
for making the map. A knowledge of weather elements and the instruments used to
measure them is therefore of importance to the mariner who hopes to benefit from
weather forecasts.

Instruments of various types have been developed to aid in making weather ob-
servations. Some have been in use for many years, while others have been developed
only recently. Electronic devices have aided materially, but the full impact of elec-
tronics upon meteorology has not yet been felt. Several new types of electronic weather
instruments are in various stages of development.

3702. Atmospheric pressure measurement.—The sea of air surrounding the earth .
exerts a pressure of about 14.7 pounds per square inch on the surface of the earth. This
atmospheric pressure, sometimes called barometric pressure, varies from place to
place, and at the same place it varies with time.

Atmospheric pressure is one of the basic elements of a meteorological observation.
When the pressure at each station is plotted on a synoptic chart, lines of equal at-
mospheric pressure, called isobars, are drawn to indicate the areas of high and low `
pressure and their centers. These are useful in making weather predictions, because
certain types of weather are characteristic of each type area, and often the wind
patterns over large areas are deduced from the isobars.

Atmospheric pressure is measured by means of a barometer. A mercurial barom-
eter does this by balancing the weight of a column of air against that of a column of
mercury. The aneroid barometer has a partly evacuated, thin-metal cell which is
compressed by atmospheric pressure, the amount of the compression being related to
the pressure.

Early mercurial barometers were calibrated to indicate the height, usually in inches
or millimeters, of the column of mercury needed to balance the column of air above the
point of measurement. While the units inches of mercury and millimeters of mercury
are still widely used, many modern barometers are calibrated to indicate the centimeter-
gram-second unit of pressure, the millibar, which is equal to 1,000 dynes per square
centimeter. A dyne is the force required to accelerate a mass of one gram at the

rate of one centimeter per second per second. A reading in any of the three units
765

766 WEATHER OBSERVATIONS

of measurement can be converted to the equivalent
reading in either of the other units by means of table
14, or the conversion factors given in appendix D.

3703. The mercurial barometer was invented by
Evangelista Torricelli in 1643. In its simplest form
it consists of a glass tube a little more than 30 inches
in length and of uniform internal diameter; one
end being closed, the tube is filled with mercury, and
inverted into a cup of mercury. The mercury in the
tube falls until the column is just supported by the
pressure of the atmosphere on the open cup, leaving a
vacuum at the upper end of the tube. The height of
the column indicates atmospheric pressure, greater
pressures supporting higher columns of mercury. A
shipboard type is shown in figure 3703.

The mercurial barometer is subject to rapid vari-
ations in height, called pumping, due to pitch and
roll of the vessel and temporary changes in atmos-
pheric pressure in the vicinity of the barometer.
Because of this, the care required in the reading of
the instrument, its bulkiness, and its vulnerability to
physical damage, the mercurial barometer has been
largely replaced at sea by the aneroid barometer.

3704. The aneroid barometer (fig. 3704) meas-
ures atmospheric pressure by means of the force
exerted by the pressure on a partly evacuated, thin-
metal element called a sylphon cell. A small spring is
used, either internally or externally, to partly coun-
teract the tendency of the atmospheric pressure to
Pēdas ss A crush the cell. Atmospheric pressure is indicated

mercurial barometer. directly by a scale and a pointer connected to the

cell by a combination of levers. The linkage pro-

vides considerable magnification of the slight motion of the cell, to permit readings
to higher precision than could be obtained without it.

An aneroid barometer should be mounted permanently. Prior to installation, the
barometer should be carefully set to station pressure (art. 3706). An adjustment
screw is provided for this purpose. The error in the reading of the instrument is
determined by comparsion with a mercurial barometer or a standard precision aneroid
barometer. If a qualified meteorologist is not available to make this adjustment, it is
good practice to remove only one-half the apparent error. The case should then be
tapped gently to assist the linkage to adjust itself, and the process repeated. If the
remaining error is not more than half a millibar (0.015 inch), no attempt should be
made to remove it by further adjustment. Instead, a correction should be applied to
the readings. The accuracy of this correction should be checked from time to time.

A precision aneroid barometer used at weather stations ashore, and for comparison
of shipboard instruments, is constructed and tested to more exacting tolerances than
the ordinary barometer, and provides readings to greater accuracy.

3705. The barograph (fig. 3705) is a recording barometer. Basically, it is the
same as a nonrecording aneroid barometer except that the pointer carries a pen at its

WEATHER OBSERVATIONS

CHES OF MERG
URy
AES.

` 1000 $

MILLIÐAR§

FIGURE 3704.—An aneroid barometer.

CLOCK CHART CLOCK CHART PEN PEN
WINDING KEY HOLDING CLIP UNIT CYLINDER LIFTING ROD ARM

CONSTANT
PRESSURE
BEARING

CURRENT
PRESSURE
ADJUSTMENT

HINGED
COVER IN OPEN FRAME SYLPHON PEN LIFTING
POSITION PLATE CELL LEVER

Figure 3705.—A barograph.

767

768 WEATHER OBSERVATIONS

outer end, and the scale is replaced by a slowly rotating cylinder around which a
prepared chart is wrapped. A clock mechanism inside the cylinder rotates the cylinder
so that a continuous line is traced on the chart to indicate the pressure at any time.

A microbarograph is a precise barograph with greater magnification of deforma-
tions due to pressure changes, and a correspondingly expanded chart. Two sylphon
cells are used, one being mounted over the other in tandem. Minor fluctuations due to
shocks or vibrations are eliminated by damping. Since oil-filled dashpots are used for
this purpose, the instrument should not be inverted.

The barograph is usually mounted on a shelf or desk in a room open to the atmos-
phere, and in a location which minimizes the effect of the ship’s vibration. Shock-
absorbing material such as sponge rubber is placed under the instrument to minimize
the transmission of shocks.

The pen should be checked and the inkwell filled each time the chart is changed,
every week in the case of the barograph, and each four days in the case of the micro-
barograph. The dashpots of the microbarograph should be kept filled with dashpot
oil to within three-eighths inch of the top.

Both instruments require checking from time to time to insure correct indication
of pressure. The position of the pen is adjusted by a small knob provided for this
purpose. The adjustment should be made in stages, eliminating half the apparent
error, tapping the case to insure linkage adjustment to the new setting, and then
repeating the process.

3706. Adjustment of barometer readings.—Atmospheric pressure as indicated by
a barometer or barograph may be subject to several errors, as follows:

Instrument error. Any inaccuracy due to imperfection or incorrect adjustment
of the instrument can be determined by comparison with a standard instrument. The
U. S. Weather Bureau provides a comparison service. In certain ports a repre-
sentative brings a standard barometer on board ships which participate in the
cooperative observation program of that Bureau. If a barometer is taken to the
Weather Bureau, comparison can be made there. The correct sea-level pressure can
be obtained by telephone. The shipboard barometer should be corrected for height,
as explained below, before comparison with this telephoned value. If there is reason
to believe that the barometer is in error, it should be compared with a standard, and
if an error is found, the barometer should be adjusted to the correct reading, or a
correction applied to all readings.

Height error. Since atmospheric pressure is caused by the weight of air above
the place, the pressure decreases as height increases. The correct value at the barometer
is called station pressure. Isobars adequately reflect wind conditions and geographic
distribution of pressure only when they are drawn for pressure at constant height (or
the varying height at which a constant pressure exists). On synoptic charts it is
customary to show the equivalent pressure at sea level, called sea level pressure. This
is found by applying a correction to station pressure. The correction, given in table
11, depends upon the height of the barometer and the average temperature of the air
between this height and the surface. The outside air temperature taken aboard ship is
sufficiently accurate for this purpose. This is an important correction which should be
applied to all readings of any type barometer.

Gravity error. Mercurial barometers are calibrated for standard sea-level gravity
at latitude 45732/40^. If the gravity differs from this amount, an error is introduced.
The correction to be applied to readings at various latitudes is given in table 12. This
correction does not apply to readings of an aneroid barometer. Gravity also changes with

height above sea level, but the effect is negligible for the first few hundred feet, and
so is not needed for readings taken aboard ship.

WEATHER OBSERVATIONS 769

Temperature error. Barometers are calibrated at a standard temperature of 32°F.
The liquid of a mercurial barometer expands as the temperature of the Mercury rises,
and contracts as it decreases. The correction to adjust the reading of the instrument
to the true value is given in table 13. This correction is to be applied to readings of
mercurial barometers only. Modern aneroid barometers are compensated for tempera-
ture changes by the use of different metals having unequal coefficients of linear
expansion.

3707. Determination of height by barometer.—Since atmospheric pressure is re-
lated to height, a barometer can be used to determine height. This is the principle
of the barometric altimeter commonly used in aircraft.

Ordinary barometers can be used for determination of height difference, a problem
which often arises in surveying. Simultaneous pressure and temperature readings
should be made at both places (heights), if practicable. If this cannot be done, and
more than a few minutes will elapse between readings, better values can be obtained
by making a reading at the first height, then at the second, and then returning and
making another reading at the first station, with approximately equal time intervals
between readings. The average of the two readings at the first station is used. All
appropriate corrections should be applied except that for height. If P, and P, are the
atmospheric pressures at the two heights, the difference in height can be computed
by Babinet’s formula:

Bi ~P:

Diff. in height=C X php
1 2

If T, and T; are the air temperatures at the two places in degrees Fahrenheit, and
difference in height is in feet,

C=52,494 (1 i

If temperature is in degrees Celsius (centigrade), and difference in height is in meters,

2(T,+T»)
C=16,000 LE

For differences of not more than a few hundred feet, approximate results can be
obtained by dividing the pressure difference in inches by 0.0011 inch, to obtain the
answer in feet. This is almost the same as multiplying the pressure difference in
hundredths of an inch by nine. For large differences, Babinet's formula is not strictly
accurate, although the results should meet most requirements.

3708. Wind measurement consists of determination of the direction from which
the wind is blowing, and the speed of the wind. Wind direction is measured by a
wind vane, and wind speed by an anemometer.

A wind vane consists of a device pivoted on a vertical shaft, with more surface
area on one side of the pivot than on the other, so that the wind exerts more force on
one side, causing the smaller end to point into the wind. An indicator may be con-
nected to the shaft to provide continuous measurement of wind direction.

In its simplest form, an anemometer consists of a number of cups mounted on
short horizontal arms attached to a longer vertical shaft which rotates as the wind
blows against the cups. "The speed at which the shaft rotates is directly proportional
to the wind speed. The number of rotations may be indicated by a counter or by
marks on a revolving drum, or the speed may be indicated directly by a device similar
to an automobile speedometer. Still another method is to connect a buzzer or flashing
light so calibrated that the number of signals per unit time is the speed in knots or
miles per hour.

770 WEATHER OBSERVATIONS

The standard anemometer used aboard ship has three cups. Some anemometers
have four cups, and certain naval vessels use a type called the bridled cup anemometer,
which has a large number of cups mounted on a shaft which does not rotate freely.
An anemometer which uses a propeller as the rotor to measure wind speed, and has a
streamlined, tail-type vane to indicate direction, is being installed on some ships. Sim-
ilar equipment is used ashore, customarily mounted on a guyed mast 13 feet high.
Wind direction is transmitted to an indicator or recorder by a synchronous motor,
while wind speed is transmitted as a voltage generated by a direct-current magneto
driven by the propeller. A synchro system is connected to some wind-measuring
equipment to provide remote indication of the velocity (both direction and speed).
Lightweight, portable, hand-held instruments for measuring and indicating wind speed
in knots are used on some ships, principally aircraft carriers.

Several types of wind speed and direction recorders are available. Each instru-
ment is normally supplied with a description and complete operating instructions.

If no anemometer is available, wind speed can be estimated by its effect upon the
sea and objects in its path, as explained in article 3710.

Measurement of winds aloft is discussed in articles 3717-3722.

3709. True and apparent wind.—An observer aboard a vessel proceeding through
still air experiences an apparent wind which is from dead ahead and has an apparent
speed equal to the speed of the vessel. Thus, if the actual or true wind is zero and
the speed of the vessel is ten knots, the apparent wind is from dead ahead at ten knots.
If the true wind is from dead ahead at 15 knots, and the speed of the vessel is ten knots,
the apparent wind is 15+10=25 knots from dead ahead. If the vessel makes a 180?
turn, the apparent wind is 15—10=5 knots from dead astern.

In any case, the apparent wind is the vector sum (art. O18) of the true wind and
the reciprocal of the vessel's course and speed vector. Since wind vanes and anemom-
eters measure apparent wind, the usual problem aboard a vessel equipped with an
anemometer is to convert this to true wind. There are several ways of doing this.
Perhaps the simplest is by the graphical solution illustrated in the following example:

Example 1.—A ship is proceeding on course 150? at a speed of 17 knots. The
apparent wind is from 40? off the starboard bow, speed 15 knots.

Required.—The relative direction, true direction, and speed of the true wind.

Solution (fig. 3709a).—Starting at the center of a maneuvering board (art. 1212)
or other suitable form, draw a line in the relative direction from which the apparent
wind is blowing. Locate point 1 on this line, at a distance from the center equal to
the speed of the apparent wind (2:1 scale is used in figure 3709a). From point 1,
draw a line vertically downward. Locate point 2 on this line at a distance from point
1 equal to the speed of the vessel in knots, to the same scale as the first line. The
relative direction of the true wind is from point 2 (120°) toward the center, and the
speed of the true wind is the distance of point 2 from the center, to the same scale
used previously (11 kn.). The true direction of the wind is the relative direction plus
the true heading, or 120°-+150°=270°.

Answers.—True wind from 120° relative, 270° true, at 11 knots.

A quick solution can be made without an actual plot, in the following manner:
On a maneuvering board (H.O. 2665-10), label the circles 5, 10, 15, 20, etc., from the
center, and draw vertical lines tangent to these circles. Cut out the 5:1 scale and
discard that part having graduations greater than the maximum speed of the vessel.
Keep this equipment for all solutions. (For durability, the two parts can be mounted
on cardboard or other suitable material.) To find true wind, spot in point 1 by eye.
Place the zero of the 5:1 scale on this point and align the scale (inverted) by means of
the vertical lines. Locate point 2 at the speed of the vessel as indicated on the 5:1

WEATHER OBSERVATIONS A

AC Jb

MANEUVERING BOARD +) EE ERE «inā d R Si
FIGURE 3709a.—Finding true wind by maneuvering board.

scale. It is always vertically below point 1. Read the relative direction and the speed
of the true wind using eye interpolation if needed. The U.S. Weather Bureau dis-
tributes a wind vector computer called a Shipboard Wind Plotter (fig. 3709b). Solution
by means of this plotter is illustrated in the following example:

Example 2.—A ship is proceeding on course 270° at a speed of 14.5 knots. The
apparent wind is from 40° off the starboard bow, speed 20 knots.

Regutred.—The relative direction, true direction, and speed of the true wind by
U.S. Weather Bureau Shipboard Wind Plotter.

Solution (fig. 3709b).—The true direction of the apparent wind is determined by
adding the apparent wind direction to the ship’s heading if the wind is from off the
starboard bow and subtracting the apparent wind direction if the wind is from off the
port bow. In this example, the true direction of the apparent wind is 310°. In this
solution the red arrowhead is considered the top of the plotter. Set ship’s course, 270°,
to the top of the plotter by rotating the protractor disk to set 270° at the red arrow.
Using a convenient linear scale, measure vertically downward from the center peg of the

12 WEATHER OBSERVATIONS

plotting board a distance equivalent to 14.5 knots. Mark this point “S” for ship.
Rotate the protractor disk of the plotting board until 310? is at the red arrowhead at
the top of the plotting board. Using the same linear scale as for ship's speed, plot
vertically downward from the center peg of the plotting board a distance equivalent to
20 knots. Mark this point ^W". Rotate the protractor disk until the “S” is vertically
above the “W”, using the vertical lines on the plotting board to line.up the two points.
Read the true wind direction at the top of the plotting board. "The distance between
points “S” and “W” is the true wind speed, using the same scale as in plotting points
DOS and DONT,
Answers.—True wind direction is 357°, true wind speed is 13 knots.

m

ES
N
DA P
M ”
SQ =
S& =
=v re
S
o =

Q

=O 2
EMEN a
= oz
= O Bs
== JE
= CN ==
= co =
=O
2 et:
2s =
= 2
= i
=a =
2 ~
Á

OL!

Ire

Ficure 3709b.—Finding true wind by Weather Bureau Shipboard Wind Plotter.

WEATHER OBSERVATIONS Ken

Such problems can be solved by the use of true directions and a regular vector
solution, but the use of relative directions simplifies the plot because that component
of the apparent wind due to the vessel's motion is always parallel (but reversed) to
the vessel's motion, and the apparent wind is always forward of the true wind.

A tabular solution based upon the same principle can be made by means of table
10. The entering values for this table are the apparent wind speed in units of ship’s
speed, and the difference between the heading and the apparent wind direction. The
values taken from the table are the relative direction (right or left) of the true wind,
and the speed of the true wind in units of ship’s speed. 1f a vessel is proceeding at 12
knots, six knots constitutes one-half (0.5) unit, 12 knots one unit, 18 knots 1.5 units, 24
knots two units, etc.

Example 3.—A ship is proceeding on course 270° at a speed of ten knots. The
apparent wind is from 10° off the port bow, speed 30 knots.

Required.—The relative direction, true direction, and speed of the true wind by
table 10.

Solution.—The apparent wind speed is 193.0 ship's speed units. Enter table
10 with 3.0 and 10? and find the relative direction of the true wind to be 15? off the
port bow (345? relative), and the speed to be 2.02 times the ship's speed, or 2.02 X 10=20
knots, approximately. The true direction is 345? 4-270? —255?.

Answers.—True wind from 345? relative, 255? true, at 20 knots.

By variations of this problem, one can find the apparent wind from the true wind,
the course or speed required to produce an apparent wind from a given direction or
speed, or the course and speed to produce an apparent wind of a given speed from a
eiven direction. Such problems arise in aircraft carrier operations.

Wind speed determined by appearance of the sea (art. 3710) 1s the speed of the true
wind. The sea also provides an indication of the direction of the true wind, because
waves move in the same direction as the generating wind, not being deflected by earth
rotation (art. 3302). If a wind vane is used, the direction of the apparent wind thus
determined can be used with the speed of the true wind to determine the direction
of the true wind by vector diagram. If a maneuvering board is used, draw a circle
about the center equal to the speed of the true wind. From the center, plot the ship's
vector (true course and speed). From the end of this vector draw a linein the direction
in which the apparent wind is blowing (reciprocal of the direction from which it is
blowing) until it intersects the speed circle. This line is the apparent wind vector, its
length denotes the speed. A line from the center of the board to the end of the ap-
parent wind vector is the true wind vector. The reciprocal of this vector is the direction
from which the true wind is blowing. If the true wind speed is less than the speed of
the vessel, two solutions are possible. If solution is by table 10, the true speed, in units
of ship’s speed, is found in the column for the direction of the apparent wind. The
number to the left is the relative direction of the true wind. The number on the same
line in the side columns is the speed of the apparent wind in units of ship’s speed.
Again, two solutions are possible if true wind speed is less than ship’s speed.

3710. Wind and the sea.—The action of the wind in creating ocean currents and
waves is discussed in chapters XXXII and XXXIII, respectively. There is a relation-
ship between the speed of the wind and the state of the sea in the immediate vicinity
of the wind. This is useful in predicting the sea conditions to be anticipated when
future wind speed forecasts are available. It can also be used to estimate the speed of
the wind, which may be desirable when an anemometer is not available.

774 WEATHER OBSERVATIONS

Wind speeds are usually grouped in accordance with the Beaufort scale named after
Admiral Sir Francis Beaufort, who devised it in 1806. As adopted in 1838, Beaufort
numbers ranged from 0, calm, to 12, hurricane. They have now been extended to
17. The Beaufort scale, with certain other pertinent information, is given in appen-
dix R. The appearance of the sea at different Beaufort scale numbers from 0 through
12 is shown in figures 3710a through 3710m.

FIGURE 3710a.— Beaufort scale 0. FIGURE 3710b.— Beaufort scale 1.

FIGURE 3710c.— Beaufort scale 2. FIGURE 3710d.— Beaufort scale 3.

FIGURE 3710e.— Beaufort scale 4.

FiavnE 3710g.— Beaufort scale 6. FIGURE 3710h.— Beaufort scale 7

WEATHER OBSERVATIONS 775

FIGURE 3710i.— Beaufort scale 8. FIGURE 3710j.—Beaufort scale 9.

FIGURE 3710k.—Beaufort scale 10. FIGURE 37101.—Beaufort scale 11.

FiGURE 3710m.—Beaufort scale 12.

3711. Temperature is the intensity or degree of heat. It is measured in degrees.
Several different temperature scales are in use.

On the Fahrenheit (F) scale commonly used in the United States and other
English-speaking countries, pure water freezes at 32° and boils at 212°.

On the Celsius (C) scale commonly used with the metric system, the freezing
point of pure water is 0° and the boiling point is 100°. This scale has been known by
various names in different countries. In the United States it was formerly called the
centigrade scale. The Ninth General Conference of Weights and Measures, held in
France in 1948, adopted the name Celsius to be consistent with the naming of other
temperature scales after their inventors, and to avoid the use of different names in
different countries. On the original Celsius scale, invented in 1742 by a Swedish
astronomer named Anders Celsius, the numbering was the reverse of the modern scale,
0° representing the boiling point of water, and 100° its freezing point.

Réaumur temperature is based upon a scale in which water freezes at 0° and boils
at 80°.

Absolute zero is considered to be the lowest possible temperature, at which there
is no molecular motion and a body has no heat. For some purposes, it is convenient to
express temperature by a scale at which 0° is absolute zero. This is called absolute

776 WEATHER OBSERVATIONS

temperature. If Fahrenheit degrees are used, it may be called Rankine (R) temperature;
and if Celsius, Kelvin (K) temperature. The Kelvin scale is more widely used than
the Rankine. Absolute zero is at (—) 459°67 F or (—) 273°15C.

` Temperature by one scale can be converted to that at another by means of the
relationship that exists between the scales. Thus,

5
=9(F—32)
and

F=?C +32.

A temperature of (—)40° is the same by either the Celsius or Fahrenheit scale. Similar
formulas can be made for conversion of other temperature scale readings. Table 15
gives the equivalent values of Fahrenheit, Celsius, and Kelvin temperatures.

The intensity or degree of heat (temperature) should not be confused with the
amount of heat. If the temperature of air or some other substance is to be increased
(the substance made hotter) by a given number of degrees, the amount of heat that
must be added is dependent upon the amount of the substance to be heated. Also,
equal amounts of different substances require the addition of unequal amounts of heat
to effect equal increase in temperature because of their difference of specific heat
(art. 3012). Units used for measurement of amount of heat are the British thermal
unit (BTU), the amount of heat needed to raise the temperature of one pound of water
one degree Fahrenheit; and the calorie, the amount of heat needed to raise the tem-
perature of one gram of water one degree Celsius.

3712. Temperature measurement is made by means of a thermometer. Most
thermometers are based upon the principle that materials expand with increase of tem-
perature, and contract as temperature decreases. In its most usual form (fig. 3712a)
a thermometer consists of a bulb filled with mercury and connected to a tube of very
small cross-sectional area. The mercury only partly fills the tube. In the remainder
is a vacuum created during construction of the instrument. The air is driven out by
boiling the mercury, and the top of the tube is then sealed by a flame. As the mercury
expands or contracts with changing temperature, the length of the mercury column in
the tube changes. Temperature is indicated by the position of the top of the column
of mercury with respect to a scale etched on the glass tube or placed on the thermom-
eter support.

A maximum thermometer has a constriction in the tube, near the bulb. As tem-
perature increases, the expanding mercury is forced past the constriction, but will not
return as temperature decreases. Thus, it indicates the highest temperature which
has occurred since the last setting. This principle is utilized in clinical thermometers,
used for measuring body temperature. The mercury can be forced back into the bulb
by centrifugal force applied by swinging the arm rapidly. Meteorologists have a
device called a “Townsend support” for accomplishing this with less effort and less
possibility of breakage.

A minimum thermometer (fig. 3712b) uses alcohol instead of mercury. The
upper part of the tube contains air under slight pressure, to prevent evaporation of
the alcohol with resultant “breaks” in the column as the alcohol later condenses. The
thermometer contains an index which is so constructed as to allow alcohol to flow past
it up the tube with rising temperatures, but which moves downward in the tube if the
temperature falls below it, being drawn down by the effect of surface tension exerted
by the bottom of the meniscus (curved upper surface) of the column of alcohol as it
reaches the index. Due to this effect, the index remains at the lowest temperature

WEATHER OBSERVATIONS (ewe

' d vag] may ARA» UÁ Ds

I 1
INVERT BULB 5° BELOW HORIZONTAL
FOR SETTING RAL POSITION
H

——

tn

MENISCUS

BLACK OF ALCOHOL
TOWNSEND GLASS INDEX COLUMN
SUPPORT Z
[PENES DITA, US
RAG m IM ==> |
THERMOMETER | 1 1
CLEAR READ CURRENT
ALCOHOL MINIMUM TEMPERATURE
IN BORE TEMPERATURE

HERE

FIGURE 3712b.—A minimum thermometer.

CHART CYLINDER CLOCK PEN ARM RANGE CURRENT
AND WINDING PEN PIVOT ADJUSTMENT TEMPERATURE

CLOCK UNIT KEY ARM X BEARING THUMBSCREW ADJUSTMENT
UPPER
GUARD
BRACKET
& PIVOT
BEARING
g BOURDON
A EMO BE

ELEMENT
LOWER
GUARD
BRACKET

FIGURE

3712a.—

A ther-

pone THERMOGRAPH

er for E (WITH COVER REMOVED )

measur- HOLDING LIFTING LIFTING

ing air CLIP ROD LEVER

temper-

ature. FIGURE 3712c.—A thermograph with cover removed.

which has occurred since the last setting. Setting is accomplished by tilting the ther-
mometer until the bulb is uppermost, when the index returns to the current tempera-
ture. The thermometer is normally maintained at an angle of about 5° to the hori-
zontal, with the bulb at the lower end. A Townsend support is used for this purpose.

Temperature can be measured by means of a thermograph (fig. 3712c), which
is a recording thermometer. In its outward appearance this instrument is similar to a
barograph (fig. 3705). The pen arm is connected, through a linkage, to the ther-
mometric element, which usually consists of a metal tube shaped in the form of an
arc and containing alcohol. As the alcohol expands with temperature increase, it
tends to straighten the tube; and as the temperature decreases, the contracting alcohol
permits the tube to resume its curved shape. The linkage magnifies these variations
and transmits them to the pen, which records the temperature on a chart placed around
a clock-driven, revolving cylinder.

The freezing point of mercury is about (—)38?F. Various substances are used
to measure lower temperatures, the most common being some form of alcohol, which
has a freezing point well below (—) 100? F. For even lower temperatures, below those

778 WEATHER OBSERVATIONS

ever recorded in the atmosphere, gas may be used instead of a liquid. Thermometers
based upon other principles, such as unequal expansion of dissimilar metals, melting
point of a substance, color, etc., are sometimes used, particularly for temperatures
considerably higher or much lower than those occurring in the atmosphere.

Temperature measuring equipment should be placed in a shelter which protects
it from mechanical damage and direct rays of the sun. The shelter should have louvered
sides to permit free access of air. Aboard ship, the shelter should be placed in an
exposed position as far as practicable from metal bulkheads. On vessels where shelters
are not available, the temperature measurement should be made in shade at an exposed
position on the windward side.

Sea water temperature is normally measured at the condenser intake. Although
this is not a true measure of surface water temperature, the error is generally small.
Measurement should be made near the entrance of the intake.

If the temperature of the water at the surface is desired, a sample should be ob-
tained by bucket, preferably a canvas bucket, from a forward position well clear of any `
discharge lines. The sample should be taken immediately to a place where it is shel-
tered from wind and sun. The water should then be stirred with the thermometer,
keeping the bulb submerged, until an essentially constant reading is obtained.

3713. Humidity is the condition of the atmosphere with reference to its water
vapor content. Absolute humidity is a measure of the mass of vapor per unit volume
of air. Relative humidity is the ratio (stated as a percentage) of the existing vapor
pressure to the vapor pressure corresponding to saturation at the prevailing tempera-
ture and atmospheric pressure. This is very nearly the ratio of the amount of water
vapor present to the amount that the air could hold at the same temperature and
pressure if it were saturated.

As air cools, its capacity for holding water vapor decreases. Therefore, as air
temperature decreases, the relative humidity increases. At some point, saturation
takes place, and any further cooling results in condensation of some of the moisture.
The temperature at which this occurs is called the dew point, and the moisture deposited
upon natural objects is called dew if it forms in the liquid state, or frost if it forms in
the frozen state.

The same process causes moisture to form on the outside of a container of cold
liquid, the liquid cooling the air in the immediate vicinity of the container until it
reaches the dew point. When moisture is deposited on man-made objects, it is usually
called sweat. It occurs whenever the temperature of a surface is lower than the dew
point of the air in contact with it. It is of particular concern to the mariner because
of its effect upon his instruments, and possible damage to his ship or its cargo. Lenses
of optical instruments may sweat, usually with such small droplets that the surface
has a “frosted” appearance. When this occurs, the instrument is said to “fog” or
“fog up,” and is useless until the moisture is removed. Damage is often caused by
corrosion or direct water damage when pipes sweat and drip, or when the inside of the
shell plates of a vessel sweat. Cargo may sweat if it is cooler than the dew point of
the air. One of the principal problems of preserving ships of the reserve fleet is the
protection against moisture. An important step is the draining of all water, sealing
of compartments, and drying of the air.

Clouds and fog form by "sweating" of minute particles of dust, salt, etc., in the air.
Each particle forms a nucleus around which a droplet of water forms. If air is completely
free from solid particles on which water vapor may condense, the extra moisture remains
in the vapor state, and the air is said to be supersaturated.

Relative humidity and dew point are measured by means of a hygrometer. The
most common type, called a psychrometer, consists of two thermometers mounted

WEATHER OBSERVATIONS 779

SWIVEL
LINK

FIGURE 3713.—A sling psychrometer.

together on a single strip of material, as shown in figure 3713. One of the thermometers
is mounted a little lower than the other, and has its bulb covered with muslin. When
the muslin covering is thoroughly moistened and the thermometer well ventilated,
evaporation cools the bulb of the thermometer, causing it to indicate a lower reading
than the other. A sling psychrometer, illustrated in figure 3713, is ventilated by
whirling the thermometers. Some psychrometers use a fan. Dry-bulb temperature
is indicated by the uncovered dry-bulb thermometer, and wet-bulb temperature is
indicated by the muslin-covered wet-bulb thermometer. The difference between
these two temperatures, and the dry-bulb temperature, are used to enter psychrometric
tables to find the relative humidity (tab. 16) and dew point (tab. 17). If the wet-
bulb temperature is above freezing, reasonably accurate results can be obtained by a
psychrometer consisting of wet- and dry-bulb thermometers mounted so that air can
circulate freely around them without special ventilation. This type of installation
is common aboard ship.

Example.—The dry-bulb temperature is 65°F and the wet-bulb temperature is
619 F.

Required. — (1) Relative humidity, (2) dew point.

Solution.—The difference between readings is 49%. Entering table 16 with this
value and a dry-bulb temperature of 65°, the relative humidity is found to be 80
percent. From table 17 the dew point is found to be 58”.

Answers.—(1) Relative humidity 80 percent, (2) dew point 58°.

A recording hygrometer, called a hygrograph, provides a continuous record of rela-
tive humidity. In outward appearance this instrument is similar to a barograph (fig.
3705) and a thermograph (fig. 3712c), using the same clock movement and chart
cylinder. The measuring element, however, generally consists of a number of strands
of human hair separated into groups kept apart.by a spreader device. The hairs are
kept taut by a counterbalance. As the relative humidity rises, the hairs increase in
length, and as the relative humidity falls, they decrease in length. A linkage magnifies
these changes and transmits them to a pen which records the relative humidity on a
chart placed around the clock-driven, revolving cylinder. The hygrograph is a con-
venient device, but lacks accuracy, lags considerably behind changes in relative humid-
ity, and is not reliable at low temperatures. It requires frequent calibration.

A hygrothermograph combines the features of both the hygrograph and the thermo-
graph, providing a continuous record of both relative humidity and air temperature
for seven days on a single chart. It has the same limitations as the hygrograph and
the thermograph and its indications should be checked daily by psychrometer and
thermometer.

3714. Clouds are visible assemblages of numerous tiny droplets of water, or ice
crystals, formed by condensation of water vapor in the air, with the bases of the assem-
blages above the surface of the earth. Fog is a similar assemblage in contact with the
surface of the earth.

780 WEATHER OBSERVATIONS

The shape, size, height, thickness, and nature of a cloud depend upon the conditions
under which itis formed. Therefore, clouds are indicators of various processes occurring
in the atmosphere. The ability to recognize different types and a knowledge of the
conditions associated with them are useful in predicting future weather.

Although the variety of clouds is virtually endless, they may be classified according
to general type. Clouds are grouped generally into four “families” according to some
common characteristic. High clouds are those having a mean lower level above 20,000
feet. They are composed principally of ice crystals. Middle clouds have a mean level
between 6,500 and 20,000 feet. They are composed largely of water droplets, although
the higher ones have a tendency toward ice particles. Low clouds have a mean upper
level of less than 6,500 feet. These clouds are composed entirely of water droplets.
Clouds with vertical development are a distinctive group formed by rising air which is
cooled as it reaches greater heights. When it reaches the height of the dew point,
some of its water vapor condenses. Therefore, the bottoms of such clouds are
usually flat. Clouds with vertical development may begin at almost any level, but .
generally within the low cloud range. They may extend to great heights, well above
the lower limit of high clouds. They form as water droplets, but toward the top
they may freeze.

Within these four families are ten principal cloud types. The names of these are
composed of various combinations and forms of the following basic words, all from
Latin:

Cirrus, meaning “curl.”

Cumulus, meaning “heap.”

Stratus, meaning “layer.”

Alto, meaning “high.”

Nimbus, meaning “rain.”

The first three are the basic cloud types. Individual cloud types recognize certain
characteristics, variations, or combinations of these. The ten principal cloud types are:

High clouds. Cirrus (Ci) are detached high clouds of delicate and fibrous appear-
ance, without shading, generally white in color, and often of a silky appearance (figs.
3714a and 3714d). Their fibrous and feathery appearance is due to the fact that they
are composed entirely of ice crystals. Cirrus appear in varied forms such as isolated
tufts; long, thin lines across the sky; branching, feather-like plumes; curved wisps which
may end in tufts, etc. These clouds may be arranged in parallel bands which cross the
sky in great circles and appear to converge toward a point on the horizon. This may
indicate, in a general way, the direction of a low pressure area. Cirrus may be brilliantly
colored at sunrise and sunset. Because of their height, they become illuminated be-
fore other clouds in the morning, and remain lighted after others at sunset. Cirrus
are generally associated with fair weather, but if they are followed by lower and thicker
clouds, they are often the forerunner of rain or snow.

Cirrocumulus (Cc) are high clouds composed of small white flakes or scales, or of
very small globular masses, usually without shadows and arranged in groups or lines,
or more often in ripples resembling those of sand on the seashore (fig. 3714b). One
form of cirrocumulus is popularly known as “mackerel sky” because the pattern re-
sembles the scales on the back of a mackerel. Like cirrus, cirrocumulus are composed
of ice crystals and are generally associated with fair weather, but may precede a storm
if they thicken and lower. They may turn gray and appear hard before thickening.

Cirrostratus (Cs) are thin, whitish, high clouds (fig. 3714c) sometimes covering the
sky completely and glving 1t a milky appearance and at other times presenting, more
` t distinctly, a formation like a tangled web. The thin veil is not sufficiently dense

o blur the outline of sun or moon. However, the ice crystals of which the cloud is

WEATHER OBSERVATIONS 781

FIGURE 3714b.—Cirrocumulus.

FIGURE 3714c.— Cirrostratus. FIGURE 3714d.—Cirrus and cirrostratus.

composed refract the light passing through in such a way that halos (art. 3819) may
form with the sun or moon at the center. Figure 3714d shows cirrus thickening and
changing into cirrostratus. In this form it is popularly known as “mares” tails." If it
continues to thicken and lower, the ice crystals melting to form water droplets, the
cloud formation is known as altostratus. When this occurs, rain may normally be
expected within 24 hours. The more brushlike the cirrus when the sky appears as in
figure 3714d, the stronger the wind at the level of the cloud.

Middle clouds. Altocumulus (Ac) are middle clouds consisting of a layer of large,
ball-like masses that tend to merge together. The balls or patches may vary in thick-
ness and color from dazzling white to dark gray, but they are more or less regularly
arranged. They may appear as distinct patches (fig. 3714e) similar to cirrocumulus
(fig. 3714b) but can be distinguished by the fact that individual patches are generally
larger, and show distinct shadows in some places. They are often mistaken for
stratocumulus (fig. 3714i). If this form thickens and lowers, it may produce thundery
weather and showers, but it does not bring prolonged bad weather. Sometimes the
patches merge to form a series of big rolls that resemble ocean waves, but with streaks
of blue sky (fig. 3714f). Because of perspective, the rolls appear to run together near
the horizon. These regular parallel bands differ from cirrocumulus in that they occur
in larger masses with shadows. These clouds move in the direction of the short dimen-
sion of the rolls, as do ocean waves. Sometimes altocumulus appear briefly in the form
shown in figure 3714g, usually before a thunderstorm. They are generally arranged in

Figure 3714e.—Altocumulus in patches. FIGURE 3714f.—Altocumulus in bands.

782 WEATHER OBSERVATIONS

Figure 3714g.—Turreted altocumulus. FIGURE 3714h.—Altostratus.

a line with a flat horizontal base, giving the impression of turrets on a castle. The
turreted tops may look like miniature cumulus and possess considerable depth and great
length. These clouds usually indicate a change to chaotic, thundery skies.

Altostratus (As) are middle clouds having the appearance of a grayish or bluish,
fibrous veil or sheet (fig. 3714h). The sun or moon, when seen through these clouds, `
appears as if it were shining through ground glass, with a corona (art. 3820) around it.
Halos are not formed. If these clouds thicken and lower, or if low, ragged “scud” or
rain clouds (nimbostratus) form below them, continuous rain or snow may be expected
within a few hours.

Low clouds. Stratocumulus (Sc) are low clouds composed of soft, gray, roll-
shaped masses (fig. 37141). They may be shaped in long, parallel rolls similar to altocu-
mulus (fig. 3714f), moving forward with the wind. The motion is in the direction of
their short dimension, like ocean waves. These clouds, which vary greatly in altitude,
are the final product of the characteristic daily change that takes place in cumulus
clouds. They are usually followed by clear skies during the night.

Stratus (St) is a low cloud in a uniform layer (fig. 3714j) resembling fog. Often
the base is not more than 1,000 feet high. A veil of thin stratus gives the sky a hazy
appearance. Stratus is often quite thick, permitting so little sunlight to penetrate
that it appears dark to an observer below it. From above, it looks white. Light mist
may descend from stratus. Strong wind sometimes breaks stratus into shreds called
“fractostratus.””

Nimbostratus (Ns) is a low, dark, shapeless cloud layer, usually nearly uniform,
but sometimes with ragged, wet-looking bases. Nimbostratus is the typical rain cloud.
The precipitation which falls from this cloud is steady or intermittent, but not showery.

Clouds with vertical development. Cumulus (Cu) are dense clouds with vertical
development. They have a horizontal base and dome-shaped upper surface, with
protuberances extending above the dome. Cumulus appear in small patches, and never
cover the entire sky. When the vertical development is not great, the clouds appear
in patches resembling tufts of cotton or wool, being popularly called “woolpack” clouds
(fig. 3714k). The horizontal bases of such clouds may not be noticeable. These are

FIGURE 37141.—Stratocumulus. FIGURE 3714j.—Stratus.

WEATHER OBSERVATIONS 783

Figure 3714k.—Cumulus. Figure 37141.—Cumulonimbus.

called “fair weather” cumulus because they always accompany good weather. How-
ever, they may merge with altocumulus, or may grow to cumulonimbus before a thunder-
storm. Since cumulus are formed by updrafts, they are accompanied by turbulence,
causing “bumpiness” in the air. The extent of turbulence is proportional to the vertical
extent of the clouds. Cumulus are marked by strong contrasts of light and dark.

Cumulonimbus (Cb) is a massive cloud with great vertical development, rising in
mountainous towers to great heights (fig. 37141). The upper part consists of ice crys-
tals, and often spreads out in the shape of an anvil which may be seen at such distances
that the base may be below the horizon. Cumulonimbus often produces showers of
rain, snow, or hail, frequently accompanied by thunder. Because of this, the cloud is
often popularly called a “thundercloud” or “thunderhead.” The base is horizontal,
but as showers occur it lowers and becomes ragged.

3715. Cloud height measurement.—At sea, cloud heights are often determined by
estimate. This is a difficult task, particularly at night. A searchlight may be of some as-
sistance. Radar operating at the higher frequencies, particularly three-centimeter radar,
indicates returns from some clouds. Certain models permit measurement of height.

Ceiling balloons can be used to determine height of low clouds with reasonable
accuracy. Any type balloon having a known rate of ascent is suitable. The following
balloons are in use:

1. A 10-gram spherical balloon with 40 grams of hydrogen or 43 grams of helium.
Used at Navy and Air Force stations.

2. A 10-gram spherical balloon with 45 grams of helium. Used at civil stations.

3. A 30-gram balloon with 125 grams of hydrogen or 139 grams of helium. Used
at civil and Navy stations.

4. A 30-gram balloon with 132 grams of hydrogen or 147 grams of helium. Used
at Air Force stations.

The ascent of these four balloons, in feet, is

Minutes 1 2 8 4
1 480 500 710 720
2 850 960 1,360 1,380
ə 1,210 1,420 2,010 2,040
4 1,570 1,880 2,630 2, 670
5 1,930 2,300 3,250 3,300
6 2,290 2,720 3,840 3,900
7 2,650 3,140 4,430 4, 500

8 3,010 3,560 5,020 5, 100.

For elapsed times greater than eight minutes, the rate is 360 feet per minute for balloon
1, 420 feet per minute for balloon 2, 590 feet per minute for balloon 3, and 600 feet
per minute for balloon 4.

784 WEATHER OBSERVATIONS

Cloud height is determined by measurement of the elapsed time from release of
the balloon until it disappears in the clouds. Horizontal motion due to wind generally
has negligible effect upon the rate of ascent.

The height of the base of clouds formed by vertical development (any form of
cumulus), if formed in air that has risen from the surface of the earth, can be deter-
mined by psychrometer, because the height to which the air must rise before condensa-
tion takes place is proportional to the difference between surface air temperature and
the dew point. At sea, this difference multiplied by 236 gives the height in feet. That
is, for every degree difference between surface air temperature and the dew point, the
air must rise 236 feet before condensation will take place. Thus, if the dry-bulb
temperature is 80°F, and the wet-bulb temperature is 77°F, the dew point (from
tab. 17) is 76°F, or four degrees lower than the surface air temperature. The height
of the cloud base is A 236= 944 feet.

Ashore, cloud height measurement can be made at night by means of a ceiling
light projector and clinometer (fig. 3715). The projector throws a beam of light -
vertically upward, casting a spot of light on the clouds. An observer at a known dis-
tance from the projector measures the angle of elevation of the spot of light. This is
usually done by means of a clinometer, a single hand-held sighting device with a pointer

CEILING =

BASE LINE X TANGENT S OBSERVER PIECE `
OF CLINOMETER ANGLE U WITH CLINOMETER
S
BASE LINE Na

Figure 3715.— Ceiling light projector and clinometer for measuring cloud height at
night.

which hangs freely and indicates elevation angle on an arc. The height of the cloud
base is equal to the tangent of the elevation angle times the distance between the
projector and observer, the curvature of the earth being neglected. Thus, if the ob-
server is 400 feet from the projector, and the angle of elevation is 739, the height of
the base of the clouds is 400X3.2709—1,308 feet. If two ships are in company, an
approximation of cloud height might be determined in this way, using a searchlight on
one ship and a clinometer (a sextant can be used if the horizon is distinguishable) on
the other. For low clouds, this might be performed on a single vessel, mounting the
searchlight at one end of the vessel, and placing the observer at the other end. Reason-
ably accurate results might be obtained at sea if the searchlight can be stabilized in the
vertical.

Measurements can be made both day and night by means of a ceilometer. This
device consists of a projector, detector, and recorder to provide a continuous record of
cloud height above the observing station, both day and night. The ceilometer uses
a beam of light that is pulse modulated (art. 1016) like radar signals. The projector
and detector are some distance apart, height being determined by the same principle
used with the ceiling light projector and clinometer. Either the projector or detector
continuously scans a 90° arc from the vertical to the horizontal, and back, in line with

WEATHER OBSERVATIONS 785

the other instrument, which remains vertical. When the spot of light is in the line of
sight of the detector, a photoelectric cell detects it, and actuates the recorder, which
reads directly in height. The ceilometer is not suitable for use at sea.

3716. Visibility measurement.—Visibility is the extreme horizontal distance at
which prominent objects can be seen and identified by the unaided eye. It is usually
measured directly by the human eye. Ashore, the distances of various buildings, trees,
lights, and other objects are measured and used as a guide in estimating the visibility.
At sea, however, such an estimate is difficult to make with accuracy. Other ships
and the horizon may be of some assistance.

Visibility is sometimes measured by a transmissometer, a device which measures
the transparency of the atmosphere by passing a beam of light over a known short
distance, and comparing it with a reference light.

3717. Upper air observations. —Upper air information provides the third dimension
to the weather map. Unfortunately, the equipment necessary to obtain such in-
formation is quite expensive, and the observations are time consuming. Consequently,
the network of observing stations is quite sparse compared to that for surface observa-
tions, particularly over the oceans and in isolated land areas. Where facilities exist,
upper air observations are made by means of unmanned balloons in conjunction with
theodolites, radiosondes, radar, and radio direction finders. Observations are
sometimes made by aircraft.

3718. Pilot balloons are free balloons released at the surface of the earth and fol-
lowed by optical means to determine their movement in relation to the point from which
released. They are of neoprene latex (occasionally of natural rubber latex) a few
thousandths of an inch thick, and have a nominal weight of either 30 or 100 grams.
The balloons are inflated with helium or hydrogen to a definite free-lift capacity for
which ascensional rate tables have been prepared. The neck of each balloon is then
securely fastened to prevent leakage of the gas, and the balloon is released. A theod-
olite is trained on the balloon, which is kept in the field of vision of the instrument
throughout the observation.

By means of a buzzer signal the observer is warned five seconds prior to the end of
each minute after release. The cross hairs of the theodolite are then brought to bear
on the balloon at the end of each minute (also signalled by the buzzer), and the hori-
zontal and vertical angles are read to the nearest tenth of a degree. These data are
then plotted on polar coordinate paper similar to a maneuvering board (art. 1212), and
the wind speed and direction at each selected level (each 1,000-foot level) are determined.

An observation of winds aloft made in this manner is called a pibal, from pilot
balloon observation. If the same procedure is used with a sounding balloon (art. 3720),
the observation is called a rabal, from radio balloon observation,

3719. The theodolite—Survey theodolites are discussed in article 4004. The
instrument by the same name used for pilot balloon observations is constructed on
the same principle, but with some differences to suit the use for which it is intended.

The shore-type theodolite used by the meteorologist is essentially a telescope so
mounted that the horizontal and vertical angles of its axis can be measured. The
telescope is mounted in a yoke secured to a base plate. The base plate is mounted ona
tripod or pipe support, with provision for accurate leveling. By means of a 45° prism,
the line of sight is bent through an angle of 90°. The eyepiece is mounted on the
horizontal axis of the theodolite. Tangent-screw controls permit adjustment in both
the horizontal and vertical directions.

The shipboard-type theodolite (fig. 3719) differs considerably from the shore
type, being mounted on gimbals atop a tripod. A counterbalance is provided to serve

786 WEATHER OBSERVATIONS

INDEX ARTIFICIAL HORIZON
MIRROR BUBBLE MOUNT

COLORED `
RAY FILTERS

BUBBLE

SHADE GLASS ADJUSTMENT KNOB

FOCUSING
ADJUSTMENT

HORIZON LENS — N
SS

ELEVATION
QUADRANT ARM

AZIMUTH
ENGAGEMENT
KNOB

Cu "72
(A
4 A
) 3 ;

BUBBLE
\ HORIZON LEVER

a ali

—|

AZIMUTH
TANGENT SCREW
8 VERNIER DRUM

ELEVATION
ENGAGEMENT KNOB

ELEVATION
TANGENT SCREW
AND

VERNIER DRUM

AZIMUTH
WINDOW

GIMBAL RING

swept

i
FIE

Egi i

ri
lij
CH H

TELESCOPIC
STEEL
TRIPOD LEG

ADJUSTABLE
COUNTER

Figure 3719.—A shipboard-type meteorological theodolite.

WEATHER OBSERVATIONS 787

as a pendulum in maintaining the instrument approximately horizontal. The instru-
ment is aligned with the longitudinal axis of the craft, so that relative bearings are
observed. Elevation angles are measured in a manner similar to the measurement of
altitudes of celestial bodies, an image of the balloon being brought into coincidence
with the direct view of the horizon. A bubble artificial horizon is also provided.

3720. Radiosondes are miniature radio transmitters carried aloft by sounding
balloons which ascend at the rate of about 1,000 feet per minute, to a height of nearly
100,000 feet. The transmitter, powered by a compact battery, transmits on a fre-
quency of 72, 403, or 1,680 megacycles per second. In the United States the 72-
megacycle instruments have been replaced by 403-megacycle radiosondes.

As the radiosonde ascends, it transmits a continuous-wave radio signal on its
assigned frequency. This signal is modulated (art. 1016) by pressure, temperature,
and relative humidity in turn.

The transmitted radio signals are received by an antenna and radio receiver at
the surface. They are fed through an electronic frequency meter, and then recorded.
By this means a continuous record is made to the height at which the balloon bursts
or its signals can no longer be received.

An observation made in this way is called a raob, from radiosonde observation.

3721. Electronic measurement of winds aloft.—If either a pilot balloon (art.
3718) or sounding balloon (art. 3720) is fitted with a metal target and tracked by
radar, height, slant distance, and bearing are available, permitting determination of
wind speed and direction. Radio direction finder equipment which permits measure-
ment of both horizontal and vertical directions has been developed and is in use ashore
for tracking radiosondes. Similar equipment for use aboard ship is under development.
An observation made by tracking with either radar or radio direction finder is called
a rawin, from radio winds-aloft observation. A combined raob (art. 3720) and rawin
is called a rawinsonde.

3722. Observations by aircraft.—Reports from aircraft are helpful in making
upper air observations. By this means, winds, heights of clouds, visibility, etc., can
be determined. An aircraft flying over the ocean and equipped with both absolute
and barometric altimeters can supply valuable information on the height of the pres-
sure level at which it is flying. Such reports are used in connection with pressure
pattern navigation (art. 2807). They are also useful in establishing positions of high
and low pressure centers.

The Air Weather Service of the U. S. Department of Defense makes regular flights
to collect weather information. These flights are made along established routes
over the oceans and in the arctic where adequate coverage is not otherwise avail-
able. In addition, the U. S. Navy and U. S. Air Force, in cooperation with the
Weather Bureau, make flights into tropical cyclones (ch. XXXIX) to collect useful
information.

Prior to the advent of the radiosonde (art. 3720), an instrument known as the
aerograph or aerometeorograph was widely used by most weather services. In effect,
this instrument is a combination barograph (art. 3705), thermograph (art. 3712), and
hygrograph (art. 3713). The instrument is attached to an aircraft, and during flight
it makes a continuous trace of pressure, temperature, and relative humidity on a
chart or “smoked sheet” attached to the drum of a clock-driven cylinder. By means
of electrical connections to the pens, the pilot of the airplane indicates the time at
which he enters and leaves phenomena such as haze, fog, clouds, rain, snow, etc. Since
the heights reached are restricted by the ceiling of the aircraft, they are generally
less than those attained by radiosondes. The use of the aerograph is now limited
principally to storm reconnaissance.

788 WEATHER OBSERVATIONS

3723. Storm detection radar.—During World War II, it was found that certain
radar equipment gave an indication of weather fronts (art. 3812) and precipitation
areas. It was of particular value near hurricanes and typhoons. Since the close of
that war a great amount of work has been done in perfecting radar equipment for use
in weather observation. It has proved of immense value in detecting, tracking, and
interpreting weather activity out to a distance of as much as 400 miles from the ob-
serving station.

3724. Precipitation measurement.—Any type of condensed water vapor that falls
to the earth’s surface is called precipitation. It may be liquid, freezing, or frozen when
it arrives at the surface. Measurement of precipitation normally includes only the
determination of the amount of rain or snow that has fallen in a given period of time.
For purposes of comparison, snow measurement is obtained by melting the snow to its
water equivalent. Depth of snow is also measured to determine the amount of
snowfall.

The usual type of nonrecording precipitation gage consists of a collector ring, funnel,
and measuring cylinder set within a receiver. All precipitation falling on the area
encompassed by the collector ring descends through the funnel into the measuring
cylinder, where it is measured directly by means of a rod graduated in tenths of an
inch. Since the cross-sectional area of the measuring cylinder is exactly one-tenth that
of the collector ring, each 0.1 inch collected is a measure of 0.01 inch of precipitation.
When precipitation is in the form of snow, the measuring tube is removed, permitting
the snow to collect in the larger receiver. The receiver is placed in a container of
warm water until the snow melts. The resulting liquid is then poured into the meas-
uring tube and measured.

The most representative measurement of precipitation from snow is obtained by
removing the collector ring and funnel, and using a slat screen to reduce the effect of
wind.

One type of recording rain gage is known as the “tipping-bucket rain gage." The
rainfall from a funnel-shaped collector is directed into one of two small buckets so
arranged that when 0.01 inch of rain is collected, the bucket is forced downward,
causing the other bucket to move into the collecting position. When a bucket is in the
"down" position, its water runs into the base of the collector, where it can be meas-
ured later. As each bucket lowers in its turn, it causes a small cam to rotate into
contact position and close a battery-powered electric circuit. This causes a magnetic
relay at the recorder to operate a pen arm, which marks the additional 0.01 inch of
rainfall on a chart secured to a clock-driven drum.

Another type of recording rain gage, used principally at locations which are not
continuously attended, employs a weighing device which actuates a pen arm, causing
it to trace measurements on a chart secured to a clock-driven drum.

The precipitation gage, whatever its form, should be placed in an exposed position
as far as practicable from obstructions. Precipitation measurement is not ordinarily
made aboard ship because the motions of the vessel, and the possibility of collecting
salt spray, introduce errors into the measurement.

3725. Automatic weather stations provide regularly scheduled transmissions of
meteorological measurements by radio. They are used at isolated and relatively
inaccessible locations from which weather data are of great importance to the weather
forecaster. The measurements usually obtained are of wind speed and direction,
atmospheric pressure, temperature, and relative humidity.

3726. Recording observations. —Aboard ship, weather observations are recorded
on the Ship Weather Observation Sheet (fig. 3726). Instructions for using this sheet are
given in OPNAV Instruction 3140.37C, Manual for Ship's Surface Weather Observations.

WEATHER OBSERVATIONS 789

PI 4
OPNAV FORM 3144-1 (9-64) DEPARTMENT OF THE NAVY

SHIP WEATHER OBSERVATION SHEET

USS eee
DATE (GMT) 19
AT/P
ASSAGE FROM TO
TABLE |
WINDS >.
TEMPERATURE SEA ]
viet.
qime | EV IF ESTIMATED | gi. [WEATHER] BAROMETER Ep Sone TEMS Se MSL
I `
(GMT) | Direction | Force (cs) (Symbols) (Inches) Ory Wet Amount (Degrees i
(Troe) | (Knots) Dy wer Anaont mā Type Sei Direction | Perlod Direction | Period Height
tenths) (True) | (Seconds) (True) | (Seconds) | (Feet)
e ak
01 T
E
02 T
03 1 +
tE
04
E
05
e
06
Tm
i" T
|
L
Tm +
10
ep FT
n T
z = |
12
Es
13
14
15
16
| zr
17 T
E
18
19
20
21 lg
2
23
=!
TABLE Il
SYNOPTIC OBSERVATIONS
3-HOUR
POSITION OF SHIP WIND WEATHER |PRESSURE CLOUDS & | _ | PRESSURE | SIGNIFICANT CLOUD
D 2 | € | TENDENCY
FIRST GROUP El Total um Af ale =
OF O! | Oc- | Latitude | Longitude | TIME | Cloud) __ bil- ki zr EH AE: 2
MESSAGE Week| san | (Degrees | (Degrees |(GMT)| Ame. [Direction] Speed | ity [present] Post | Canero TEMP. = 30 |330 [O [5 215 |5 El „| _ f
(1-7) (0-3) nd d DEE neve) (00-99) | (0-9) | Cerreeted | CO lEgls [zos |5 | e| S13 lege] 5 |52 Height
a ch (Coded) (00-36) | (Knots) | (90-99) (Mb) SO Sole cl Els ESSI
(GMT)| (5-8) | tenths) tenths) ¿slo [o: [lo aa 5| 28/53/2531 5 23 &
ESE ESEST SRA £ ES
1 20003 4 5 sl: 8 9 10 | m |12 13 4 (15 | 16 | 17] 18 | 19 J 20] 20] 2| 23 |24 |25 |26| 27
vil Qype es | K ESTA Ga ff Wit ww) (T pop. TA se cene dE m S NA
SHIP 00 8
e |
SHIP 06 8
3!
SHIP 12 8
IS
SHIP 18 8
SEA WAVES SWELL WAVES ICE ACCRETION SEA ICE DO NOT TRANSMIT
AR. | oe S
lee T tes e — s i OS Dry Bulb Wet Bulb ilā
5 2 | 2 el = 23 $:3 5 M Indi 5 {3 5 = k
3 (Coded) 3 i4 33 53 $ i 33 es Big E 8 indicator 5 2 5 E E H En (nā
= ī|ēd [28/23 E | šo $59|298| 8 |3 Ea Zi vāli ās bails puede ond tenths)
+
| 2 30 | a | 32 |.33.) 34 fasi 36 | 37 | 38 39 | 40 | 41 | 42 43 44 | 45 | 46 | 47 | 48 A, Ay Ay
+
ON RE EE E CIR COE S C KLM UC E K ESE S ICE a Vēji | = | Celsius Celsius Celsius
0 1 1 2 ICE
- =I
0 1 1 2 ICE
0 1 1 2 ICE
0 1 1 2 ICE
REMARKS EXAMINED USN, NAVIGATOR

D-11814

FIGURE 3726.—Ship Weather Observation Sheet.

790 WEATHER OBSERVATIONS

To assist in the preparation of synoptic observations for transmission, Table II
(which is similar to WB Form 615-5, Ship’s Weather Observations, for merchant ships
which participate in the cooperative observation program of the U.S. Weather Bureau)
is arranged in the correct code form with the five-digit groups separated by heavy lines.
Two wave groups are given because two separate wave systems are sometimes persent.

The symbols to use in the “weather” column of Table I are as follows:

CLR Clear or a few clouds
SCT Scattered clouds—0.1 to 0.5 clouds
BKN Broken clouds—0.6 to 0.9 clouds
OVC Overcast—more than 0.9 clouds

T Thunderstorm

R Rain
RW Rain showers
L Drizzle

ZR Freezing rain
ZL Freezing drizzle
E Sleet
F Fog
GF Shallow fog (ground fog)
EW Sleet showers
S Snow
SW Snow showers
IC Ice crystals

A Hai
IF Ice fog
H Haze
K Smoke
D Dust

BY Blowing spray

Problems

3709a. A ship is proceeding on course 180? at a speed of 22 knots. The apparent
wind is from 70? off the port bow, speed 20 knots.

Required.— The relative direction, true direction, and speed of the true wind by
maneuvering board or Weather Bureau plotter.

Answers.—True wind from 231? relative, 051? true, at 24.3 knots.

3709b. A ship is proceeding on course 050? at a speed of 13.5 knots. "The apparent
wind is from broad on the starboard bow, speed 20 knots.

Required.—The relative direction, true direction, and speed of the true wind by
table 10.

Answers.—True wind from 086° relative, 136° true, at 14.3 knots.

3709c. A ship is proceeding on course 020° at a speed of 16 knots. The true wind
is estimated to be from 110° on the port bow, speed 10 knots.

WEATHER OBSERVATIONS 791

Required.—The relative direction, true direction, and speed of the apparent wind
by maneuvering board or Weather Bureau plotter.

Answers.—Apparent wind from 323° relative, 343° true, at 15.6 knots.

3709d. A ship is proceeding on course 190% at a speed of 14 knots. The true

wind is estimated to be from broad on the starboard quarter, speed 20 knots.

Required.—The relative direction, true direction, and speed of the apparent wind
by table 10.

Answers.—Apparent wind from 090° relative, 280° true, at 14.0 knots.

3709e. The true wind has been determined to be from 210°, speed 12 knots. The
captain of an aircraft carrier desires an apparent wind of 30 knots from 10% on the
port bow for launching aircraft.

Required.—The course and speed of the aircraft carrier.

Answers.—C 235°, S 18.6 kn. (The required apparent wind could also be pro-
duced by C 005°, S 40.5 kn.)

3709f. A ship is proceeding on course 255% at a speed of 15 knots. The wind
vane indicates the apparent wind is broad on the starboard beam. From the appear-
ance of the sea the navigator estimates the speed of the true wind as Beaufort 5 (19
knots).

Required.—(1) Relative and true directions of the true wind, (2) speed of the
apparent wind. Use the maneuvering board.

Answers.—(1) True wind from 142° relative, 037° true; (2) apparent wind speed
11.6 knots.

3709g. A ship is proceeding on course 135° at a speed of 18 knots. The wind vane
indicates the apparent wind is 40° on the starboard bow. From the appearance of
the sea the navigator estimates the speed of the true wind as Beaufort 6 (24.5 knots).

Required.—(1) Relative and true directions of the true wind, (2) speed of the
apparent wind. Use table 10.

Answers.—(1) True wind from 069° relative, 204° true; (2) apparent wind speed
36 knots.

3709h. A ship is proceeding on course 330° at a speed of 20 knots. The wind vane
indicates the apparent wind is 30° on the port bow. From the appearance of the sea
the navigator estimates the speed of the true wind as Beaufort 4 (13.5 knots).

Required.—(1) Relative and true directions of the true wind, (2) speed of the
apparent wind. Solve first by maneuvering board and then by table 10.

Answers.—Graphical solution: (1) true wind from 199° relative, 169° true or
from 282° relative, 252° true; (2) apparent wind speed 8.5 knots or 26.3 knots. Table
10 solution: (1) true wind from 197° relative, 167° true or from 283° relative, 253°
true; (2) apparent wind speed 8.0 knots or 26.0 knots.

3713. The dry-bulb temperature is 41°F and the wet-bulb temperature is 35°F.

Required.—(1) Relative humidity, (2) dew point.

Answers.—(1) Relative humidity 53 percent, (2) dew point 26°.

3715a. A 30-gram balloon with 139 grams of helium is released, and 10”12* later
it disappears in the clouds.

Reguired.—Height of the base of the clouds.

Answer.—Height 6,318 feet.

3715b. The dry-bulb temperature is 72°F and the wet-bulb temperature is 58°F.

Required.—Height of the base of cumulonimbus clouds formed in air which has
risen from the surface of the sea.

Answer.—Height 5,900 feet.

792 WEATHER OBSERVATIONS

3715c. An observer 1,000 feet from a ceiling light projector measures the elevation
angle of the spot of light on the base of the clouds as 68°.

Required.—Height of the base of the clouds.

Answer.—Height 2,475 feet.

References

Berry, F. A., Bollay, E., and Beers, N. R. Handbook of Meteorology. New York,
McGraw-Hill, 1945.

Burgess, C. R. Meteorology for Seamen. Glasgow, Brown, 1950.

Byers, H. R. General Meteorology. 2nd ed. New York, McGraw-Hill, 1944.

Haynes, B. C. Techniques of Observing the Weather. New York, Wiley, 1947.

Knight, A. M. Modern Seamanship. 12th ed. New York, Van Nostrand, 1953.

Middleton, W. E. K., and Spilhaus, A. F. Meteorological Instruments. Toronto,
U. of Toronto, 1953.

Smithsonian Institution. Smithsonian Meteorological Tables. 6th ed. Washington,
Smithsonian Inst., 1951.

U.S. Weather Bureau. Manual of Barometry. Vol. 1. 1st ed. Washington, U.S.
Govt. Print. Off., 1963

U.S. Weather Bureau. Manual of Marine Meteorological Observations. Circular M.
12th ed. Washington, U.S. Govt. Print. Off., 1964.

U.S. Weather Bureau. Weather Surveillance Radar Manual. Washington, U.S.
Govt. Print. Off., 1960.

CHAPTER XXXVIII
WEATHER AND WEATHER FORECASTS

3801. Introduction.—Weather is the state of the earth's atmosphere with respect
to temperature, humidity, precipitation, visibility, cloudiness, etc. In contrast, the
term climate refers to the prevalent or characteristic meteorological conditions of a
place or region.

All weather may be traced ultimately to the effect of the sun on the earth, including
the lower portions of the atmosphere. Most changes in weather involve large-scale,
approximately horizontal, motion of air. Air in such motion is called wind. This
motion is produced by differences of atmospheric pressure, which are largely attribut-
able to differences of temperature.

The weather is of considerable interest to the mariner. The wind and state of the
sea affect dead reckoning. Reduced horizontal visibility limits piloting. The state of the
atmosphere affects electronic navigation and radio communication. If the skies are
overcast, visual celestial observations are not available; and under certain conditions
refraction and dip are disturbed. When wind was the primary motive power, knowledge
of the areas of favorable winds was of great importance. This consideration led Matthew
Fontaine Maury, more than a century ago, to seek information from ships' logs to es-
tablish speed and direction of prevailing winds over the various trade routes of the world.
The information thus gathered was shown on pilot charts. By means of these charts,
the mariner could select a suitable route for a favorable passage. Even power vessels
are affected considerably by wind and sea. Less fuel consumption and a more com-
fortable passage are to be expected if wind and sea are moderate and favorable. Pilot
charts are useful in selecting suitable routes. Since longer range forecasts have become
possible, some experimental work has been done in routing ocean vessels to take ad-
vantage of anticipated conditions during passage.

3802. The atmosphere is a relatively thin shell of air, water vapor, dust, smoke,
etc., surrounding the earth. The air is a mixture of transparent gases (art. 1410) and,
like any gas, is elastic and highly compressible. Although extremely light, it has a
definite weight which can be measured. A cubic foot of air at standard sea-level tem-
perature and pressure weighs 1.22 ounces, or about 1/817th part of the weight of an
equal volume of water. Because of this weight, the atmosphere exerts a pressure upon
the surface of the earth, amounting to about 15 pounds per square inch.

As altitude increases, less atmosphere extends upward, and pressure decreases.
With less pressure, the density decreases. More than three-fourths of the air is con-
centrated within a layer averaging about seven statute miles thick, called the tropo-
sphere. This is the region of most “weather,” as the term is commonly understood.

The top of the troposphere is marked by a thin transition zone called the tropopause.
Beyond this lie several other layers having distinctive characteristics, as listed in
article 1410, and shown in figure 1410. The average height of the tropopause ranges
from about five miles or less over the poles to about 11 miles over the equator.

The standard atmosphere is a conventional vertical structure of the atmosphere
characterized by standard sea level pressure of 29.92 inches of mercury (1013.25 mil-
libars), sea level temperature of 59°F (15°C), and a uniform decrease of temperature

793

794 ' WEATHER AND WEATHER FORECASTS

and moisture content of the air with height, the rate of temperature decrease being
3?6 F (2°C) per thousand feet to 11 kilometers (36,089 feet) and thereafter a constant
temperature of (—)69°7F (—56°5C). The rate of temperature decrease with height
in the standard atmosphere is called the standard temperature lapse rate.

Meteorologists are continually learning more of the characteristics of atmospheric
processes above the lowest portions of the atmosphere. In recent years, greatly in-
creased attention has been directed to such features as the jet stream, a meandering
stream of air which circles the globe at speeds of 100 to more than 250 knots at heights
of about 20,000 to 40,000 feet. Some similarity has been noted between major wind
streams such as the jet stream, and ocean currents such as the Gulf Stream (art. 3206).

3803. Wind.—When air is not confined, changes in temperature produce changes in
volume, heated air expanding and cooled air contracting. If a large volume of air
near the surface of the earth is cooled, it contracts, causing a downdraft. Air from
neighboring regions aloft moves horizontally to fill the void. This results in a greater
mass of air over the region, and the pressure is correspondingly increased. By a similar
process in reverse, heating of air near the surface causes expansion and an updraft,
resulting in decreased pressure over the heated area. Near the surface of the earth,
the air tends to move from an area of high pressure to one of low pressure. Thus, a
circulation is set up, air moving across the surface of the earth from an area of high
pressure and low temperature to one of low pressure and high temperature, then
vertically upward, then horizontally at high altitudes from the area of low pressure
to that of high pressure, where it moves vertically downward to complete the circuit.
The actual circulation is much more complex than this, due to such factors as rotation of
the earth and continual changes in temperature and pressure.

If there were no heating and cooling, the temperature at any given altitude remain-
ing everywhere the same, there would be no tendency for the air to move from one place
to another. Air would lie sluggish and at rest on the earth's surface. There wouid
be no wind and no variation in weather.

As a result of the position and motion of the earth in relation to the sun, and the
physieal processes involving radiation and absorption of energy, certain regions of
the earth are always warmer than others. For similar reasons, the air over some parts
of the earth is seasonally warmer than that over other parts. This general pattern is
modified to a varying degree by the local heating and cooling which is continually taking
place. Consequently, winds in some areas are relatively steady in both direction and
speed, others are seasonal, and this general circulation is continually being modified
by local conditions.

3804. General circulation of the atmosphere.—The heat required for warming the
air is supplied originally by the sun. As radiant energy from the sun arrives at the
earth, about 43 percent is reflected back into space by the atmosphere, about 17
percent is absorbed in the lower portions of the atmosphere, and the remaining 40
percent (approximately) reaches the surface of the earth and much of it is reradiated
into space. "This earth radiation is in comparatively long waves relative to the short-
wave radiation from the sun, since it emanates from a cooler body. Long-wave
radiation, being readily absorbed by the water vapor in the air, is primarily responsible
for the warmth of the atmosphere near the earth's surface. Thus, the atmosphere
acts much like the glass on the roof of a greenhouse. It allows part of the incoming
solar radiation to reach the surface of the earth, but is heated by the terrestrial radiation
passing outward. Over the entire earth and for long periods of time, the total outgoing
energy must be equivalent to the incoming energy (minus any converted to another
form and retained), or the temperature of the earth, including its atmosphere, would
steadily increase or decrease. In local areas, or over relatively short periods of time,

WEATHER AND WEATHER FORECASTS 795

such a balance is not required, and in fact does not exist, resulting in changes such as
those occurring in the different seasons, and in different parts of the day.

As shown in figure 1419b, the more nearly perpendicular the rays of the sun
strike the surface of the earth, the more heat energy per unit area is received at that
place. Physical measurements show that in the tropics more heat per unit area is
received than is radiated away, and that in polar regions the opposite is true. Unless
there were some process to transfer heat from the tropics to polar regions, the tropics
would be much warmer than they are, and the polar regions would be much colder.
The process which brings about the required transfer of heat is the general circulation
of the atmosphere.

If the earth had a uniform surface, did not rotate on its axis (but received sun-
light equally all around the equator), and did not revolve around the sun (with its
axis tilted), a simple circulation would result, as shown in figure 3804a. However, the
surface of the earth is far from uniform, being covered with an irregular distribution of
land of various heights, and water; the earth rotates about its axis once in approximately
24 hours, so that the portion heated by the sun continually changes; and the axis of
rotation is tilted so that as the earth moves along its orbit about the sun, seasonal
changes occur in the exposure of specific areas to the sun's rays, resulting in variations
in the heat balance of these areas. These factors, coupled with others, result in con-
stantly changing large-scale movements of air. Based upon averages over long periods,
however, a general circulation is discernible. Figures 3804b and 3804c give a gen-
eralized picture of the world's pressure distribution and wind systems as actually
observed. A simplified diagram of the general pattern is shown in figure 3804d.

The rotation of the earth diverts the air from a direct path between high and low
pressure areas, the diversion being toward the right in the northern hemisphere and
toward the left in the southern hemisphere. At some distance above the surface of the

NORTH POLE

POLAR REGION
Area of Least Heating

EQUATORIAL REGION
Area of Greatest Heating

POLAR REGION
Area of Least Heating

SOUTH POLE

Figure 3804a.—Ideal atmospheric circulation for a uniform, nonrotating, nonrevolving earth.

796 WEATHER AND WEATHER FORECASTS

80° 60° 40° 20° 0° 20° 40° 60° 80° 100° 120° 140° 160° 180° 160° 140°

80° 60° 40° 20° 0° 20° 40° 60° 80° 100° 120° 140° 160° 180° 160° 140° 120°

FIGURE 3804b.—Generalized pattern of actual surface winds PREVAILING WINDS

in January and February. LENGTH of arrow indicates generalized degree of
CONSTANCY OF WIND DIRECTION
WIDTH of arrow indicates average FORCE OF WIND
20+ Knots
15—20 Knots
10—15 Knots
10— Knots
= DIRECTION OF MOVE-
MENT OF AIR MASS
60° 80° 100° 120°

60° 80° 100° 120° 140° 160°

180° 160° 140° 120°

FIGURE 3804c.— Generalized pattern of actual surface winds in July and August.

d WEATHER AND WEATHER FORECASTS 797

- . NORTH POLE

A
PREVAILI

Å ~ |
> PREVAILING WESTERLIES

N SOUTHEAST
SW < D ERLIES
TS GE

Ficure 3804d.—Simplified diagram of the general circulation of the atmosphere.

earth, the wind tends to blow along the isobars, being called the geostrophic wind if
the isobars are straight (great circles), and gradient wind if they are curved. Near
the surface of the earth, friction tends to divert the wind from the isobars toward the
center of low pressure. At sea, where friction is less than on land, the wind follows
the isobars more closely.

The decrease of pressure with distance is called the pressure gradient. It is
maximum along a normal (perpendicular) to the isobars, decreasing to zero along the
isobars. Speed of the wind is directly proportional to the maximum pressure gradient.

3805. The doldrums.—The belt of low pressure near the equator occupies a position
approximately midway between high pressure belts at about latitude 30° to 35° on
each side. Except for slight diurnal changes, the atmospheric pressure along the
equatorial low is almost uniform. With almost no pressure gradient, wind is practically
nonexistent. The light breezes that do blow are variable in direction. Hot, sultry
days are common. The sky is often overcast, and showers and thundershowers are
relatively frequent.

The area involved is a thin belt near the equator, the eastern part in both the
Atlantic and Pacific being wider than the western part. However, both the position
and extent of the belt vary somewhat with the season. During February and March it
lies immediately to the north of the equator and is so narrow that it may be considered
virtually nonexistent. In July and August the belt is centered on about latitude 7°N,
and is several degrees in width, even at the narrowest point.

3806. The trade winds blow from the belts of high pressure, toward the equatorial
belt of low pressure. Because of the rotation of the earth, the moving air is deflected

798 WEATHER AND WEATHER FORECASTS

toward the west. Therefore, the trade winds in the northern hemisphere are from the
northeast and are called the northeast trades, while those in the southern hemisphere
are from the southeast and are called the southeast trades. Over the eastern part of
both the Atlantic and Pacific these winds extend considerably farther from the equator,
and their original direction is more nearly along the meridians, than in the western part
of each ocean.

The trade winds are generally considered among the most constant of winds.
Although they sometimes blow for days or even weeks with little change of direction or
speed, their constancy is sometimes exaggerated. At times they weaken or shift direc-
tion, and there are regions where the general pattern is disrupted. A notable example
is the island groups of the South Pacific, where they are practically nonexistent during
January and February. Their highest development is attained in the South Atlantic
and in the South Indian Ocean. Everywhere they are fresher during the winter than
during the summer.

In July and August, when the belt of equatorial low pressure moves to a position
some distance north of the equator, the southeast trades blow across the equator, into
the northern hemisphere, where the earth's rotation diverts them toward the right,
causing them to be southerly and southwesterly winds. The “southwest monsoons””
of the African and Central American coasts have their origin partly in such diverted
southeast trades.

Cyclonic storms generally do not enter the regions of the trade winds, although
hurricanes and typhoons (ch. XXXIX) may originate within these areas.

3807. The horse latitudes.—Along the poleward side of each trade-wind belt, and
corresponding approximately with the belt of high pressure in each hemisphere, is
another region with weak pressure gradients and correspondingly light, variable winds.
These are called the horse latitudes. The weather is generally clear and fresh, unlike
that in the doldrums, and periods of stagnation are less persistent, being of a more
intermittent nature. The difference is due primarily to the fact that rising currents
of warm air in the equatorial low carry large amounts of moisture which condenses as
the air cools at higher levels, while in the horse latitudes the air is apparently descending
and becoming less humid as it is warmed at lower heights.

3808. The prevailing westerlies.—On the poleward side of the high pressure belt
in each hemisphere the atmospheric pressure again diminishes. The currents of air set
in motion along these gradients toward the poles are diverted by the earth’s rotation
toward the east, becoming southwesterly winds in the northern hemisphere and north-
westerly in the southern hemisphere. These two wind systems are known as the
prevailing westerlies of the temperate zones.

In the northern hemisphere this relatively simple pattern is distorted considerably
by secondary wind circulations, due primarily to the presence of large land masses.
In the North Atlantic, between latitudes 40° and 50°, winds blow from some direction
between south and northwest during 74 percent of the time, being somewhat more
persistent in winter than in summer. They are stronger in winter, too, averaging about
25 knots (Beaufort 6) as compared with 14 knots (Beaufort 4) in the summer.

In the southern hemisphere the westerlies blow throughout the year with a steadi-
ness approaching that of the trade winds (art. 3806). "The speed, though variable, is
generally between 17 and 27 knots (Beaufort 5 and 6). Latitudes 40°S to 5098 (or
555) where these boisterous winds occur, are called the roaring forties. These winds
are strongest at about latitude 50? S.

The greater speed and persistence of the westerlies in the southern hemisphere are
due to the difference in the atmospheric pressure pattern, and its variations, from that
of the northern hemisphere. In the comparatively landless southern hemisphere,

WEATHER AND WEATHER FORECASTS 799

the average yearly atmospheric pressure diminishes much more rapidly on the poleward
side of the high pressure belt, and has fewer irregularities due to continental interference,
than in the northern hemisphere.

3809. Winds of polar regions.—Because of the low temperatures near the geo-
graphical poles of the earth, the pressure tends to remain higher than in surrounding
regions. Consequently, the winds blow outward from the poles, and are deflected
westward by the rotation of the earth, to become northeasterlies in the arctic, and
southeasterlies in the antarctic. Where these meet the prevailing westerlies, the
winds are variable.

In the arctic, the general circulation is greatly modified by surrounding land
masses. Winds over the Arctic Ocean are somewhat variable, and strong surface winds
are rarely encountered.

In the antarctic, on the other hand, a high central land mass is surrounded by
water, a condition which augments, rather than diminishes, the general circulation.
The high pressure, although weaker than in some areas, is stronger than in the arctic,
and of great persistence near the south pole. The upper air descends over the high
continent, where it becomes intensely cold. As it moves outward and downward toward
the sea, it is deflected toward the west by the earth’s rotation. The winds remain
strong throughout the year, frequently attaining hurricane force, and sometimes reach-
ing speeds of 100 to 200 knots at the surface. These are the strongest surface winds
encountered anywhere in the world, with the possible exception of those in well-
developed tropical cyclones (ch. X XXIX).

3810. Modifications of the general circulation.—The general circulation of the
atmosphere as described in articles 3804-3809 is greatly modified by various conditions.

The high pressure in the horse latitudes is not uniformly distributed around the
belts, but tends to be accentuated at several points, as shown in figures 3804b and 3804c.
These semipermanent highs remain at about the same places with great persistence.

Semipermanent lows also occur in various places, the most prominent ones being
west of Iceland, and over the Aleutians (winter only) in the northern hemisphere, and
at the Ross Sea and Weddell Sea in the antarctic. The areas occupied by these semi-
permanent lows are sometimes called the graveyards of the lows, since many lows
move directly into these areas and lose their identity as they merge with and reinforce
the semipermanent lows. The low pressure in these areas is maintained largely by
the migratory lows which stall there, but partly by the sharp temperature difference
between polar regions and warmer ocean areas.

Another modifying influence is land, which undergoes greater temperature changes
than does the sea. During the summer, a continent is warmer than its adjacent
oceans. Therefore, low pressures tend to prevail over the land. If a belt of high pres-
sure encounters such a continent, its pattern is distorted or interrupted. A belt of
low pressure is intensified. The winds associated with belts of high and low pressure
are distorted accordingly. In winter, the opposite effect takes place, belts of high
pressure being intensified over land and those of low pressure being interrupted.

The most striking example of a wind system produced by the alternate heating
and cooling of a land mass is the monsoons of the China Sea and Indian Ocean. A
portion of this effect is shown in figures 3810a and 3810b. In the summer (fig. 3810a),
low pressure prevails over the warm continent of Asia, and high pressure over the
adjacent sea. Between these two systems the wind blows in a nearly steady direction.
The lower portion of the pattern is in the southern hemisphere, extending to about
10° south latitude. Here the rotation of the earth causes a deflection to the left, re-
sulting in southeasterly winds. As they cross the equator, the deflection is in the
opposite direction, causing them to curve toward the right, becoming southwesterly

800 WEATHER AND WEATHER FORECASTS

FIGURE 3810a.—The summer monsoon. FiGURE 3810b.— The winter monsoon.

winds. In the winter (fig. 3810b), the positions of high and low pressure areas are
interchanged, and the direction of flow is reversed.

In the China Sea the summer monsoon blows from the southwest, usually from
May to September. The strong winds are accompanied by heavy squalls and thun-
derstorms, the rainfall being much heavier than during the winter monsoon. As the
season advances, squalls and rain become less frequent. In some places the wind
becomes a light breeze which is unsteady in direction, or stops altogether, while in
other places it continues almost undiminished, with changes in direction or calms
being infrequent. The winter monsoon blows from the northeast, usually from Octo-
ber to April. It blows with a steadiness similar to that of the trade winds, often attain-
ing the speed of a moderate gale (28-33 knots). Skies are generally clear during this
season, and there is relatively little rain.

The general circulation is further modified by winds of cyclonic origin (art. 3813),
and various local winds (art. 3814).

3811. Air masses.—Because of large differences in physical characteristics of the
earth’s surface, particularly the oceanic and continental contrasts, the air overlying
these surfaces acquires differing values of temperature, moisture, etc. The processes
of radiation and convection in the lower portions of the troposphere act in differing,
characteristic manners for a number of well-defined regions of the earth. The air over-
lying these regions acquires characteristics common to the particular area, but con-
trasting to those of other areas. Each distinctive part of the atmosphere, within
which common characteristics prevail over a reasonably large area, is called an air
mass.

Air masses are named according to their source regions. Four such regions are
generally recognized: (1) equatorial (E), the doldrum area between the north and south
trades; (2) tropical (T), the trade wind and lower temperate regions; (3) polar (P),
the higher temperate latitudes; and (4) arctic (A), the north polar region of ice and
snow (or, by extension, the antarctic). This classification is a general indication of
relative temperature, as well as latitude of origin.

Tropical and polar air masses are further classified as maritime (m) or continental
(c), depending upon whether they form over water or land. This classification is an
indication of the relative moisture content of the air mass. Since the moisture content
of equatorial and arctic air is essentially independent of the surface over which they
form, these sub-classifications are not applied to them. Tropical air, then, might be
designated maritime tropical (mT) or continental tropical (cT). Similarly, polar air may
be either maritime polar (mP) or continental polar (cP).

A third classification sometimes applied to tropical and polar air masses indi-
cates whether the air mass is warm (w) or cold (k) relative to the underlying surface.
Thus, the symbol mTw indicates maritime tropical air which is warmer than the under-

WEATHER AND WEATHER FORECASTS 801

lying surface, and cPk indicates continental polar air which is colder than the under-
lying surface. The w and k classifications are primarily indications of stability. If the
air is cold relative to the surface, the lower portion of the air mass is being heated
resulting in instability as the warmer air tends to rise by convection. Conversely if
the air is warm relative to the surface, the lower portion of the air mass is oled
tending to remain close to the surface. This is a stable condition. i

Two other types of air masses are sometimes recognized. These are monsoon (M),
a transitional form between cP and E; and superior (S), a special type formed in the
free atmosphere by the sinking and consequent warming of air aloft.

3812. Fronts.—As air masses move within the general circulation, they travel
from their source regions and invade other areas dominated by air having different
characteristics. There is little tendency for adjacent air masses to mix. Instead,
they are separated by a thin zone in which air mass characteristics exhibit such sharp
gradients as to appear as discontinuities. This is called a frontal surface. The
intersection of a frontal surface and a horizontal plane is called a front, although the
term “front” is commonly used as a short expression for “frontal surface” when this
will not introduce an ambiguity.

FIGURE 3812a.—First stage in the development of a frontal wave (top view).

Because of differences in the motion of adjacent air masses, “waves” form along
the frontal surface between them.

Before the formation of frontal waves, the isobars (lines of equal atmospheric
pressure) tend to run parallel to the fronts. As a wave is formed, the pattern is dis-
torted somewhat, as shown in figure 3812a. In this illustration, colder air is north of
warmer air. Isobars are shown at intervals of three millibars. The wave tends to
travel in the direction of the general circulation, which in the temperate latitudes is
usually in a general easterly and slightly poleward direction.

Along the leading edge of the wave, warmer air is replacing colder air. This is called
the warm front. The trailing edge is the cold front, where colder air is replacing
warmer air.

The warm air, being less dense, tends to ride up over the colder air it is replacing,
causing the warm front to be tilted in the direction of motion. The slope is gentle,
varying between 1:100 and 1:300. Because of the replacement of cold, dense air with
warm, light air, the pressure decreases. Since the slope is gentle, the upper part of a
warm frontal surface may be many hundreds of miles ahead of the surface portion.
The decreasing pressure, indicated by a “falling barometer,” is often an indication of

802 WEATHER AND WEATHER FORECASTS

the approach of such a wave. In a slow-moving, well-developed wave, the barometer
may begin to fall several days before the wave arrives. Thus, the amount and nature
of the change of atmospheric pressure between observations, called pressure tendency,
is of assistance in predicting the approach of such a system.

The advancing cold air, being more dense, tends to cut under the warmer air at
the cold front, lifting it to greater heights. The slope here is in the opposite direction,
at a rate of about 1:25 to 1:100, being steeper than the warm front. Therefore, after
a cold front has passed, the pressure increases—a “rising barometer.”

In the first stages, these effects are not marked, but as the wave continues to grow,
they become more pronounced, as shown in figure 3812b. As the amplitude of the
wave increases, pressure near the center usually decreases, and the “low”” is said to
“deepen.” As it deepens, its forward speed generally decreases.

The approach of a well-developed warm front is usually heralded not only by
falling pressure, but also by a more-or-less regular sequence of clouds. First, cirrus
appear. These give way successively to cirrostratus, altostratus, altocumulus, and
nimbostratus. Brief showers may precede the steady rain accompanying the nimbo-
stratus.

As the warm front passes, the temperature rises, the wind shifts to the right (in
the northern hemisphere), and the steady rain stops. Drizzle may fall from low-lying
stratus clouds, or there may be fog for some time after the wind shift. During passage
of the warm sector between the warm front and the cold front, there is little change in
temperature or pressure. However, if the wave is still growing and the low deepening,
the pressure might slowly decrease. In the warm sector the skies are generally clear
or partly cloudy, with cumulus or stratocumulus clouds most frequent. The warm
air is usually moist, and haze or fog may often be present.

As the faster moving, steeper cold front passes, the wind shifts abruptly to the
right (in the northern hemisphere), the temperature falls rapidly, and there are often
brief and sometimes violent showers, frequently accompanied by thunder and lightning.
Clouds are usually of the convective type. A cold front usually coincides with a well-
defined wind-shift line (a line along which the wind shifts abruptly from southerly or
southwesterly to northerly or northwesterly in the northern hemisphere and from
northerly or northwesterly to southerly or southwesterly in the southern hemisphere).
At sea a series of brief showers accompanied by strong, shifting winds may occur
along or some distance (up to 200 miles) ahead of a cold front. These are called
squalls, and the line along which they occur is called a squall line. Because of its
greater speed and steeper slope, which may approach or even exceed the vertical near
the earth’s surface (due to friction), a cold front and its associated weather passes
more quickly than a warm front. After a cold front passes, the pressure rises, often
quite rapidly, the visibility usually improves, and the clouds tend to diminish.

As the wave progresses and the cold front approaches the slower moving warm
front, the low becomes deeper and the warm sector becomes smaller. This is shown
in figure 3812c.

Finally, the faster moving cold front overtakes the warm front (fig. 3812d), re-
sulting in an occluded front at the surface, and an upper front aloft (fig. 3812e). When
the two parts of the cold air mass meet, the warmer portion tends to rise above the
colder part. The warm air continues to rise until the entire system dissipates. As
the warmer air is replaced by colder air, the pressure gradually rises, a process called

filling.” This usually occurs within a few days after an occluded front forms, but

the process is sometimes delayed by a slowing of the forward motion of the wave. In
general, however, a filling low increases in speed.

WEATHER AND WEATHER FORECASTS 803

FīcuRE 3812b.—A fully developed frontal wave (top view).

FIGURE 3812c.—A frontal wave nearing occlusion (top view).

804 WEATHER AND WEATHER FORECASTS

FIGURE 3812d.—An occluded front (top view).

The sequence of weather associated with a low depends greatly upon location with
respect to the path of the center. That described above assumes that the observer
is so located that he encounters each part of the system. If he is poleward of the path
of the center of the low, the abrupt weather changes associated with the passage of
fronts are not experienced. Instead, the change from the weather characteristically
found ahead of a warm front to that behind a cold front takes place gradually, the
exact sequence being dictated somewhat by distance from the center, as well as severity
and age of the low.

Although each low follows generally the pattern given above, no two are ever
exactly alike. Other centers of low pressure and high pressure and the air masses
associated with them, even though they may be 1,000 miles or more away, influence

FIGURE 3812e.—An occluded front (cross section).

WEATHER AND WEATHER FORECASTS 805

the formation and motion of individual low centers and their accompanying weather.
Particularly, a high stalls or diverts a low. This is true of temporary highs as well as
semipermanent highs.

3813. Cyclones and anticyclones.—An approximately circular portion of the atmos-
phere in the vicinity of a low pressure area is called a cyclone. A similar portion in
the vicinity of an atmospheric high is called an anticyclone. These terms are used
particularly in connection with the winds associated with such centers. Wind tends
to blow from an area of high pressure to one of low pressure, but due to rotation of the
earth, they are deflected toward the right in the northern hemisphere and toward the
left in the southern hemisphere (art. 3804).

Because of the rotation of the earth, therefore, the circulation tends to be counter-
clockwise around areas of low pressure in the northern hemisphere (figs. 3812c and
3812d), and clockwise around areas of high pressure, the speed being proportional to
the spacing of isobars. In the southern hemisphere, the direction of circulation is
reversed. Based upon this condition, a general rule (Buys Ballot’s Law) can be stated
thus:

If an observer in the northern hemisphere faces the wind, the center of low pressure
is toward his right, somewhat behind him; and the center of high pressure is toward his left
and somewhat in front of him.

If an observer in the southern hemisphere faces the wind, the center of low pressure
is toward his left and somewhat behind him; and the center of high pressure is toward his
right and somewhat in front of ham.

In a general way, these relationships apply in the case of the general distribution
of pressure, as well as to temporary local pressure systems.

The reason for the wind shift along a front is that the isobars have an abrupt change
of direction along these lines, as shown in figures 3812a-3812d. Since the direction
of the wind is directly related to the direction of isobars, any change in the latter results
in a shift in the wind direction.

In the northern hemisphere, the wind shifts toward the right when either a warm
or cold front passes. In the southern hemisphere, the shift is toward the left. When
the wind shifts in this direction (clockwise in the northern hemisphere and counter-
clockwise in the southern hemisphere), it is said to veer. If it shifts in the opposite
direction, as when an observer is on the poleward side of the path of a frontal wave, it
is said to back.

In an anticyclone, successive isobars are relatively far apart, resulting in light
winds. In a cyclone, the isobars are more closely spaced. With a steeper pressure
gradient, the winds are stronger.

Since an anticyclonic area is a region of outflowing winds, air is drawn into it from
aloft. Descending air is warmed, and as air becomes warmer, its capacity for holding
uncondensed moisture increases. Therefore, clouds tend to dissipate. Clear skies are
characteristic of an anticyclone, although scattered clouds and showers are sometimes
encountered.

In contrast, a cyclonic area is one of converging winds. The resulting upward
movement of air results in cooling, a condition favorable to the formation of clouds and
precipitation. More or less continuous rain and generally stormy weather are usually
associated with a cyclone.

Between the two belts of high pressure associated with the horse latitudes (art.
3807), cyclones form only occasionally, generally in certain seasons, and always in
certain areas at sea. These tropical cyclones are usually quite violent, being known
under various names according to their location. They are discussed in chapter

XXXIX.

806 WEATHER AND WEATHER FORECASTS

In the areas of the prevailing westerlies (art. 3808), cyclones are a common occur-
rence, the cyclonic and anticyclonic circulation being a prominent feature of temperate
latitudes. These are sometimes called extratropical cyclones to distinguish them from
the more violent tropical cyclones. Although most of them are formed at sea, their
formation over land is not unusual. As a general rule, they decrease in intensity when
they encounter land, and increase when they move from the land to a water area. In
their early stages, cyclones are elongated, as shown in figure 3812a, but as their life
cycle proceeds, they become more nearly circular (figs. 3812b-3812d).

3814. Local winds.—In addition to the winds of the general circulation (arts. 3804—
3809) and those associated with cyclones and anticyclones (art. 3813), there are num-
erous local winds which influence the weather in various places.

The most common of these are the land and sea breezes, caused by alternate heating
and cooling of land adjacent to water. The effect is similar to that which causes the
monsoons (art. 3810), but on a much smaller scale, and over shorter periods. By day
the land is warmer than the water, and by night it is cooler. This effect occurs along
many coasts during the summer. Between about 0900 and 1100 the temperature of
the land becomes greater than that of the adjacent water. The lower levels of air
over the land are warmed, and the air rises, drawing in cooler air from the sea. This
is the sea breeze. Late in the afternoon, when the sun is low in the sky, the tempera-
ture of the two surfaces equalizes and the breeze stops. After sunset, as the land cools
below the sea temperature, the air above it is also cooled. The contracting cool air
becomes more dense, increasing the pressure. This results in an outflow of winds to
the sea. This is the land breeze, which blows during the night and dies away near
sunrise. Since the atmospheric pressure changes associated with this cycle are not
great, the accompanying winds do not exceed gentle breezes. The circulation is gen-
erally of limited extent, reaching a distance of perhaps 20 miles inland, and not more
than five or six miles offshore, and to a height of a few hundred feet. In the tropics, this
process is repeated with great regularity throughout most of the year. As the latitude
increases, it becomes less prominent, being masked by winds of cyclonic origin (art.
3813). However, the effect may often be present to reinforce, retard, or deflect stronger
prevailing winds.

Varying conditions of topography produce a large variety of local winds throughout
the world. In light airs, winds tend to follow valleys, and to be deflected from high
banks and shores. Many local winds have been given distinctive names. An anabatic
wind is one which blows up an incline, as one which blows up a hillside due to surface
heating. A katabatic wind is one which blows down an incline due to cooling of the air.
The cooler air becomes heavier than surrounding air and flows downward along the
incline under the force of gravity.

A dry wind with a downward component, warm for the season, is called a foehn.
The foehn occurs when horizontally moving air encounters a mountain barrier. As it
blows upward to clear the barrier, it is cooled below the dew point, resulting in loss of
moisture by cloud formation and perhaps rain. As the air continues to rise, its rate of
cooling is reduced because the condensing water vapor gives off heat to the surrounding
atmosphere. After crossing the mountain barrier, the air flows downward along the
leeward slope, being warmed by compression as it descends to lower levels. Thus, since
it loses less heat on the ascent than it gains during descent, and since it loses moisture
during ascent, it arrives at the bottom of the mountains as very warm, dry air. This
accounts for the warm, arid regions along the eastern side of the Rocky Mountains and
in similar areas. In the Rocky Mountain region this wind is known by the name
chinook. It may occur at any season of the year, at any hour of the day or night, and
have any speed from a gentle breeze to a gale. It may last for several days, or for a very

WEATHER AND WEATHER FORECASTS 807

short period. Its effect is most marked in winter, when it may cause the temperature to
rise as much as 20°F to 30°F within 15 minutes, and cause snow and ice to melt within
a few hours. On the west coast of the United States, the name “chinook” is given to a
moist southwesterly wind from the Pacific Ocean, warm in winter and cool in summer.
Cloudy weather and rain may accompany or follow this wind, which is thus quite differ-
ent from the other chinook mentioned above. A foehn given the name Santa Ana blows
through a pass and down a valley by that name in Southern California. This wind
usually starts suddenly, without warning, and blows with such force that it may capsize
small craft off the coast.

A cold wind blowing down an incline is called a fall wind. Although it is warmed
somewhat during descent, as is the foehn, it is cold relative to the surrounding air.
It occurs when cold air is dammed up in great quantity on the windward side of a moun-
tain and then spills over suddenly, usually as an overwhelming surge down the other
side. It is usually quite violent, sometimes reaching hurricane force. A different
name for this type wind is given at each place where it is common. The williwaw of
the Aleutian coast, the tehuantepecer of the Mexican and Central American coast, the
pampero of the Argentine coast, the mistral of the western Mediterranean, and the
bora of the eastern Mediterranean are examples of this type wind.

Many other local winds common to certain areas have been given distinctive
names.

A blizzard is a violent, intensely cold wind laden with snow mostly or entirely
picked up from the ground, although the term is often used popularly to refer to any
heavy snowfall accompanied by strong wind. A dust whirl is a rotating column of air
about 100 to 300 feet in height, carrying dust, leaves, and other light material. This
wind, which is similar to a waterspout at sea (art. 3825), is given various local names
such as dust devil in southwestern United States and desert devil in South Africa. A
gust is a sudden, brief increase in wind speed followed by a slackening, or the violent
wind or squall that accompanies a thunderstorm. A puff of wind or a light breeze
affecting a small area, such as would cause patches of ripples on the surface of water,
is called a cat’s paw.

3815. Fog, like a cloud (art. 3714), is a visible assemblage of numerous tiny
droplets of water, or ice crystals, formed by condensation of water vapor in the air.
However, the base of a cloud is above the surface of the earth, while fog is in contact
with the surface.

Radiation fog forms over low-lying land on clear, calm nights. As the land
radiates heat and becomes cooler, it cools the air immediately above the surface. This
causes a temperature inversion to form, the temperature for some distance upward
increasing with height. If the air is cooled to its dew point (art. 3713), fog forms.
Often, cooler and more dense air drains down surrounding slopes to heighten the
effect. Radiation fog is often quite shallow, and is usually thickest at the surface.
After sunrise the fog may “lift,” as shown in figure 3815, and gradually dissipate,
usually being entirely gone by noon. At sea the temperature of the water undergoes
little change between day and night, and so radiation fog is seldom encountered more
than ten miles from shore.

Advection fog forms when warm, moist air blows over a colder surface and is cooled
below its dew point. This type, most commonly encountered at sea, may be quite
thick and often persists over relatively long periods. The maximum density might
be at nearly any height. Advection fog is common over cold ocean currents. If the
wind is strong enough to thoroughly mix the air, condensation may take place at some
distance above the surface of the earth, forming low stratus clouds (art. 3714) rather
than fog.

308 WEATHER AND WEATHER FORECASTS

Off the coast of California, winds create an offshore current which displaces the
warm surface water, causing an upwelling of colder water. Moist air being transported
along the coast in the same wind system is cooled, and advection fog results. In the
coastal valleys, fog is sometimes formed when moist air blown inland during the after-
noon is cooled by radiation during the night. Both of these are called California fog
because they are peculiar to California and its coastal valleys.

RADIATION FOG

ATT NIGHT
44°F (CLEAR, COOL, AND WITH LIGHT BREEZE)
AU FOG FORMS

38'F vou S UE CS
lp —————

41°F AFTER SUNRISE—FOG MAY “LIFT”
44°F
41°F py
39°F

ķ Kan DA
ym)
44°F eiert

41°F BEFORE NOON—FOG DISSIPATES
44°F NS)
47°F HE is
4 i /
50°F |

T | /
525 F wee g tI Ms
FiGURE 3815.— Formation and dissipation of radiation fog.

When very cold air moves over warmer water, wisps of visible water vapor may
rise from the surface as the water “steams,” as shown in figure 2505. In extreme cases
this frost smoke, or arctic sea smoke, may rise to a height of several hundred feet,
the portion near the surface constituting a dense fog which obscures the horizon and
surface objects, but usually leaves the sky relatively clear.

Fog consisting of ice crystals is called ice fog, or pogonip by Western American
Indians. Thin fog of relatively large particles, or very fine rain lighter than drizzle,
is called mist. A mixture of smoke and fog is called smog.

WEATHER AND WEATHER FORECASTS 809

Haze consists of fine dust or salt particles in the air, too small to be individually
apparent, but in sufficient number to reduce horizontal visibility and cast a bluish or
yellowish veil over the landscape, subduing its colors and making objects appear
indistinct. This is sometimes called dry haze to distinguish it from damp haze, which
consists of small water droplets or moist particles in the air, smaller and more scattered
than light fog. In international meteorological practice, the term “haze” is used to
refer to a condition of atmospheric obscurity caused by dust and smoke.

3816. Mirage.—As explained in article 1613, light is refracted as it passes through
the atmosphere. When refraction is normal, objects appear slightly elevated, and the
visible horizon is farther from the observer than it otherwise would be. Since the
effects are uniformly progressive, they are not apparent to the observer. When re-
fraction is not normal, some form of mirage may occur. A mirage is an optical phe-
nomenon in which objects appear distorted, displaced (raised or lowered), magnified,
multiplied, or inverted due to varying atmospheric refraction which occurs when a
layer of air near the earth’s surface differs greatly in density from surrounding air.
This may occur when there is a rapid and sometimes irregular change of temperature
or humidity with height.

If there is a temperature inversion (increase of temperature with height), par-
ticularly if accompanied by a rapid decrease in humidity, the refraction is greater than
normal. Objects appear elevated, and the visible horizon is farther away. Objects
which are normally below the horizon become visible. This is called looming. If
the upper portion of an object is raised much more than the bottom part, the object
appears taller than usual, an effect called towering. If the lower part of an object is
raised more than the upper part, the object appears shorter, an effect called stooping.
When the refraction is greater than normal, a superior mirage may occur. An in-
verted image is seen above the object, and sometimes an erect image appears over the
inverted one, with the bases of the two images touching. Greater than normal refraction
usually occurs when the water is much colder than the air above it.

If the temperature decrease with height is much greater than normal, refraction
is less than normal, or may even cause bending in the opposite direction. Objects
appear lower than normal, and the visible horizon is closer to the observer. This is
called sinking. Towering or stooping may occur if conditions are suitable. When
the refraction is reversed, an inferior mirage may occur. A ship or an island appears to
be floating in the air above a shimmering horizon, possibly with an inverted image
beneath it. Conditions suitable to the formation of an inferior mirage occur when
the surface is much warmer than the air above it. This usually requires a heated land
mass, and therefore is more common near the coast than at sea.

When refraction is not uniformly progressive, objects may appear distorted, taking
an almost endless variety of shapes. The sun when near the horizon is one of the objects
most noticeably affected. A fata morgana is a complex mirage characterized by marked
distortion, generally in the vertical. It may cause objects to appear towering,
magnified, and at times even multiplied.

3817. Sky coloring.—White light is composed of light of all colors. Color is
related to wave length, the visible spectrum varying from about 0.000038 to 0.000076
centimeters (art. 1003). The characteristics of each color are related to its wave
length (or frequency). Thus, the shorter the wave length, the greater the amount of
bending when light is refracted. It is this principle that permits the separation of light
from celestial bodies into a spectrum ranging from red, through orange, yellow, green,
and blue, to violet, with long-wave infrared (black light) being slightly outside the
visible range at one end and short-wave ultraviolet being slightly outside the visible

810 WEATHER AND WEATHER FORECASTS

range at the other end. Light of shorter wave length is scattered and diffracted more
than that of longer wave length.

Light from the sun and moon is white, containing all colors. As it enters the earth’s
atmosphere, a certain amount of it is scattered. The blue and violet, being of shorter
wave length than other colors, are scattered most. Most of the violet light is absorbed
in the atmosphere. Thus, the scattered blue light is most apparent, and the sky
appears blue. At great heights, above most of the atmosphere, it appears black.

When the sun is near the horizon, its light passes through more of the atmosphere
than when higher in the sky, resulting in greater scattering and absorption of blue and
green light, so that a larger percentage of the red and orange light penetrates to the
observer. For this reason the sun and moon appear redder at this time, and when
this light falls upon clouds, they appear colored. This accounts for the colors at sunset
and sunrise. As the setting sun approaches the horizon, the sunset colors first appear as
faint tints of yellow and orange. As the sun continues to set, the colors deepen. Con-
trasts occur, due principally to difference in height of clouds. As the sun sets, the clouds
become a deeper red, first the lower clouds and then the higher ones, and finally they
fade to a gray.

When there is a large quantity of smoke, dust, or other material in the sky, unusual
effects may be observed. If the material in the atmosphere is of suitable substance
and quantity to absorb the longer wave red, orange, and yellow radiations, the sky
may have a greenish tint, and even the sun or moon may appear green. If the green
light, too, is absorbed, the sun or moon may appear blue. A green moon or blue moon
is most likely to occur when the sun is slightly below the horizon and the longer wave
length light from the sun is absorbed, resulting in green or blue light being cast upon the
atmosphere in front of the moon. The effect is most apparent if the moon is on the same
side of the sky as the sun.

3818. Rainbows.—The familiar arc of concentric colored bands seen when the sun
shines on rain, mist, spray, etc., is caused by refraction, internal reflection, and diffrac-
tion of sunlight by the drops of water. The center of the arc is a point 180° from the
sun, in the direction of a line from the sun, through the observer. The radius of the
brightest rainbow is 42%. The colors are visible because of the difference in the amount
of refraction of the different colors making up white light, the light being spread out to
form a spectrum (art. 3817). Red is on the outer side and blue and violet on the
inner side, with orange, yellow, and green between, in that order from red.

Sometimes a secondary rainbow is seen outside the primary one, at a radius of
about 50°. The order of colors of this rainbow is reversed. On rare occasions a faint
rainbow is seen on the same side as the sun. The radius of this rainbow and the order
of colors are the same as those of the primary rainbow.

A similar arc formed by light from the moon (a lunar rainbow) is called a moonbow.
The colors are usually very faint. A faint, white are of about 39° radius is occasionally
seen in fog opposite the sun. This is called a fogbow, although its origin is controver-
sial, some considering it a halo (art. 3819).

3819. Halos.— Refraction, or a combination of refraction and reflection, of light by
ice crystals in the atmosphere (cirrostratus clouds, art. 3714) may cause a halo to appear.
The most common form is a ring of light of radius 22° or 46° with the sun or moon at the
center. Occasionally a faint, white circle with a radius of 90° appears around the sun.
This is called a Hevelian halo. It is probably caused by refraction and internal reflec-
tion of the sun’s light by bipyramidal ice crystals. A halo formed by refraction is

usually faintly colored like a rainbow (art. 3818), with red nearest the celestial body,
and blue farthest from it.

WEATHER AND WEATHER FORECASTS 811

A brilliant rainbow-colored arc of about a quarter of a circle with its center at the
zenith, and the bottom of the arc about 46° above the sun, is called a circumzenithal arc.
Red is on the outside of the arc, nearest the sun. It is produced by the refraction and
dispersion of the sun's light striking the top of prismatic ice erystals in the atmosphere.
It usually lasts for only about five minutes, but may be so brilliant as to be mistaken
for an unusually bright rainbow. A similar arc formed 46° below the sun, with red on
the upper side, is called a circumhorizontal arc. Any arc tangent to a heliocentric halo
(one surrounding the sun) is called a tangent arc. As the sun increases in elevation,
such ares tangent to the halo of 22° gradually bend their ends toward each other. If
they meet, the elongated curve enclosing the circular halo is called a cireumscribed
halo. The inner edge is red.

A halo consisting of a faint, white circle through the sun and parallel to the horizon
is called a parhelic circle. A similar one through the moon is called a paraselenic circle.
They are produced by reflection of sunlight or moonlight from vertical faces of ice
crystals.

A parhelion (plural parhelia) is a form of halo consisting of an image of the sun
at the same altitude and some distance from it, usually 22°, but occasionally 46°. A
similar phenomenon occurring at an angular distance of 120° (sometimes 90° or 140°)
from the sun is called a paranthelion. One at an angular distance of 180°, a rare oc-
currence, is called an anthelion, although this term is also used to refer to a luminous,
colored ring or glory sometimes seen around the shadow of one’s head on a cloud or fog
bank. A parhelion is popularly called a mock sun or sun dog. Similar phenomena
in relation to the moon are called paraselene (popularly a mock moon or moon dog),
parantiselene, and antiselene. The term parhelion should not be confused with
perthelion, that orbital point nearest the sun when the sun is the center of attraction
(art. 1407).

A sun pillar is a glittering shaft of white or reddish light occasionally seen extending
above and below the sun, usually when the sun is near the horizon. A phenomenon
similar to a sun pillar, but observed in connection with the moon, is called a moon pillar.
A rare form of halo in which horizontal and vertical shafts of light intersect at the sun
is called a sun cross. It is probably due to the simultaneous occurrence of a sun pillar
and a parhelic circle.

3820. Corona.—When the sun or moon is seen through altostratus clouds (art.
3714), its outline is indistinct, and it appears surrounded by a glow of light called a
corona. This is somewhat similar in appearance to the corona seen around the sun
during a solar eclipse (art. 1424). When the effect is due to clouds, however, the glow
may be accompanied by one or more rainbow-colored rings of small radii, with the
celestial body at the center. These can be distinguished from a halo by their much
smaller radii and also by the fact that the order of the colors is reversed, red being on
the inside, nearest the body, in the case of the halo, and on the outside, away from the
body, in the case of the corona.

A corona is caused by diffraction of light by tiny droplets of water. The radius
of a corona is inversely proportional to the size of the water droplets. A large
corona indicates small droplets. If a corona decreases in size, the water droplets are
becoming larger and the air more humid. This may be an indication of an approach-
ing rainstorm.

The glow portion of a corona is called an aureole. M"

3821. The green flash.—As light from the sun passes through the atmosphere, it is
refracted. Since the amount of bending is slightly different for each color, separate
images of the sun are formed in each color of the spectrum. The effect is similar to that

812 WEATHER AND WEATHER FORECASTS

of imperfect color printing in which the various colors are slightly out of register.
However, the difference is so slight that the effect is not usually noticeable. At the
horizon, where refraction is maximum, the greatest difference, which occurs between
violet at one end of the spectrum and red at the other, is about ten seconds of arc. At
latitudes of the United States, about 0.7 second of time is needed for the sun to change
altitude by this amount when it is near the horizon. The red image, being bent least
by refraction, is first to set and last to rise. The shorter wave blue and violet colors
are scattered most by the atmosphere, giving it its characteristic blue color (art. 3817).
Thus, as the sun sets, the green image may be the last of the colored images to drop out
of sight. If the red, orange, and yellow images are below the horizon, and the blue
and violet light is scattered and absorbed, the upper rim of the green image is the only
part seen, and the sun appears green. This is the green flash. The shade of green
varies, and occasionally the blue image is seen, either separately or following the green
flash (at sunset). On rare occasions the violet image is also seen. These colors may
also be seen at sunrise, but in reverse order. They are occasionally seen when the sun
disappears behind a cloud or other obstruction.

The phenomenon is not observed at each sunrise or sunset, but under suitable con-
ditions is far more common than generally supposed. Conditions favorable to obser-
vation of the green flash are a sharp horizon, clear atmosphere, a temperature inversion
(art. 3815), and an attentive observer. Since these conditions are more frequently
met when the horizon is formed by the sea than by land, the phenomenon is more
common at sea. With a sharp sea horizon and clear atmosphere, an attentive observer
may see the green flash at as many as 50 percent of sunsets and sunrises, although a
telescope may be needed for some of the observations.

Duration of the green flash (including the time of blue and violet flashes) of as
long as ten seconds has been reported, but such length is rare. Usually it lasts for a
period of about half a second to two and one-half seconds with about one and a quarter
seconds being average. ‘This variability is probably due primarily to changes in the
index of refraction (art. 1613) of the air near the horizon.

Under favorable conditions, a momentary green flash has been observed at the
setting of Venus and Jupiter. A telescope improves the chances of seeing such a flash
from a planet, but is not a necessity.

3822. Crepuscular rays are beams of light from the sun passing through openings
in the clouds, and made visible by illumination of dust in the atmosphere along their
paths. Actually, the rays are virtually parallel, but because of perspective appear to
diverge. Those appearing to extend downward are popularly called backstays of the
sun, or sun drawing water. Those extending upward and across the sky, appearing
to converge toward a point 180° from the sun, are called anticrepuscular rays.

3823. The atmosphere and radio waves.—Radio waves traveling through the at-
mosphere exhibit many of the properties of light, being refracted, reflected, diffracted,
and scattered. These and other effects are discussed in chapter X.

3824. Atmospheric electricity.—Various conditions induce the formation of elec-
trical charges in the atmosphere. When this occurs, there is often a difference of
electron charge between various parts of the atmosphere, and between the atmosphere
and earth or terrestrial objects. When this difference exceeds a certain minimum
value depending upon the conditions, the static electricity is discharged, resulting in
phenomena such as lightning or St. Elmo's fire.

Lightning is the discharge of electricity from one part of a thundercloud (art.

3714) to another, from one such cloud to another, or between such a cloud and the
earth or a terrestrial object.

WEATHER AND WEATHER FORECASTS 813

Enormous electrical stresses build up within thunderclouds and between such
clouds and the earth. At some point the resistance of the intervening air is overcome.
At first the process is a progressive one, probably starting as a brush discharge (St.
Elmo's fire) and growing by ionization. The breakdown follows an irregular path
along the line of least resistance. A hundred or more individual discharges may be
necessary to complete the path between points of opposite polarity. When this
“leader stroke” reaches its destination, a heavy “main stroke” immediately follows in
the opposite direction. This main stroke is the visible lightning, which may be tinted
any color, depending upon the nature of the gases through which it passes. The
illumination is due to the high degree of ionization of the air, which causes many of the
atoms to be in excited states and emit radiation.

Thunder, the noise that often accompanies lightning, is caused by the heating
and ionizing of the air by lightning, which results in rapid expansion of the air along its
path and the sending out of a compression wave. Thunder may be heard at a distance
of as much as 15 miles, but generally does not carry that far. The elapsed time
between the flash of lightning and reception of the accompanying sound of thunder is
an indication of the distance, because of the difference in travel time of light and sound.
Since the former is comparatively instantaneous, and the speed of sound is about 1,117
feet per second, the approximate distance in nautical miles is equal to the elapsed time
in seconds, divided by 5.5. If there is no accompanying thunder, the flash is called
heat lightning.

St. Elmo's fire is a luminous discharge of electricity from pointed objects such
as the masts and yardarms of ships, lightning rods, steeples, mountain tops, blades of
grass, human hair, arms, etc., when there is a considerable difference in the electrical
charge between the object and the air. It appears most frequently during a storm. An
object from which St. Elmo’s fire emanates is in danger of being struck by lightning, since
this type discharge may be the initial phase of the leader stroke. Throughout history
those who have not understood St. Elmo's fire have regarded it with superstitious awe,
considering it a supernatural manifestation. This view is reflected in the name corposant
(from “corpo santo," meaning “body of a saint") sometimes given this phenomenon.

The aurora is a luminous glow appearing in varied forms in the thin atmosphere
high above the earth, due to radiation from the sun. This phenomenon is discussed in
article 2526.

3825. Waterspouts.—A waterspout is a small, whirling storm over the ocean or
inland waters. Its chief characteristic is a funnel-shaped cloud extending, in a fully
developed spout, from the surface of the water to the base of a cumulus type cloud
(fig. 3825). The water in a spout is mostly confined to its lower portion, and may be
either salt spray drawn up by the sea surface, or fresh water resulting from condensa-
tion due to the lowered pressure in the center of the vortex creating the spout. Water-
spouts usually rotate in the same direction as cyclones (counterclockwise in the northern
hemisphere and clockwise in the southern hemisphere), but the opposite rotation is
occasionally observed. They are found most frequently in tropical regions, but are
not uncommon in higher latitudes.

Waterspouts may be divided into two classes, according to their different origins
and appearances. In the true waterspout, the vortex is formed in clouds by the inter-
action of air currents flowing in opposite directions. This type occurs mainly in the
vicinity of a squall line (art. 3812). A similar disturbance over land is called a tornado.
The second type, which may be considered a pseudo waterspout, originates just above
the water surface, in unstable air, and builds upward, frequently under clear skies.

814 WEATHER AND WEATHER FORECASTS

FIGURE 3825.— Waterspouts.

This type is identical to the whirling pillars of sand and dust often seen on deserts
(art. 3814) and usually occurs only over very warm water surfaces.

Waterspouts vary in diameter from a few feet to several hundred feet, and in
height from a few hundred feet to several thousand feet. Sometimes they assume
fantastic shapes and may even seem to coil about themselves. Since a waterspout is
often inclined to the vertical, its actual length may be much greater than indicated by
its height. The highest waterspout on record was one of 5,014 feet observed near New
South Wales, Australia, on May 16, 1898.

3826. Deck ice.—Ships traveling through regions where the air temperature is
below freezing may acquire thick deposits of ice as a result of salt spray freezing on

WEATHER AND WEATHER FORECASTS 815

the rigging or deck areas (fig. 3826). Also, precipitation may freeze to the superstruc-
ture and exposed areas of the vessel, increasing the load of ice.

On small vessels in heavy seas and freezing weather, deck ice may accumulate
very rapidly and increase the topside weight to such an extent as to reduce seriously
the stability of the vessel.

3827. Forecasting weather.—The prediction of weather at some future time is
based upon an understanding of weather processes, and observations of present condi-
tions. Thus, one learns that when there is a certain sequence of cloud types (art.
3714), rain can usually be expected to follow within a certain period. If the sky is
cloudless, more heat will be received from the sun by day, and more heat will be radiated
outward from the warm earth by night than if the sky is overcast. If the wind is in
such a direction that warm, moist air will be transported to a colder surface, fog can be

" RW
SEH
T

ui 3 ` à

FIGURE 3826.— Deck ice.

expected. A falling barometer indicates the approach of a “low,” probably accom-
panied by stormy weather. Thus, before the science of meteorology was developed,
many individuals learned to interpret certain phenomena in terms of future weather,
and to make reasonably accurate forecasts for short periods into the future.

With the establishment of weather observation stations, additional information
became available. As such observations expanded, and communication facilities
improved, knowledge of simultaneous conditions over wider areas became available.
This made possible the collection of these “synoptic” reports at civilian forecast
centers and Navy Fleet Weather Centrals.

The individual observations are made at government-operated stations on shore,
and aboard vessels at sea. Observations aboard merchant ships at sea are made
and transmitted on a voluntary and cooperative basis. The various national mete-
orological services supply shipmasters with blank forms, printed instructions, and other
materials essential to the making, recording, and interpreting of observations. Any
shipmaster can render a particularly valuable service by reporting all contacts with
tropical cyclones (ch. XXXIX).

816 WEATHER AND WEATHER FORECASTS

Symbols and numbers are used to indicate on a synoptic chart, popularly called x
weather map, the conditions at each observation station. Isobars are drawn ee
lines of equal atmospheric pressure, fronts are located and marked by symbol (fig.
3827), areas of precipitation and fog are indicated, etc. E

Ordinarily, surface charts are prepared every six hours, but at a few centers they
are drawn every three hours. In addition, synoptic charts for selected heights are

LEGEND

Type Symbol Coloring
COLD FRONT PVN VVS BLUE LINE
WARM FRONT GG GVN NEU RED LINE
OCCLUDED FRONT L4 AA QA AA AA ) PURPLE LINE
STATIONARY FRONT Y ALTERNATE RED & BLUE
UPPER COLD FRONT DOT DNA DASHED BLUE LINE

FIGURE 3827.— Designation of fronts on weather maps.

prepared two to four times per day. Knowledge of conditions aloft is of value in estab-
lishing the three-dimensional structure of the atmosphere at any time, and the motions
upon which forecasts are based.

By studying the latest synoptic weather chart and comparing it with previous
charts, a trained meteorologist having a knowledge of local weather peculiarities can
draw certain inferences regarding future weather, and issue a forecast. Weather
forecasts are essentially a form of extrapolation (art. P6). Past changes and present
trends are used to predict future events. In areas where certain sequences follow with
great certainty, the probability of an accurate forecast is very high. In transitional
areas, or areas where an inadequate number of synoptic reports is available, the fore-

WEATHER AND WEATHER FORECASTS 817

casts are less reliable. Forecasts, then, are based upon the principles of probability
(ch. XXIX), and where nature provides low probability, high reliability should not
be expected. In any area, the probability of a given event occurring decreases with
the lead time. Thus, a forecast for six hours after a synoptic chart is drawn should be
more reliable than one for 24 hours ahead. Long-term forecasts for two weeks or a
month in advance are limited to general statements. For example, a prediction is
made as to which areas will have temperatures above or below normal, and how
precipitation will compare with normal, but no attempt is made to state that rainfall
will occur at a certain time and place.

Forecasts are issued for various areas. The national meteorological services of
most maritime nations, including the United States, issue forecasts for ocean areas and
warnings of the approach of storms. The efforts of the various nations are coordi-
nated through the World Meteorological Organization.

3828. Dissemination of weather information is carried out in a number of ways.
Forecasts are widely broadcast by commercial and government radio stations, and
printed in newspapers. Shipping authorities on land are kept informed by telegraph and
telephone. Visual storm warnings are displayed in various ports, and storm warnings
are broadcast by radio.

Through the use of codes, a simplified version of synoptic weather charts is
transmitted to various stations ashore and afloat. Rapid transmission of completed
maps has been made possible by the development of facsimile transmitters and re-
ceivers. This system is based upon detailed scanning, by a photoelectric detector,
of properly illuminated black and white copy. The varying degrees of light intensity
are converted to electric energy which is transmitted to the receiver and converted

back to a black and white presentation.

Complete information on dissemination of weather information by radio is given
in H.O. Pubs. Nos. 118-A and 118-B, Radio Weather Aids. This publication lists
broadcast schedules and weather codes. Information on day and night visual storm
warnings is given in the various volumes of sailing directions and coast pilots.

3829, Interpreting the weather.—The factors which determine weather are numer-
ous and varied. Ever-increasing knowledge regarding them makes possible a contin-
ually improving weather service. However, the ability to forecast is acquired through
study and long practice, and therefore the services of a trained meteorologist should
be utilized whenever available.

The value of a forecast is increased if one has access to the information upon
which it is based, and understands the principles and processes involved. It is some-
times as important to know the various types of weather that might be experienced as
it is to know which of several possibilities is most likely to occur.

At sea, reporting stations are unevenly distributed, sometimes leaving relatively
large areas with incomplete reports, or none at all. Under these conditions, the loca-
tions of highs, lows, fronts, etc., are imperfectly known, and their very existence may
even be in doubt. At such times the mariner who can interpret the observations made
from his own vessel may be able to predict weather during the next 24 hours more
reliably than a trained meteorologist some distance away with incomplete information.

Knowledge of the various relationships given in chapters XXXVII, XXXVIII,
and XXXIX is of value, but only the more elementary principles are presented. Fur-
ther information can be obtained from meteorological publications such as those
listed at the ends of the weather chapters. The information obtained from these
references will provide a background for proper interpretation of individual experience.
If one uses every opportunity to observe and interpret weather sequences, he can
develop knowledge and skill that will serve as a valuable supplement to information

818 WEATHER AND WEATHER FORECASTS

given in weather broadcasts, or to supply information for areas not covered by such
broadcasts.

3830. Influencing the weather.—Meteorological activities are devoted primarily
to understanding weather processes, and predicting future weather. However, as
knowledge regarding cause-and-effect relationships increases, the possibility of being
able to induce certain results by artificially producing the necessary conditions becomes
greater. The most promising results to date have been in the encouraging of precipi-
tation by “seeding” supercooled clouds with powdered dry ice or silver iodide smoke.
The effectiveness of this procedure is controversial. Various methods of decreasing
the intensity of tropical cyclones, or of diverting their courses, have been suggested,
but a satisfactory method has not been devised.

If a way is found to influence weather on a major scale, legal and possibly moral
problems will be created due to conflicting interests.

References

American Meteorological Society. Compendium of Meteorology. Boston, American
Meteorological Society, 1951.

American Meteorological Society. Glossary of Meteorology. Boston, American
Meteorological Society, 1959.

Burgess, C. R. Meteorology for Seamen. Glasgow, Brown, 1950.

Byers, H. R. General Meteorology. 2nd ed. New York, McGraw-Hill, 1944.

Halpine, C. G. A Pilot's Meteorology. 2nd ed. New York, Van Nostrand, 1953.

Knight, A. M. Modern Seamanship. Revised by Capt. John V. Noel, Jr., U.S. Navy.
13th ed. New York, Van Nostrand, 1960.

Neuberger, Hans. Introduction to Physical Meteorology. State College, Pennsylvania
State University, 1951.

Petterssen, Sverre. Introduction to Meteorology. 2nd ed. New York, McGraw-Hill,

1958.
Shaw, Napier. The Drama of Weather. 2nd ed. [London] Cambridge University
Press, 1939.
Tannehill, I. R. Weather Around the World. 2nd ed. Princeton, Princeton University
Press, 1951.

Trewartha,G.T. An Introduction to Climate. 3rd ed. New York, McGraw-Hill, 1953.

U.S. Department of the Navy. Meteorology for Naval Aviators. NAVAER 00-80U-
24. Washington, Chief of Naval Operations, 1958.

U. S. Department of the Navy. U. S. Navy Marine Climatic Atlas of the World,
vol. I, North Atlantic Ocean, NAVAER 50-1C-528; vol. II, North Pacific Ocean,
NAVAER 50-1C-529. |

U.S. Weather Bureau. Preparation and Use of Weather Maps at Sea. Circular R.
4th ed. Washington, U.S. Govt. Print. Off., 1961.

CHAPTER XXXIX
TROPICAL CYCLONES

3901. Introduction.—A tropical cyclone is a violent cyclone (art. 3813) originating
in the tropics. Although it generally resembles the extratropical cyclone originating
in higher latitudes, there are important differences, the principal one being the con-
centration of a large amount of energy into a relatively small area. Tropical cyclones
are infrequent in comparison with middle- and high-latitude storms, but they have a
record of destruction far exceeding that of any other type of storm. Because of their
fury, and the fact that they are predominantly oceanic, they merit the special attention
of all mariners, whether professional or amateur.

Rarely does the mariner who has experienced a fully developed tropical cyclone
at sea wish to encounter a second one. He has learned the wisdom of avoiding them
if possible. The uninitiated may be misled by the deceptively small size of a tropical
cyclone as it appears on a weather map, and by the fine weather experienced only a
few hundred miles from the reported center of such a storm. The rapidity with which
the weather can deteriorate with approach of the storm, and the violence of the fully
developed tropical cyclone, are difficult to visualize if they have not been experienced.

3902. Areas of occurrence.—Tropical cyclones occur almost entirely in six rather
distinct regions, four in the northern hemisphere and two in the southern hemisphere,
as shown in figure 3902. The name by which such a disturbance is commonly known
varies somewhat with the locality, as follows:

Region I. North Atlantic (West Indies, Caribbean Sea, Gulf of Mexico, and
waters off the East Coast of the United States). A tropical cyclone with winds of 64
knots or greater is called a hurricane.

1209501 EES CEEE FT
7 E

90° 120° 150° 180° 150° 120°

FIGURE 3902.— Areas in which tropical cyclones occur, and their approximate tracks.
819

820 TROPICAL CYCLONES

Region II. Southeastern North Pacific (waters off west coast of Mexico and
Central America). The name hurricane is applied, as in Region I.

Region III. Far East (the entire area west of the Mariana and Caroline Islands,
across the Philippines and the China Sea, and northeastward to China and Japan).
A fully developed storm with winds of 60 knots or greater is called a typhoon or, locally
in the Philippine Islands, a baguio.

Region IV. A. Arabian Sea. B. Bay of Bengal. In these areas the storms
are called cyclones.

Region V. South Indian Ocean (in the vicinity and to the east of Madagascar).
As in Region IV, the tropical cyclone is called a cyclone.

Region VI. A. Australian waters (to longitude 160°E). B. South Pacific (the
western portion, east of longitude 160? E). Several names are applied in this area,
cyclone being the most common. One originating in the Timor Sea and moving south-
west and then southeast across the interior of northwestern Australia is called a willy-
willy. One to the east of Australia may be called a hurricane.

The only tropical ocean area in which tropical cyclones have not been encountered
at some time is the South Atlantic.

As a tropical cyclone moves out of the tropics to higher latitudes, it normally
loses energy slowly, expanding in area until it gradually dissipates or acquires the
characteristics of extratropical cyclones. At any stage, a tropical cyclone normally
loses energy at a much faster rate if it moves over land.

3903. Season and frequency of occurrence.—In Region III tropical cyclones may
be encountered in any month of the year, though less frequently in winter than in
summer. In the other regions, they occur only in the summer or autumn of that area,
as shown in figure 3903. The total number for the northern hemisphere reaches a sharp
peak in September. In general, this is the month of greatest frequency in each of the
first four regions, although the Far East reaches its maximum in August, and in the
Arabian Sea there are two peaks, one in June, and the other in late October. In the
southern hemisphere, the maximum number is not as sharply peaked, being distributed
nearly equally over January, February, and March, the summer season of that
hemisphere.

The occurrence of tropical cyclones in an area is not as regular as might be inferred
from a curve such as any of those of figure 3903, which are averages over a great many
years. Even near the peak of a tropical cyclone season in any area there are periods
when no tropical storms are observed. At the other extreme, as many as three hurri-
canes have been in progress at the same time in the North Atlantic, and as many as four
typhoons in the Far East. The average total number of tropical cyclones occurring
per year is 43 in the Northern Hemisphere and 13 in the Southern Hemisphere, or 56
throughout the world. However, the actual number in an area varies greatly from year
to year. In the North Atlantic, where the greatest irregularity occurs, there have been
as few as two and as many as 21 in a year, although the average number is seven. In
the Far East, the number has varied from 13 to 25.

3904. Storm tracks.— Tropical cyclones form over the ocean, in low latitudes. As
one forms, it drifts slowly westward with the current of free air in which it forms. As
it reaches the edge of a subtropical anticyclone, the storm, together with the general
mass of air, drifts farther from the equator, in many instances curving poleward and
then eastward with the winds of the general circulation (art. 3804). In general, a
tropical cyclone moves very slowly at first, its speed varying from about five to 20
knots. The speed gradually increases as the storm progresses, and may, in a few
instances, reach a value of 50 knots or more when the storm reaches temperate latitudes.

m

TROPICAL CYCLONES 821

The average track varies somewhat as the season progresses, and individual storm
tracks may differ widely from the average. Region I, the North Atlantic, is typical of
the changes. In August, about 80 percent originate in the southern North Atlantic
and the eastern Caribbean, and about 20 percent in the western Caribbean and Gulf of
Mexico. About 60 percent curve toward theright, roughly paralleling the coast of North
America, and about 40 percent continue on westward, as shown in figure 3904a.

By the peak of the season, in September, the number forming in the southern North
Atlantic and eastern Caribbean has dropped to 70 percent, but the number curving to-

10

KEY

REGION = |—NORTH ATLANTIC
8 REGION II—5S.E. N. PACIFIC

à REGION III—FAR EAST
REGION IV—ARABIAN SEA

BAY OF BENGAL
REGION V—S. INDIAN OCEAN
7 REGION VI—W. OF 160°E.

E. OF 160°E.
NORTHERN HEMISPHERE
SOUTHERN HEMISPHERE

JANUARY
FEBRUARY
AUGUST
SEPTEMBER
NOVEMBER
DECEMBER

FIGURE 3903.—Average number of tropical disturbances per month in the various regions.

ward the right has increased to about the same percentage. The normal track has
moved a little farther offshore in the lower latitudes, but has straightened somewhat
so as to pass over eastern Newfoundland. This is shown in figure 3904b.

By October, the number originating in the southern North Atlantic and eastern
Caribbean has dropped to 50 percent; and 80 percent of them curve, but at a point
farther west, and more sharply, as shown in figure 3904c. By November, the change
has been somewhat back toward the condition in September. As the season progresses,
the deviation from average becomes greater and more common.

TROPICAL CYCLONES

80° 70° 50°

FIGURE 3904a.—Average North Atlantic storm tracks in August.

90° 80°

30°

409 `

20*

10°

3 10°
60° 50 40° 30°

Figure 3904b.— Average North Atlantic storm tracks in September.

TROPICAL CYCLONES 823

70° 60°

50°

FIGURE 3904c.— Average North Atlantic storm tracks in October.

The differences, both in the averages and in individual tracks, are due to differ-
ences in the pressure pattern, particularly the location and movement of highs, which
any cyclone tends to avoid.

3905. Life cycle.—The life cycle of a tropical cyclone may be considered to consist
of four rather distinct stages, as follows:

Formation. A cyclonic circulation (art. 3813) develops, and wind speed increases
to hurricane force (64 knots) over a restricted area near the center. Atmospheric
pressure drops to about 1,000 millibars (29.53 inches). This stage may occupy several
days, or may be completed in a period of 12 hours or less.

Immaturity. The pressure at the center continues to fall (the storm ''deepens”)
and the wind speed increases, but the storm is still confined to a small area.

Maturity. The pressure at the center remains about the same, but the area of
hurricane winds expands, to a radius of perhaps 150 to 200 miles, with winds of gale
force (app. R) extending to perhaps 300 miles. Individual storms may differ con-
siderably from these averages.

Decay. The area continues to increase, the pressure at the center rises, and the
wind speed decreases. The storm loses its tropical characteristics and gradually
dissipates, a process that may require several days over an ocean area. Over land the
decay is more rapid.

3906. Origin and development.—Tropical cyclones originate between the doldrums
(art. 3805) and the zones of the strongest trade winds. This accounts, at least partly,
for the absence of such storms in the South Atlantic, for the Atlantic doldrums remain
several degrees north of the equator except for occasional brief periods.

Some of the details regarding the formation of tropical cyclones are not understood,
but the fact that such storms form only over water, and dissipate rapidly if they en-

824 TROPICAL CYCLONES

counter land, probably indicates the need for a supply of water vapor. Over the
tropical ocean this is abundantly available in the lower portion of the atmosphere.
When a low develops over tropical oceans, hot, vapor-laden air flows in from adjacent
regions. This air ascends near the center of the low, and condensation occurs. Each
pound of water vapor that condenses into cloud or rain liberates approximately 970
British thermal units (art. 3711) of heat. This heat warms the surrounding air, thus
increasing further the instability, and hastening the ascent of the air. Thus, the pressure
continues to drop and the winds increase in speed, bringing in an increasing quantity
of warm, moist air from the regions surrounding thelow. Atsome height, the ascending
air flows outward from the center of the cyclonic circulation. This process of inward
flow, rising air current, condensation, warming, and high-level outflow causes the low
to deepen and the wind speed to increase. Thus, as long as conditions remain suitable,
the storm grows more intense.

While the actual mechanics of tropical cyclone formation are somewhat more
involved than just described, the essential steps are given. Several theories exist
regarding the details of initial formation of the low pressure area. Dropping pressure
at the surface due to disturbances at high levels of the atmosphere; interaction of two
air streams to produce a cyclonic eddy, causing convergence of surface air and the
resulting ascent; and the joining of minor disturbances in the wind and pressure
patterns in the atmosphere are all considered possibilities. The process is probably
begun by several factors which combine in just the right relationship.

When it becomes fully developed, a tropical cyclone covers a well-defined area,
more or less circular in shape, within which the atmospheric pressure decreases rapidly
toward the center. This decrease of pressure may amount to a maximum of 0.01 or
even 0.02 inch per mile. Because of the rapid decrease of pressure with distance, the
wind speed is high, being greatest at the regions of steepest pressure gradient.

At the center of the storm, there is normally an area five to 30 miles in diameter
(most often ten to 15 mules) within which the wind speed drops to a relative calm,
usually ten to 15 knots or less. This is the eye of the storm. Ascending air causes
the dense cover of clouds to give way to a thin layer of low clouds with holes through
which the sun may shine. Around the edge of the eye, the wind speed increases from
the relative calm to the full fury of maximum speed within a distance of a few feet.
Here the heavy cloud seems thickest, and the torrential rains surrounding the central
area appear concentrated. This is the wall of the eye. When a tropical cyclone moves
to higher latitude, its eye becomes less clearly defined as the maximum wind moves
outward from the center, the wall of the eye becomes more indistinct, and its cloud
cover increases.

3907. Locating and tracking a tropical cyclone.—By means of radio, organized
meteorological services collect weather observations daily from island stations, ships
at sea, and aircraft. When a tropical cyclone is located, usually in its early formative
stage, it is followed closely. In the North Atlantic, aircraft of the U. S. Navy and
U.S. Air Force, in cooperation with the Weather Bureau, make frequent flights to the
vicinity of such storms to provide information needed for tracking the hurricane and
determining its intensity. Bulletins are broadcast to ships several times daily, giving
information on each storm’s location, intensity, and movement. As a further aid,
the mariner may obtain weather reports by radio directly from other ships in the vicinity
of a tropical cyclone. Radar may be used to follow the movements of the precipitation
areas when they are within range.

Although these aids normally prove adequate for locating and avoiding a tropical
cyclone, knowledge of the appearance of the sea and sky in the vicinity of such a storm
is useful to the mariner. This information is given in article 3908.

TROPICAL CYCLONES 825

3908. The passage of a tropical cyclone at sea is an experience not soon to be
forgotten.

An early indication of the approach of such a storm is the presence of a long swell.
In the absence of a tropical cyclone, the crests of swell in the deep waters of the Atlantic
pass at the rate of perhaps eight per minute. Swell generated by a hurricane is
about twice as long, the crests passing at the rate of perhaps four per minute. Swell
may be observed several days before arrival of the storm.

When the storm center is 500 to 1,000 miles away, the barometer usually rises a
little, and the skies are relatively clear. Cumulus clouds, if present at all, are few in
number and their vertical development appears suppressed. The barometer usually
appears restless, pumping up and down a few hundredths of an inch.

As the tropical cyclone comes nearer, a cloud sequence begins which resembles
that associated with the approach of a warm front in middle latitudes (art. 3812).
Snow-white, fibrous “mare's tails" (cirrus) appear when the storm is about 300 to
600 miles away. Usually these seem to converge, more or less, in the direction from
which the storm is approaching. This convergence is particularly apparent at about
the time of sunrise and sunset.

Shortly after the cirrus appears, but sometimes before, the barometer starts a
long, slow fall. At first the fall is so gradual that it only appears to alter somewhat
the normal daily cycle (two maxima and two minima in the tropics). As the rate of
fall increases, the daily pattern is completely lost in the more or less steady fall.

The cirrus becomes more confused and tangled, and then gradually gives way to a
continuous veil of cirrostratus. Below this veil, altostratus forms, and then strato-
cumulus (art. 3714). These clouds gradually become more dense, and as they do so,
the weather becomes unsettled. A fine, mist-like rain begins to fall, interrupted from
time to time by showers. The barometer has fallen perhaps a tenth of an inch.

As the fall becomes more rapid, the wind increases in gustiness, and its speed
becomes greater, reaching a value of perhaps 22 to 40 knots (Beaufort 6-8). On the
horizon appears a dark wall of heavy cumulonimbus (art. 3714), the bar of the storm.
Portions of this heavy cloud become detached from time to time and drift across the
sky, accompanied by rain squalls and wind of increasing speed. Between squalls, the
cirrostratus can be seen through breaks in the stratocumulus.

As the bar approaches, the barometer falls more rapidly and wind speed increases.
The seas, which have been gradually mounting, become tempestuous. Squall lines,
one after the other, sweep past in ever increasing number and intensity.

With the arrival of the bar, the day becomes very dark, squalls become virtually
continuous, and the barometer falls precipitously, with a rapid increase in wind speed.
The center may still be 100 to 200 miles away in a fully developed tropical cyclone.
As the center of the storm comes closer, the ever-stronger wind shrieks through the
rigging and about the superstructure of the vessel. As the center approaches, rain
falls in torrents. The wind fury increases. The seas become mountainous. The tops
of huge waves are blown off to mingle with the rain and fill the air with water. Objects
at a short distance are not visible. Even the largest and most seaworthy vessels become
virtually unmanageable, and may sustain heavy damage. Less sturdy vessels do not
survive. Navigation virtually stops as safety of the vessel becomes the prime con-
sideration. The awesome fury of this condition can only be experienced. Words are
inadequate to describe it.

If the eye of the storm passes over the vessel, the winds suddenly drop to a breeze
as the wall of the eye passes. The rain stops, and the skies clear sufficiently to permit
the sun to shine through holes in the comparatively thin cloud cover. Visibility
improves. Mountainous seas approach from all sides, apparently in complete confu-

826 TROPICAL CYCLONES

sion. The barometer reaches its lowest point, which may be an inch and a half or two
inches below normal in fully developed tropical cyclones. As the wall on the opposite
side of the eye arrives, the full fury of the wind strikes as suddenly as it ceased, but
from the opposite direction. The sequence of conditions that occurred during approach
of the storm is reversed, and pass more quickly, as the various parts of the storm are
not as wide in the rear of a storm as on its forward side.

Typical cloud formations associated with a hurricane are shown in figure 3908.

FIGURE 3908.—Typical hurricane cloud formations.

3909. Locating the center of a tropical cyclone.—If intelligent action is to be
taken to avoid the full fury of a tropical cyclone, early determination of its location and
direction of travel relative to the vessel is essential. The bulletins and forecasts are
an excellent general guide, but they are not infallible and may be sufficiently in
error to induce a mariner in a critical position to alter course so as to unwittingly increase
the danger to his vessel. Often it is possible, using only those observations made
aboard ship, to obtain a sufficiently close approximation to enable the vessel to ma-
neuver to the best advantage.

As stated in article 3908, the presence of an exceptionally long swell is usually
the first visible indication of the existence of a tropical cyclone. In deep water it
approaches from the general direction of origin (the position of the storm center when
the swell was generated). However, in shoaling water this is a less reliable indication
because the direction is changed by refraction, the crests being more nearly parallel
to the bottom contours (art. 3307).

When the cirrus clouds appear, their point of convergence provides an indication
of the direction of the storm center. If the storm is to pass well to one side of the
observer, the point of convergence shifts slowly in the direction of storm movement.
If the storm center will pass near the observer, this point remains steady. When the
bar (art. 3908) becomes visible, it appears to rest upon the horizon for several hours.
The darkest part of this cloud is in the direction of the storm center. If the storm is
to pass to one side, the bar appears to drift slowly along the horizon. If the storm is
heading directly toward the observer, the position of the bar remains fixed. Once
within the area of the dense, low clouds, one should observe their direction of move-

PT» T

H

v + / Mem Term

TROPICAL CYCLONES 827

ment, which is almost exactly along the isobars, with the center of the storm being 90°
from the direction of cloud movement (left of direction of movement in the northern
hemisphere, and right in the southern hemisphere).

The winds are probably the best guide to the direction of the center of a tropical
cyclone. The circulation is cyclonic (art. 3813), but because of the steep pressure
gradient near the center, the winds there blow with greater violence and are more
nearly circular than in extratropical cyclones.

According to Buys Ballot’s law (art. 3813) an observer who faces into the wind
has the center of the low pressure on his right in the northern hemisphere, and on his
left in the southern hemisphere, and in each case somewhat behind him. If the wind
followed circular isobars exactly, the center would be exactly eight points, or 90°, from
dead ahead when facing into the wind. However, the track of the wind is usually
inclined somewhat toward the center, so that the angle from dead ahead varies be-
tween perhaps 8 and 12 points (90° to 135%). The inclination varies in different parts
of the same storm. It is least in front of the storm, and greatest in the rear, since the
actual wind is the vector sum of that due to the pressure gradient and the motion of

Wind Arrow

Wind Arrow

Wind Arrow

Wind Arrow

Wind Arrow

Wind Arrow

1 pt.=11%*

Figure 3909a.—Approximate relationship of wind to isobars and storm center in the northern
hemisphere.

828 TROPICAL CYCLONES

the storm along the track. A good average is perhaps ten points in front, and 11 or 12
points in the rear. These values apply when the storm center 1s still several hundred
miles away. Closer to the center, the wind blows more nearly along the isobars, the
inclination being reduced by one or two points at the wall of the eye. Since wind direc-
tion usually shifts temporarily during a squall, its direction at this time should not be
used for determining the position of the center. The approximate relationship of wind
to isobars and storm center in the northern hemisphere is shown in figure 3909a.

When the center is within radar range, it might be located by this equipment.
However, since the radar return is predominantly from the rain, results can be decep-
tive, and other indications should not be neglected. Figure 3909b shows a typical
radar PPI presentation of a tropical cyclone.

Distance from the storm center is more difficult to determine than direction.
Radar is perhaps the best guide. However, the rate of fall of the barometer is some
indication. If a vessel is hove-to in front of a storm which is advancing directly
toward it, the fall of pressure per hour might be about as shown in figure 3909c. How-
ever, this is an imperfect indication, for the rate of fall may be quite erratic, and will
vary somewhat with the depth of the low at the center, the speed of the storm center
along its track, and the stage in the life cycle of the storm. The usefulness of this
information is further reduced by the fact that a vessel would not normally remain
hove-to in the path of a tropical cyclone.

3910. Maneuvering to avoid the storm center.—The safest procedure with re-
spect to tropical cyclones is to avoid them. If action is taken sufficiently early, this
is simply a matter of setting a course that will take the vessel well to one side of the
probable track of the storm, and then continuing to plot the positions of the storm
center, as given in the weather bulletins, revising the course as needed.

However, such action is not always possible. If one finds himself within the storm
area, the proper action to take depends in part upon his position relative to the storm
center and its direction of travel. It is customary to divide the circular area of the
storm into two parts. In the northern hemisphere, that part to the right of the storm
track (facing in the direction toward which the storm is moving) is called the dangerous
semicircle. It is considered dangerous because (1) the actual wind speed is greater
than that due to the pressure gradient alone, since it is augmented by the forward
motion of the storm, and (2) the direction of the wind and sea is such as to carry a vessel
into the path of the storm (in the forward part of the semicircle). The part to the left
of the storm track is called the navigable semicircle. In this part, the wind is decreased
by the forward motion of the storm, and the wind blows vessels away from the storm
track (in the forward part). Because of the greater wind speed in the dangerous semi-
circle, the seas are higher here than in the navigable semicircle. In the southern hemi-
sphere, the dangerous semicircle is to the left of the storm track, and the navigable
semicircle is to the right of the storm track.

A plot of successive positions of the storm center should indicate the semicircle in
which a vessel is located. However, if this is based upon weather bulletins, it is not a
reliable guide because of the lag between the observations upon which the bulletin is
based and the time of reception of the bulletin, with the ever present possibility of a
change in the direction of motion of the storm. The use of one’s radar eliminates this
lag, but the return is not always a true indication of the center. Perhaps the most
reliable guide is the wind. Within the cyclonic circulation, a veering wind (one changing
direction to the right in the northern hemisphere and to the left in the southern hemi-
sphere) indicates a position in the dangerous semicircle, and a backing wind (one chang-
ing in a direction opposite to a veering wind) indicates a position in the navigable semi-
circle. However, if a vessel is underway, its motion should be considered. If it is

Zn» 1

TROPICAL CYCLONES 829

outrunning the storm or pulling
rapidly toward one side (which
is not difficult during the early
stages of a storm, when its
speed is low), the opposite effect
occurs. This should usually be
accompanied by a rise in atmos-
pheric pressure, but if motion
of the vessel is nearly along an
isobar, this may not be a reliable
indieation. If in doubt, the
safest action is usually to stop
long enough to determine defi-
nitely the semicircle. The loss
in valuable time may be more
than offset by the minimizing
of the possibility of taking the
wrong action and increasing the
danger Eo the Vessel. SE FiGURE 3909b.— Typical radar PPI presentation of a tropical
wind direction remains steady cyclone.

(for a vessel which is stopped),

with increasing speed and falling barometer, the vessel is in or near the path of the
storm. If it remains steady with decreasing speed and rising barometer, the vessel
is on the storm track, behind the center.

The first action to take if one finds himself within the cyclonic circulation, is to
determine the position of his
vessel with respect to the storm
center. While the vessel can
still make considerable way
through the water, a course
should be selected to take it as
far as possible from the center.
If the vessel can move faster
than the storm, it is a relatively
simple matter to outrun the
storm if sea room permits. But
when the storm is faster, the
solution is not as simple. In
this case, the vessel, if ahead
of the storm, will approach
nearer to the center. The prob-
lem is to select a course that
will produce the greatest possi-
ble minimum distance. This is
best determined by means of a
relative movement plot, as
shown in the following example
solved on a maneuvering board
(arta 1212):

Example.—A tropical cy-

*URE 3909c.— ical average pressure drop as tropical A í À
C... RE cd ; clone is estimated to be moving

FALL OF BAROMETER PER HOUR

00 50 100 150 200 250 300
MILES FROM CENTER

830 TROPICAL CYCLONES

in direction 320° at 19 knots. Its center bears 170°, at an estimated distance of 200
miles from a vessel which has a maximum speed of 12 knots. |

Required.—(1) The course to steer at 12 knots to produce the greatest possible
minimum distance between the vessel and the storm center.

(2) The distance of the storm center at nearest approach.

(3) Elapsed time until nearest approach.

Solution (fig. 3910).—Consider the vessel remaining at the center of the plot
throughout the solution, as on a radar PPI.

(1) Plot point C at a distance of 200 miles (scale 20:1) in direction 170? from the
center of the diagram, to locate the position of the storm center relative to the vessel.
From the center of the diagram, draw RA, the speed vector of the storm center, in
direction 320?, speed 19 knots (scale 2:1). From A draw a line tangent to the 12-knot
speed circle (labeled 6 at scale 2:1) on the side opposite the storm center. From the

FicuRE 3910.— Solution to determine course for avoiding storm center.

TROPICAL CYCLONES 831

center of the diagram draw a perpendicular to this tangent line, locating point B.
The line RB is the required speed vector for the vessel. Its direction, 011°, is the
required course.

(2) The path of the storm center relative to the vessel, will be along a line from C in
the direction BA, if both storm and vessel maintain course and speed. The point of
nearest approach will be at D, the foot of a perpendicular from the center of the diagram.
This distance, at scale 20:1, is 187 miles.

(3) The length of the vector BA (14.8 knots) is the speed of the storm with respect
to the vessel. Mark this on the lowest scale of the nomogram at the bottom of the
diagram. "The relative distance CD is 72 miles, by measurement. Mark this (scale
10:1) on the middle scale at the bottom of the diagram. Draw a line between the two
points and extend it to intersect the top scale at 29.2 (292 at 10:1 scale). The elapsed
time is therefore 292 minutes, or 4 hours 52 minutes, or 5 hours approximately.

Answers.—(1) C 011°, (2) D 187 mi., (3) t 5^ (approximately).

The storm center will be dead astern at its nearest approach.

As a very general rule, for a vessel in the northern hemisphere, safety lies in placing
the wind on the starboard bow in the dangerous semicircle and on the starboard quarter
in the navigable semicircle. If on the storm track ahead of the storm, the wind should
be put about two points on the starboard quarter until the vessel is well within the
navigable semicircle, and the rule for that semicircle then followed. A study of figure
3909a should indieate why these headings are desirable. In the southern hemisphere
the same rules hold, but with respect to the port side. With a faster than average vessel,
the wind can be brought a little farther aft in each case. However, as the speed of the
storm increases along its track, the wind should be brought farther forward. If land
interferes with what would otherwise be the best maneuver, the solution should be
altered to fit the circumstances. If the speed of a vessel is greater than that of the
storm, it is possible for the vessel, if behind the storm, to overtake it. In this case, the
only action usually needed is to slow enough to let the storm pull ahead.

In all cases, one should be alert to changes in the direction of movement of the
storm center, particularly in the area where the track normally curves toward the pole.
If the storm maintains its direction and speed, the ship's course should be maintained
as the wind shifts.

If it becomes necessary for a vessel to heave to, the characteristics of the vessel
should be considered. A power vessel is concerned primarily with damage by direct
action of the sea. A good general rule is to heave to with head to the sea in the
dangerous semicircle or stern to the sea in the navigable semicircle. This will result
in greatest amount of headway away from the storm center, and least amount of leeway
toward it. If a vessel handles better with the sea astern or on the quarter, it may be
placed in this position in the navigable semicircle or in the rear half of the dangerous
semicircle, but never in the forward half of the dangerous semicircle. It has been
reported that when the wind reaches hurricane speed and the seas become confused,
some ships ride out the storm best if the engines are stopped, and the vessel is permitted
to seek its own position. In this way, it is said, the ship rides with the storm instead
of fighting against it.

In a sailing vessel, while attempting to avoid a storm center, one should steer
courses as near as possible to those prescribed above for power vessels. However, if
it becomes necessary for such a vessel to heave to, the wind is of greater concern than
the sea. A good general rule always is to heave to on whichever tack permits the
shifting wind to draw aft. In the northern hemisphere this is the starboard tack in

332 TROPICAL CYCLONES

the dangerous semicircle and the port tack in the navigable semicircle. In the southern
hemisphere these are reversed. |

While each storm requires its own analysis, and frequent or continual resurvey of
the situation, the general rules for a steamer may be summarized as follows:

NORTHERN HEMISPHERE

Right or dangerous semicircle.—Bring the wind on the starboard bow (045° rela-
tive), hold course and make as much way as possible. If obliged to heave to, do so
with head to the sea.

Left or navigable semicircle.—Bring the wind on the starboard quarter (135° rela-
tive), hold course and make as much way as possible. If obliged to heave to, do so
with stern to the sea.

On storm track, ahead of center.—Bring the wind two points on the starboard
quarter (157°5 relative), hold course and make as much way as possible. When well
within the navigable semicircle, maneuver as indicated above.

On storm track, behind center.—Avoid the center by the best practicable course,
keeping in mind the tendency of tropical cyclones to curve northward and eastward.

SOUTHERN HEMISPHERE

Left or dangerous semicircle.—Bring the wind on the port bow (315? relative), hold
course and make as much way as possible. If obliged to heave to, do so with head
to the sea.

Right or navigable semicircle.—Bring the wind on the port quarter (225° relative),
hold course and make as much way as possible. If obliged to heave to, do so with
stern to the sea.

On storm track, ahead of center.—Bring the wind two points on the port quarter
(20275 relative), hold course and make as much way as possible. When well within
the navigable semicircle, maneuver as indicated above.

On storm track, behind center.—Avoid the center by the best practicable course,
keeping in mind the tendency of tropical cyclones to curve southward and eastward.

Whenever a tropical cyclone is encountered, the wise procedure is to begin pre-
paring the vessel for heavy weather in sufficient time to permit thorough preparation,
so that damage may be minimized. One should be particularly careful to keep free
surfaces of liquids to a minimum.

3911. Coastal effects.—' The high winds of a tropical cyclone inflict widespread
damage when such a storm leaves the ocean and crosses land. Aids to navigation may
be blown out of position or destroyed. Craft in harbors, unless they are properly
secured, drag anchor or are blown against obstructions. Ashore, trees are blown over,
houses are damaged, power lines are blown down, etc. The greatest damage usually
occurs in the dangerous semicircle a short distance from the center, where the strongest
winds occur. As the storm continues on across land, its fury subsides faster than it
would if it had remained over water.

Along the coast, particularly, greater damage may be inflicted by water than by
the wind. There are at least four sources of water damage. First, the unusually high
seas generated by the storm winds pound against shore installations and craft in their
way. Second, the continued blowing of the wind toward land causes the water level
to increase perhaps three to ten feet above its normal level. This storm tide, which
may begin when the storm center is 500 miles or even farther from the shore, gradually
increases until the storm passes. The highest storm tides are caused by a slow-moving
tropical cyclone of large diameter, because both of these effects result in greater dura-
tion of wind in the same direction. The effect is greatest in a partly enclosed body

TROPICAL CYCLONES 833

of water, such as the Gulf of Mexico, where the concave coastline does not readily
permit the escape of water. It is least on small islands, which present little obstruction
to the flow of water. Third, the furious winds which blow around the wall of the eye
create a ridge of water called a storm wave, which strikes the coast and often inflicts
heavy damage. The effect is similar to that of a seismic sea wave, caused by an earth-
quake in the ocean floor. Both of these waves are popularly called tidal waves. Storm
waves of 20 feet or more have occurred. About three or four feet of this is due to the
decrease of atmospheric pressure, and the rest to winds. Like the damage caused by
wind, that due to high seas, the storm tide, and the storm wave is greatest in the
dangerous semicircle, near the center. The fourth source of water damage is the heavy
rain that accompanies a tropical cyclone. This causes floods that add to the damage
caused in other ways.

When proceeding along a shore recently visited by a tropical cyclone, a navigator
should remember that time is required to restore aids to navigation which have been
blown out of position or destroyed. In some instances the aid may remain but its
light, sound apparatus, or radiobeacon may be inoperative. Landmarks may have
been damaged or destroyed.

References

Burgess, C. R. Meteorology for Seamen. Glasgow, Brown, 1950.

Byers, H. R. General Meteorology. 2nd ed. New York, McGraw-Hill, 1944.

Colon, J. A. “A Study of Hurricane Tracks for Forecasting Purposes.” Monthly

feather Review. March 1953. Washington, U. S. Govt. Print. Off. |

McDonald, W. F. “On a Hypothesis Concerning the Normal Development and
Disintegration of Tropical Hurricanes.” Monthly Weather Review. January
1942. Washington, U. S. Govt. Print. Off.

Nimitz, Chester W., et. al. “Typhoon Doctrine." U.S. Naval Institute Proceedings,
vol. 82, No. 1 (January 1956), pp. 83-93.

Riehl, Herbert. Tropical Meteorology. New York, McGraw-Hill, 1954.

Tannehill, I. R. Hurricanes. 9th ed. Princeton, Princeton University Press, 1956.

U. S. Weather Bureau. The Hurricane. Washington, U. S. Govt. Print. Off., 1956.

M i ntis: PARI A
De at «kis fiat

"ie

H

» R ` ! d * = M R I
ee ermal ` ` Å
1 Kë £ y LA i PUN wn »
M us EL ve 1! Wo velt) 74 "m Bd "LA VY Á one’s
ei LL INM- a "dns Y uma y ka Hat uf AR 195 K - Kit n

a
BE nat? ada olun QUA

T L€ ' y 00) t vt *: i 4 otf
ews rs gati kb el ! CH Li | s. fr
4 Mol on ml’. te
+4 -
D V P LI
P |
|
:
H
i 4 4
l
J
2 e

PART EIGHT
HY DROGRAPHY

PART EIGHT

HYDROGRAPHY

CHAPTER XL. Instruments for Hydrographic Surveying

CHAPTER XLI. Hydrographic Surveying
CHAPTER XLII. Oceanic Soundings
CHAPTER XLIII. Photogrammetry
CHAPTER XLIV. Production of Nautical Charts

Page
837
848
868
874
886

CHAPTER XL
INSTRUMENTS FOR HYDROGRAPHIC SURVEYING

4001. Introduction.— Although the expression “hydrographic surveying” denotes
investigation of water areas to obtain information for use in making nautical charts,
land surveying methods are frequently used to establish points on shore from which
positions of all hydrographic observations such as soundings, currents, etc., can be
related. Therefore, this chapter describes such instruments as the astrolabe, theodo-
lite, level, and special drafting equipment, as well as tide gages, current meters, and
other instruments directly associated with hydrography. Instruments used in hydro-
graphic surveying, but described elsewhere, include the sextant (ch. XV), echo sounder
(art. 619), and electronic equipment (ch. XIII). In general, surveying instruments are
characterized by a high order of accuracy, as compared with navigation instruments.

4002. Astrolabe.—Unlike the earlier instrument of the same name (art. 124),
the modern astrolabe is used in hydrographic surveying to determine the instant at
which various celestial bodies arrive at a preselected altitude. From a number of such

FicGuRE 4002a.—A prismatic astrolabe.

observations, the position of the instrument can be calculated. Astrolabes now avail-
able use an altitude of 45° or 60°.

As its name implies, the prismatic astrolabe (fig. 4002a) depends upon an accurately-
ground prism to maintain the fixed angle of observation. In addition, the prism per-
mits the observation of a second image of a star by reflection from an artificial horizon,
which is a small pan of mercury placed below the prism. In figure 4002b, a light ray
(R) from a star enters directly the upper surface of the prism and is reflected through
the horizontal observing telescope. A parallel ray (R’) from the same star is reflected
from the mercury surface, enters the lower surface of the prism, and is then reflected
through the telescope. Since the latter image is a doubly reflected one, its apparent
motion will be opposite that of the former (fig. 4002b, rays (a) and (a’) and inset (1)).
When the direct and reflected light rays are perpendicular to the upper and lower
surfaces of the prism, respectively, the two images are coincident and the star is at
the altitude fixed by the angle between the surfaces of the prism. i

In practice, the prism is turned slightly on an axis coincident with the telescope
axis so that the images will, at the fixed altitude, be side by side on a horizontal line

837

838 INSTRUMENTS FOR HYDROGRAPHIC SURVEYING

PRISMATIC ASTROLABE OPTICS

R and R’ are parallel light rays from star
f is focal plane of objective lens (1) Star I z

Before Passage

30x FINDER

w
=
R
o
ul
=
a
o

(a^)
(b) (b^)
(a)
80x OBSERVING SEES
(2) Star Images
MERCURY HORIZON At Fixed Altitude

Passage

FIGURE 4002b.— Optics of the prismatic astrolabe.

(fig. 4002b, rays (b) and (b’) and insert (2)) rather than coincident. This permits
easier, more accurate observation.

In addition to the basic parts already mentioned, the prismatic astrolabe is
provided with level bubbles and three leveling screws to adjust it to the horizontal.
For orienting to north and setting at desired azimuths, it is equipped with a mag-
netic compass and an azimuth circle. Adjusting screws are provided for collima-
tion; that is, making the vertical surface of the
prism perpendicular to the axis of the telescope.
There is also an erecting screw which rotates the
prism about the axis of the telescope. Flash-
light batteries supply power to illuminate the
azimuth circle and reticle, the intensity of the
latter being controlled by a rheostat.

A prism actuated by a lever deflects the light
rays upward to a 30-power, wide field-of-view
eyepiece to facilitate finding the star. Once the
star is located, final observations are made through
the 80-power observing eyepiece. Accessories
for screening the mercury from wind and dust,
and equipment for cleaning the surface of the
mercury are included with the instrument.

The pendulum astrolabe (fig. 4002c) fixes
the observation altitude by directing the light
rays from a star down a 60° objective tube to a
pendulum-supported horizontal mirror, from which
it is reflected up a 60° eyepiece tube. Thus, in
a sense, it is a telescope bent at 60° with a
FIGURE 4002c.—A pendulum astrolabe. pendulum mirror to reflect the light rays accord-

ingly (fig. 4002d). Since only one star image
is seen, the exact time of star passage is noted as being the mean of the times at
which it passes a set of horizontal cross hairs.

In addition to the 80-power observing telescope, it has an 11-power finder tele-

scope. This instrument also has internal illumination and is provided with means for
leveling and setting in azimuth.

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING 839

4903. Timing equipment.—
The timing equipment used in ri} PENDULUM ASTROLABE OPTICS
conjunction with astrolabes : f is focal plane of objective
consists of a chronometer, a R is ray oleh from star
radio, a chronograph, and a
break-circuit key (fig. 4003).
The chronometer is set to run
on sidereal time and is con-
nected through an amplifier to
the chronograph, which records
a tick mark on moving paper at
each one-second break except
the 59th second of every minute. (a) Star Image At First Crosswire
This is omitted so that the be- a wire
ginning of each minute can be
easily identified on the record.

The radio, also, is connect-
ed to the chronograph recorder
through the amplifier, and is
used to receive standard time sig-
nals for determining chronom-
eter correction and rate. The
break-circuit key is tapped by
the observer at the instant of
star passage, making a tick
mark on the chronograph paper.
The chronometer time of star
passage can be scaled off the
chronograph record. By appli-
cation of chronometer correc-
tion and rate, one can determine FīcuRe 4003.— Timing equipment.
the GM'T of the observation.

4004. Theodolite.— A theodolite is an instrument designed to measure precise
horizontal and vertical angles. Thus, it can be used for determining the bearing
(called “azimuth” by surveyors) of a line by observing the angle between that line and
the azimuth line of a star. It can be used to measure the angles in a triangulation net,
and to measure vertical angles for the trigonometric computation of elevations.

The direction theodolite (fig. 4004a) consists essentially of two graduated circles
(one horizontal and one vertical), equipment for leveling and centering the instrument,
an observing telescope, and an eyepiece for reading the circles. Horizontal angles can
be read directly to the nearest 0.2 second of arc on the instrument illustrated. A smaller,
lighter model can be read directly to the nearest second of arc, and tenths can be
estimated.

Both circles are completely enclosed, and are read at one eyepiece through a system
of prisms within the instrument. As the upper portion of the instrument turns about
a vertical axis, two sets of prisms scan diametrically opposite sides of the horizontal
circle. "This upper portion can be clamped and final pointing on target can be made with
a slow-motion tangent screw. The vertical cross hair is brought exactly on target,
and the instrument is collimated and read. The horizontal circle can be set at any
desired initial reading.

When the telescope is turned about its horizontal axis, two sets of prisms scan

840 INSTRUMENTS

FicurE 4004a.—A direction theodolite.

FOR HYDROGRAPHIC SURVEYING

diametrically opposite sides of the vertical circle.
This motion also has a clamp and slow-motion
tangent screw. Collimation is effected before
reading. The vertical circle is read through the
same eyepiece as the horizontal circle, by turning
a knob near the bottom of the rear face of the
right-hand standard. When the line on this knob
is horizontal, the horizontal circle is seen, and
when the line is vertical, the vertical circle is seen.
Since the vertical circle reads zero when the tele-
scope is pointed directly toward the zenith, the
angles read are zenith distances.

Accessory equipment for this type instrument
includes an optical centering device, internal il-
lumination for night observations, prismatic eye-
pieces, and accurate levels. Complete instruc-
tions for use of the instrument are furnished by
the manufacturer.

The repeating theodolite (fig. 4004b), unlike
the direction theodolite, has a lower motion clamp
screw and slow-motion tangent screw. Thus,
with the upper portion clamped and the lower

motion free, the horizontal circle and upper portion of the instrument carrying the
telescope and two verniers rotate as a unit about the vertical axis. With the lower

motion clamped and the upper motion
free, the circle remains fixed and the upper
portion only rotates, indicating angles by
the position of the verniers relative to the
horizontal circle. Also, the circle is ex-
posed at the verniers for reading through
a magnifying glass. These verniers can
be read to the nearest ten seconds of arc.

Since the vertical circle is graduated
to read zero when the telescope is horizon-
tal, other readings are either elevation
or depression angles. The verniers of the
vertical circle read directly to the nearest
15 seconds of arc.

4005. Transit.—The surveyor’s
transit (fig. 40058) is similar to the
repeating theodolite, except that it is
smaller, lighter, and less precise. It rests
on four leveling screws rather than three,
and some models read only to the nearest
minute of arc.

The camera transit (fig. 4005b) con-
sists essentially of a surveyor's transit with
à camera mounted between widely sep-
arated standards. A transit telescope is
mounted on top of the camera. In use,
the instrument is pointed on a known con-

FIGURE 4004b.— repeating theodolite.

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING 841

di IR m a
a

FIGURE 4005a.—A surveyor's transit. FIGURE 4005b.—A camera transit.

trol point as if it were an ordinary transit. A photograph is taken, then the instrument
is turned in azimuth and another picture is obtained. This is repeated until a complete
panorama of overlapping pictures is obtained around the observation point. During
this procedure, the instrument may be pointed on other known points to obtain addi-
tional control. Prints of these pictures can be used for determining angles to additional
points for supplementary hor-
izontal and vertical control. A
somewhat similar instrument,
consisting of a combination
camera and theodolite, is called
a phototheodolite.

4006. Level.—The pre-
cise level (fig. 4006) is used
for determining precise eleva-
tion differences between two
points. The instrument illus-
trated has generally supplanted
the “Wye” level formerly used
in most hydrographic surveys.
The split image of a sensitive
level bubble is seen through an
eyepiece adjacent to the tele-
scope eyepiece, and as long as
the two parts remain matched,
the telescope line of sight is in
the horizontal.

Ficure 4006.—A precise level.

842 INSTRUMENTS FOR HYDROGRAPHIC SURVEYING

For reconnaissance or other rough work, a small hand level may be used. The
Locke type hand level determines only a horizontal line of sight. The Abney type
adds a small vertical arc which can be used for observing elevation angles. Neither
should be considered a precision instrument. Å

4007. Distance measurement can be accomplished by any of several different
methods and procedures. For precise work, special tapes which have a low coefficient
of expansion and have been calibrated by the National Bureau of Standards under
controlled temperature, tension, and support conditions are used. They are used in the
field under standard tension and support, and the temperatures and support eleva-
tions are observed and recorded so that corrections can be applied to the measured
distances to adjust them to the corrected horizontal distances. If such precision is
not required, a surveyor’s steel tape may ve used.

Slightly less precise, but more rapid, is the measurement of distance by means of a
subtense bar (fig. 4007). In this method, a direction theodolite is used to measure the
angle between the end points of a distant Invar bar. The bar is mounted horizontally
on a tripod and is oriented to be perpendicular to the line between its center and the
theodolite by a small telescope mounted on it for this purpose. The size of the angle
subtended by this bar is a measure of the distance from theodolite to bar. Tables

FIGURE 4007.—A subtense bar.

of angles and corresponding distances are available from the manufacturer, or can be
computed.

Another still less precise method of measuring distance is by a stadia, a graduated
rod. In addition to the cross hairs used in angle measurement, a transit is equipped
with two other horizontal cross hairs so spaced that they will subtend one foot on a
vertical stadia rod at 100 feet distance. At any distance the stadia cross hairs will
intercept on the rod a length of about Mooth of that distance. If the ratio is other than
1:100, a stadia constant is furnished with the instrument or can be determined by
comparing a stadia measurement of distance with the value of that same distance as
carefully measured with a tape.

4008. Bottom samplers.—Samples of the bottom are obtained by means of snapper
or scoopfish type bottom samplers. The former is secured to the base of a sounding
lead and is used while the craft is lying to. Two clamshell-shaped castings are snapped
together by a heavy spring when triggered by hitting the bottom, and a handful-size
sample is thus obtained. The scoopfish is designed for use with the vessel underway.
It is essentially a hollow tube with diving fins aft, and a special towing bridle. When
properly set and towed, it dives to the bottom. When it strikes the bottom, a sample is
forced into the tube, the bridle suspension point is automatically shifted forward so

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING 843

that the instrument will no longer dive but can be hoisted up, and a cover flips into
position over the forward end of the tube to retain the sample.

j 4009. Tide gage.—It is necessary to obtain as complete a record as possible of the
tide in the survey area during operations. The information furnished by this record
is used to determine the reference plane, or datum, for all heights and depths. It is also
used for adjusting all original observations to that datum, and from it is computed
the tidal data which is printed on the chart, such as mean sea level, spring rise, neap
rise, lunitidal interval, etc. Å

The portable automatic recording tide gage (fig. 4009) is a light, compact instru-
ment which records on single sheets of special paper a graph of the tide. The paper is
clipped onto a drum which is rotated at one-half revolution per day by an eight-day
clock movement contained inside. A float is suspended by a wire inside a pipe-float well

Fiaure 4009.—A portable automatic recording tide gage.

which protects it from wave and current action, yet permits long-period water level
variations through a small aperture in the bottom of the pipe.

The float wire is guided up to the gage over an idler pulley centered over the top
of the pipe. At the gage, the wire is wound around a grooved drum. Inside this drum
is a spring which keeps tension on the wire so that as the float rises with the water, the
drum rotates and takes up the slack. When the water level falls, the weight of the
float overcomes the tension of the spring and the drum rotates in the opposite direction.
The axle of the float-wire drum is geared to a long-pitch screw on which rides a stylus.
This screw moves the stylus across the paper parallel to the axis of the record drum.
Thus, while the record drum is rotated by its clock, the stylus is moved back and forth
across the drum as the water level rises and falls. The record paper is black or red and
coated with white wax. The stylus scratches the wax, drawing a graph of the water
level variations with time as abscissa around the drum and height as ordinate across the

drum.

844 INSTRUMENTS FOR HYDROGRAPHIC SURVEYING

Record paper is furnished in different height scales and corresponding sets of gears
are used to vary the stylus motion. Thus, the instrument can be adapted for use in
accordance with the range of the tide.

The standard automatic recording tide gage operates in a similar manner, with the
following exceptions: the paper, fed from a supply roller, passes over a main roller
across which a pencil rides, and is taken up by a receiving roller. The paper is long
enough to accommodate a continuous one-month tide record. Two clocks are used; one
to advance the paper by rotating the main roller, and the other to strike hour marks on
the paper. The receiving roller, which winds the paper, is actuated by a weight sus-
pended by a cord which is wound around a drum. Friction springs retard the supply
roll so it will not unwind too fast. A counterpoise weight is suspended by a wire which
runs over a drum secured to the same shaft as the float-wire drum. This keeps tension
on the float wire and takes up the slack as the tide rises. In addition to the tide-
marking pencil, this instrument is equipped with a datum-marking pencil. This is set
to draw a straight line at the datum height. Scale changes to accommodate various
ranges of tide are accomplished by using float-wire drums of varying circumference,
different pencil screw pitch, and corresponding counterpoise weights.

A number of other methods may be used for observing tidal data. Most important
is the tide staff. This is a graduated board from which the water height is read at
regular time intervals. It can be installed vertically or, with properly exaggerated
graduations, inclined. The latter installation is best used in calm water with small
range of tide. Other devices for measuring tide include the float gage, tape gage, and
pipe gage. These are all nonregistering.
A number of gages have been designed
to operate on the bottom. Their mecha-
nisms are actuated by pressure changes
caused by variations in the depth of water.
This type of gage is not in general use.

4010. Current observations are also
an integral part of hydrographic survey-
ing. When printed on the chart, the
information is valuable to navigators,
especially in channels and other areas of
limited maneuvering space. Types and
designs of current meters are so varied that
only those features which are common to
most of them will be presented here.

In general, current speed is deter-
mined by counting the number of rev-
olutions of a propeller per unit time.
FicGuRE 4010.—A device for measuring current Propeller turna are counted in MAA

speed. One type is illustrated in figure 4010.
Direction of the current is indicated
by one of many methods of determining the heading of the meter relative to a
compass magnet. The meters are kept headed into the current by fins.

4011. Drafting instruments.—Certain drafting instruments are of special value in
plotting the information obtained in hydrographic surveys. Distance measurements in
chart drafting are taken from a metal diagonal metric scale direct to the nearest 0.0001
meter. This device consists of a flat metal bar a little more than one meter long.
Vertical lines (fig. 4011a) are spaced at intervals of one centimeter (0.01 meter) and
graduated 0 to 100. To the left of the meter is an additional centimeter with diagonal

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING 845

5 O | 2 3 4 5 6 7

8 9 10
10
9 ii. |
8
K |
7 |Ë a

: EH | T
E n" —
F

| i [al
AY e

4 5 6 Tá 8

FIGURE 4011a.—A diagonal metric scale.

lines permitting measurement to two additional decimal places. Along the bottom
horizontal line this additional centimeter is divided into ten equal parts. Hundredths
are obtained by making the measurement on the corresponding horizontal line. Thus,
a distance of 7.43 centimeters is measured horizontally along line 3, from vertical line
7 on the right to diagonal line 4 on the left. When the distance is greater than can
be accommodated by the usual dividers or compasses, beam compasses (fig. 4011b)
are used. This consists of a wood or metal
bar on which slide two beam heads earry-
ing steel points, exchangeable for an inking
pen or pencil point. A thumb screw on
each point clamps it in position on the bar,
and one is equipped with a slow-motion
screw for fine adjustment.

A three-arm protractor is used for
rapid plotting of three-point fixes. It can
also be used for plotting angles to secondary
survey stations. The center arm of a
three-arm protractor is secured to, or a
part of, a graduated circle. The left and Figure 4011b.—Beam compasses.
right arms are pivoted about the center
of this circle and are equipped with clamping devices. A plastic type has a two-
minute vernier on each movable arm, and angles can be set to the nearest estimated
one minute. This type is easy and rapid when plotting three-point fixes on signals
which are comparatively near the boat position. For more precise plotting and
for fixes on distant signals, the metal protractor (fig. 4011c) is used. The verniers
of this instrument read to the nearest one minute. A magnifying glass 18 attached
to facilitate reading the verniers, and slow motion screws are provided to permit
fine adjustments. Detachable extension arms are furnished for use on distant
objects. Since only one arm can be set to small angles down to zero, this instrument is
manufactured in left- and right-hand models, on which the left and right angles, respec-
tively, may be set to zero.

Proportional dividers (fig. 4011d) are an aid to transferring measurements between
charts or other drawings which are not to the same scale. This device consists of two

846

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING

FIGURE 4011d.—Pro-
portional dividers. FIGURE 4011e.—Spacing dividers.

INSTRUMENTS FOR HYDROGRAPHIC SURVEYING 847

legs, each with a point at each end, and a movable pivot. When the pivot is at the
middle, the two leg openings are equal. If the pivot is moved toward one end, the leg
opening at that end is less than at the other, at a fixed ratio. The path of travel of the
pivot is graduated so that a predetermined ratio can be set on the instrument.
Spacing dividers (fig. 4011e) are useful in subdividing distances into equal parts,
such as spacing soundings along a line between two boat positions.
so that as they are opened, the spaces between points are equal.

Other, commonly used drawing instruments such as scales, triangles, etc., are also
used in chart work.

They are designed

CHAPTER XLI
HYDROGRAPHIC SURVEYING

Introduction

D

4101. Hydrography is that science which deals with the measurement and descrip-
tion of the physical features of the oceans, seas, lakes, rivers, and other waters, and their
adjoining coastal areas, with particular reference to their use for navigational purposes.
The process of making the measurements upon which the description depends is called
surveying. Precise determination and marking of positions on land, and accurate
measurement of a reference direction and distance, taking into account the earth’s
curvature, constitute a geodetic control survey. Measurement of details of water
areas and appropriate details of adjoining coastal areas is called a hydrographic
survey. In addition to delineation of coast lines and location and measurement
of submerged features, a hydrographic survey usually includes measurement of
magnetic declination (variation) and dip, tides, currents, and meteorological ele-
ments. Limited surveys may be conducted to satisfy particular requirements. Before
a hydrographic survey can be conducted, a geodetic control survey may be needed
if available information does not provide adequate control of positions.

The principal objective of most hydrographic surveys is to obtain information
on water areas and adjacent coastal regions, to serve as source material for nautical
charts, sailing directions or coast pilots, and other nautical publications of value to the
mariner. The results of the surveys are also used for planning harbor improvements
and seaplane anchorages; for studies of silting and erosion, oceanographic features, and
earth sciences; and for military defense projects.

Nearly 71 percent of the earth’s surface is covered by water. Only a small part of
this area has been adequately surveyed, and much of the land area has not been accu-
rately measured. The changes caused by nature and man, and the continual increase in
requirements of more precise and more nearly automatic systems and methods of
navigation, render obsolete the charts or surveys once considered adequate. Con-
sequently, the need for ever more accurate, more complete surveys continues, with
no end in sight.

Surveys are usually conducted by personnel who have been given specialized train-
ing, and are provided with complete equipment. A modern survey ship is shown in
figure 4101. Detailed information on the conducting of such a survey is given in
Special Publication No. SP-4, Hydrographic Office Technical Specifications for US.
Naval Surveys and Supplementary Data; and in U.S. Coast and Geodetic Survey Pub.
No. 20-2, Hydrographic Manual. The purpose of the present chapter is to acquaint
the mariner with the principles of surveying, to provide him with sufficient knowledge
to conduct an exploratory survey (art. 4127) of a previously uncharted area, and to
obtain and record in suitable form new data for the correction and improvement of
existing charts.

4102. Planning a survey.—As in other operations, an efficient and adequate sur-
vey requires advance preparation. In addition to a knowledge of surveying, one
should acquaint himself with the available information on the area. A study of all
available charts, aerial photographs, and written material should be the first step.

Work sheets or planning charts can be prepared showing the location of principal
848

HYDROGRAPHIC SURVEYING 849

FIGURE 4101.—A modern survey ship, the USS Maury (AGS16).

landmarks; general configuration of coast lines; tentative anchorage areas, landing
beaches, and camp sites; probable sites for the erection of signals to mark the various
stations; and possible tide gage locations. Several copies should be made.

When the survey craft arrive at the area to be surveyed, several reconnaissance
parties should be sent out to verify the information on the work sheets or planning
charts. Tentative anchorage areas should be the first investigated. Protection during
foul weather is essential to the safety as well as the comfort of the personnel who will
man the small craft used for inshore soundings.

In the selection of landing beaches, safety of personnel and equipment is the pri-
mary consideration. Surf conditions, beach gradients, and bottom characteristics should
be observed. The convenience of the locations and access to good routes of travel on
shore are also important.

The selection of sites for signal marks should be made by an experienced surveyor,
if one is available. Visibility from the sea is the most important consideration, but
intervisibility among stations, or with those used for a geodetic control survey, are im-
portant to the accurate establishment of the positions of the stations. High points and
conspicuous features of the terrain should be utilized to the fullest extent, not only for
hydrographic control, but also as aids in controlling aerial photography. A helicopter
is a valuable aid in making such a study, permitting rapid reconnaissance of the whole
area.

Particular care should be exercised in the selection of a tide station. It should be
located in a protected area where there is little wave action, but where access of sea
water is adequate and representative of the area. A depth of at least five feet below
the predicted lowest tide is desirable. The tide gage should be installed on a rigid
structure, which may have to be constructed if one is not already available. Wharves
are most frequently used, but the gage should be so located that it will not be damaged
by operations in the area.

A decision will have to be made as to whether or not a geodetic control survey is

needed and, if so, its extent.

850 HYDROGRAPHIC SURVEYING

Geodetic Control Survey

4103. Origin of survey.—An important requirement of a survey is to establish
the position of each feature measured. The first step is to determine carefully the
location of one reference point. This should be established as accurately as circum-
stances permit, for all other positions are located relative to this one point, called the
origin. Any error in the origin is carried over to the entire survey.

If an accurate land survey has been made in the vicinity, the origin of the new
survey might be determined with respect to the earlier survey, so that there will be
no discontinuity between surveys. If this method is not available, an astronomical
position is customarily obtained.

4104. Astronomical observations are made by the best method available. The
most accurate available in the field is generally by astrolabe (art. 4002). Both lati-
tude and longitude are determined by a single set of observations. If a direction
theodolite (art. 4004) is used, latitude and longitude are determined separately and
somewhat less accurately. If neither of these methods is available, position is deter-
mined by the best available means. However careful the measurement, all astro-
nomical positions are subject to a possible error due to deflection of the vertical (art.
1610).

Surveyors generally time observations by means of a chronometer rated to side-
real time, and set approximately to GST. The chronometer error on GST is deter-
mined by finding the GST at the time of comparison (using the American Ephemeris
and Nautical Almanac) and comparing this with the reading of the chronometer.
Usually, the longitude of an assumed position is converted to time units and combined
algebraically with the chronometer error (or correction) on GST to find chronometer
error (or correction) on LST. Thus, if the chronometer is 8?15*2 fast on GST and the
longitude is 5°06™23°4 east (76°35'51"0E), the chronometer is 4°58™0882 slow on
LST.

For survey accuracy, the Nautical Almanac does not provide sufficiently precise
data. The American Ephemeris and Nautical Almanac or other source should be used.
If observations are timed by sidereal time, local hour angle is found by subtracting right
ascension (art. 1426) from LST. Similarly, the sight reduction methods commonly
used by navigators are not sufficiently precise for use in surveying. In general, only
those computations necessary to the conducting of the survey are made in the field.
All of the data should be sent to the appropriate government charting agency, where
detailed computations are made to check and perhaps refine those already made, and
to supply the additional answers needed for interpreting and utilizing the information.
The important part of the field work is to make all measurements carefully and accu-
rately, and supply all needed data, suitably labeled, so that the end products will be
reliable. All measurements should be made to a higher order of precision than in
ordinary navigation.

4105. Observation by astrolabe.— The astrolabe is set up and carefully leveled.
Star lists are available to indicate the name and constellation, right ascension, magni-
tude, azimuth, and local sidereal time at which various stars will have the desired alti-
tude, neglecting refraction. A body near the prime vertical should be observed first
to provide a check on the local sidereal time, which is used for timing observations.
As each additional star approaches the fixed altitude of the astrolabe, the observer
picks it up and centers it in the lower power eyepiece. He then shifts to the higher-
power eyepiece, and as the body reaches the fixed altitude, he presses a telegraph key,

recording a mark on a chronometer-chronograph record tape. If available, about 100
celestial bodies are thus measured.

HYDROGRAPHIC SURVEYING 851

About ten or 12 of these stars, well distributed in azimuth around the entire hori-
zon, are selected. The zenith distance of each star is computed for the time of obser-
vation. Computation is customarily made by means of the navigational triangle;
assumed latitude, meridian angle, and declination of the body being known. With a
good assumed position, the computed zenith distance of most bodies will be greater
than that indicated by the astrolabe used (30° for a 60° astrolabe; 45° for a 45° astro-
labe) because of refraction. The differences in zenith distances, computed minus
assumed (30° or 45°), are plotted as distances in seconds of arc along the azimuth line
of the body, from the assumed position. A negative difference is plotted along the
reciprocal of the azimuth line. At the points so determined, lines are drawn perpen-
dicular to the azimuth lines. These are lines of position. If they are accurate, they

350 P 10
ASTROLABE PLOTTING SHEET 340 vadu null, y 39
\ 1
STATION Carupano . 32 NES "n, EE
A /
DEIA erly dar T n E NS í
V
PLOTTED BY AD. tara dd S
N AM
N
SS
POS
N
D
Gs
=
o US
d ET
VS —o
S-= =
v= =8
NAS =
2 SI
Q = = Q
^ nc: =
Se =8
ne Zo
KK =
7
97
Xe. E
ASSUMED POSITION 2
+40? AQUEL nin ee
a V nj
TOS- IS- 00.00 W. OFZ
SCALE: e D
One mm division=..L second of arc o le,
NOTE Zo (rdg pps o
^ S y /
Show positions thus: Findet zi 200 (huot (um 62
190 180 170

FIGURE 4105.—A typical plot of astrolabe observations.

are tangent to a circle which can be drawn within the figure formed by them. The
radius of the circle is the constant error of observation, the principal component of
which is refraction. The center of the circle is the position of the observer. Its lati-
tude and longitude can be found by applying corrections to the assumed position.
highly accurate results, a correction is applied for convergency of the meridians.
typical plot of astrolabe observations is shown in figure 4105.

For

4106. Observation by direction theodolite.—When accuracy requirements are less
exacting, as for a magnetic observation station, a position can be obtained in consider-
ably less time by means of a direction theodolite.

Zenith distances of two stars are measured when they are within 5% of the prime
vertical (one east, the other west) and their altitudes do not differ by more than 1°.
If convenient, a minimum altitude of 30° should be used. Two sets of such observa-

852 HYDROGRAPHIC SURVEYING

tions are made, each observation being carefully timed. The meridian angle at the
time of observation can be computed by time sight formula (art. 2106). This can be
converted to LHA, which can then be compared with GHA to determine longitude.
Surveyors generally compute local sidereal time and compare this with the Greenwich
sidereal time of the observation. »

The selection of stars near the prime vertical can be made by measuring the hori-
zontal angle from Polaris or any other star near the meridian.

Latitude is determined from theodolite observations of northerly and southerly
stars near the celestial meridian. In north latitude, Polaris is usually used for the
northerly star. The two stars should have altitudes which do not differ by more than
1°, and should be within about 2° (azimuth) of the meridian.

4107. High-latitude observations.—The methods described in articles 4105 and
4106 are unsuitable in high latitudes because of the nearly-horizontal apparent motion
of celestial bodies, and the continuous daylight during the summer, when surveys are
customarily conducted.

The method usually employed is to set up a direction theodolite and observe the
zenith distance of the sun at approximately hourly intervals. Timing is probably best
done by means of a stop watch, which is started at the moment of observation and
stopped at a convenient chronometer time shortly thereafter. Chronometer time at
comparison minus the interval recorded by stop watch is the chronometer time of the
observation. The chronometer should be checked by radio time tick immediately
before and after observations, and the difference in chronometer error distributed
evenly over the period of observation.

Local hour angle is determined and converted to meridian angle. With assumed
latitude, declination, and meridian angle, the zenith distance of the sun is computed.
This is compared with the observed value corrected for refraction. The difference is
used to plot the line of position as in ordinary navigation. Since zenith distances are
used, a greater computed value results in a toward situation. The navigator may find
it less confusing to convert all zenith distances to the more familiar altitudes. If all
observations and computations are completely accurate and the actual refraction does
not vary from that used in the computation, all lines of position will intersect at a
common point. However, this is rarely the case, and the center of the plotted figure
is used, as in ordinary navigation.

4108. Direction.—A reference direction for a survey is established by carefully
determining the angle between a meridian and the straight line connecting two prom-
inently marked points. The angle is measured clockwise from south, as astronomers
usually measure azimuth. This direction is determined at one of the marks by
observation of the azimuth of a celestial body. The reference direction, which a
navigator would call a “bearing” (measured from south), of the second mark from the
observer is customarily referred to by surveyors as an “azimuth.”

Azimuth is established by observation of a celestial body. A body having a
nearly constant azimuth during the period of observation is the most desirable to use.
In the northern hemisphere (except in very low or high latitudes) Polaris is ideal for
id DOE ED Kri it should be observed when it is at its greatest

€ E RS 1e nort celestial pole, for at this time its movement is most
d Ve d ia V east change in azimuth occurs. If another body is used, it

ka Ka ši Se i Kis its motion is most nearly vertical. A body that crosses the
doce dot cross the. MCN M e LT
observer, and of the same name), the desired dit vus when OP ee i
, , the desired condition occurs when the body is

HYDROGRAPHIC SURVEYING 853

nearest the prime vertical. This time can be determined by means of table 25, or
by an inspection table such as H.O. Pub. No. 214. When H.O. Pub. No. 214 is
used, the desired condition is indicated by a number of identical, or nearly identical,
azimuth angles in consecutive entries in a column. The meridian angle at the most
favorable moment can be converted to LHA, and this to GHA, which can be used with
an almanac or the ephemeris to determine the time to make the observation (art.
2107).

Azimuth is determined by measuring the horizontal angle between the celestial
body and the mark indicating the second place, using a theodolite. The azimuth of
the celestial body is computed to the nearest 071, and the horizontal angle is added
(subtracted if measured counterclockwise from the body) to determine the desired
azimuth. For best results, celestial bodies having low altitudes should be selected, if
such are available.

A direction measured at the same point at which an astronomical longitude is
determined is called a Laplace azimuth. Positions and directions at a second place,
determined by a series of measurements of direction or distance, or both, do not, in
general, coincide with values obtained by astronomical observation at the second sta-
tion because of a difference in deflection of the vertical at the two places. The position
as determined by a series of measurements from a “known” position is called a geodetic
position. The geodetic azimuth differs from the astronomical azimuth by the
amount of the Laplace correction, which is equal to (Aa— 2g) sin Lg, where X, is the
astronomical longitude, As is the geodetic longitude, and Lg is the geodetic latitude.
The accumulated error in a series of measurements is far greater in azimuth than in
longitude. The Laplace correction, which assumes all the error is in the computed
geodetic azimuth and none in the computed geodetic longitude, is applied to the
astronomical azimuth at the second place to find the corrected geodetic azimuth.

4109. The base line.—Following the determination of a single accurate position
and a reference direction, the length of a base line is measured, to serve as the basis for
other measurements of distance. The length of the base line should be at least one-fifth
that of the average side of the principal network of lines of the survey.

The length of the base line should be determined as accurately as equipment and
conditions permit. For field surveys conducted by the U. S. Navy Hydrographic
Office, the maximum error is specified as one part in 150,000. This is one foot in about
25 nautical miles, or about half an inch per nautical mile. The probable error (art.
2904) specified is one part in 500,000.

For such accuracy a carefully calibrated, low-expansion-coefficient, Invar tape is
used under a standard tension which allows for sag and stretching. Corrections are
applied for temperature, height above sea level, and inclination (if the ground is not
level). With standard professional methods this accuracy can be obtained over moder-
ately rough terrain with slopes up to 20°. The base line is divided into sections about
one kilometer (a little more than half a nautical mile) in length. Each section is meas-
ured in each direction, using separate tapes, if available. It may be necessary to clear
the line of brush or other growth to provide an unobstructed view. Stakes are driven at
each tape length, and the distance between stakes is measured. A precise level (art.
4006) is used to determine the inclination. In making the measurement, care should
be exercised to prevent kinks, abrasion, and tension greater than that prescribed.

The measurement of a base line can require a considerable amount of time. An
approximate length can be determined quickly by means of a subtense bar (art. 4007)
or even by a stadia, making the measurements in lengths of about 300 feet. Results
obtained in this way are sufficiently accurate for graphic plotting done in the craft

854 HYDROGRAPHIC SURVEYING

running sounding lines. If later measurement indicates the need for adjustment, this
can be provided by multiplying all distances by the ratio of accurate distance to pre-
liminary distance. For a plot, only the scale need be changed. , k

If the survey covers a limited area, as a harbor, a single base line is sufficient.
However, if the survey is to extend over a considerable area, additional base lines are
needed as checks.

4110. Triangulation.—A network or chain of triangles with vertices at selected
points on the ground is established in the area to be surveyed. In the selection of these
points, which are commonly called stations, consideration is given to both topographic
features and geometric factors. By carefully measuring the angles at the vertices of
each triangle and using these measurements together with the position of the origin of
the survey, and the length and direction of the base line, one is able to compute the
position of each station. This forms a triangulation net (fig. 4110) covering the area
and serving as the framework or skeleton to which all other positions are referred. The
stations should be selected carefully to provide a strong net. This net, with its refer-
ence to the origin and observed azimuth, is called the geodetic control of the survey.
Those control points which are used for fixing position during survey of the water area
constitute the hydrographic control.

4111. Trilateration.—If a network of lines similar to a triangulation net is estab-
lished by measuring the length of each line instead of the angles between lines, the process
is called trilateration, and the system of lines is called a trilateration net. If lengths are
measured by tape, as explained in article 4109, this is a time-consuming and often diffi-
cult or impossible process. However, with the development of electronic methods of
measuring distance, trilateration became a practical method. In periods of low visi-
bility, or where lines are too long for visual observation (as between off-lying islands and
the shore), it may be the only method available.

4112. Traverse.—In some areas the best, or only available, method is by measuring
both direction and distance of a series of lines. This is a traverse. It might be used
where a clear view of one station is not available from others, or along an irregular beach.
The application is usually limited, so that a traverse is generally somewhat subsidiary
to the main triangulation or trilateration.

In planning a traverse, one should select a route affording reasonably long legs as
free as possible from obstacles. When the traverse is used to connect two parts of a
net, reciprocal directions should be measured at the two ends, to provide a check. This
provides two routes by which a line of the triangulation or trilateration can be carried
through to a line of the traverse. Where the traverse follows a route with many curves,
as along a stream or beach, it should be connected to the main triangulation or tri-
lateration net at several points. If this is not practicable, an azimuth line should be
established between points several legs apart, so that directions can be carried forward
with greater accuracy. All main traverse stations should be permanently marked, but
intermediate stations need not be permanently established.

4113. Signals.—As each station is established, a conspicuous structure or signal
is constructed or designated to mark the site. It is essential that the signal be accur-
ately centered over the station, which for principal stations is marked by & bronze
marker set in concrete. The signals take different forms depending upon the distance
over which they are to be seen, obstructions, the need for identification, background,
and the availability of existing structures. The shape, target area, and color are
factors to be considered. The color is selected with particular reference to the back-
ground. The three types of signal most used for principal stations are:

Tower. A tower is used when needed to clear obstructions, where the distance is
so great that the curvature of the earth is a consideration, or where a smaller target

HYDROGRAPHIC SURVEYING 855

vf 21°29'13.4"N
SPIRE 39°10/57.3"E

Tal
N tallest building)

9Min
\ (minaret)

Ficure 4110.—A typical triangulation net.

might not be sufficiently conspicuous. The type of tower generally used is an open-
framework, prefabricated structure of galvanized steel, which can be assembled rapidly
by an experienced crew (fig. 4113a). It consists of an inner tower to furnish instrument
support, and an outer independent structure to support a platform for the observer.
The tower is constructed in sections, to a maximum height of 113 feet. It can be made

856 HYDROGRAPHIC SURVEYING

smaller by omitting one or more of the bottom sections. Part of the outside may be
covered with cloth to make it more conspicuous.

Tripod. A wooden tripod (fig. 4113b) is the signal used most frequently when
the observer has good visibility from the ground. Usually, the lumber is cut aboard
ship and assembled at the site. It is generally about 25 to 30 feet high and covered
with cloth or provided with latticed lumber to make it more conspicuous. It is firmly
anchored and guyed by wires as necessary.

Existing structures. Conspicuous church spires, chimneys, flagpoles, lighthouses,
etc., can be used. For a complex structure, the specific part used should be specified.
If there is any reasonable possibility of confusion, as when several chimneys are close
together, the structure should be avoided. When an existing structure is used, a
permanent marker is not installed. Usually it is necessary to observe from some point
nearby, called an eccentric point, and provide a correction to the observations made
from the station. This is done by measuring (1) the distance (D) between the structure

FIGURE 4113a.—A tower survey signal. FIGURE 4113b.—A tripod survey signal.

and the point of observation; and (2) the angle (a), at the point of observation, between
a line to the structure and one to another signal, at an approximate distance (s) from
the site. The correction (C) in seconds of arc to be applied to the direction of the
distant station observed is then

_ D sin a

s sin 17

Secondary signals for intermediate stations may be improvised from any suitable
material available. Examples are a single pole with cross-lattice work or a flag, a
whitewashed tree trunk or rock, a whitewashed box or barrel filled with Stories
earth and surmounted by a flag, a piece of sheeting wrapped around a bush, etc.

It is common practice to give each station a short name, for easy identification.

4114. Records.—It is of importance that measurements be made carefully, and
that complete records be kept. Each observer should be provided with a EAR in
which to make notes as the survey progresses. At the end of each period of observa-

HYDROGRAPHIC SURVEYING 857

tion these notes should be converted to good form for the permanent record of the
survey.

All information should be evaluated as it is received. In many instances this
requires at least preliminary computations to determine whether the work is of accept-
able accuracy. Surveyors usually measure distances in meters to the nearest 0.01
meter and angles to the nearest 071, and compute geodetic positions to the nearest
0:01. In a triangle formed by survey lines, the three angles should equal 180% plus
the spherical excess due to curvature of the earth. This amounts to about 070175 per
square nautical mile of area. If facilities are not available for computation, large-
scale, carefully drawn plots may suffice. As the various positions are determined,
they are plotted on a polyconic projection (art. 315). Any results that seem incon-
sistent with others should be measured again.

A complete description of each station, preferably with a sketch, should be pre-
pared. It is generally desirable that preliminary descriptions be prepared indepen-
dently by two observers, who should then collaborate in preparing the final descrip-
tion. This information may be needed if the station is to be reoccupied, perhaps many
years later.

When a regular survey party is sent out, it is provided with standard computation
forms, tables, and blank books for recording observations, as well as the instruments
and other equipment needed to do the work. Others make the best use of whatever
is available.

When the survey is completed, all of the records are forwarded to the government
agency responsible for charting the area. For United States personnel, this is the
U. S. Coast and Geodetic Survey for United States territory, and the U. S. Navy
Hydrographic Office for foreign areas.

Hydrographic Survey

4115. Control.—Hydrographic surveys differ in several respects from geodetic
control surveys. The surface of the water is relatively flat, and the water obscures
vision of the relief of the bottom. As a result, sharp discontinuities in the bottom
level, such as pinnacles, might escape detection. Permanent stations are not estab-
lished at sea, and the lack of a stable platform precludes precision measurement of
angles with the type of equipment used ashore. Measurement of distances by tape
is impractical over water.

The principal function of a hydrographic survey is to determine depths of water.
The positions at which soundings are obtained are determined by reference to estab-
lished points on shore. In addition to locating the points at their correct geographical
positions, this practice results in the land and marine features being in correct rela-
tionship to each other. This is an important consideration because the marine navi-
gator near a coast also locates himself relative to the land, in many instances using the
same landmarks used by the surveyor.

The means used for determining the position of the sounding craft is called
control. The two kinds of hydrographic control in common use are visual and elec-
tronic. At great distances from the shore, celestial navigation might be used.

4116. Visual control is the determination of position by visual reference to con-
spicuous landmarks. The most commonly used method is to obtain horizontal sex-
tant angles and plot the position by means of a three-arm protractor (art. 4011). This
is called the three-point fix method.

Any conspicuous object which has been accurately located can be used. Geo-
detic control survey signals might be available. Natural objects such as prominent

858 HYDROGRAPHIC SURVEYING

trees or sharp mountain peaks are often used. Existing structures such as lighthouses
and church steeples make satisfactory marks. When marks are not available at desired
locations, a signal might be constructed. The type most commonly used is a a
mast 20 to 30 feet high, to which three triangular skirts are attached at angles of 120
to each other (fig. 4116). A flag of distinctive color may be attached to the top to aid
in identification. Floating signals may be used in shoal areas to extend control be-
yond the limits of shore visibility. The signal generally used consists of a mast pro-
vided with skirts or wooden slats, and supported
on an anchored floating structure. The location of
such a signal should be checked frequently, as it
might be displaced by wind and wave action.

The distance between signals depends upon the
scale of the survey, general contour, and visibility.
In general, signals should be one-half to one mile
apart for harbor and anchorage surveys, and one to
two miles apart for coastal surveys.

The signals used for hydrographic surveys are
normally positioned by reference to geodetic control
survey stations. This is usually done by one of the
following methods:

Intersection of bearing lines from three or more
stations, the position being determined either by
computation or plotting.

Resection by observing the bearing of three or
EE survey More stations from the position to be determined.

signal. Traverse from established stations.
A "ship-shore" method is occasionally used.
Horizontal sextant angles between the signal to be located and an established point
are observed aboard ship at the same instant that the shore party measures angles
from known points to locate the ship.

4117. Electronic control is used in periods of low visibility, and beyond the range
of normal visibility from shore. Any electronic positioning system meeting the ac-
curacy requirements might be used. Those which have been extensively used are
radio acoustic ranging (art. 1205); radar (art. 1208), usually with transponder beacons
(art. 1108); shoran (art. 1213); electronic position indicator (art. 1213); Lorac (art
1310); Decca (art. 1309); and Raydist (arts. 1214, 1311). Radio acoustic ranging,
electronic position indicator, and radar are no longer in common use for control.

To provide survey accuracy, the electronic equipment should be accurately tuned
and calibrated, and should be operated within the closest practicable tolerances.

The direct ranging methods (radio acoustic ranging, radar, shoran, and electronic
position indicator) provide results that can be used without special equipment. Ranges
are usually plotted by means of a number of concentric circular arcs drawn in advance
on the plotting sheet, or in some cases by means of a beam compass and a diagonal
metric scale (art. 4011). The accuracy of such readings varies with conditions, but
about the best that can be expected for single readings is 15 yards for shoran, 75 yards
for electronic position indicator, and 150 yards for radar with transponder beacons.

The hyperbolic systems (Lorac, Decca, and Raydist) require location of the hyper-
bolas. These are plotted at intervals, and intermediate values are obtained by inter-

polation. The accuracy of these systems varies with position relative to the
transmitters, but is sufficient for offshore surveys.

HYDROGRAPHIC SURVEYING 859

4118. Plotting sheets. When the approximate extent of the area to be surveyed
has been determined, a master plotting sheet is prepared, usually on the polyconic
projection (art. 315). The scale depends upon the contour and the amount of detail
to be shown. As the various items of information are determined, they are plotted on
this survey sheet. Smaller sheets are prepared for use of the parties conducting the
survey. Close to the beach these are of the same scale as the master sheet, but farther
out they may be of smaller scale. These smaller sheets may be called boat sheets,
ship sheets, shore line sheets, etc., as appropriate.

4119. Topography.—The positions of the shore line, streams, mountains, hills,
etc., may be available from a land survey. If this information is not available, it is
determined as part of the hydrographic survey.

The position of the shore line is best determined by means of vertical aerial photog-
raphy (ch. XLIII). If this method is not available, positions are obtained, usually by
horizontal sextant angles, at short intervals along the beach. The beach line is sketched
in through the established points.

Inland features are located by horizontal sextant angles or by transit angles from
triangulation stations. The heights of hills near the shore can be determined by
vertical angle measurement and table 9 (or more accurately by computation), or by
difference in the reading of a barometer, using table 11 or the formula of article 3707.
If enough information is available, contours should be sketched in. The location of a
summit should be indicated by a dot, and the height indicated by a number.

4120. Hydrographic features.—Depth is determined by running a series of parallel
sounding lines. Usually, these are run normal to the general trend of the beach, but
in areas of shoals or other dangers, they should be run in such direction as to provide
the best indication of the bottom features. The sounding lines should be spaced at
intervals of two-tenths of an inch on the plotting sheet. Check lines should be run
perpendicular to the main group, at intervals of perhaps two inches on the plot. When
these sheets are prepared, the desired lines should be drawn lightly in pencil to serve
as a guide to the sounding craft. Bottom samples should be taken at intervals of not
more than two inches on the plotting sheet, except in depths greater than 50 fathoms,
where bottom samples normally are not taken unless required for the oceanographic
aspects of the survey.

In shoal water and sheltered areas, sounding lines are run by small craft. Farther
from shore larger craft, including the survey ship itself, run the lines.

For harbor and anchorage surveys, the scale of the plotting sheets is generally
1:5,000, 1:10,000, or occasionally 1:25,000. A fix should be obtained every two minutes.
Soundings should preferably be obtained by a recording echo sounder, to provide a
bottom profile. Every 15 seconds the sounding should be recorded in a sounding book
provided for this purpose. If the depth is not greater than 11 fathoms, soundings should
be recorded to the nearest foot. For greater depths, the nearest one-half fathom is
sufficient.

For channel surveys, the scale of the plotting sheet may be 1:10,000, 1:25,000, or
even 1:50,000 in some cases. Fixes should be obtained at intervals of two minutes, and
soundings recorded every 15 seconds unless the scale of the survey is 1:50,000, when
every 30 seconds should suffice.

For coastal surveys, the scale should be about 1:50,000 to a depth of 20 fathoms,
1:100,000 between 20 and 100 fathoms, and 1:250,000 for greater depths. The in-
terval between fixes should be about three, five, or ten minutes, respectively, for the
three scales. Soundings should be recorded every 30 seconds for a 1:50,000 plot, and
every minute for smaller scales.

860 HYDROGRAPHIC SURVEYING

Sometimes it is necessary to sound an area well offshore, as a bank in the open
sea. The individual circumstances govern the choice of technique to use. Control is
provided by the best means available. If the area is beyond the range of the electronic
position indicator, celestial navigation or loran might be used. If the water is sufficiently
shoal to permit anchoring, a relatively large number of observations might be made to
establish one position from which others can be determined. Open ocean surveys are
further discussed in chapter XLII.

In any hydrographic survey, an area in which the existence of a shoal or other
obstruction is suspected should be sounded thoroughly by a number of closely spaced
lines, to be reasonably certain that the least depths have been found and their positions
accurately determined. The surest way of determining that the least depth has been
found is to use a wire drag. This is particularly important in rocky or coral areas,
where individual pinnacles may not be found by sounding, however thorough. Basic-
ally, a drag consists of a submerged horizontal “ground wire" suspended by upright
wires from buoys and held at a constant depth by weights and submerged floats. The
ground wire is towed over the area between two vessels, and will strike or hang on
obstructions extending above the depth at which it is towed. If the ground wire
rides up over the obstruction, the fact is indicated by the falling over of the supporting
buoys. The depth at which the ground wire is towed can be varied by altering the
length of the upright wires. The depth usually used is 42 feet. The wire drag was
developed by the U. S. Coast and Geodetic Survey. A detailed description of the
construction and use of the device is given in Publication No. 20-1 of that organization.
Since wire drag surveys are costly and time-consuming, they are normally used only
in critical areas such as important harbors, anchorages, and channels.

A pier and its surrounding area should be surveyed carefully. Its direction and
dimensions should be established accurately. Hand lead soundings should be taken
every 20 feet along the face of the pier. Additional sounding lines should be run
parallel to the pier at distances of 20, 40, and 60 feet.

In general, a small stream is sufficiently surveyed for chart purposes if a few lines
of soundings are run in the navigable part, parallel to the principal reaches, with an
estimate of the distances to each shore. However, individual circumstances should
govern.

4121. Tide and tidal current observations.—Tide observations should begin as soon
as practicable, using the appropriate equipment (art. 4009). A permanent tide station
may be installed, but more often temporary stations are used in surveying. If the
area to be surveyed is extensive, or if local conditions indicate a possible wide variation
in tidal conditions at different points in the area, several stations should be established
at representative points. Observations should continue throughout the period of the
survey, or longer if practicable. It is desirable that the period of observation extend
over an entire synodical month (29% days).

A sufficient number of tidal current observations should be made to establish the
current pattern for the area, with particular reference to the direction and maximum
speed in the principal channels, and the times of all maximum speeds and slacks.
| If a current meter (art. 4010) is not available, observations can be made by: an
improvised method. A current pole consists of a pole weighted so as to float vertically,
and having a log line attached. The pole is placed in the water from an anchored
vessel or fixed point, and permitted to drift with the current. The amount of drift
in a timed interval can be determined by measuring the length of line paid out. A
simple computation can be used to convert this to speed. The direction can be deter-
mined by noting the direction the log line tends. This method is particularly adapted
to current measurement at the anchorage of the survey ship. In the channels, a

HYDROGRAPHIC SURVEYING 861

launch can be permitted to drift with the current, its position being determined at
short intervals by horizontal sextant angles and three-arm protractor, or other suitable
method. Occasionally, current can be measured by water-soluble dyes.

4122. Magnetic measurements.—If specialized magnetic instruments are avail-
able, a magnetic observatory can be set up ashore to determine all magnetic elements
for which equipment is available. Observations might continue throughout the period
of the survey. If such equipment is not available, a magnetic compass might be taken
ashore, free from the deviating influence of the vessel, and the variation determined
by carefully measuring the magnetic direction of any accurately measured line of the
survey. If no such line is available, magnetic azimuths of the sun or other celestial
body can be measured and compared with the computed true azimuth at the same
instants. A dip needle might be available to measure the magnetic dip.

It is desirable to take readings at a number of places, to check for anomalies. In
the water areas, anomalies which affect variation can be detected by steering a steady
course and measuring the compass bearings of established shore points from a series
of known positions as the vessel proceeds. These can then be compared with computed
or measured true directions to determine compass error, which should remain essentially
constant as long as the course remains unchanged.

At the principal shore station, observations should preferably continue over the
period of the survey, to eliminate the effects of any magnetic disturbances. Because of
possible diurnal change, readings should be taken at different times during the day.
If this is not practicable, readings are best made at about noon.

4123. Geographic names.—The correct names and spellings of all named places
and features in the area covered by the survey should be determined from reliable
local sources, noting any established variations. Full information on names should
be submitted with the survey records.

4124. Aids to navigation.—The location of each aid to navigation should be deter-
mined carefully. A description of the aid should be prepared and, if lighted, its
characteristics should be timed. Any discrepancies between actual conditions and
information given in the light lists or sailing directions should be noted. The promi-
nence of the aids with respect to their backgrounds should be observed, and any advis-
able precautions with respect to the aids should be recorded. Lines of demarkation
between color sectors should be measured carefully. The directions and lengths of
ranges should be measured. If aids are moved from time to time because of changes
in hydrographic features or seasonal ice or weather conditions, detailed information
should be recorded. Signal stations and other prominent landmarks which might be
useful to a navigator should be located and described.

4125. Miscellaneous information.—In addition to the various measurements,
descriptive information forms an important part of a hydrographic survey. This is
useful in the interpretation of the measurements, and it provides a major source of
information for notes on the charts, and for compilation of sailing directions or coast
pilots. The amount and detail of the information to be collected varies with individual
circumstances. The surveyor should be alert to note any items that should be included,
recording the appropriate details as they come to his attention. Even negative infor-
mation is helpful when it answers a question that might logically come to the mind of
the mariner. Examples of the items that might be included are: vus

Errors, omissions, or ambiguous statements in publications such as sailing directions
or light lists. -—

A description of the general trend, features, and aspect of the coast as 1t 18 ap-
proached. This description might well be supplemented with pictures or radar scope
photographs from stated positions and heights.

862 HYDROGRAPHIC SURVEYING

The color and extent of discolored water.

The nature and extent of meteorological and seasonal influences.

The kind and type of ice.

The location of fishing stakes, nets, and fishing boat operations.

The location, landing places, and shore markers of submarine cables; and the
location and height of overhead cables.

The location of ferry crossings and other areas where local traffic may be heavy.

The location of restricted or military operating areas, with a statement of the regu-
lations pertaining to them.

The location and extent of overfalls, rips, etc.

A description of the various awash dangers at various stages of the tide.

The location and nature of all wrecks, with all pertinent information regarding
their visibility, depth, markers, etc.

Whether or not channels are dredged, and the probability of their filling with
sediment.

Safe speed to use through channels, confined waters, etc.

Suitability of anchorages with respect to holding qualities, availability of mooring
buoys, freedom from obstructions, direction and speed of wind and currents, amount and
direction of swell, etc.

Location and description of special anchorages, with the regulations concerning
their use.

Prevalence of fog and other visibility-limiting phenomena.

Any needed explanatory information on tides and currents.

The appearance and effect of mirages, abnormal refraction, phosphorescent seas,
ete”

Local harbor regulations.

Port and aerodrome facilities.

Pertinent information regarding shore settlements.

4126. Records.—As information is collected, it should be evaluated and incor-
porated in the one master record. Each item should be verified as it is recorded. When
the survey has been completed, the smooth copy of the completed information should
be sent to the appropriate government charting agency. When an acknowledgement
of the receipt of this information is received, the additional records such as sounding
books, angle books, etc., should be forwarded.

Limited Surveys

4127. Exploratory survey.—When time or lack of equipment does not permit, or
where desired results do not justify the carrying out of a standard geodetic control or
hydrographic survey, a limited exploratory survey may be conducted. This might be
an advance investigation to determine the desirability of making a full detailed survey,
an operation to make a preliminary chart of an anchorage, an investigation of a reported
shoal, etc. The principles and techniques in general conform to those described earlier
in this chapter, but are adapted to meet the requirements, instrument limitations, and
training of personnel. This is the type of survey that might well be assigned to a
nonsurvey vessel.

When the area to be surveyed is covered by maps or charts of reasonable relia-
bility, it is customary to establish the origin of the survey by scaling the position of one
landmark from the chart. When this source of information is not available, the origin
might be determined by careful measurement of electronic or celestial information
needed for a position. If the position is determined from celestial observations ashore,

HYDROGRAPHIC SURVEYING 863

a theodolite or transit should be used if available. If it is not, an artificial horizon might
be used with a sextant. It is desirable to observe at least 12 bodies well distributed
around the horizon. At sea, it is desirable to anchor, or remain in the vicinity of an
anchored aid to navigation.

A reference direction is best determined by astronomical means. If a theodolite or
transit is not available, a sextant might be used with a body at low altitude, measure-
ment being made of the horizontal angle. If visibility limitations or available time does
not permit, a gyro compass might be used, as follows: With the ship at anchor, bearings
of an observer on shore are observed. The observer measures the horizontal angle
between the ship's gyro repeater used for the observation, and a landmark, using a
theodolite, transit, or sextant. The reciprocal of the gyro repeater bearing, with the
measured angle applied, is the direction from the observer to the landmark.

If the length of the base line cannot be measured by one of the methods described
in article 4109, an approximation of sufficient accuracy for some purposes might be
determined by measurement from the ship, using any available means, such as radar.
Either of two methods might be used. A base line across navigable water might be
selected. As the ship steams across the base line the distance to each shore station is
measured. The least sum of the two distances is the length of the base line. The
average of several such determinations should be used. By the second method, the
distance to a single shore station is measured. At thé same moment, an observer at the
shore station measures the angle between the ship's radar antenna and a second shore
station. At the second station an observer measures the angle between the antenna and
the first shore station. With this information, the length of the line between the two
shore stations can be computed.

Tf triangulation is needed, it is carried out as accurately as time and equipment
permit. If horizontal sextant angles are used, the stations should be at nearly the
same height if practicable.

An essential part of an exploratory survey of a harbor or anchorage is to delineate
the shore line and coastal topography as accurately and completely as time permits.
The quickest and best method is to use vertical aerial photography, if available. If
this is used, established control points should be marked and described. If this method
is not available, a reasonably accurate method is to run a traverse along the beach.
A quick method of obtaining a rough approximation consists of determining radar
bearings and distances to a number of shore points, from an anchored ship, and sketch-
ing in the shore line. A photograph or trace of a radar PPI presentation is another
possibility.

Heights might be determined by transit or sextant angles, or by air search radar,
with table 9.

Sounding lines are run as close together as conditions and time permit. Fixes are
obtained by horizontal sextant angles, cross bearings, or radar at such intervals as
warranted by the requirements of the survey and available time and equipment. Fixes
at three-minute intervals are commonly used in harbor areas. The position of a sound-
ing boat might be determined relative to the anchored survey ship, using radar. The
sounding lines should be run in a systematic manner, with shoal areas being given
extra attention. Soundings should be plotted directly on the work sheet, and fathom
curves sketched in as the information becomes available.

Tide and current observations should be made as completely as time and condi-
tions permit. A tide staff is usually used with half-hourly readings of the height.
Current is usually measured by an improvised current pole (art. 4121). .

A complete and accurate record should be made and forwarded to the appropriate
government authority upon completion of the work.

864 HYDROGRAPHIC SURVEYING

4128. Running survey.—A limited survey can be conducted as a ship steams
along a coast. The position at the beginning of the run is determined as accurately
as conditions permit. If accurately charted landmarks are not available, it may be
possible to send a landing party ashore to establish a good astronomical position.

As the survey progresses, the ship steams at a safe distance from the shore, deter-
mining its courses and speeds as accurately as practicable. Natural ranges may be
available from time to time to provide good courses. If charted shore objects are
available, frequent fixes can be determined and the dead reckoning between them
adjusted to avoid gaps in the plot. As the ship proceeds, continuous soundings are
taken, preferably by a recording echo sounder. Bottom samples are taken at frequent
intervals if conditions permit, and if required.

If the shore has not been accurately surveyed and charted, positions of various
prominent landmarks are established by a series of horizontal sextant angles or bear-
ings, or by radar, as the vessel proceeds. A minimum of three readings should be
made on each object, so that its plotted position will be reasonably accurate, and to be
sure of identification. Since errors in this method are cumulative—the positions of
landmarks being established from the ship, and then future positions of the ship
established by means of the same landmarks—it is desirable to make all measurements
as accurately as practicable. Generally it is best to steam at moderate and constant
speed, stopping only if this contributes to the establishment of better positions.

If available, one or more launches might proceed along parallel courses between
the ship and the shore to obtain additional lines of soundings. Their positions might
be determined by a series of bearing and distance measurements, as by radar, or what-
ever means are available. These launches can collect additional information regarding
the shore line and beach topography. Under some conditions a launch might contrib-
ute most to the survey by proceeding at will, obtaining angles and making sketches
and notes, rather than taking soundings. With a recording echo sounder it might
serve both functions.

All observations should be recorded, and all positions plotted as soon as received,
so that apparent errors might be corrected while the landmarks are still visible. Be-
cause of the approximate nature of the survey, a large scale plotting sheet is not justi-
fied, a scale of 1:100,000 usually being adequate. Sketches and descriptions of various
details along the coast can serve useful purposes later. If shore parties are landed,
distingvishing marks might be established at some points. The amount of detail
recorded depends primarily upon the time available, and perhaps upon the require-
ments of the survey. Discrepancies are certain to occur. These are resolved as accu-
rately and completely as available information permits.

4129. Beach survey.—The most common purpose of a beach survey is to provide
preliminary data for use in planning the constructions of piers, docks, or other harbor
facilities. Another common purpose is to obtain data useful for landing supplies,
equipment, and personnel directly on the beach from landing craft or amphibious
vehicles.

Since a beach survey seeks detailed information about a relatively small area,
accurate control (position) is essential. Several methods are in use:

Range and distance. Several ranges are established on shore, accurately meas-
ured by transit and tape, and marked by suitable markers. These ranges are estab-
lished perpendicular to the general trend of the coast, and numbered for identification.
The sounding boat runs lines of soundings in line with the ranges, determining distance
offshore by stadia (with the rod in the boat and the observer on shore), or by attaching

a line to an object on the beach and streaming out the line as the boat proceeds along
the range, away from the shore.

HYDROGRAPHIC SURVEYING 865

Two ranges. Where the trend of the beach permits, two series of ranges can be
established nearly perpendicular to each other, so that distance measurements are not
needed.

Two transits can be set up at accurately determined positions on shore. Angles
to the sounding boat are observed simultaneously at frequent intervals. This method
is precise, but does not provide guidance to the sounding boat, since positions are
determined on shore at a later time.

Horizontal sextant angles can be determined simultaneously by two observers in
the boat, the results being plotted by three-arm protractor. This method is not
attractive unless the area to be sounded is extensive.

Depth of water may be determined by echo sounder or pressure gage where prac-
ticable, but generally soundings close to the beach are made by hand lead or sounding
pole. If the bottom is very soft, the lower end of the lead or pole should be fitted with
a disk to prevent excessive penetration.

Chart projections are seldom required for a beach survey. A plane coordinate
grid oriented with respect to an origin on shore, or the ranges, is sufficient for most
purposes. The scale should be appropriate to the area and accuracy requirements,
1 inch=100 feet being commonly used. Soundings should be recorded to the nearest
one-half foot out to the depth considered critical for the project.

Tide observations should be recorded continuously during the survey and, if
practicable, should be extended to cover a synodical month (29% days). One or more
permanent bench marks should be established, and the height of the water level de-
termined relative to the nearest foot mark if a tide staff is used.

Current measurements should be made to determine any current along the shore,
and also maximum ebb and flood.

If the beach is to be used for landing vehicles, the suitability of the beach and
backshore for landing and operating the type vehicles involved should be determined
by inspection and also by penetration and other tests, as practicable. Wind, sea and
swell, coastal currents, and character of beach materials are factors which govern pos-
sible sedimentation or erosion, and so should receive attention in the survey.

If the sea approaches have not been surveyed, these areas should be given attention
in connection with the beach survey.

4130. Bathymetric survey.—Sounding lines run at sea are of assistance in adding
detail to existing charts, or in constructing special charts to serve particular purposes.
Most of the required information is obtained by ships proceeding between ports, either
singly or in company with other ships. The important factors are accurate depths
and accurate positions. These operations are given more detailed attention in chapter
XLII.

4131. Checking accuracy of existing charts.—A mariner can perform a real service
to himself and others by being continually alert to detect errors on the charts or in
sailing directions. When such errors are suspected, an opinion that an error exists,
or the submission of a chart with corrections shown, is of relatively little value to a
charting agency. Chart requirements demand a higher order of accuracy than that of
a vessel fixing its position by normal methods of navigation.

Positions of shoals, aids to navigation, landmarks, etc., should be determined
carefully by whatever method is available. The average ship is provided with means
for determining position to accepted accuracy. For instance, if an uncharted shoal is
found, a launch should be sent to investigate. A sounding lead, two sextants, a chart,
a three-arm protractor (improvised if necessary), and plotting board may be all that is
needed. As the launch moves back and forth across the shoal, soundings are taken and
simultaneous horizontal sextant angles between conspicuous charted objects are meas-

866 HYDROGRAPHIC SURVEYING

ured. If a single sextant is available, angles may be measured in quick succession,
followed by a second measurement of the first angle, at approximately the same time
interval as that between the first two measurements. If the objects are at a considerable
distance, so that angles change slowly, the average of the two readings of the first angle
can be used without significant error. Positions are then plotted and soundings
recorded. The height of tide should be noted by tide table or other available means.
The investigation should be continued over a sufficient area, and with enough thorough-
ness, to obtain an accurate indication of the nature and extent of the feature. If time
permits, the surrounding area should be investigated to determine other possible shoals.

Points on land might be located by a number of bearing or distance measurements
from different accurately located positions of the ship, or by measurements of direction
made on land. A new structure might be located by information obtainable ashore,
or by reference to other nearby structures. If a charted landmark is missing or has
been moved, information should be sought ashore to determine the permanency of the
change, and perhaps precise information regarding position, height, etc.

The number of variations is almost limitless, but the important thing to remember
is the need to be alert to detect possible errors in the chart, and to obtain as complete
and accurate information as practicable, submitting all details and an evaluation of the
reliability of the data submitted. If complete information is not available, send what
can be obtained, to at least alert the charting agency of the need for a correction. In
the case of man-made changes, a possible source of complete information is helpful if
the data itself cannot be obtained.

The mariner himself is one of the most valuable sources of information. By pro-
viding reliable data, he can help keep his charts and sailing directions accurate, current,
and complete.

References

Bilby, J. S. Signal Building. U.S. Coast and Geodetic Survey Special Publication
No. 234. Washington, U.S. Govt. Print. Off., 1943.

Breed, C. B. and Hosmer, G. L. The Principles and Practice of Surveying. Vol. I,
Elementary Surveying. 8th ed., 1945. Vol. II, Higher Surveying. 6th ed., 1947.
New York, Wiley.

Gossett, F. R. Manual of Geodetic Triangulation. U.S. Coast and Geodetic Survey
Special Publication No. 247. Rev.ed. Washington, U.S. Govt. Print. Off., 1959.

Hoskinson, A. J. and J. A. Duerkson. Manual of Geodetic Astronomy. U.S. Coast and
Geodetic Survey Special Publication No. 237 (1952 reprint). Washington, U.S.
Govt. Print. Off., 1952.

Hosmer, G. L. Geodesy. 2d ed. New York, Wiley, 1930.

Jeffers, K. B. Hydrographic Manual. U.S. Coast and Geodetic Survey Publication
20-2. Washington, U.S. Govt. Print. Off., 1960.

Mitchell, H. C. Definition of Terms Used in Geodetic and Other Surveys. U.S. Coast
and Geodetic Survey Special Publication No. 242. Washington, U.S. Govt.
Print. Off., 1948.

Mussetter, William. Manual of Reconnaissance for Triangulation. U.S. Coast and
Geodetic Survey Special Publication No. 225. Rev. ed. Washington, U.S. Govt.
Print. Off., 1959.

Reynolds, W. F. Manual of Triangulation Computation and Adjustment. U.S. Coast

and Geodetic Survey Special Publication No. 138 (1955 reprint). Washinot
U.S. Govt. Print. Off., 1934. ly gton,

HYDROGRAPHIC SURVEYING 867

Ulm, K. S. Wire Drag Manual. U.S. Coast and Geodetic Survey Publication 20-1.
Washington, U.S. Govt. Print. Off., 1959.

U.S. Coast and Geodetic Survey. Formulas and Tables for the Computation of Geodetic
Positions. U.S. Coast and Geodetic Survey Special Publication No. 8. 7th ed.
(1963 reprint). Washington, U.S. Govt. Print. Off., 1963.

U.S. Coast and Geodetic Survey. Horizontal Control Data. U.S. Coast and Geodetic
Survey Special Publication No. 227 (Revised 1957. Reprinted in 1961 with minor
corrections). Washington, U.S. Govt. Print. Off., 1961.

U.S. Coast and Geodetic Survey. Manual of Current Observations. U.S. Coast and
Geodetic Survey Special Publication No. 215. Rev. ed. Washington, U.S.
Govt. Print. Off., 1950.

U.S. Coast and Geodetic Survey. Manual of Tide Observations. U.S. Coast and
Geodetic Survey Publication 30-1. Washington, U.S. Govt. Print. Off., 1965.

U.S. Department of the Army. Special Surveys. Technical Manual TM 5-235.
Washington, 1964.

U.S. Navy Hydrographic Office. Hydrographic Office Technical Specifications for U.S.
Naval Surveys and Supplementary Data. U.S. Navy Hydrographic Office Special
Publication No. SP-4. Washington, 1961.

CHAPTER XLII
OCEANIC SOUNDINGS

4201. Introduction.—Relatively little is known of the surface features of the nearly
71 percent of the earth covered by water. However, enough has been learned to indicate
that the unseen topography beneath the oceans has all the features common to that
above water. It is known that there are submerged mountains extending to greater
heights above their surroundings than do the Rockies, and depressions deeper than the
Grand Canyon.

While many of the general features are known, details are lacking. A very large
number of accurately located soundings are needed to provide sufficient information to

m

EH
= "d

ANTE

Figure 4201.—Contour lines and hachures (top) may be used to show underwater relief (bottom).

describe adequately the underwater relief. Tf sufficient information is available, such
relief can be delineated on nautical charts by means of contours and Hachures A
simplified chart of this type is shown in the upper part of figure 4201. The bras»: art
of the figure is a block diagram of the area shown on the chart. Only a small part AC the
oceans has been sounded sufficiently to provide the detailed information needed for
such a chart. Even in narrow strips along many coasts, along the route of the North

Atlantic cable, and along a strip of the Pacific from California to the Carolines, where
868

OCEANIC SOUNDINGS 869

soundings have been most numerous, the underwater relief is not known with the desired
completeness and accuracy.

As long as oceanic soundings could be made only by a vessel stopping and lowering
a weight, a process which might require several hours for a single sounding in very deep
water, it was impractical for most vessels to obtain very much depth information at
sea. With the development of the echo sounder, however, this situation has changed.
Witha recording echo sounder, a ship can obtain a profile along its track from continent
to continent without slowing, using about a yard of recording paper per day. Such
information, if reliable, is of great assistance to charting agencies in preparing more
adequate charts of.the ocean areas.

4202. Sounding equipment.—While lead lines and sounding machines have been
used at sea, almost all deep-sea soundings are now taken by echo sounder (art. 619).
If a depth recording device is available, it should be used, as the profile thus produced
is a better indication of the bottom than even the most closely spaced visual readings.

All echo sounding equipment is subject to certain errors unless the operator has a
clear understanding of the operating characteristics and limitations of the instrument.
The routine checks recommended by the manufacturer should be made at every change
of the watch, or oftener. In addition, the operator should be alert for certain possible
errors peculiar to his instrument. A close watch should be kept on the proper function-
ing of the stylus, recorder speed, the zero adjustment, and the frequency of the electric
current. The percentage error in the recorded depth is the same as that of the electric
current frequency. Thus, at 3,000 fathoms, the error of a 60-cycle echo sounder is
100 fathoms if the actual frequency is in error by two cycles.

4203. Evaluating results.—Inaccurate results may be worse than no information
at all. Therefore, every effort should be made to obtain reliable data. Particularly,
soundings which conflict with known or charted depths should be carefully analyzed.
Even when the equipment is operating correctly, false returns might be received due to
sources external to the vessel. A shoal “phantom bottom" may be due to marine life,
there may be multiple echoes or interference, or no return may be received because of
aeration of the water or suspended matter in it. Such errors are further discussed
in article 3504. Unusual local conditions may be a source of error. If an error is
believed probable, but no source is detected, full information should be submitted
with the soundings, for the charting agency may be able to interpret the results. This
action is particularly important where the measured depths are less than those shown
on the chart. If no error can be found, the charting agency may have no alternative
but to enter the shoal soundings upon the charts affected, and take the first opportunity
to send a survey vessel to verify or disprove them.

The speed at which sound travels in water varies with the salinity, temperature,
and pressure. When these are known, corrections can be applied to obtain more ac-
curate results. However, this is normally done only for scientific purposes. Those
soundings submitted to a charting agency should be the uncorrected values obtained
by using an assumed standard speed of 4,800 feet per second.

4204. Deep sea sounding lines.—Most deep sea soundings are obtained by ships
proceeding between ports. Soundings should be taken at every opportunity. Those
taken in well-surveyed areas can be of assistance to the navigator in locating his position.
If they conflict with values shown on the chart, and no error is found, they should be
sent to the appropriate charting agency, with full particulars. All soundings in areas
for which little depth information is shown on the chart should be submitted.

In addition to reliable soundings, accurate positions are needed. Navigation should
be in accordance with standard practice, using every practicable means to reduce error
and provide frequent checks on position.

OCEANIC SOUNDINGS

870

When two or more ships are operating together, they should steam on parallel
courses about five miles apart, maintaining stations abeam of each other by continuous
monitoring by radar and pelorus, or other available means. Only one ship should
perform the navigation used for controlling the survey.

4205. Investigating small areas.—If a feature of particular interest, such as an
isolated shoal or a seamount, is found or reported in the vicinity of the vessel, a service
can be rendered by conducting a further investigation in the vicinity of the feature.

Two methods are in common use for this purpose:
Radial. A system of radial lines 20° apart are laid out from a central control point,

preferably at the center of the feature to be investigated. These are extended outward
for a distance of about 30 miles, and the ends of alternate ones are connected, as shown

in figure 4205a. These form a series of course lines as shown.
Parallel. A north-south, east-west square is laid out with perhaps 60-mile sides,

the center of the feature of interest being at the center of the square. A series cf course
lines are drawn parallel to one side of the square, at intervals of about five miles. The
ends of alternate parallel course lines are connected, as shown in figure 4205b.

Y
— ——— — Center Control Point

FIGURE 4205a.— Radial course line pattern,

0 miles

OCEANIC SOUNDINGS 871

/-«— Reported Shoal

60 miles

60 miles
FIGURE 4205b.— Parallel course line pattern.

During such an investigation, by either method, the best control of position can
usually be obtained by anchoring a buoy, if practicable, at the center of the area. In
some instances, several buoys might be used. Any rig having buoyancy adequate to
support the necessary length of anchor cable is satisfactory. The type generally used
consists of a steel drum or mooring buoy with a weight attached to a cable, in the case
of a large buoy, or piano wire if the buoy is small and of insufficient buoyancy to support
a cable. A chain is not generally used. Buoys of this type have been successfully
anchored in depths to 2,500 fathoms. The position of the buoy is determined as ac-
curately as practicable, using celestial navigation, loran, or whatever means are avail-
able. Position of the vessel is determined relative to the buoy or buoys, using visual
or radar bearings and ranges at intervals of half an hour orless. Beyond this range, the
best available means are used. A balloon with a suspended radar reflector might be
attached to the buoy to extend its range of usefulness. The securing line of the balloon
should be at least 400 feet long, if practicable.

Sonar ranging, if available, should be used to assist in the location of shoal areas.

4206. Records.— While a reliable trace of the bottom is being obtained, the recorder
should be operated continuously. Each hour, preferably on the hour, the time should
be written on the graph, with an arrow pointing to the correct position on the trace.
A fix marker may be used if the recorder is provided with one. In addition, the time
of sharp changes in depth and other interesting features should be recorded. The date
should be entered each watch, and the ship's name given at each end of the graph. Other
pertinent information should be recorded. Figure 4206a illustrates a properly marked

OCEANIC SOUNDINGS

872

“AGO UMP di 5 MIO

i iU AMA UI KE de icu el

LULA RN BRL VAR A AI V E

ESTADO r TU RUE BATUR RTI Dër UR MH N
~- -
Sar a
EEN

E

MEN
a

FīGuRE 4206a.—A properly marked depth recorder graph.

S.

sounding

adjusted plot with

FIGURE 4206b.—An

OCEANIC SOUNDINGS 873

graph. When a reliable trace is not recorded, visible or audible soundings should be
recorded in a log at least every five minutes. The time and date of the entries should
be included in the log.

A plot of the.track should be made on a plotting sheet. On this plot the dead
reckoning lines and times should be adjusted to provide a continuous run, without gaps.
Pertinent navigational data should be included, but no extraneous information should
be given. Soundings should be spaced about one-quarter inch apart on the plot. The
position of each sounding should be indicated by a tick with the sounding in fathoms
given alongside, at an angle to the track line. Most plotting sheets have printed labels
for the parallels of latitude. It is necessary that labels for the meridians be recorded.
an item that should not be overlooked. The date of the soundings and the name of the
vessel should also be recorded. Accuracy is essential, and neatness is desirable.
4206b illustrates a typical adjusted plot.

When the work has been completed, all necessary information should be sent to
the appropriate charting agency, usually the U. S. Navy Hydrographic Office. This
should include the unadjusted plot used for navigation, the adjusted plot; data for each
fix, with the navigator’s evaluation of its reliability, and appropriate comments on
weather conditions, etc.; depth recorder trace; and sounding log (if kept). The com-
manding officer’s or captain’s forwarding letter should indicate where the soundings
were taken, type of sounding equipment, any difficulties encountered, and pertinent
remarks regarding estimated reliability of the data. Additional information of value
to cooperating observers is given in H.O. Pub. No. 606-b.

Figure

CHAPTER XLIII
PHOTOGRAMMETRY

4301. Introduction.—One of the most significant contributions to modern map
making has been the development of the precision aerial camera and the techniques for
interpreting and utilizing the information appearing on the photographs made by it.
Such photographs constitute a detailed and permanent record of all unobscured natural
and man-made features of a given section of the earth’s surface, and as such, furnish
more completely than any other means the information required for making maps.
However, all photographs, whether aerial or terrestrial, are perspective views, and it is
necessary to change these to orthographic views in order to obtain reliable map informa-
tion. Although an aerial photograph is often map-like in appearance, there are many
errors, both systematic and random, which prevent the photograph from being a true
map. The science of photogrammetry is used to eliminate or correct these errors and
also to properly record all the photographed information into a true map presentation.
Its development into a complex and exact science has made photogrammetry the most
efficient, accurate, and economical method for mapping large areas.

It is not the purpose of this chapter to present the detailed theory or working
procedure of photogrammetric instruments and methods, but rather to acquaint the
reader with the fact that such methods and instruments do exist and also to present
simple formulas and techniques that a nonphotogrammetrist can utilize to obtain
valuable, map-like information from aerial and ground (or shipboard) photographs.

4302. General photography classifications.—Photography used in map making
is of three general classifications:

Vertical (aerial) photography, made with the optical axis of the camera vertical to
the earth, or approximately so.

Oblique (aerial) photography, made with the optical axis of the camera at an angle
to the vertical.

Terrestrial (ground) photography, made with the camera’s optical axis in a gener-
ally horizontal position.

Each of these types of photography has its own particular field of usefulness,
but the vertical aerial photograph is the type most widely used for mapping, since
it most nearly resembles a map.

4303. Vertical photography.—The vertical photograph is not a map, but a per-
spective projection of three-dimensional terrain onto a two-dimensional photograph.
This results in the photographic images being displaced from their true horizontal
relationships due to the relief of the terrain features and any tilt of the aerial camera.
This in turn results in a photograph which does not havea uniform scale. These dis-
placements of image positions prevent the accurate determination of either distance
or direction directly from the photograph. Figure 4303a illustrates the principle of
image displacements due to the relief of terrain features.

For regular photogrammetric mapping purposes, vertical aerial photography is
accomplished with less than 3° of tilt and in such a manner that there is approximately
60 percent overlap between photographs in line-of-flight, and approximately 20 percent
sidelap between adjacent strips of photographs. The 60 percent overlap provides at

874

PHOTOGRAMMETRY

875

NEGATIVE
PLANE

D2 “¡DOS P

a] a2 C142

Focal Length

ELEVATION

SHOWING DISPLACEMENT DUE TO RELIEF
1. Shows Map Position
2. Shows Photograph Position
Datum Plane usually means Mean Sea Level

FiaunE 4303a.— Displacement due to relief.

876 PHOTOGRAMMETRY

least two different views of all features photographed. This is necessary to achieve
the stereoscopic effect by which interpretation and measurements can be accom-
plished. By understanding and utilizing the geometric properties of this photography,
one can obtain the information required to make a map; and accurate vertical, as well
as horizontal, measurements can be made.

The radial line plot is one method of compiling a planimetric map (one showing
horizontal position only) from overlapping vertical aerial photographs. Displacement
due to relief and small amounts of tilt is corrected graphically by the radial-line inter-
section method. The center of each photograph is located, and any ground control
points are identified and marked on the photographs. Auxiliary control points are
selected on all photographs to strengthen the network. Radial-line intersections are
taken from successive photograph centers to all control points. These intersections
define the distances and directions of the points on the photographs.

The ground control points are plotted on a grid or map projection for the purpose
of orienting the photographs. The intersecting of the radial lines and the orienting of
the photographs to the plotted control network can be done graphically or mechanically
through the use of arms or templates. After all the auxiliary control points have been
correctly plotted on the manuscript, planimetric detail can be traced from the photo-
graphs by aligning corresponding points on the manuscript and photographs.

There are photogrammetric instruments capable of utilizing the basic photographic
information to plot a standard topographic map manuscript. These instruments
encompass a tremendous range from relatively simple monocular devices to highly
complex optical and mechanical instruments. In basic theory, they recreate the three-
dimensional view as photographed from aircraft, and permit the plotting of these ter-
rain features onto a map manuscript.

Figure 4303b shows the working principle of one of these instruments, the multi-
plex. Nine-inch square aerial negatives are reduced by the use of a reduction printer to
small transparencies called diapositives. These are placed in projectors held by
brackets above a flat table. The brackets have adjustments by which the relation-
ship that existed between the pictures at the time of exposure can be reestablished to
scale with the two projectors. As many as 24 projectors can be placed on a frame.
Thus, control established at a known point on the earth can be extended many miles.

The projectors are oriented in such a way that corresponding rays from the adja-
cent diapositives intersect at the image space above the table. By this means a stereo-
scopic model of the terrain appearing on the original negatives is precisely created.
The adjacent diapositives are projected in complementary colors (red and green)
onto a tracing table at any level of the stereoscopic model as a two-color anaglyph, and
the operator views this model through spectacles in which one glass is red and the
other green. Briefly, the tracing table consists of a round white disk called a platen,
in the center of which is a very small illuminated hole. The platen is supported by
two columns, and by means of a knurled screw it can be raised and lowered. In this
way, the point of light can be made to appear on the surface of the ground, and dif-
ferences in elevations can be read on a counter mounted on one of the columns. A
pencil holder is mounted directly beneath the illuminated point, and the whole device
is mounted on agate foot pads so that it can be easily moved over a piece of suitable
drawing material. In this way, the operator can trace the horizontal position of se-
lected data, including relief features, in an orthographic presentation of the earth’s
surface corresponding to the photographic coverage.

4304. Scale of vertical photograph.—The scale of the vertical aerial photograph,
usually expressed as a representative fraction (e.g. 1:40,000), denotes only the average

877

PHOTOGRAMMETRY

MULTIPLEX
PROJECTORS

Principles of the multiplex.

FiGURE 4303b.

TRACING

878

PHOTOGRAMMETRY

or approximate scale, for even on an untilted vertical photograph there can be no

uniform scale due to the varying elevations to the terrain.

If the scale of an aerial

photograph is to be determined, two items of basic information must be known: (1)
the focal length of the aerial camera, and (2) the flight altitude of the photographic

aircraft above the terrain.

FIGURE 4305.— Determination of height by image
displacement.

The scale is determined by the ratio of these factors.

For example: If the focal length (f)=6
inches=0.5 feet, and the flight altitude
(H) =20,000 feet, then:

Pro r1 coss a
paoro sen ` 20,000 40,000

=1:40,000.

The approximate scale of the vertical
aerial photograph can also be established
by comparison of distances on the photo-
graph with corresponding distances on a
map of known scale.

4305. Height determination.—If the
foreshortened side of an object of consider-
able height, such as a tower or lighthouse,
appears on a vertical aerial photograph,
a simple application of the geometric
properties of a photograph can determine
the true height. The factors which must
be known are: (1) the flight altitude of
the aircraft above the terrain, (2) the
length of the foreshortened side of the
object on the photograph, and (3) the dis-
tance between the top of the object as it
appears on the photograph and the center
of the photograph. Refer to figure 4305
for the development of the height-deter-
mination formula. In the figure, H is the
flight altitude above terrain, h is the

height of the object, r is the distance from the top of the object image to photograph
center, d is the length of the foreshortened image of the object, and f is the focal

length of the aerial camera.
By the geometry of the figure:

(1) triangles LVC, ABC, and LV'a are similar, with angles a equal.

(2) triangles LBC and Lba are similar.

(A) From (1):

RADE rh
tan a H Le De
(B) From (1) and (2):
DR. od
db Va
From (A) and (B):
o csl
DS tate
Therefore: rh=dH
dH.

and

PHOTOGRAMMETRY 879

Thus, if the foreshortened image of a lighthouse appearing on a vertical aerial
photograph (d) is measured as 0.08 inch, the distance on the photograph from the light-
house top to the center of the photograph (r) is measured as 3.75 inches, and the
flight altitude above terrain (H) is 3,750 feet, the height of the lighthouse is

dH 3750

h =F —0.08X 4757-80 feet.

4306. Oblique photography.—Oblique aerial photographs are obtained by tilting
the optical axis of the camera from the vertical. The oblique camera has the advantage
of being able to photograph vast areas in a single exposure. Oblique mapping photo-
graphs are of two types: the high oblique, which shows the horizon line; and the low
oblique, which does not show the horizon. Sometimes two high obliques are exposed
in opposite directions simultaneously with a vertical, in order to provide photographic
coverage from horizon to horizon, perpendicular to the line of flight. Although this
method (named trimetrogon after the three metrogon lenses used in the camera sys-
tem) of employing two obliques and one vertical photograph enables relatively rapid
map compilation of large areas, the type of information obtained from obliques is
adequate for only small-scale maps of a reconnaissance nature. The use of high oblique
photos for mapping is more limited than that of verticals because the methods entailed
are more time consuming and the results obtained are ordinarily less accurate. This is
due to the perspective distortion of the oblique, and the masking of distant features by
closer ones.

Twin low-oblique photography is obtained with a twin-camera arrangement con-
sisting of a pair of wide-angle precision aerial cameras coupled rigidly together. The
optical axes of the two cameras lie in a common vertical plane and form an angle of 20?
with a plumb line (assuming no tilt) and 40? with each other.

4307. Maps from oblique photography.—High oblique photographs can be used
for reconnaissance mapping, particularly in areas where the relief of the terrain 1s slight
and the required map is essentially planimetric. Methods and instruments for use by
trained personnel are available for extracting elevations from high obliques, but the
procedure is involved, and will not be covered here. "Transfer of planimetric detail
from the oblique photograph to a map manuscript may be simply and effectively
accomplished by a graphical process known as the perspective grid method. In basic
principle, this method permits sketching of the linear detail (shore line, lakes, rivers,
town lines, etc.) from a perspective grid at the picture plane to a rectangular grid at
the map plane. For the reconnaissance study of unmapped flat areas, it is feasible for
a nonphotogrammetrist to prepare his own base maps by this method, even using pictures
taken by himself. It is required only that a distinct and regular horizon line should be
visible on the photograph, and that certain basic factors be known, as explained in
articles 4308 and 4309.

4308. Construction of the perspective grid.—The perspective grid is drawn on &
transparent medium which is positioned securely over the photograph. In the con-
struction of the perspective grid, three factors are required:

1. The altitude of the photographic aircraft.

2. The focal length of the camera lens.

3. The true, as distinguished from the apparent, depression angle of the photo-
graph. This factor can be computed from measurements, as explained in step (7)
below. KA

The first consideration in construction of the perspective grid is the scale to use
for the drawing; that is, the size the squares of the map grid are to be, and what distance
on the ground each side of the square will represent. Suppose that the perspective

880 PHOTOGRAMMETRY

MARGIN OF PHOTOGRAPHY

ATTE

PHOTOGRAPH=7 x 7 INCHES

Figure 4308.— Construction of a perspective grid for a high oblique aerial photograph.

grid shown in figure 4308 is to be drawn, and it is decided that the map grids are to be
one inch square, and that each side of the square will represent 660 feet on the ground.
Suppose, further, that H, the flight altitude, was 5,000 feet; that f, the focal length of
the camera lens, is 5.216 inches; and that the photograph is seven inches by seven
inches. The grid construction follows (shown to reduced scale in fig. 4308) :

(1) On the photograph, draw a line along the apparent horizon.

(2) On the photograph, draw a line perpendicular to the apparent horizon and
through the principal point (the center or point of intersection of the two diagonals,
designated P), extending this line from one edge of the photograph to the opposite edge.

These two lines are the only ones to be drawn on the photograph.

(3) Lay the material to be used for the perspective grid over the photograph, and
on it trace the two lines drawn on the photograph (steps (1) and (2)).

(4) Measure the distance PH;. Suppose this is three inches.

(5) Compute the a depression angle by the formula: tangent of the ap-

1 3
fi 05,216
29543, which is the angle of apparent depression.

(6) Compute the dip (D) by: D in seconds= 58.82 yH in feet. In the example,
58.82 4/5,000— 4,159 seconds, or 1°09/3. (In the Nautical Almanac, dip is now deter-
mined by using 58.2 for the constant 58.82. The value 58.8 was formerly used for
almanac dip tables. In this example, the use of 58.2 gives a dip of 1%08/6. With
either value of D the answer to step (8) is the same.

(7) Add the dip to the apparent depression angle, to obtain 0, the true depression
angle: 29°54'3+1°09/3=31°03/6.

(8) Compute the distance from the principal point to the celestial horizon by:
PH,=f tan 0=5.216X0.60229=3.14 inches.

(9) Scale this distance (3.14 inches) from P, along the principal line to Ha, and
draw the line V,A,V, through it, parallel to the apparent horizon.

(10) The scale of the map grid has already been decided upon as being one inch=
660 feet. Compute the distance from the celestial horizon to the front ground line
at G, where one inch on the front ground line subtends 660 feet on the ground trace
of the photograph, by the formula: Haat S00 9 5,000X4 16737 gg inches.

parent depression Nola tius

=0.57515. The angle having this tangent is

PHOTOGRAMMETRY 881

(11) Scale this distance (8.84 inches) from Hp, along the principal line to G, and
draw D, GD, parallel to V,H,V..

(12) From G, in both directions along D,GD;, measure off one-inch divisions, and
from these points draw lines through the vanishing point H». These are the meridian
lines of the perspective grid (not geographic meridians).

(13) Determine the vanishing points V,, V; for the diagonals, by the formula:
H,V,=H2V.2=f sec 0=5.216X1.16737=6.09 inches.

(14) Determine D,, D, by the formula: GD.— GD— y x pao 5.70=
2

3.14
11.06 inches.

(15) Draw the diagonals V; D; and V,D,. These lines will cross at P if the drawing
and computations have been carefully done.

(16) Draw a horizontal line through each intersection of a diagonal and a meridian
line, as shown in figure 4308.

(17) Lay out the limits of the photograph, and ink all lines within the photograph
limits except the construction lines.

4309. Use of the perspective grid.— Prepare a grid of one inch squares on a separate
sheet of paper large enough to take the entire plottable area covered by the photograph.
Superimpose the transparent perspective grid over the photograph in its proper position.
By inspection, transfer the detail from the photograph to the square grid. This is
illustrated in figures 4309a and 4309b. Figure 4309a represents a transparent perspec-
tive grid, as if superimposed on a photograph showing a main shore line and offlying
islands. Figure 4309b shows the transfer of the shore line and islands from the photo-
graph to the plotting or map grid. "The entire area of figure 4309a is not included, to
permit a larger scale illustration. "The scale of the map grid is one-third the scale of
the perspective grid.

4310. Terrestrial (ground) photography is comparable to shipboard photography,
and both may be utilized in a similar manner. The principles of the perspective grid
method previously described can be adapted for use with terrestrial photography.
Another method of determining horizontal positions is to obtain two photographs of
the same area taken from different camera stations. The positions of the camera
stations must be known and the horizontal directions of the camera axis at the time of
each exposure must be determined. The focal length of the camera must also be
known. Where the reproduction is not at the same scale as the negative, the reduction
or enlargement must be known so that the focal length value may be altered proportion-
ately. Preferably, the celestial horizon should run through the principal point of the
photographs and be parallel to the top and bottom margins. |

Place a sheet of transparent material over each photograph. Select the points
(A, B, O, D, fig. 4310a) for which the positions are desired, making certain that all
points are included in both photographs. Through each of these points and also P,
the principal point (located by diagonals, as shown), draw a line perpendicular to the
horizon. Near the bottom of each photograph draw a line (JK) parallel to the horizon,
intersecting all vertical lines at right angles (A’, B’, C', D’, and P'). Extend Vara
line PP’ (through the principal point), and from P’ measure off the focal length, P S,
locating the camera station, S. Connect point S with points A”, B’, C", and D'. Next,
place each overlay on the chart with its point S over the correct camera position, and
line SP in the direction the camera was facing when the picture was taken. The
location of point A on the chart is at the intersection of the two SA’ lines, extended
if necessary. The other points are located similarly. | ;

If the position of the camera station for any photograph is unknown, it can be
determined if there are several correctly positioned points on a chart that are readily

882 PHOTOGRAMMETRY

CELESTIAL HORIZON

APPARENT HORIZON

FIGURE 4309a.— Perspective grid as if superimposed upon a photograph.

identifiable on the photograph. The procedure described above is applied to the
single photograph, but using the identifiable points (fig. 4310b). The transparent
overlay is positioned on the chart so that the radial lines pass through the corresponding
points on the chart. The position of the camera station is thus determined by resection
(art. 4116).

4311. Photo-interpretation is the examination of photographic images of objects
for the purpose of identifying the objects and deducing their significance. In identi-
fying objects from their photographic images, the following characteristics should be
considered :

Shape relates to the general form, configuration, or outline of an individual object.
The shape of an object appearing on a vertical photograph may differ widely from its
shape when viewed from the ground. Because of this, a certain amount of practice
and experience is necessary in order to make a reliable identification.

PHOTOGRAMMETRY 883

FIT

KBB

FIGURE 4309b.—Section of a map grid from the perspective grid of figure 4309a.

The size of an object as compared with another object can be of invaluable assist-
ance in determining the size of the second object. A truck on a road gives an idea of
the width of the road.

Pattern refers to the spatial arrangements of objects. Many objects, both natural
and man-made, conform to certain repetitious patterns. For example, streams which

884 PHOTOGRAMMETRY

DIAGONALS LOCATE PRINCIPAL POINT

<
Æ

RO CES
S
`

2 KNOWN CAMERA STATIONS SS A

S S

Figure 4310a.—Determination of horizontal positions from two photographs.

branch and reunite in a braided pattern are readily distinguished from simple meander-
ing streams.

Tone refers to the shade of gray in which an object appears on a photograph.
The tone of an object may differ on two adjacent photographs because the light is
reflected back at different angles in different amounts. The image of smooth water
may appear light on one photograph and dark on the next. Most roads are good
reflectors of light over a wide angle and almost invariably appear as light lines on the
photograph.

Texture is the nature of the surface photographed, with particular reference to
size and arrangement of individual units. For example, the photographic texture of
the beach area on which an amphibious landing is contemplated may indicate the
coarseness of particles composing the beach and, thereby, the ability of the beach to
support military vehicles. i

Shadows frequently give the best indication of the profile view of an object, thus
facilitating the identification of the object. Shadows will give an indication as to
heights of trees and buildings, types of bridges and towers, and depth of cuts, quarries,
etc. Frequently, it is possible to obtain some idea of the character of the relief from
the shadows on a single photograph.

Site is the location of an object in relation to its surroundings. It is important in
the interpretation of both man-made and natural features. Many types of vegetation

are confined to specific topographic sites such as swamps, stream banks, sandy flats, or
rock knolls.

PHOTOGRAMMETRY 885

DIAGONALS LOCATE
PRINCIPAL POINT

FOCAL LENGTH

LOCATION OF CAMERA STATION

FIGURE 4310b.— Determination of camera station from one photograph.

References

American Society of Photogrammetry. Manual of Photogrammetry. 2nd ed. [Wash-
ington, 1952.]

McNeil, G. T. Photographic Measurements, Problems, and Solutions. New York,
Pitman, 1954.

U.S. Department of the Army.Map Reading.Field Manual FM 21-26.Washington, 1965.

U. S. Departments of the Army, Navy, and Air Force. Cartographic Aerial Photog-
raphy. Department of the Army Technical Manual TM 5-243. Department of
the Navy Hydrographic Office Publication H.O. Pub. No. 595. Department of the
Air Force Technical Order AFM 95-6. [Washington, U.S. Govt. Print. Off.] 1964.

U. S. Departments of the Army, Navy, and Air Force. Photographic Interpretation
Handbook. Department of the Army Technical Manual TM 30-245. Depart-
ment of the Navy NAVAER 10-35-610. Department of the Air Force Manual
AFM 200-50. Washington, U.S. Govt. Print. Off., 1954.

CHAPTER XLIV
PRODUCTION OF NAUTICAL CHARTS

The Production of Charts

4401. Introduction.—The nautical chart has become so reliable and readily avail-
able that one unacquainted with the tremendous amount of material, labor, and time
involved in its production might easily fail to appreciate the contribution made by
charting agencies. So dependent has the mariner become upon this commonplace
but important aid, that he generally considers it essential to safe navigation.

The four preceding chapters describe briefly the collection of survey data. This
chapter sets forth the basic techniques used in the production of nautical charts from
survey data and other source material. The information is given so that the mariner
might have a better understanding of his chart and its limitations. Thus equipped, he is
capable of more effective, reliable navigation. Further, the mariner is an important
source of data used in the production and correction of nautical charts. If he is familiar
with the use made of these data, he can better evaluate the information which comes to
his attention, and can forward it in form that will be of value to the charting agencies.
With such information, these agencies can produce more accurate charts of greater
usefulness to the mariner. ;

4402. Federal charting agencies.—The U. S. Navy Hydrographic Office has
responsibility for producing and maintaining nautical charts of any area of interest
to the United States Navy or merchant marine which is not the responsibility of other
U. S. charting agencies. The U. S. Coast and Geodetic Survey, of the Department
of Commerce, has responsibility for charting the coastal waters of the United States
and its territories and possessions. The U. S. Lake Survey, of the U. S. Army Corps
of Engineers, has similar responsibilities for the Great Lakes. Consequently, the
Hydrographic Office limits its activities to foreign waters and the high seas, except in
time of war or national emergency. Under these circumstances, charting activities
would be carried out under a coordinated program.

The charting activities of these agencies seek to provide maximum navigational
safety and facility to vessels of the United States Navy and merchant marine. They
keep informed of new navigational requirements, and utilize the latest developments
in the production of charts. Many new methods and instruments originate with these
agencies.

While the information given in this chapter relates primarily to the methods, tech-
niques, etc., of the U. S. Navy Hydrographic Office, it applies, with minor variations,
to those in use by the U. S. Coast and Geodetic Survey and other charting organiza-
tions, both domestic and foreign.

4403. Improvements in charts.—The nautical chart has kept pace with the latest
developments in the field of marine transportation and navigation. Special-purpose
nautical charts have been produced to satisfy specific navigational requirements, such
as those of loran and radar. New or improved developments in electronic positioning
systems, magnetic observations, and aerial photographic coastal and topographic
delineations are some of the factors instrumental in improved chart accuracy.

886

PRODUCTION OF NAUTICAL CHARTS 887

Presentation of data is planned to conform with standard specifications which
have been established by U. S. Government charting agencies and the International
Hydrographic Bureau, located in the Principality of Monaco. This organization,
established in 1921, is composed of more than 30 of the leading maritime nations of the
world. Its purpose is to promote international agreement in the form of nautical
charts and publications, and to effect collaboration in the common task of collecting and
disseminating hydrographic information. Adoption of chart standards and the prac-
tice of exchanging cartographic information and techniques among various agencies
and scientific and professional societies have aided materially in improving the nautical
chart. Some of the prominent innovations which have improved the appearance
and utility of the nautical chart are the following: use of colors to accentuate naviga-
tional hazards, revision and simplification of typography for improved legibility, use
of tint shading in combination with contours to give a pictorial presentation of relief.
The transition in presentation has been gradual, with convenience to the chart user
being constantly kept in mind.

4404. Sources of chart data.—The preferred source of data used in the construc-
tion of nautical charts is the hydrographic survey (ch. XLI). The completed survey
usually covers more extensive areas than the charts because of chart size limitations
and the absence of chart requirements in areas without special naval or economic
significance. However, hydrographic survey plans generally include a proposed chart
layout to insure sufficient detail at suitable scale in potential chart areas.

In addition to surveys, chart data are collected from many other sources. Foreign
data, the main source for U. S. Navy Hydrographic Office nautical charts, are col-
lected in published chart form on a continuing basis under exchange agreements with
member states of the International Hydrographic Bureau and with other maritime
countries. Various government agencies, engineering firms, educational institutions,
and private individual sources furnish documented information which is incorporated
into nautical charts. Each week, the Hydrographic Office receives more than 400
documents which are evaluated for use in preparing charts and publications. The
published chart does not outwardly reflect the amount of information which is screened
during its construction. The following list of source material is representative of the
type from which useful information is obtained:

Surveys and charts of the United States and foreign countries (hydrographic data).

Maps (transportation, topography, planimetry, and communications data).

Periodicals, travel folders, atlases, and gazetteers (place names, town plans, and

descriptive data).

Photographs (aerial mapping and others).

Mariners’ reports of port facilities and other miscellaneous information (harbor and

dock construction work, conspicuous aids and dangers to navigation, etc.).

Sketches (used to verify and amplify other information).

Notice to Mariners (navigational data).

4405. Chart production methods.—Four common methods of producing nautical
charts are in use at the U. S. Navy Hydrographic Office: construction of the chart
from modern U. S. Navy surveys; production of the chart from a compilation mosaic
(art. 4416), based upon numerous foreign charts; redraft of an existing foreign chart;
and facsimile reproduction of an existing foreign chart. The last method is employed
only in emergencies, and the facsimile is not sold to the public. A fifth method of in-
creasing popularity is the modified facsimile reproduction of foreign charts (based
upon bilateral agreement), which are sold as H.O. charts.

Copper engraving of nautical charts is no longer carried on by the U. S. Navy

888 PRODUCTION OF NAUTICAL CHARTS

Hydrographic Office, having been replaced by methods considered more economical.
Plastic engraving (engraving on plastic) of the chart original, recently introduced, is a
promising source of further reduction in time and cost.

Photolithography is the principal chart reproduction method used. Negatives are
made on glass, film, or plastic, with reproduction plates of zinc or aluminum.

4406. Chart terminology.—The following terminology is in use at the U. S. Navy
Hydrographic Office: i

New chart. A chart published for the first time, covering an area not previously
charted at the same scale by the same organization.

New edition. A chart incorporating corrections too numerous or extensive to be
reported in Notice to Mariners. A new edition makes previous printings obsolete.

Corrected (New) print. A chart incorporating corrections which have been
published in Notice to Mariners, and other information of insufficient importance to
justify a new edition. Chart dates are discussed in article 506.

Reprint. A chart reprinted without any corrections or changes.

Field chart. A chart published on board a survey vessel, and reprinted by the
Hydrographic Office. It is identified by the letter “F” preceding the chart number.

Chartlet. A graphic supplement to Notice to Mariners of corrections which are too
extensive for the narrative version.

Proof. A copy of a chart made prior to release for final processing. Photo proofs
are made from negatives. Litho proofs are made from the printing plates, in any desired
color. A composite proof is a combined proof of more than one color plate. A watercote
is a composite proof, in color, from negatives.

Withdrawal. A chart removed temporarily from issue with the intention of re-
placement or reissue at a future date. All copies are destroyed, except standards for
record purposes. The printing plates may either be retained or destroyed.

Cancellation. A chart permanently removed from issue. All copies and printing
plates are destroyed, except standard copies for historical purposes.

Discontinuance. Removal from issue of a reproduction of a foreign chart.

Elements of Chart Construction

4407. Drafting instruments.—The ordinary drafting instruments are employed in
making charts. In addition, the following have proved useful in compilation and
drafting of a nautical chart:

Pantograph (fig. 4407a), a parallelogram-linkage device for reproducing a drawing
at a different scale. A pantograver, a pantograph which corrects for distortion due to
unequal expansion or contraction of the paper of the source material, is used by the
U. S. Navy Hydrographic Office to make corrections on wet (glass) plates.

Projection-ruling machine (fig. 4407b), a device for drawing the meridians and
parallels of a map projection.

Vertical projector (fig. 4407c), a device for projecting a vertical aerial photograph
(arts. 4302-4305), drawing, or other chart onto a work table at-any scale between speci-
fied limits, so that details can be traced onto a map manuscript (art. 4303). The pro-
jector shown is portable, stands 74 inches high when the movable carriage is at the top
of its travel, and provides for any scale from % to 3% times the original.

Light table, a table with a glass top over a light source, to facilitate inspection by
direct comparison of different charts of the same scale, and the tracing of a drawing at
the same scale. Light tables are available in a variety of sizes and shapes. They may
be part of another device, as shown in figure 4407b, or separate. A portable version
requiring a table or desk for support is called a light box.

PRODUCTION OF NAUTICAL CHARTS 889

WEIGHTED STAND
SUSPENSION WIRES

VERNIER FOR PRECISE SETTINGS

RECOIL SPRING
AND HOUSING

CORD TO RAISE OR
LOWER PENCIL POINT

PENCIL OR DOTTING PIN TRACE

FIGURE 4407a.—A suspended pantograph.

Three-arm protractor (fig. 4011c), a device for plotting a position from horizontal
sextant angles.
Proportional dividers (fig. 4011d), a device for transferring distances at a different
scale.
Spacing dividers (fig. 4011e), a device for dividing a length into equal segments.
Beam compasses (fig. 4011b), a device for drawing circles of large radius, or meas-
uring distances too great for ordinary compasses or dividers.

1. Metric bar scale(s), subdivisions in millimeters. 2.

Figure 4407b.—Projection-ruling machine.
pes for reading metric bar scales. 3. Metal

Power supply to illuminate light table and microsco
spline—can be set to rule straight or curved lines. 4. Gear tracks for carriage(s) to travel on.

5. Microscope for reading metric bar scales. 6. Dials for setting curvature in metal spline. 7.
Ruling pen carriage. 8. Ruling pen. 9. Fluorescent light. 10. Transparent glass table top
(light table). 11. Rectangular (X— Y) coordinate plotting device. 12. Microscope for reading

scale on movable plate.

890 PRODUCTION OF NAUTICAL CHARTS

FIGURE 4407c.—Portable vertical projector.

Road pen (fig. 4407d), a device with a double pen, to permit drawing of two
curved lines with constant distance between them.

Plastic splines, long narrow strips of plastic material, which can be bent into a
large variety of curves, to form a pen guide for drawing curved lines.

Border-scale subdividing device (fig. 4407e), a mechanical device for drawing
equal subdivisions of a border (latitude and longitude) or similar scale. The illustra-
tion shows: A, a steel straightedge 60 inches long which is secured, by weights or clamps,
parallel to the inside border or neat line of the chart; B, steel divider plate, one of 12
plates measuring 9 X4 X Me inches and cut with deep, diverging grooves; C, steel triangle
to be placed with its base against the divider plate; D, clamp screws for securing the
divider plate to the straightedge; E, knob for controlling a screw to move the divider
point toward or away from the straightedge; F, divider point, which rests in the grooves
of the divider plate; and G, a set screw to prevent creeping of the divider point. When
the device is set up, the divider point is set so that the distance between consecutive
grooves is the required distance between graduations of the scale. For a variable scale
such as that for latitude on a Mercator chart, this setting must be changed periodically
for accurate results.

Diagonal metric scale (fig. 40112), a device for measuring distances in metric scale
units.

ai sada rw i

PRODUCTION OF NAUTICAL CHARTS

4408. Drawing material.—The draw-
ings for a nautical chart should be made
on a dimensionally stable drafting medium
for maximum accuracy. Plastics, “Duco”
plate, and metal-laminated paper, all have
minimum distortion qualities and good
inking surfaces. The vinyl resins, intro-
duced in the United States in 1928, are
among the more recent materials receiving
widespread use. Plastics, known under
many trade names, are produced in
opaque, transparent, and translucent
sheets. The “Duco” plate is a grained
zinc lithographic printing plate, sprayed
with a good grade of enamel paint, which
produces a good drafting surface. Metal-
laminated paper is produced by mounting
a good grade of drawing paper (Bristol
board) on a metal plate, using an adhesive
and pressure. The metal plate used is
normally a zinc or aluminum lithographic
printing plate. Use of this type of draw-
ing medium has lost much of its popularity
since the introduction of plastics.

4409. Reduction methods.—Source
material at the same or larger scale as the

891

FīGURE 4407d.—Swivel road pen in contour
penholder.

compilation manuscript is frequently employed in cartography. This practice avoids
inaccuracies which might be introduced in enlarging smaller scale data to the scale of

the compilation.

The four principal methods of reduction are by camera, projector,

FiaunE 4407e.— Border-scale subdividing device.

892 PRODUCTION OF NAUTICAL CHARTS

Figure 4409.—The “diagonal square” method of sketch plotting.

pantograph, or “diagonal squares.” The camera method is the most accurate and is
preferred when reduction is the only consideration. In this method the source material
is photographed to the desired scale. The projector (fig. 4407c) and pantograph (fig.
4407a) are used when the work is not extensive, and some alterations are to be made.
The “diagonal square" method is used to *sketch-plot" data from one scale or pro-
jection to another, for example shore line data from a Mercator chart replotted onto a
gnomonic or an azimuthal equidistant projection. This method, similar to the per-
spective grid method of photogrammetry (art. 4309), is illustrated in figure 4409.

4410. Datums.—As explained in chapter XLI, each survey has an “origin,” and
geographic coordinates of other points are determined with reference to this control
point. In some regions, a single origin has been used as control for an extensive area.
A system of control points established with reference to a single origin is called a datum
(plural in this usage is datums, not data), and given an identifying name. Examples
are the North American Datum of 1927, Tokyo Datum, Nahrwan Datum, and the
Kelienphur Datum. Since each origin was determined independently, coordinates
determined with reference to one datum will not agree with coordinates of the same
point determined with reference to a second datum. Normally, there is no confusion
because various points are generally defined with reference to a single datum, which
is used for the entire area. The limits of a given datum are usually defined by some
natural barrier such as an ocean, uninhabited area, etc., so that transitions do not
generally occur at a troublesome place. Occasionally, political boundaries of adjacent
countries prevent the establishment of geographic coordinate agreement at common
stations.

A datum which controls geographic positions of points on the earth is called a
horizontal datum to distinguish it from a reference level for heights and depths, called
a vertical datum. For depths, the reference level found to be most realistic for measur-
ing the height of tide is used for charts. This varies in different parts of the world,
as indicated in appendix M. This reference level is sometimes referred to as the chart
datum. In nearly all instances it is some form of low water. Heights are nearly
always indicated with reference to mean sea level or high water. Therefore, two differ-
ent vertical datums are generally used for the same chart.

PRODUCTION OF NAUTICAL CHARTS 893

When the information is available, both horizontal and vertical datums are in-
dicated in the chart legend. If a chart extends over more than one datum, itis normally
of such small scale that differences between datums are not of significance.

4411. Borders and scales.—Selection of the border style to use depends primarily.
upon the scale of the chart, but consistency with other charts in the vicinity is a factor.
In general, some form of plan border (fig. 4411a) is used for charts of scale larger than
1:50,000; and a scale border (fig. 4411a) for charts of smaller scale.

On large-scale charts, graphic scales are usually added. On recent charts with
plan borders, yard scales are placed along the right and left sides, and both kilometer
and nautical mile scales at the top. On charts with scale borders, and older plan border
charts, graphic scales are shown at a convenient location inside the border. When this

RIAN"BORDERS

41' 45” 30” 15” 24°40' 55”
a "ëm bt a Rte E leeë SI T T E ir aA. MD i
44' 43' 42' 30” 41' 840' 39 38
15" 42' 45" 30" 15” At 45" 30" 15" 40' 45" 30" 15" 39'

PEER
20’ 30’

LLI FITI ET 3
F D Li À D o 3 1
180° 30 179° 30 178 30 Ei

a e ——— IE ESA EE
118°

Figure 4411a.—Border styles.

894 PRODUCTION OF NAUTICAL CHARTS

For use on charts of scale 1:5,000 or larger
Yards

100 50 0 100 200 300 400 500
Meters
[sa a Ts pe pel = ZAAPA Puestos oS eee Se S|
100 50 0 100 200 300 400 500

For use on charts of scale 1:5,001 to 10,000
Yards

EEE Lp 8 é6 HEAT EE
100 0 500 1000
Meters
[EC IR mero =E ET 5 i 7000
100 (0)

Figure 4411b.— Typical graphic scales.

is done, a nautical mile scale is given first, followed by a yard scale and a meter scale.
The number of yards and meters shown is dependent upon the amount of space avail-
able, the scale of the chart, and the overall size of the chart. Figure 4411b illustrates
typical graphic scales.

4412. Charted details.—The standard symbols and abbreviations which have
been approved for use on nautical charts published by the United States of America
are shown in appendix K. These are in substantial agreement with the recommenda-
tions of the International Hydrographic Bureau. From time to time changes in the
standards are made to keep pace with changing requirements.

Topographic data are normally obtained from aerial photogrammetric compila-
tions, surveys, and existing maps and charts.

Depths are indicated by soundings or explanatory notes. Only a small percentage
of the soundings obtained in a hydrographic survey can be shown on a nautical chart.
The least depths are generally selected first, and a pattern built around them to provide
a representative indication of bottom relief. In shallow water, soundings may be
spaced 0.2 to 0.4 inch apart. The spacing is gradually increased as water deepens, until
a spacing of 0.8 to 1.0 inch is reached in deeper waters offshore. Where a sufficient
number of soundings are available to permit adequate interpretation, depth curves
are drawn in at 1-, 3-, 6-, 10-, 20-, 30-, 50-, and 100-fathom depths. Other features
are shown as indicated in chapter V and appendix K.

Aids to navigation are shown by symbol and legend, as indicated in chapter V and

appendix K.
Å Place names are given according to sources and decisions recommended by the
United States Board on Geographic Names. The general policy is to use the local
source. Foreign names are used in foreign areas. Generally, international features
such as the Gulf of Mexico or a river that flows through several countries (for instance,
the Danube) are given the commonly accepted English name. The names of countries
are also given in English. When appropriate, the English equivalents of foreign terms
are shown in a glossary on the chart.

All letters and numbers shown on a chart are printed on sheets of cellulose acetate
or white paper, backed with a suitable adhesive which adheres to the drafting material
when pressed into place. This practice promotes uniformity and legibility. Various
type styles are used to distinguish between different kinds of features and to provide
a pleasing appearance.

Notes are used to convey information which does not lend itself to convenient
symbolization.

PRODUCTION OF NAUTICAL CHARTS 895

Compass roses are placed where they are readily available for use, yet obscure a
minimum of chart information. The number, size, and location are suited to the
individual chart.

The chart title is placed at a location that will result in minimum loss of chart
information, preferably on land and in one of the corners.

The official seal of the charting agency is generally placed above the chart title.

The chart number is placed at several convenient locations in the margin. When
a chart is cancelled, its number is not reassigned to another chart for several years.
When a series of charts is planned, a block of numbers is reserved to provide continuity
throughout the series.

When a chart is prepared by a government charting agency, and printed by a
different government agency or commercial printing establishment; or if a government
charting agency prints a chart for another office or department of the government, a
suitable imprint note is placed in the bottom margin.

From Requirement to Printed Chart

4413. Requirement.—A new or altered chart comes into being as a result of
recognition of a requirement. This requirement may be established by the charting
agency itself, from its continual review of existing charts, the receipt of new information,
and the needs of operating units; or it may originate with the operating forces or mili-
tary planners. Whatever its source, the requirement precedes all other steps in the
production of the chart.

4414. Estimate of the situation.—Having recognized the requirement, the
charting agency having jurisdiction then studies the situation to determine priority and
availability of source information. The intended use, required scale, and urgency
are considered in selecting the chart production method (art. 4405).

If a survey is needed, the type, extent, and thoroughness are determined according
to the availability of survey vessels, personnel, and other pertinent factors. A thorough
hydrographic survey is a slow and costly process. If it must be preceded by geodetic
control or aerial photographic surveys, the time and expense are increased. Several
weeks may be needed to thoroughly survey a single harbor of moderate size. Survey
operations are generally planned on a long-range basis to provide adequate coverage for
an entire area once operations have begun. In time of war or national emergency, such
plans may have to be abandoned and survey ships sent into forward areas. During
World War II, survey ships went into the Pacific with the fleet, and it was not uncom-
mon for survey parties to be in operation on shore before fighting had ceased. To
meet urgent requirements, the larger survey ships were provided with drafting and
printing facilities so that charts could be produced almost as soon as the data were
collected. In time of peace such urgency is not generally required.

4415. Research and planning.—Before construction of a chart begins, all available
data are investigated and evaluated. All details of the chart are planned, and specifica-
tions and procedures are prepared. The best sources of data are recommended. The
area is selected to provide maximum usefulness consistent with limitations imposed by
scale, size of sheets that can be accommodated by the printing press, land and water
configuration, etc. The use expected to be made of the chart is an important con-
sideration. Port and harbor charts normally portray the most important hydrographic
region centered on the sheet, while approach charts embrace maximum sea room and
only a limited amount of land area, sufficient to include the prominent features of naviga-
tional value. Care is exercised to avoid omission of important aids to navigation, river
entrances, channels, etc. This often results in some overlapping of adjoining charts.
The extent of adequate survey and other compilation data are also considerations.

896 PRODUCTION OF NAUTICAL CHARTS

The chart projection is selected to meet the requirements. N early all nautical charts
are on the Mercator projection, but the gnomonic, Lambert conformal, and other
projections are used for special-purpose charts. This subject is further discussed in
chapters III, V, and XXV.

4416. Compilation.—From the recommended sources, the compiler selects the
data to be used. The task of determining what to include and what to omit may be
of considerable magnitude, particularly when some of the information is inconsistent
or of questionable reliability. The skill and wisdom with which this assignment is
filled has a direct bearing upon the value of the completed chart.

Various methods of compilation are in use depending upon the amount and nature
of the data. When most of it comes from published charts, the compiler may prepare
a film positive compilation mosaic. To do this he computes and drafts the graticule
(latitude and longitude lines for the map projection used) and plots the control points
at their correct positions. The source material is photographed to the scale of the
chart, and film positives are provided. These are secured to the graticule in their
proper geographic positions. If necessary, the film positives are cut into small pieces,
so that errors in positions of distorted features can be proportionately distributed be-
tween control points. Deletions and corrections are then made, and broken lines are
connected.

The compilation is carefully reviewed for completeness and accuracy before a
contact negative is made. Black-line paper prints are made for specification sheets,
and light blue-line plastic prints for drafting. The blue-line prints are made on stable
plastic material so that drafting can be done directly on the print. Since light blue
does not photograph, only those features inked in black will appear on the negative to
be made of each finished drawing for chart reproduction. The black-line prints are
used to indicate which items to include on the finished drawing. Generally, separate
prints are used for indicating topographic and cultural features, hydrographic features,
type faces and sizes, and approved geographic names.

4417. Drafting of the chart original is done on a medium having minimum dis-
tortion qualities. The graticule and borders are drawn first, followed by planimetric
(horizontal) detail, and then relief. Next, the lettering is added. The chart title,
notes, etc., are added last, so they will not interfere with charted features.

A separate drawing is made for black and for each color to be shown on the chart.
The use of several draftsmen on the same chart permits the work on the various draw-
ings to go forward simultaneously and makes better use of the difference in experience
and skill of the various draftsmen. The preparation of the chart originals for a single
chart may require several months of continuous drafting.

4418. Review and edit.—When drafting has been completed, the chart original is
reviewed by an experienced cartographer. He carefully checks every detail for accu-
racy, and consults the latest Notice to Mariners and all other sources, to be certain
that nothing that should be charted has been omitted, and that the latest data have
been used. Any corrections to be made are indicated on a transparent overlay which
is returned with the chart original to the draftsman for action.

When all corrections have been made and checked, the chart original goes to a
chart editor. Here it is checked to see that the line work is sharp and clear, the type
is securely fastened, and that all work is in accordance with established standards.
Another check is made to be sure that the latest and most complete information has
been used.

When the chart editor is satisfied that the chart original meets the foregoing re-
quirements and is safe for navigation, he releases it for reproduction. The various steps
in preparing a chart original by the mosaic process are shown in figure 4418.

PRODUCTION OF NAUTICAL CHARTS 897

CONSTRUCTION OF A NAUTICAL CHART
INFORMATION SOURCES

Surveys

Geodetic control survey, hydro-
graphic survey, limited surveys.

RESEARCH 8 PLANNING

Available data evaluated, and best
sources recommended. Specifica-
tions prepared and procedures
designated.

Aerial Photography
Compilations from aerial photogra-
phy, liaison for data from other U.S.
Government charting agencies.

COMPILATION

Data selected from recommended
sources. Layout, film positive
mosaic, guide sheets, titles, notes,
etc. prepared. Hydrographic fea-
tures and type sizes selected.

PHOTOGRAPHY

Film positives made to scale from
compilation data. From mosaic a
blue-line plastic is made, on which
the chart original will be drafted.
Photo prints furnished for guides.

Foreign Sources
Foreign surveys & charts, charts
€ scientific data on exchange

agreements.
REVIEW

Film positive mosaic reviewed DRAFTING

pile E Chart original drafted on blue-line
tion of compilation guides. Blue- Dae Thi hendes Gal d
line plastic and guides forwarded Pipette: a8 meindes MADE an
to Drafting, Drawn chart original stickup of lettering and soundings.

Publications given final review. Late data

Notices to Mariners, Light Lists, dos tegen

Radio Navigational Aids.

EDITING

Final chart original edited for
conformance to standards. Chart
approved for navigational safety.
Chart released for reproduction.

PHOTOLITHOGRAPHY

Production of the printed chart.
See figure 4419.

Miscellaneous
Periodicals, travel booklets, plans,
sketches, etc. Data from private
corporations i.e. petroleum, steam-
ship, mapping companies, etc.

Figure 4418.—Flow of work in the construction of a nautical chart by the mosaic method.

4419. Reproduction.—Three basic processes of reproduction (printing) are in use
commercially: letterpress prints directly from raised type or other image; gravure
prints directly from a depressed image; and lithography prints indirectly (by offset)
from a surface that is neither raised nor depressed, operating on the principle of the
mutual repulsion of grease and water. The lithographic printing plate has a grease
image which is receptive to greasy ink, and a nonprinting portion which is receptive to
water. Charts are usually reproduced by photolithography, which uses photography in
the preparation of the lithographic plates. The essential steps in the reproduction of a
chart by this process are shown in figure 4419. |

In this process, the results of each step are checked carefully. A chart editor edits
black photo proofs made from the negatives, and color litho proofs made from the
plates. During printing, a continual check is made by the pressman to insure uni-

898

PRODUCTION OF NAUTICAL CHARTS

PHOTOLITHOGRAPHIC PROCESSING OF A NAUTICAL CHART

CHART ORIGINAL

In chart making, the copy is known as the
chart original. This original may be either a
drawn or engraved chart. After approval by
the chart editor it is sent to the Lithographic
Division to be processed for reproduction by
photolithography.

PLATE COATING

The coating operation is done in a whirler. It
has many variables such as grain texture,
whirler speed, drying heat, and fluidity of the
coating material. These variables affect coating
thickness, which is critical to the quality of the
finished plate.

PHOTOGRAPHY

Photography is done by a camera equipped
with lights, movable lens, a movable copy holder,
and a camera back that supports the photo
plates. The dark room type of camera is pre-
ferred for chart reproduction work. The copy is
mounted and the proper exposure settings deter-
mined. The camera is focused, copy illuminated,
and the exposure made.

PHOTO FINISHING

After exposure, the photo-sensitive material
is processed. Normally, nautical charts are
photographed on a glass negative (wet plate
process). Film or plastic negatives are also
used. Procedure, emulsion, and developer used
depends upon the type of negative being made.

PRINTING FRAME

Photo mechanical plates are exposed in a
vacuum printing frame. The coated press plate
is held firmly in contact with the negative by
creating and maintaining a vacuum. It is then
exposed to light which passes through the nega-
tive image onto the light sensitive press plate.

OPAQUING & RETOUCHING

(NEGATIVE ENGRAVING)

Imperfections which are not part of the image
are opaqued. Then the negative engravers re-
store or improve line work, lettering, and make
late additions and corrections. The negative is
is next placed into a printing frame with the
press plate for exposure.

PLATE PROCESSING

After exposure, the plate is developed by rub-
bing it up with a developing ink. A solution of
ammonia and water is then used to wash and
flush away the unexposed albumen, leaving only
the positive image of the chart on the plate.

PLATE GRAINING

Metal plates such as zine or aluminum are
grained to give the surface a matte finish. The
tiny depressions produced by graining the sur-
face act as reservoirs to hold the coating and
the dampening fluid (water). For economy,
prepared grained plates are stored in large quan-
tities suitable for immediate use.

PLATE TRANSFER

As received, the plate is sensitive to grease and
additions or corrections can be made on it by
drafting or hand transfer. The plate is then
given a desensitizing treatment making the non-
printing area no longer receptive to grease.
Then it is treated with an asphaltum base to
protect the image.

PRESS

The rotary offset press is widely used in print-
ing charts. Printing from a plate to a blanket
which in turn offsets the image onto the paper
gives this press its name. The basic parts area
plate cylinder, blanket cylinder, impression cylin-
der, ink reservoir, and water fountain. Multicol-

ored presses print several colors in one operation.

FIGURE 4419.—Flow of work in the photolithographic processing of a nautical chart.

formity of impressions and accurate "register" (each color being printed at the correct
place on the chart). 'The highest standards possible are maintained throughout the
entire operation.

When printing is completed, the plates are removed from the cylinders, cleaned,
and the image side given a protective coating of soluble gum arabic and asphaltum.
The plates are then stored in vertical racks. The glass negatives have already been
stored. A photographic duplicate of the chart original may have been made, and the
original and a copy stored at separate locations for possible future use.

PRODUCTION OF NAUTICAL CHARTS 899

4420. Chart record.—A record of each chart is maintained to provide a history,
from the authorization of its first edition to the date of the last action, perhaps many
editions and printings later. The record accompanies the chart original throughout
production, with appropriate entries being made as it progresses through the various
steps. Included in the record are such data as sources of information used, method of
construction, the map projection graticule computation, geodetic control used, and
decisions rendered.

A well-written chart record is valuable in the prevention of duplicative effort.
Also, it is the medium through which research is conducted when questions arise as to
why certain data were shown on or removed from any issue of the chart.

us IE

A J S "m awl ves » RN up
Se 4 ` “tx + TAS T
Be y A = id «d mera de
EM P H

=
> D
e +
e
E R `
>
=
=>
e Ke
£ =
- 4
`
tæ
y
4
r
=
c

=

Bii EE
y ON EE odpira
lian apres dtumed. et, cotan;

Sah EE 54 Wade courant,
Palama correcto

LDL 4
q...

T. ie : MT RS o po OEE FRAO PO xa: `
Pg BOP WISHEY 10 = aad E s Lio Satin U Tada
See, a ARDEN DICES mug pay

LE
NDI S kuta labrt , xianagah ——
Aðditinn al j

an obaniidy’ nad

MY E Bite? zixwaesd,
HE

its M D xia aah
Ip eg a xis zu ^

++

“e

APPENDIX A.
APPENDIX B.
APPENDIX C.
APPENDIX D.
APPENDIX E.
APPENDIX F.
APPENDIX G.
APPENDIX H.
APPENDIX JI.
APPENDIX J.
APPENDIX K.
APPENDIX L.
APPENDIX M.
APPENDIX N.
APPENDIX O.
APPENDIX P.
APPENDIX Q.
APPENDIX R.
APPENDIX S.
APPENDIX T.
APPENDIX U.
APPENDIX V.
APPENDIX W.
APPENDIX X.
APPENDIX Y.
APPENDIX Z.
APPENDIX AA.
APPENDIX BB.
APPENDIX CC.

APPENDICES

Abbreviations and Symbols 00 S
Greek Alphabets 29 3 007 S S
Glossary ue ves n ve de da eec c
Miscellaneous Data ms c
Navigational Coordinates. 022. A
Planets... cv. 4242 cart ced eMe E
Identification of Navigational Stars_____.._.--------------
Navigational Stars and the Planets: ---... == =
CQonstellatiors....-.27 Tvs
Buoyage Systems... crespo. S CE
Chart Symbols... 0222022206 0222.53 S
Units of Depth Measurement on Charts of Various Nations. __
Tidal Datums in Use in Various Areas
Sources of Charts and Publications
Mathematics
Interpolation
Work Forms

Long-term Almanac ECB EE
Extracts from H.O. Pub. No.
Extracts from H.O. Pub. No.
Extracts from H.O. Pub. No.
Extracts from H.O. Pub. No.
Extracts from H.O. Pub. No.

APPENDIX A
ABBREVIATIONS AND SYMBOLS

A more complete listing of abbreviations and symbols is given in H.O. Pub. No.
220, Navigation Dictionary, of which this is an abridgment.

A, amplitude; augmentation; away (alti-

tude difference).

a, altitude difference (Ho~Hc); altitude
factor (change of altitude in one minute

. of time from meridian transit) ; assumed.

Ao, first Polaris correction.

a, second Polaris correction.

a2, third Polaris correction.

AC, alternating current.

add'l, additional.

AF, audio frequency.

aL, assumed latitude.

AM, amplitude modulation.

AM, ante meridian (before noon).

antilog, antilogarithm.

AP, assumed position.

approx., approximate, approximately.

AU, astronomical unit.

a), assumed longitude.

B, atmospheric pressure correction (alti-
tude); bearing, bearing angle.

Ba, difference between heading and ap-
parent wind direction.

Bn, bearing (as distinguished from bearing
angle).

Bpge, bearing per gyro compass.

Br, difference between heading and true
wind direction.

C, acceleration correction (altitude);
Celsius (centigrade); chronometer time;
compass (direction); correction; course,
course angle.

CB, compass bearing.

CC, compass course.

CCU, chart comparison unit.

CE, chronometer error; compass error.

CH, compass heading.

cm, centimeter, centimeters.

Cn, course (as distinguished from course
angle).

co-, the complement of (90° minus).

colog, cologarithm.

corr., correction.

cos, cosine.

cot, cotangent.

COV, COVersine.

Cpgc, course per gyro compass.

cps, cycles per second.

csc, cosecant.

CW, continuous wave.

CZn, compass azimuth.

D, deviation; dip (of horizon); distance.

d, declination (astronomical); difference.

d, declination change in one hour.

DC, direct current.

dec., declination.

Dev., deviation.

DG, degaussing.

diff., difference.

dist., distance.

DLo, difference of longitude (arc units).

DR, dead reckoning, dead reckoning
position.

DRE, dead reckoning equipment.

DRM, direction of relative movement.

DRT, dead reckoning tracer.

D,, dip short of horizon.

dur., duration.

da, difference of longitude (time units).

E, east.

e, base of Naperian logarithms.

e, eccentricity.

EHF, extremely high frequency.

EP, estimated position.

EPI, electronic position indicator.

Eq.T, equation of time.

ETA, estimated time of arrival.

F, Fahrenheit; fast; longitude factor;
phase correction (altitude).

f, latitude factor.
903

904

FM, frequency modulation.

ft., foot, feet.

G, Greenwich, Greenwich meridian (up-
per branch); grid (direction).

g, acceleration due to gravity; Greenwich
meridian (lower branch).

GAT, Greenwich apparent time.

GB, grid bearing.

GC, grid course.

GE, gyro error.

GH, grid heading.

GHA, Greenwich hour angle.

GMT, Greenwich mean time.

GP, geographical position.

Gr., Greenwich.

GST, Greenwich sidereal time.

GV, grid variation.

GZn, grid azimuth.

H, high (loran PRR); horizontal inten-
sity of earth’s magnetic field; sea tilt
correction (altitude).

h, altitude (astronomical); height above
sea level.

ha, approximate altitude.

hav, haversine.

He, computed altitude.

Hdg., heading.

HE, heeling error; height of eye.

HF, high frequency.

HHW, higher high water.

HLW, higher low water.

H.O., Hydrographic Office.

Ho, observed altitude.

HP, horizontal parallax.

Hp, precomputed altitude.

Hpgc, heading per gyro compass.

hr, rectified altitude.

hr., hour.

hrs., hours.

hs, sextant altitude.

ht, tabulated altitude.

HW, high water.

I, dip (magnetic); instrument correction.

IC, index correction.

in., inch, inches.

int., interval.

ISLW, Indian spring low water.

J, irradiation correction (altitude).

K, Kelvin (temperature); constant of the
cone; constant proportional to required
length of Flinders bar.

APPENDIX A: ABBREVIATIONS AND SYMBOLS

ke, kilocycle, kilocycles; kilocycles per
second.

km, kilometer, kilometers.

kmc, kilomegacycle, kilomegacycles; kilo-
megacycles per second.

kn., knot, knots.

L, latitude; low (loran PRR); lower limb
correction for moon (from Nautical
Almanac) ; wave length (water).

l, difference of latitude; logarithm, loga-
rithmic.

LAN, local apparent noon.

LAT, local apparent time.

lat., latitude.

LF, low frequency.

LHA, local hour angle.

LHW, lower high water.

LL, lower limb.

LLW, lower low water.

Lm, middle latitude.

LMT, local mean time.

log, logarithm, logarithmic.

log., natural logarithm (to the base e).

logis, common logarithm (to the base 10).

long., longitude.

LST, local sidereal time.

LW, low water.

M, celestial body; meridian (upper
branch); magnetic (direction); me-
ridional parts; nautical mile, miles.

m, meridian (lower branch); meridional
difference (M;—Mj;); meter, meters;
statute mile, miles.

mag., magnetic; magnitude.

MB, magnetic bearing.

mb, millibar, millibars.

MC, magnetic course.

mc, megacycle, megacycles; megacycles
per second.

MF, medium frequency.

MH, magnetic heading.

MHHW, mean higher high water.

MHW, mean high water.

MHWN, mean high water neaps.

MHWS, mean high water springs.

mi., mile, miles.

mid, middle.

min., minute, minutes.

MLLW, mean lower low water.

MLW, mean low water.

MLWN, mean low water neaps.

APPENDIX A: ABBREVIATIONS AND SYMBOLS

MLWS, mean low water springs.

mm, millimeter.

mo., month.

mos., months.

mph, miles (statute) per hour.

MPP, most probable position.

MSL, mean sea level.

MZn, magnetic azimuth.

N, north; tilt correction (altitude).

n, natural (trigonometric function).

Na, nadir.

P, atmospheric pressure; parallax; planet;
pole; wave period (water).

p, departure, polar distance.

PC, personal correction.

pge, per gyro compass.

P in A, parallax in altitude.

PM, pulse modulation.

PM, post meridian (after noon).

Pn, north pole; north celestial pole.

PPI, plan position indicator.

PRR, pulse repetition rate.

Ps, south pole; south celestial pole.

psc, per standard compass.

p stg c, per steering compass.

Pub., publication.

PV, prime vertical.

Q, Polaris correction (Air Almanac).

QQ’, celestial equator.

R, Rankine (temperature) ; refraction.

RA, right ascension.

rad, radian, radians.

RAR, radio acoustic ranging.

Ra. Ref., radar reflector.

RB, relative bearing.

R Bn, radiobeacon.

RDF, radio direction finder.

rev., reversed.

RF, radio frequency.

R Fix, running fix.

RZn, relative azimuth.

S, sea-air temperature difference correc-
tion (altitude); slow; south; special
(loran PRR); speed.

s, 4 (h+ L+p); standard deviation.

Sa, speed of apparent wind in units of
ship's speed.

SD, semidiameter.

sec, secant.

sec., second, seconds.

semidur., semiduration.

905

SH, ship's head (heading).

SHA, sidereal hour angle.

SHF, super high frequency.

sin, sine.

SRM, speed of relative movement.

Sr, speed of true wind in units of ship’s
speed.

T, air temperature correction (altitude);
table; temperature; time; toward (alti-
tude difference); true (direction).

t, dry-bulb temperature; elapsed time;
meridian angle.

t’, wet-bulb temperature.

tab., table.

tan, tangent.

TB, true bearing; air temperature-atmos-
pheric pressure correction (altitude).

TC, true course.

TcHHW, tropic higher high water.

TcHLW, tropic higher low water.

TcLHW, tropic lower high water.

TcLLW, tropic lower low water.

Ta, ground-wave reading (loran).

Tas, ground-wave-sky-wave reading
(loran).

TH, true heading.

TR, track.

Tr., transit.

Ts, sky-wave reading (loran).

Tsc, sky-wave-ground-wave reading
(loran).

TZn, true azimuth.

U, upper limb correction for moon (from
Nautical Almanac).

UHE, ultra high frequency.

UL, upper limb.

UT, universal time.

V, deflection of the vertical; variation;
vertex.

v, excess of GHA change from adopted
value for one hour.

Var., variation.

ver, versine.

VHF, very high frequency.

VLF, very low frequency.

VPR, virtual PPI reflectoscope.

W, watch time; wave-height correction
(altitude); west.

WE, watch error.

WT, war time.

X, parallactic angle.

906

yd., yard.

yds., yards.

yr., year.

yrs., years.

Z, azimuth angle; Coriolis correction
(altitude); vertical intensity of earth’s
magnetic field; zenith.

z, zenith distance.

ZD, zone description.

Zn, azimuth (as distinguished from azi-
muth angle).

Znpge, azimuth per gyro compass.

APPENDIX A: ABBREVIATIONS AND SYMBOLS

ZT, zone time.

a, damping error (gyro compass).

A, a small increment, or the change in one
quantity corresponding to unit change
in another.

6, speed error (gyro compass).

A, longitude; shielding factor; wave length
(radiant energy).

u, index of refraction; permeability.

us, microsecond.

m, ratio of circumference of circle to
diameter=3.14159+.

Positions

© Dead reckoning position; fix, running
fix.

© Estimated position.

Mathematical Symbols

Plus (addition)

Minus (subtraction)
Plus or minus
Absolute difference
Times (multiplication)
Divided by (division)
Square root

ee He ir

=

V nth root
= Equals
> Is greater than
< Is less than
J Integral sign
œ Infinity
... Repeating decimal

Celestial Bodies

Sun
Moon
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Star

zk mée RH DO oe

*-P Star-planet altitude correction (al-
titude)
Lower limb
Center
Upper limb
New moon
Crescent moon
First quarter
Gibbous moon
Full moon
‘Gibbous moon
Last quarter
Crescent moon

a Qo

eéeoooe*eeen|nj^

Signs of the Zodiac

Aries (vernal equinox)
Taurus

Gemini

Cancer (summer solstice)
Leo

Virgo

d49b5muec-3

= Libra (autumnal equinox)
M Scorpius

1 Sagittarius

V3 Capricornus (winter solstice)
Aquarius

Pisces

AA 8

APPENDIX A: ABBREVIATIONS AND SYMBOLS 907

Miscellaneous Symbols

Y Years * Interpolation impractical
™ Months ° Degrees
d Days ^ Minutes of arc

Seconds of arc
" Minutes of time ó Conjunction
* Seconds of time $ Opposition

ER Remains below horizon O Quadrature

Q

V

^ Hours

CJ Remains above horizon Ascending node
//// Twilight all night Descending node

APPENDIX B
GREEK ALPHABET

Aaa Alpha Nv Nu

B 66 Beta E Xi

Da Gamma Oo Omicron
Að Delta ras Pi

Ee Epsilon P p Rho
AG Zeta Dos Sigma
H 7 Eta T7 Tau
009 Theta Tu Upsilon
It Iota ae Phi

K x Kappa Xx Chi
AA Lambda Y y Psi

Mu Mu N w Omega

APPENDIX C
GLOSSARY

This appendix is an abridgment of the definitions of H.O. Pub. No. 220, Navigation

Dictionary, to which reference should be made for complete definitions.

abeam. Bearing approximately 090° relative (abeam to starboard) or 270° relative
(abeam to port).

aberration. The apparent displacement of a celestial body in the direction of
orbital motion of the earth.

abscissa. The horizontal coordinate of a set of rectangular coordinates.

absolute humidity. The mass of water vapor per unit of volume of air.

absolute zero. Thelowest possible temperature, about (—) 459967 For (—) 273915 C.

aclinic line. The magnetic equator.

acoustic navigation. Sonic navigation.

acute angle. An angle less than 90°.

advance. ‘The distance a vessel moves in its original direction in making a turn.

advanced line of position. A line of position which has been moved forward
to allow for the run since the line was established.

advection. Horizontal movement of part of the atmosphere.

age of the moon. The elapsed time, usually expressed in days, since the last
new moon.

agonic line. A line connecting points of no magnetic variation.

aground. ‘Touching, resting, or lodged on the bottom.

ahead. Bearing approximately 000° relative.

aid to navigation. A device external to a craft, designed to assist in determination
of position of the craft, or of a safe course, or to warn of dangers.

air almanac. A periodical publication of astronomical data designed primarily
for air navigation.

air mass. An extensive body of air within which the conditions of temperature
and moisture in a horizontal plane are essentially uniform.

air navigation. The navigation of aircraft.

air temperature correction. That sextant altitude correction due to changes in
refraction caused by difference between the actual temperature and the standard
temperature used in the computation of the refraction table.

alidade. A telescope or other device mounted over a compass, compass repeater,
or compass rose, for measuring direction.

alignment. Adjustment of the tuned circuits of electronic equipment for optimum
performance, or synchronization of two or more components of an electronic system.

almanac. A periodical publication of astronomical data useful to a navigator.

Alnico. The trade name for an alloy composed principally of aluminum, nickel,
cobalt, and iron; used for permanent magnets.

alternating current. An electric current that continually changes in magnitude
and periodically reverses polarity.

alternating fixed and flashing light. A fixed light varied at regular intervals by
one or more flashes of greater brilliance, with color variations in either the fixed light

or flashes, or both.
909

910 APPENDIX C: GLOSSARY

alternating fixed and group flashing light. A fixed light varied at regular in-
tervals by a group of two or more flashes of greater brilliance, with color variations in
either the fixed light or flashes, or both.

alternating flashing light. A light showing one or more flashes with color variations
at regular intervals, the duration of light being less than that of darkness.

alternating group flashing light. A light showing groups of flashes with color
variations at regular intervals, the duration of light being less than that of darkness.

alternating group occulting light. A light having groups of total eclipses at
regular intervals and having color variations, the duration of light being equal to or
greater than that of darkness.

alternating light. A light having periodic color variations, particularly one with
constant luminous intensity.

alternating occulting light. A light having one or more total eclipses at regular
intervals and having color variations, the duration of light being equal to or greater than
that of darkness.

altitude. Angular distance above the horizon; the arc of a vertical circle between
the horizon and a point on the celestial sphere, measured upward from the horizon.

altitude azimuth. An azimuth determined when altitude, declination, and latitude
are known.

altitude circle. Parallel of altitude.

altitude difference. The difference between computed and observed altitudes, or
between precomputed and sextant altitudes.

altitude intercept. Altitude difference.

altocumulus. A cloud layer (or patches) within the middle level (mean height
6,500-20,000 ft.) composed of rather flattened globular masses, the smallest elements
of the regularly arranged layers being fairly thin, with or without shading. These
elements are arranged in groups, in lines or in waves, following one or two directions,
and are sometimes so close together that their edges join.

altostratus. A sheet of gray or bluish cloud within the middle level (mean height
6,500-20,000 ft.). Sometimes the sheet is composed of a compact mass of dark, thick,
gray clouds of fibrous structure; at other times the sheet is thin and through it the sun
or moon can be seen dimly as though gleaming through ground glass.

amplitude. 1. Angular distance north or south of the prime vertical; the arc of
the horizon or the angle at the zenith between the prime vertical and a vertical circle,
measured north or south from the prime vertical to the vertical circle. 2. The maxi-
mum value of the displacement of a wave or other periodic phenomenon from the zero
position.

amplitude balance. Equality in the amplitude of two or more signals.

amplitude modulation. The process of changing the amplitude of a carrier wave
in accordance with the variations of a modulating wave.

anchorage. An area where a vessel anchors or may anchor, either because of
suitability or designation.

anchorage buoy. One of a series of buoys marking the limits of an anchorage.

anchorage chart. A nautical chart showing prescribed or recommended anchor-
ages.

anchor buoy. A buoy marking the position of an anchor.

anemometer. An instrument for measuring the speed of the wind. Some in-
struments also indicate the direction from which it is blowing.

aneroid barometer. An instrument which determines atmospheric pressure by

the effect of such pressure on a thin-metal cylinder from which the air has been partly
exhausted.

APPENDIX C: GLOSSARY 911

angle. The inclination to each other of two intersecting lines, measured by the
are of a circle intercepted between the two lines forming the angle, the center of the
circle being the point of intersection.

angular distance. The angular difference between two directions, or the arc of
the great circle joining two points.

anneal. To heat (metal) to a high temperature and then allow to cool slowly, for
the purpose of softening, making less brittle, or removing permanent magnetism.

annular. Ring-shaped.

annular eclipse. An eclipse in which a thin ring of the source of light appears
around the obscuring body.

anode. The positive pole or electrode of an electron tube or an electric cell.

ante meridian. Before noon.

antenna. A conductor or system of conductors for radiating or receiving radio
waves.

antenna array. A group of antennas arranged so as to obtain directional char-
acteristics.

anticyclone. An approximately circular portion of the atmosphere, having
relatively high atmospheric pressure and winds which blow clockwise around the
center in the northern hemisphere and counterclockwise in the southern hemisphere.

antilogarithm. The number corresponding to a given logarithm.

aperiodic compass. A compass that, after being deflected, returns by one direct
movement to its proper reading, without oscillation.

aphelion. That orbital point farthest from the sun when the sun is the center
of attraction (as in the case of a planet).

apogean tides. Tides of decreased range occurring when the moon is near apogee.

apogee. "That orbital point farthest from the earth when the earth is the center
of attraction (as in the case of the moon).

apparent altitude. Rectified altitude.

apparent horizon. Visible horizon.

apparent motion. Motion relative to a specified or implied reference point which
may itself be in motion.

apparent sun. The actual sun as it appears in the sky.

apparent time. Time based upon the rotation of the earth relative to the apparent
(true) sun.

apparent wind. Wind relative to a moving point, such as a vessel.

approximate altitude. An altitude determined by inexact means, as by estimation
or by a star finder or star chart.

arc. 1. Part of acurved line, as a circle. 2. The graduated scale of an instrument
for measuring angles, as a marine sextant.

arc of visibility. The arc of a light sector, designated by its limiting bearings
as observed at points other than the light.

argument. One of the values used for entering a table or diagram.

arm. 1. An inlet. 2. A slender part of an instrument, device, or machine.

Armco. The trade name for a high-purity, low-carbon iron, used for Flinders
bars, quadrantal correctors, etc.

arming. Tallow or other substance placed in the recess at the lower end of a sound-
ing lead, for obtaining a sample of the bottom.

artificial horizon. A device for indicating the horizontal.

artificial-horizon sextant. A sextant having an artificial horizon built in.

A-scope. A cathode ray scope on which the trace appears as a horizontal or vertical
range scale and the signals appear as perpendicular deflections.

912 APPENDIX C: GLOSSARY

assumed latitude. The latitude at which an observer is assumed to be located
for an observation or computation.

assumed longitude. The longitude at which an observer is assumed to be located
for an observation or computation.

assumed position. A point at which a craft is assumed to be located, particularly
one used as a preliminary to establishing certain navigational data, as that point on
the surface of the earth for which the computed altitude is determined in the solution
of a celestial observation.

astern. Bearing approximately 180° relative.

astrolabe. An instrument used for determining an accurate astronomical position
ashore, as in survey work.

astronomical latitude. Angular distance between the direction of gravity and the
plane of the equator.

astronomical longitude. The angle between the plane of the reference meridian
and the plane of the celestial meridian.

astronomical position. A point on the earth determined by celestial observation.

astronomical refraction. Atmospheric refraction of a ray of radiant energy from
outer space.

astronomical tide. Tide related to the attractions of celestial bodies, particularly
the sun and moon.

astronomical triangle. The .navigational triangle, either terrestrial or celestial,
used in the solution of celestial observations.

astronomical twilight. The period of incomplete darkness when the upper limb
of the sun is below the visible horizon, and the center of the sun is not more than 18°
below the celestial horizon.

astronomical unit. The mean distance between the earth and the sun, approxi-
mately 92,900,000 statute miles, used as a unit of measurement of distance within
the solar system.

atmosphere. The envelope of air surrounding the earth or other celestial body.

atmospheric absorption. The loss of power in transmission of radiant energy by
dissipation in the atmosphere.

atmospheric noise. Static.

atmospheric pressure. The pressure exerted by the weight of the earth’s atmos-
phere. Its standard value at sea level is about 14.7 pounds per square inch.

atmospheric pressure correction. That sextant altitude correction due to changes
in refraction caused by nonstandard atmospheric pressure.

atmospheric refraction. Refraction of a ray of radiant energy passing obliquely
through the atmosphere.

A trace. The first trace of a scope having more than one, as the upper trace of a
loran indicator.

attenuation. A lessening in amount, particularly the reduction of the amplitude of
a wave with distance from the origin.

audio frequency. A frequency within the audible range, about 20 to 20,000
cycles per second.
| augmentation. The apparent increase in the semidiameter of a celestial body as
its altitude increases, due to the decreased distance from the observer.

aural null. A null detected by listening for a minimum or the complete absence
of an audible signal.

aurora. A luminous phenomena due to electrical discharge in the upper atmosphere,
most commonly seen in high latitudes.

aurora australis. The aurora in the southern hemisphere.

APPENDIX C: GLOSSARY 913

aurora borealis. 'The aurora in the northern hemisphere.

auroral zone. The area of maximum auroral activity.

automatic celestial navigation. Automatic and continuous indication of position
by a device which tracks celestial bodies and solves for geographical coordinates.

automatic radio direction finder. A radio direction finder which indicates auto-
matically and continuously the great-circle direction of the transmitter to which it is
tuned.

autumnal equinox. That point of intersection of the ecliptic and the celestial
equator occupied by the sun as it changes from north to south declination, on or
about September 23, or the instant this occurs.

awash. Situated so that the top is intermittently washed by waves or tidal
` action.

azimuth. The horizontal direction of a celestial point from a terrestrial point.
It is usually measured from 000° at the reference direction clockwise through 360°.

azimuthal equidistant projection. An azimuthal map projection in which dis-
tances from the point of tangency are accurately represented according to a uniform
scale.

azimuthal projection. A map projection in which the surface of a sphere or
spheroid, such as the earth, is conceived as developed on a tangent plane, with the
result that azimuths or bearings of any point from the center are correctly represented.

azimuth angle. Azimuth measured from 0° at the north or south reference direc-
tion clockwise or counterclockwise through 90° or 180°.

azimuth bar. A slender bar with a vane at each end, designed to fit over a central
pivot in the glass cover of a magnetic compass for measurement of compass azimuths.

azimuth circle. A ring designed to fit snugly over a compass or compass repeater,
and provided with means for observing compass bearings and azimuths.

azimuth instrument. An instrument for measuring azimuths, particularly a
device which fits snugly over a central pivot in the glass cover of a magnetic compass.

azimuth tables. Publications providing tabulated azimuths or azimuth angles.

back. Of the wind, to change direction counterclockwise in the northern hemi-
sphere and clockwise in the southern hemisphere.

back sight. An observation of a celestial body made by facing 180° from the
azimuth of the body.

ballistic damping error. That error introduced in a nonpendulous gyro compass
as a result of the method used to damp the oscillations of the gyro spin axis.

ballistic deflection error. A temporary error introduced in a gyro compass by
the accelerating force acting upon the damping mechanism when a vessel changes
course or speed.

bandwidth. The number of units (cycles, kilocycles, etc.) of frequency required
for transmission.

barograph. A recording barometer.

barometer. An instrument for measuring atmospheric pressure.

barometric pressure. Atmospheric pressure as indicated by a barometer.

barometric tendency. The change of barometric pressure within a specified time
(usually three hours) before an observation, together with the direction of change and
the characteristics of the rise or fall.

bar scale. A line or series of lines on a chart, subdivided and labeled with the
distances represented on the chart. l

base line. 1. The line between two transmitters operating together to provide
a line of position, as in loran. 2. Any line serving as the basis for measurement of
other lines, as in surveying. 3. The trace of a cathode ray tube.

914 APPENDIX C: GLOSSARY

base line delay. The time interval needed for the signal from a loran master
station to travel the length of the base line, introduced as a delay between transmis-
sion of the master and slave signals.

base line extension. The extension of a base line beyond the transmitters.

basic pulse repetition rate. The lowest pulse repetition rate of a group differing
only slightly from each other.

bathymetric chart. A topographic chart of the bed of a body of water.

bathythermograph. A recording thermometer for determining temperature of
the sea at various depths.

Bayer’s name. The Greek (or Roman) letter and the possessive form of the
Latin name of a constellation, used as a star name.

beacon. 1. A fixed aid to navigation. 2. An unlighted aid to navigation.
3. Anything serving as a signal or conspicuous indication, either for guidance or
warning.

beam width. The angular width of a beam of radiant energy between half-power
intensities.

bearing. The horizontal direction of one terrestrial point from another. It is
usually measured from 000° at the reference direction clockwise through 360°.

bearing angle. Bearing measured from 0° at the north or south reference direc-
tion clockwise or counterclockwise through 90° or 180°.

bearing bar. A slender bar with a vane at each end, designed to fit over a cen-
tral pivot in the glass cover of a magnetic compass, for measurement of compass
bearings.

bearing circle. A ring designed to fit snugly over a compass or compass repeater,
and provided with vanes for observing compass bearings.

bearing line. A line extending in the direction of a bearing.

bearing repeater. A compass repeater used primarily for observing bearings.

Beaufort scale. A numerical scale for indicating wind speed, named after Admiral
Sir Francis Beaufort, who devised it in 1806.

beset. Surrounded so closely by sea ice that steering control is lost.

binnacle. The stand in which a compass is mounted.

blinking. Regular shifting right and left of a loran signal to indicate that the
signals are out of synchronization.

blue azimuth tables. H.O. Pub. No. 261, Azimuths of Celestial Bodies.

blue magnetism. The magnetism of the south-seeking end of a freely suspended
magnet.

boat compass. A small compass mounted in a box for convenient use in small
craft.

bobbing a light. Quickly lowering the height of eye several feet and then raising
it again when a light is first sighted, to determine whether the observer is at the geo-
graphical range of the light.
) bottom sample. A portion of the material forming the bottom, brought up for
inspection.

bow and beam bearings. Successive relative bearings (right or left) of 45% and
90° of a fixed object.

boxing the compass. Stating in order the names of the points (and sometimes
fractional points) of the compass.

broad on the beam. Bearing 090? relative (“broad on the starboard beam") or
270? relative (broad on the port beam").

broad on the bow. Bearing 045? relative (broad on the starboard bow") or 315°
relative (broad on the port bow”).

APPENDIX C: GLOSSARY 915

broad on the quarter. Bearing 135? relative ("broad on the starboard quarter")
or 225? relative ("broad on the port quarter").

B trace. The second trace of a scope having more than one, as the lower trace of
a loran indicator.

bubble sextant. A sextant with a bubble to indicate the horizontal.

buoy. A floating object, other than a lightship, moored or anchored to the bottom
as an aid to navigation.

buoyage. A system of buoys.

cable. 1. A unit of distance equal to 720 feet in the U. S. Navy. 2. A chain
or strong fiber or wire rope used to anchor or moor vessels or buoys. 3. A stranded
electric conductor or several conductors laid up together.

cage. To erect a gyro or lock it in place.

calculated altitude. Computed altitude.

calibrate. To determine or rectify the scale graduations of an instrument.

calibration table. A table of calibration corrections or calibrated values.

calving. The breaking away of a mass of ice from a parent iceberg, glacier, or
ice shelf.

can buoy. A buoy the above-water part of which is in the shape of a cylinder.

candela. The United States and international unit of luminous intensity.

cardinal point. North, east, south, or west.

carrier wave. A radio wave used as a vehicle for conveying intelligence, generally
by modulation.

Cartesian coordinates. Magnitudes defining a point relative to two intersecting
lines or azes.

cartography. The art and science of making charts or maps.

cathode. The negative pole or electrode of an electron tube or an electric cell.

cathode ray tube. The “picture” tube of radar, loran, television, etc.

C-band. A radio-frequency band of 3,900 to 6,200 megacycles.

celestial body. Any aggregation of matter in space constituting a unit, such as
the sun, a planet, etc.

celestial coordinates. Any set of coordinates used to define a point on the celestial
sphere.

celestial equator. The intersection of the celestial sphere and the extended plane
of the equator.

celestial equator system of coordinates. Declination and hour angle or declina-
tion and sidereal hour angle.

celestial fix. A fix established by observation of celestial bodies.

celestial horizon. That great circle of the celestial sphere formed by the inter-
section of the celestial sphere and a plane through the center of the earth and perpendic-
ular to the zenith-nadir line.

celestial latitude. Angular distance north or south of the ecliptic; the arc of a
circle of latitude between the ecliptic and a point on the celestial sphere, measured
northward or southward from the ecliptic through 90°, and labeled N or S to indicate
the direction of measurement.

celestial line of position. A line of position established by observation of a celestial
body.

celestial longitude. Angular distance east of the vernal equinox, along the
ecliptic; the arc of the ecliptic or the angle at the ecliptic pole between the circle of
latitude of the vernal equinox and the circle of latitude of a point on the celestial
sphere, measured eastward from the circle of latitude of the vernal equinox, through

360°.

916 APPENDIX C: GLOSSARY

celestial meridian. A great circle of the celestial sphere, through the celestial
poles and the zenith.

celestial navigation. Navigation with the aid of celestial bodies.

celestial observation. Observation of celestial phenomena.

celestial poles. The intersection of the celestial sphere and the extended axis of
the earth.

celestial sphere. An imaginary sphere of infinite radius concentric with the earth,
on which all celestial bodies except the earth are imagined to be projected.

celestial triangle. A spherical triangle on the celestial sphere, especially the navi-
gational triangle.

Celsius temperature. Temperature based upon a scale in which, under standard
atmospheric pressure, water freezes at 0? and boils at 100%. Called ''centigrade
temperature” before 1948.

centering control. A control used to center the image on a cathode ray tube.

centering error. That instrumental error due to inaccurate pivoting of a moving
part.

centigrade temperature. Celsius temperature.

change of tide. A reversal of the direction of motion (rising or falling) of a tide.

characteristics of a light. The sequence and length of light and dark periods and
the color or colors by which a navigational light is identified.

character of the bottom. The type of material of which the bottom is composed.

chart. A map intended primarily for navigational use.

chart comparison unit. A device which provides simultaneous, superimposed
views of a chart and radar scope.

chart datum. The tidal datum to which soundings on a chart are referred.

charted depth. The vertical distance from the chart datum to the bottom.

charted visibility. The extreme distance, shown in numbers on a chart, at which
a navigational light can be seen under standard conditions.

chartlet. 1. A small chart. 2. A graphic supplement to Notice to Mariners.

chart projection. A map projection used for a chart.

chart reading. Interpretation of the symbols, lines, abbreviations, and terms
appearing on charts.

chronometer. A timepiece with a nearly constant rate.

chronometer error. The amount by which chronometer time differs from the
correct time to which it was set, usually Greenwich mean time.

chronometer rate. The amount gained or lost by a chronometer in unit time,
usually seconds per day.

chronometer time. Time as indicated by a chronometer.

chronometer watch. A small chronometer, especially one with an enlarged watch-
type movement.

circle of declination. Hour circle.

circle of equal altitude. A circle on the surface of the earth, on every point of
which the altitude of a given celestial body is the same at a given instant.

circle of equal declination. Parallel of declination.

circle of latitude. 1. A great circle of the celestial sphere, perpendicular to the
ecliptic. 2. A meridian of the earth.

circle of longitude. 1. A circle of the celestial sphere, parallel to the ecliptic.
2. A parallel of latitude on the earth.

circle of position. A circular line of position.

circle of right ascension. Hour circle.

circle of uncertainty. A circle within which a craft is considered to be located.

APPENDIX C: GLOSSARY 917

circle of visibility. That circle surrounding an aid to navigation in which the aid
is visible.

circumpolar. Revolving about the elevated pole without setting.

cirrocumulus. High clouds (mean lower level above 20 ,000 ft.) composed of small
white flakes or of very small globular masses, usually tmt shadows, which are
arranged in groups or lines, or more often in WAR resembling those of ad on the
seashore.

cirrostratus. Thin, whitish, high clouds (mean lower level above 20,000 ft.) some-
times covering the sky completely and giving it a milky appearance and at other times
presenting, more or less distinctly, a formation like a tangled web.

cirrus. Detached high clouds (mean lower level above 20,000 ft.) of delicate and
fibrous appearance, without shading, generally white in color, and often of a silky
appearance.

civil twilight. The period of incomplete darkness when the upper limb of the sun
is below the visible horizon, and the center of the sun is not more than 6° below the
celestial horizon.

clamp screw. A screw for holding a moving part in place, as during an observation
or reading, particularly such a device used in connection with the tangent screw of a
marine sextant.

clamp screw sextant. A marine sextant having a clamp screw for controlling the
position of the tangent screw.

cloud. A visible assemblage of numerous tiny droplets of water or ice crystals
formed by condensation of water vapor in the air, with the base above the surface of
the earth.

clutter. Atmospheric noise, extraneous signals, etc., which tend to obscure the
reception of a desired signal in a radio receiver, on a radar scope, etc.

coaltitude. Ninety degrees minus the altitude.

coarse delay. On a loran indicator, a dial for controlling relatively large changes
in the position of the B trace pedestal.

coastal current. An ocean current flowing roughly parallel to a coast, outside the
surf zone.

coastal refraction. A small change in the direction of travel of a radio signal when
it crosses a shore line obliquely.

coast chart. A nautical chart intended for use near a shore, as in entering and
leaving harbors.

coasting. Proceeding approximately parallel to a coast line and near enough to
be in pilot waters most of the time.

coast pilot. A descriptive book for the use of mariners, containing detailed infor-
mation of coastal waters, harbor facilities, etc., of an area, particularly along the coasts
of the United States.

coast piloting. The directing of the movements of a vessel near a coast, by means
of terrestrial reference points.

coastwise navigation. Navigation in the vicinity of a coast.

codeclination. Ninety degrees minus the declination.

coding delay. An arbitrary time delay in the transmission of pulse signals.

colatitude. Ninety degrees minus the latitude.

cold air mass. An air mass that is colder than surrounding air, and usually colder
than the surface over which it is moving.

cold front. That line of discontinuity, at the earth’s surface or at a horizontal
plane aloft, along which an advancing cold air mass is undermining and displacing a
warmer air mass.

918 APPENDIX C: GLOSSARY

collision bearing. A constant bearing maintained while the distance between two
craft is decreasing. i

cologarithm. The logarithm of the reciprocal of a number. k

combination buoy. A buoy having more than one means of conveying intelligence,
as by light and sound. h f

comparing watch. A hack watch having its error determined by comparison with
a chronometer. i

compass. An instrument for determining a horizontal reference direction relative
to the earth.

compass adjustment. The process of neutralizing the magnetic effect a vessel
exerts on a magnetic compass.

compass amplitude. Amplitude relative to compass east or west.

compass azimuth. Azimuth relative to compass north.

compass bearing. Bearing relative to compass north.

compass bowl. That part of a compass in which the compass card is mounted.

compass card. That part of a compass on which the direction graduations are
placed.

compass compensation. The process of neutralizing the effects which degaussing
currents exert on a marine magnetic compass.

compass course. Course relative to compass north.

compass error. The angular difference between a compass direction and the
corresponding true direction.

compasses. An instrument for drawing circles.

compass heading. Heading relative to compass north.

compass north. The direction north as indicated by a magnetic compass.

compass points. The 32 divisions of a compass, at intervals of 113°.

compass repeater. That part of a remote-indicating compass system which re-
peats at a distance the indications of the master compass.

compass rose. A circle graduated in degrees, clockwise from 0° at the reference
direction to 360°, or in compass points, or in both degrees and points.

complement. An angle equal to 90° minus the given angle.

composite sailing. A modification of great-circle sailing used when it is desired
to limit the highest latitude.

computed altitude. Altitude of the center of a celestial body above the celestial
horizon at a given time and place, as determined by computation, table, mechanical
device, or graphics.

computed point. The foot of a perpendicular from a dead reckoning position to
a celestial line of position.

conformal projection. A map projection in which all angles around any point are
correctly represented.

conic projection. A map projection in which the surface of a sphere or spheroid,
such as the earth, is conceived as developed on one or more cones which are then
spread out to form a plane.

conjunction. The situation of two celestial bodies having either the same celestial
longitude or the same sidereal hour angle.

consol. An electronic navigational system providing a number of rotating equi-
signal zones that permit determination of bearings from a transmitting station by
counting a series of dots and dashes and referring to a table or special chart.

constant error. A systematic error of unchanging magnitude and sign.

constellation. Originally, a conspicuous configuration of stars ; now, a region of
the celestial sphere marked by arbitrary boundary lines.

APPENDIX C: GLOSSARY 919

continuous wave. A series of waves of like amplitude and frequency.

contour. A line connecting points of equal elevation or equal depth.

contrary name. A name (such as north or south) opposite or contrary to that
of something else. Usually used in connection with declination and latitude.

controlling depth. The least depth in the approach or channel to an area, such as
a port, governing the maximum draft of vessels that can enter.

convergence constant. The angle at a given latitude between meridians 1° apart.

conversion angle. The angle between the rhumb line and the great circle between
two points.

coordinate. One of a set of magnitudes defining a point in space.

Coriolis force. An apparent force acting on a body in motion, due to rotation
of the earth, causing deflection to the right in the northern hemisphere and to the left
in the southern hemisphere.

corner reflector. A combination of mutually intersecting, conducting surfaces
designed to return electromagnetic radiations toward their sources, and used primarily
to render objects more conspicuous to radar observations.

correcting. The process of applying corrections, particuiarly compass corrections.

corrector. A magnet, piece of soft iron, or device used in the adjustment or
compensation of a magnetic compass.

countercurrent. A secondary current flowing adjacent and in the opposite direc-
tion to another current.

course. The intended horizontal direction of travel. It is usually measured
from 000° at the reference direction clockwise through 360°.

course angle. Course measured from 0° at the reference direction clockwise or
counterclockwise through 90° or 180°.

course error. Angular difference between the course and the course made good.

course line. 1. A line extending in the direction of a given course. 2. A line
of position approximately parallel to the course.

course made good. The direction of a point of arrival from a point of departure.

course of advance. The course expected to be made good over the ground.

course over the ground. The course actually made good over the ground.

course recorder. A device which records the headings of a vessel.

critical range. The spread of ranges in which there is an element of uncertainty
in interpretation, as in the case of ground waves and sky waves of loran.

critical table. A table in which values of the quantity to be found are tabulated
for limiting values of the entering argument.

cross bearings. Two or more bearings used as intersecting lines of position for
fixing the position of a vessel.

culmination. Meridian transit.

culture. Map details which represent cultural features, such as cities, railroads,
aids to navigation, latitude and longitude lines, etc., as contrasted with natural features.

cumulonimbus. A massive cloud with great vertical development, the summits
of which rise in the form of mountains or towers, the upper parts often spreading out in
the form of an anvil.

cumulus. A dense cloud with vertical development, having a horizontal base
and dome-shaped upper surface, exhibiting protuberances.

current. 1. Water in essentially horizontal motion. 2. A hypothetical hori-
zontal motion of such set and drift as to account for the difference between a dead
reckoning position and a fix at the same time. 3. Air in essentially vertical motion.
4. Electricity flowing along a conductor.

current chart. A chart on which current data are graphically depicted.

920 APPENDIX C: GLOSSARY

current diagram. A graph showing the average speeds of flood and ebb currents
throughout the current cycle for a considerable part of a tidal waterway.

current difference. The difference between the time of slack water or strength
of current at a subordinate station and at its reference station.

current direction. The direction toward which a current is flowing.

current meter. An instrument for measuring the speed of a current, and some-
times the direction of flow, also.

current rips. Small waves formed on the surface of water by the meeting of
opposing ocean currents.

cursor. A device used with an instrument, to provide a movable reference.

cut. The intersection of lines of position, constituting a fix, with particular
reference to the angle of intersection.

cyclone. An approximately circular portion of the atmosphere, having relatively
low atmospheric pressure and winds which blow counterclockwise around the center
in the northern hemisphere and clockwise in the southern hemisphere.

cylindrical buoy. Can buoy.

cylindrical projection. A map projection in which the surface of a sphere or
spheroid, such as the earth, is conceived as developed on a tangent cylinder, which is
then spread out to form a plane.

daily rate. The change in chronometer error or watch error in 24 hours.

damping. The progressive diminishing of amplitude of oscillations, waves, etc.

dan buoy. A buoy consisting of a ballasted float carrying a staff which supports
a flag or light.

danger angle. The maximum or minimum angle between two points (separated
either horizontally or vertically), as observed from a vessel, indicating the limit of
safe approach to an off-lying danger.

danger bearing. The maximum or minimum bearing of a point for safe passage
past an off-lying danger.

danger buoy. A buoy marking an isolated danger to navigation.

danger line. A line drawn on a chart, to indicate the limits of safe navigation
for a vessel of specific draft.

dangerous semicircle. That half of a cyclonic storm area to the right of the storm
track in the northern hemisphere, and to the left of the storm track in the southern
hemisphere. In this semicircle the winds are stronger and tend to blow a vessel into
the path of the storm.

danger sounding. A minimum sounding chosen for a vessel of specific draft in a
given area to indicate the limit of safe navigation.

date line. The boundary between the (—)12 and (4-)12 time zones, corresponding
approximately with the 180th meridian.

datum. The base value, level, direction, or position from which any quantity is
measured.

daybeacon. An unlighted beacon.

daylight saving time. A variation of zone time, usually one hour later than
standard time.

daymark. A distinctive structure serving as an aid to navigation during daylight,
whether or not the structure has a light.

day's run. The distance traveled by a vessel in one day, usually reckoned from
noon to noon.

day's work. The daily routine of the navigation of a vessel at sea.

dead ahead. Bearing 000° relative.

dead astern. Bearing 180° relative.

APPENDIX C: GLOSSARY 921

deadbeat compass. Aperiodic compass.

dead reckoning. Determination of position by advancing a previous position for
courses and distances.

dead reckoning equipment. A device that continuously indicates the dead reckon-
ing position of a vessel.

dead reckoning plot. A plot of the movements of a craft as determined by dead
reckoning.

dead reckoning position. A position determined by dead reckoning.

dead reckoning tracer. A device that automatically provides a graphical record of
the dead reckoning track.

; dead reckoning track. A line representing successive dead reckoning positions of a
crait.

Decca. An electronic navigational system by which hyperbolic lines of position
are determined by measuring the phase difference of synchronized continuous wave
signals.

decibel. A unit for expressing the loudness of sounds, one decibel being approx-
imately the least change detectable by the average human ear.

deck log. A written record of the movements of a vessel with regard to courses,
speeds, positions, and other navigational information, and important events aboard the
vessel.

declination. Angular distance north or south of the celestial equator; the arc of an
hour circle between the celestial equator and a point on the celestial sphere, measured
northward or southward from the celestial equator through 90°, and labeled N or S to
indicate the direction of measurement.

deep. An unmarked fathom point on a lead line.

deep sea lead (léd). A heavy sounding lead (about 30 to 100 pounds), usually
having a line 100 fathoms or more in length.

deflection of the vertical. The angular difference between the direction of a plumb
line (the vertical) and the perpendicular (the normal) to the reference spheroid.

deflector. An instrument for measuring the relative directive force acting on a
magnetic compass on different headings, for use in compass adjustment.

degaussing. Neutralization of the strength of the magnetic field of a vessel, by
means of suitably arranged electric coils permanently installed in the vessel.

demodulation. The process of obtaining a modulating wave from a modulated wave.

departure. 1. The distance between two meridians at any given parallel of lati-
tude, expressed in linear units, or the distance to the east or west made good by a vessel
in proceeding from one point to another. 2. Act of departing or leaving.

deperming. The process of changing the magnetic condition of a vessel by wrapping
a large conductor around it a number of times in a vertical plane, athwartships, and
energizing the coil thus formed.

depressed pole. That celestial pole below the horizon, of contrary name to the
latitude.

depth. Vertical distance from a given water level to the bottom.

depth contour. A contour connecting points of equal depth.

destination. The point of intended arrival.

deviation. The angle between the magnetic meridian and the axis of a compass
card.

deviation table. A table of the deviation of a magnetic compass on various
headings.

dew point. The temperature to which air must be cooled at constant pressure and
constant water vapor content to reach saturation.

922 APPENDIX C: GLOSSARY

diagram on the plane of the celestial meridian. A diagram in which the local
celestial meridian appears as a circle with the zenith at the top, and the horizon as a
horizontal diameter.

diaphone. A device for producing a distinctive fog signal by means of a slotted
reciprocating piston actuated by compressed air.

difference of latitude. The shorter arc of any meridian between the parallels of
two places, expressed in angular measure.

difference of longitude. The smaller angle at the pole or the shorter arc of a
parallel between the meridians of two places, expressed in angular measure.

dip. 1. The vertical angle, at the eye of an observer, between the horizontal and
the line of sight to the visible horizon. 2. The angle between the horizontal and the
lines of force of the earth’s magnetic field. 3. The first detectable decrease in the
altitude of a celestial body after reaching its maximum at or near meridian transit.

dip circle. An instrument for measuring magnetic dip.

dip correction. That correction to a sextant altitude due to dip of the horizon.

dip needle. A magnetized needle mounted so as to indicate magnetic dip.

dip of the horizon. Dip, definition 1.

direct current. An electric current which flows continuously in the same direction.

direction. The position of one point in space relative to another without ref-
erence to the distance between them.

direction finder deviation. Error in the reading of a radio direction finder due to
its environment.

direction of current. The direction toward which a current is flowing.

direction of waves or swell. The direction from which waves or swell are moving.

direction of wind. The direction from which a wind is blowing.

directive force. The force tending to cause the directive element of a compass to
line up with the reference direction.

direct wave. A radio wave which travels from transmitter to receiver without an
abrupt change due to refraction or reflection.

disposition of lights. The arrangement, order, etc., of navigational lights in an
area.

distance finding station. A radiobeacon with a synchronized sound signal.

distance marker. A device indicating distance, particularly one on a radar
indicator.

diurnal. Having a period of, occurring in, or related to a day.

diurnal circle. The apparent daily path of a celestial body.

diurnal current. Tidal current having one flood current and one ebb current each
tidal day.

diurnal inequality. The difference between the heights of the two high tides or
two low tides during the tidal day, or the difference in speed between the two flood
currents or the two ebb currents during a tidal day.

diurnal motion. The apparent daily motion of a celestial body.

diurnal tide. Tide having one high tide and one low tide each tidal day.

dividers. An instrument consisting in its simple form of two pointed legs joined
by a pivot, used principally for measuring distances or coordinates.

dock. The space between two piers, or a basin or enclosure for reception of
vessels and controlling the water level.

_ Doppler effect. The apparent change in frequency of radiant energy when the

distance between the source and the observer or receiver is changing.

double. To travel around with a near reversal of course, as to double a cape.

double pulsing. The transmitting of loran signals of two rates by a single station.

APPENDIX C: GLOSSARY 923

double tide. A high tide consisting of two maxima of nearly the same height
separated by a relatively small depression, or a low tide consisting of two minima
separated by a relatively small elevation.

doubling the angle on the bow. A method of obtaining a running fix by measuring
the distance a vessel travels while the relative bearing (right or left) of a fixed object
doubles.

draft. The depth to which a vessel is submerged.

drafting machine. An instrument consisting essentially of a protractor and one
or more arms attached to a parallel motion device.

drift. 1. The speed of a current. 2. The distance a vessel is moved by current
and wind. 3. Downwind or downcurrent motion due to wind or current.

drift current. Any broad, shallow, slow-moving ocean current.

drift lead. A lead placed on the bottom to indicate movement of a vessel.

drogue. Sea anchor.

dry compass. A compass without a liquid-filled bowl.

dumb compass. Pelorus.

earth inductor compass. A compass depending for its indications upon the current
generated in a coil revolving in the earth's magnetic field.

easting. The distance a craft makes good to the east.

ebb current. Tidal current moving away from land or down a tidal stream.

echo ranging. Determination of distance by measuring the time interval between
transmission of a radiant energy signal, usually sound, and the return of its echo.

echo sounder. An instrument used for echo sounding.

echo sounding. Determination of the depth of water by measuring the time in-
terval between emission of a sonic or ultrasonic signal and the return of its echo from
the bottom.

eclipse. The obscuration of a source of light by the intervention of an object.

ecliptic. The apparent annual path of the sun among the stars.

ecliptic diagram. A diagram of the zodiac, indicating the positions of certain
celestial bodies in this region.

ecliptic pole. On the celestial sphere, either of the two points 90? from the
ecliptic.

ecliptic system of coordinates. Celestial latitude and celestial longitude.

electrode. A terminal at which electricity passes from one medium into another.

electromagnetic energy. Radiant energy in radio waves, light waves, X-rays,
heat waves, etc.

electronic navigation. Navigation by means of electronic equipment.

electronics. The science and technology relating to the emission, flow, and effects
of electrons in a vacuum or through a semiconductor such as a gas, and to systems using
devices in which this action takes place.

elevated pole. That celestial pole above the horizon, of the same name as the
latitude.

E-link. A bracket attached to one of the arms of a binnacle to permit the mount-
ing of a quadrantal corrector in an intermediate position between the fore-and-aft
and athwartship lines through a magnetic compass.

ellipsoid. A surface whose cross-sections are all ellipses or circles, or the solid
enclosed by such a surface.

endless tangent screw. A tangent screw which can be moved over the entire
range of its arc without resetting. |

engine revolution counter. An instrument for registering the number of revolutions
of a propeller shaft.

924 APPENDIX C: GLOSSARY

ephemeris. An almanac for astronomers.

epoch. A particular instant for which certain data are given.

equal altitudes. Two altitudes numerically the same.

equation of time. Apparent time minus mean time (U. S. usage). |

equator. The primary great circle of the earth, or a similar body, perpendicular
to the polar axis. q

equatorial chart. A chart of equatorial areas or one on an equatorial projection.

equatorial projection. A map projection centered on the equator.

equatorial tides. The tides that occur when the moon is near the celestial equator,
when the difference in height between consecutive high or low tides is a minimum.

equinoctial. Celestial equator.

equinoctial tides. The tides that occur at or about the time of the equinoxes,
when the spring range is greater than average.

equinox. One of the two points of intersection of the ecliptic and the celestial
equator, or the instant the sun occupies one of these points, when its declination is 0°.

error of perpendicularity. That error in the reading of a marine sextant due to
nonperpendicularity of the index mirror to the frame.

establishment. The interval of time between the transit (upper or lower) of the
moon and the next high water.

estimated position. The most probable position of a craft, determined from
incomplete data or data of questionable accuracy.

excess of arc. That part of a sextant arc indicating negative readings.

ex-meridian observation. Measurement of the altitude of a celestial body near
the celestial meridian, for conversion to an equivalent meridian altitude; or the altitude
so measured.

explement. An angle equal to 360° minus the given angle.

extrapolation. The process of estimating the value of a quantity beyond the
limits of known values by assuming that the rate or system of change continues.

extremely high frequency. Radio frequency of 30,000 to 300,000 megacycles per
second.

eye of the storm. The center of a tropical cyclone.

fade. Of a radiant energy signal, to decrease, often temporarily, in strength
without a change of receiver controls.

Fahrenheit temperature. Temperature based upon a scale in which, under
standard atmospheric pressure, water freezes at 32° and boils at 212°.

fair tide. A tidal current which increases the speed of a vessel.

fair wind. A wind which aids a craft in making progress in a desired direction.

falling tide. A tide in which the depth of water is decreasing.

false horizon. A line resembling the visible horizon but above or below it.

far vane. That instrument sighting vane on the opposite side of the instrument
from the observer’s eye.

fata morgana. A complex mirage, characterized by marked distortion, generally
in the vertical.

fathom. A unit of length equal to six feet.

fathom curve, fathom line. A depth contour with depth measured in fathoms.

Fathometer. The trade name for a widely used echo sounder.

favorable current. A current which increases the speed of a vessel over the
ground.

favorable wind. A wind which helps a craft make progress in a desired direction.

feel the bottom. The action of a vessel in shoal water, when its speed is reduced
and it sometimes becomes hard to steer.

APPENDIX C: GLOSSARY 925

fictitious craft. An imaginary craft used in the solution of certain maneuvering
problems.

fictitious latitude, fictitious longitude. Coordinates based upon a set of fictitious
parallels and fictitious meridians similar to the geographical graticule, but offset from
it. These are usually used with a transverse or oblique map projection, or with a
navigational grid.

fictitious rhumb line. A line making the same oblique angle with all fictitious
meridians.

final great-circle course. The great-circle course at the destination.

fine delay. A dial on a loran indicator, for controlling relatively small changes
in the position of the B trace pedestal.

first estimate-second estimate method. The process of determining the value
of & variable quantity by trial and error. Used particularly for finding the time of
meridian transit at a moving craft.

first point of Aries. Vernal equinox.

fish stakes. Poles or stakes placed in shallow water to outline fishing areas, or to
support fish nets.

fix. A relatively accurate position determined without reference to any former
position.

fixed and flashing light. A fixed light varied at regular intervals by one or more
flashes of greater brilliance.

fixed and group flashing light. A fixed light varied at regular intervals by a group
of two or more flashes of greater brilliance.

fixed light. A light having constant luminous intensity.

flashing. The process of reducing the amount of permanent magnetism in a vessel
by placing a single coil horizontally around the vessel and energizing the coil.

flashing light. A light showing one or more flashes at regular intervals, the dura-
tion of light being less than that of darkness.

Flinders bar. A bar of soft unmagnetized iron placed in a vertical position near
a magnetic compass to counteract deviation caused by magnetic induction in vertical
soft iron of the craft.

float chamber. A sealed, hollow part attached to the compass card of a magnetic
compass as part of the compass card assembly.

floe. Sea ice, either a single unbroken piece or many individual pieces, covering
an area of water.

floeberg. A mass of heavily hummocked sea ice resembling an iceberg in ap-
pearance.

flood current. Tidal current moving toward land or up a tidal stream.

focal length. The distance between the optical center of a lens, or the surface of
a mirror, and its focus.

focal point. Focus.

focus (pl. foci). "That point at which parallel rays of light meet after being re-
fracted by a lens or reflected by a mirror.

fog. A visible assemblage of numerous tiny droplets of water, or ice crystals
formed by condensation of water vapor in the air, with the base at the surface of the
earth.

fog signal. A warning signal transmitted by a vessel or aid to navigation during
periods of low visibility.

form line. An approximation of a contour without a definite elevation value.

foul berth. A berth in which a vessel at anchor is in danger of striking or fouling
another vessel, the ground, or an obstruction.

926 APPENDIX C: GLOSSARY

four-point bearing. A relative bearing of 045° or oí

frequency. The rate at which a cycle is repeated. Å

frequency modulation. The process of changing the frequency of a carrier wave
in accordance with the variations of a modulating wave.

front. The intersection of a frontal surface and a horizontal plane.

frontal surface. The thin zone of discontinuity between two air masses.

frost smoke. Fog produced by apparent steaming of a relatively warm sea in the
presence of much colder air.

gain. The ratio of output voltage, current, or power to input voltage, current, or
power in electronic equipment.

galaxy. A vast assemblage of stars, nebulae, etc., composing an island universe.

gas buoy. A buoy having a gas light.

gauss. The centimeter-gram-second electromagnetic unit of magnetic induction.

Gaussin error. Deviation of a magnetic compass due to transient magnetism
which remains in a vessel's structure for short periods after the inducing force has
been removed.

gee. An electronic navigation system providing hyperbolic lines of position
similar to those of loran.

general chart. A nautical chart intended for offshore coastwise navigation.

geocentric latitude. The angle between the plane of the equator and a line from
a point on the surface of the earth to the center of the earth.

geocentric parallax. The difference in the apparent direction or position of a
celestial body as observed from the center of the earth and a point on its surface.

geodesic line. The shortest line, on a mathematically derived surface, between
two points on that surface.

geodesy. That science which deals mathematically with the size and shape of
the earth, and with surveys in which this is considered.

geodetic latitude. The angle between the plane of the equator and a normal
to the spheroid.

geodetic line. A geodesic line on the spheroidal earth.

geodetic longitude. The angle between the plane of the prime meridian and the
plane through the polar axis and a normal to the spheroid.

geodetic survey. A survey which takes into account the size and shape of the
earth.

geographical mile. The length of one minute of arc of the equator, or 6087.090
feet (on the Clarke spheroid of 1866).

geographical position. 1. That point on the earth at which a given celestial body
is in the zenith at a specified time. 2. Any position on the earth defined by means of
its geographical coordinates.

geographic latitude. Geodetic latitude.

geographic longitude. Geodetic longitude.

geographic range. The extreme distance at which an object or light can be seen
when limited by the curvature of the earth and the heights of the object and the observer.

geoid. The figure of the earth as defined by mean sea level over the entire surface
of the earth.

geoidal horizon. That circle of the celestial sphere formed by the intersection
of the celestial sphere and a plane through a point on the sea-level surface of the earth,
and perpendicular to the zenith-nadir line.

geomagnetic electrokinetograph. A device for measurement of the lateral com-

ponent of the speed of an ocean current by means of two pairs of electrodes towed
astern.

APPENDIX C: GLOSSARY 927

geomagnetic equator. That terrestrial great circle everywhere 90% from the
geomagnetic poles.

geomagnetic pole. Either of two points marking the intersection of the earth’s
surface with the extended axis of a hypothetical bar magnet at the center of the earth
and approximating the source of the actual magnetic field of the earth.

geomagnetism. The magnetism of the earth.

geometrical dip. The vertical angle, at the eye of an observer, between the
horizontal and a straight line tangent to the surface of the earth.

geometrical horizon. Originally, the celestial horizon; now more commonly the
intersection of the celestial sphere and a cone tangent to the surface of the earth and
with its apex at the eye of the observer.

geometric projection. Perspective projection.

ghost. 1. A radar signal the origin of which cannot readily be determined. 2.
A signal, on a scope, which is not repeated each time a trace is made.

gibbous. Bounded by convex curves.

gimballing error. That error introduced in a gyro compass by the tilting of the
gimbal mounting system due to horizontal acceleration, as during a roll.

gimbals. A device for supporting anything, such as an instrument, in such a
manner that it remains essentially horizontal when the support tilts.

glacier. A field or stream of ice which moves or has moved slowly down an
incline.

gnomonic projection. A map projection in which points on the surface of a
sphere or spheroid, such as the earth, are conceived as projected by radials from the
center to a tangent plane.

goniometer. An instrument for measuring angles.

gradient. The change of any quantity with distance in any given direction.

gradient tints. A series of color tints used on some charts to indicate relative
heights or depths.

graduation error. Inaccuracy in the graduations of the scale of an instrument.

graph. A diagram indicating the relationship between two or more variables.

grass. Sharp, closely spaced deflections of the trace of a cathode ray tube, pro-
duced by random interference.

graticule. The network of lines representing parallels and meridians on a map,
chart, or plotting sheet.

great circle. The intersection of a sphere and a plane through its center.

great-circle bearing. The initial direction of a great circle through two terrestrial
points.

great-circle chart. A chart on which a great circle appears as a straight line or
approximately so, particularly a chart on the gnomonic projection.

great-circle course. The direction of the great circle through the point of depar-
ture and the destination.

great-circle distance. The length of the shorter arc of the great circle joining
two points.

great-circle sailing. Any method of solving the various problems involving courses,
distances, etc., as they relate to a great-circle track.

great-circle track. The track of a craft following a great circle, or a great circle
which it is intended a craft will follow approximately.

greater ebb. The stronger of two ebb currents occurring during a tidal day.

greater flood. The stronger of two flood currents occurring during a tidal day.

greatest elongation. The maximum angular distance of a body of the solar
system from the sun, as observed from the earth.

928 APPENDIX C: GLOSSARY

Greenwich apparent time. Local apparent time at the Greenwich meridian;
the arc: of the celestial equator, or the angle at the celestial pole, between the lower
branch of the Greenwich celestial meridian and the hour circle of the apparent (true)
sun, measured westward from the lower branch of the Greenwich celestial meridian
through 24 hours; Greenwich hour angle of the apparent or true sun, expressed in time
units, plus 12 hours.

Greenwich civil time. Greenwich mean time.

* Greenwich hour angle. Local hour angle at the Greenwich meridian; angular dis-
tance west of the Greenwich celestial meridian; the arc of the celestial equator, or the
angle at the celestial pole, between the upper branch of the Greenwich celestial meri-
dian and the hour circle of a point on the celestial sphere, measured westward from
the Greenwich celestial meridian through 360°.

Greenwich mean time. Local mean time at the Greenwich meridian; the arc of
the celestial equator, or the angle at the celestial pole, between the lower branch of
the Greenwich celestial meridian and the hour circle of the mean sun, measured west-
ward from the lower branch of the Greenwich celestial meridian through 24 hours;
Greenwich hour angle of the mean sun, expressed in time units, plus 12 hours.

Greenwich meridian. The meridian through Greenwich, England, serving as the
prime meridian and the reference meridan for Greenwich time.

Greenwich sidereal time. Local sidereal time at the Greenwich meridian; the
arc of the celestial equator, or the angle at the celestial pole, between the upper branch
of the Greenwich celestial meridian and the hour circle of the vernal equinox, measured
westward from the upper branch of the Greenwich celestial meridian through 24 hours;
Greenwich hour angle of the vernal equinox, expressed in time units.

grid. 1. A series of lines, usually straight and parallel, superimposed on a chart
or plotting sheet to serve as a directional reference for navigation. 2. Two sets of
mutually perpendicular lines dividing a map or chart into squares or rectangles to
permit location of any point by a system of rectangular coordinates.

grid amplitude. Amplitude relative to grid east or grid west.

grid azimuth. Azimuth relative to grid north.

grid bearing. Bearing relative to grid north.

grid course. Course relative to grid north.

grid declination. The angular difference between grid north and true north.

grid heading. Heading relative to grid north.

grid latitude. Fictitious latitude on a navigational grid.

grid longitude. Fictitious longitude on a navigational grid.

grid navigation. Navigation by the use of grid directions.

grid north. An arbitrary reference direction used with grid navigation.

grid variation. The angular difference between magnetic north and grid north.

grivation. Grid variation.

grounding. The touching of the bottom by a vessel.

ground swell. A long ocean wave, or series of waves, in shoal water, at a consid-
erable distance from its origin.

d nos tackle. The anchors, anchor chains, fittings, etc., used for anchoring a
vessel.

ground wave. That portion of a radio wave in proximity to and affected by the
ground.

group flashing light. A light showing groups of flashes at regular intervals, the
duration of light being less than that of darkness.

group occuliing light. A light having groups of eclipses at regular intervals, the
duration of light being equal to or greater than that of darkness.

APPENDIX C: GLOSSARY 929

À growler. A small iceberg, piece broken from an iceberg, or detached piece of sea
ice, large enough to be a hazard to shipping but small enough that it may escape
detection.

gyro compass. A compass having one or more gyroscopes as the directive element,
and tending to indicate true north.

gyro error. The error in the reading of the gyro compass.

gyro pilot. An automatic device for steering a vessel by means of control signals
from a gyro compass.

gyro repeater. That part of a remote-indicating gyro compass system which
repeats at a distance the indications of the master gyro compass.

` gyro sextant. A sextant provided with a gyroscope to indicate the horizontal.

hachures. Short lines on maps or charts, to indicate the slope of the ground.

hack watch. A watch used for timing observations of celestial bodies, regulating
ship’s clocks, etc.

half pulse repetition rate delay. An interval of time equal to half the pulse repeti-
tion rate of a pair of loran transmitters, introduced as a delay between transmission
of the master and slave signals.

half-tide level. The level midway between mean high water and mean low water.

hand lead (léd). A light sounding lead (7 to 14 pounds), usually having a line of
not more than 25 fathoms.

harbor chart. A nautical chart intended for navigation and anchorage in harbors
and smaller waterways.

hard iron. Iron or steel which is not readily magnetized by induction, but which
retains a high percentage of the magnetism acquired.

haul. Of the wind, to shift in a counterclockwise direction, or to shift forward
of a vessel.
IES COS

2

haze. Fine dust or salt particles in the air, too small to be individually apparent
but in sufficient number to reduce visibility and cast a bluish or yellowish veil over
the landscape, subduing its colors.

heading. The horizontal direction in which a craft is pointed. It is usually meas-
ured from 000° at the reference direction clockwise through 360°.

heading angle. Heading measured from 0° at the reference direction clockwise
or counterclockwise through 90° or 180°.

heading line. A line extending in the direction of a heading.

heading-upward plan position indicator. A plan position indicator with the head-
ing of the craft maintained at the top of the indicator.

headway. Motion in a forward direction.

heel. Lateral inclination, as of a vessel during a roll or when listed.

heeling adjuster. A dip needle with a sliding weight that can be moved along
one of its arms to balance the magnetic force, used to determine the correct position
of a heeling magnet.

heeling error. The change in the deviation of a magnetic compass when a craft
heels.

heeling magnet. A permanent magnet placed vertically in a tube under the center
of a magnetic compass, to correct for heeling error. |

height of eye correction. That correction to sextant altitude due to dip of the
horizon.

height of tide. Vertical distance from the tidal datum to the level of the water
at any time.

haversine. Half of the versine, or

930 APPENDIX C: GLOSSARY

heliocentric parallax. The difference in the apparent positions of a celestial body
outside the solar system, as observed from the earth and sun. mg

high altitude method. The establishing of a circular line of position from the
observation of the altitude of a celestial body by means of the geographical position
and zenith distance of the body.

higher high water. The higher of two high tides occurring during a tidal day.

higher low water. The higher of two low tides occurring during a tidal day.

high frequency. Radio frequency of three to 30 megacycles per second.

high tide. The maximum height reached by a rising tide.

high water. High tide.

high water full and change. The average interval of time between the transit
(upper or lower) of the full or new moon and the next high water.

high water inequality. The difference between the height of the two high tides
during a tidal day.

high water lunitidal interval. The interval of time between the transit (upper or
lower) of the moon and the next high water at a place.

hiran. High precision shoran.

homing. Navigation toward a point by maintaining constant some navigational
coordinate(s), usually bearing.

hop. Travel of a radio wave to the ionosphere and back to earth.

horizon. That great circle of the celestial sphere midway between the zenith and
nadir, or a line resembling or approximating such a circle.

horizon glass. That glass of a marine sextant attached to the frame, through which
the horizon is observed.

horizon system of coordinates. Altitude and azimuth or altitude and azimuth angle.

horizontal parallax. The geocentric parallax of a celestial body on the celestial
horizon.

hour angle. Angular distance west of a celestial meridian or hour circle; the arc
of the celestial equator, or the angle at the celestial pole, between the upper branch
of a celestial meridian or hour circle and the hour circle of a point on the celestial
sphere, measured westward through 360°.

hour circle. On the celestial sphere, a great circle through the celestial poles.

humidity. The amount of water vapor in the air.

hummock. A mound or hill in pressure ice.

hunting. Fluctuation about a mid-point, due to instability, as oscillation of the
needle of an instrument about the zero point.

hydrographic survey. A survey of a water area.

hydrography. That science which deals with the measurement of the physical
features of waters and their marginal land areas, with special reference to the elements
that affect safe navigation, and the publication of such information in a form suitable
for use of navigators.

hydrolant. An urgent notice of dangers to navigation in the Atlantic.

hydrometeor. Any product from the condensation of atmospheric water vapor,
whether formed in the free atmosphere or at the earth’s surface.

hydropac. An urgent notice of dangers to navigation in the Pacific.

hydrophone. A listening device for receiving underwater sounds.

hygrometer. An instrument for measuring the humidity of the air.

hyperbolic line of position. A line of position determined by measuring the differ-
ence in distance to two fixed points.

hypsometric tints. Gradient tints.

ice anchor. An anchor used for securing a vessel to ice.

APPENDIX C: GLOSSARY 931

ice barrier. Impenetrable ice.

iceberg. A mass of land ice which has broken away from its parent formation
on the coast and either floats in the sea or is stranded.

ice buoy. A sturdy buoy, usually a metal spar, used to replace a more easily
damaged buoy during a period when heavy ice is anticipated.

ice chart. A chart showing prevalence of ice, usually with reference to navigable
waters.

ice field. Sea ice covering an area greater than five miles across.

ice jam. An accumulation of broken ice caught in a narrow part of a stream or
blown against the shore of a lake.

ice shelf. A thick ice formation with level surface extending over the sea but
attached to the land.

ice tongue. A narrow peninsula of ice.

index chart. An outline chart showing the limits and identifying designations of
charts, volumes of sailing directions, etc.

index correction. That correction due to index error.

index error. That error in the reading of an instrument equal to the difference
between the zero of the scale and the zero of the index.

index mirror. That mirror attached to the index arm of a marine sextant.

indirect wave. Any wave which arrives by an indirect path, having undergone
an abrupt change of direction by refraction or reflection.

induced magnetism. Magnetism acquired by a piece of magnetic material while
it is in a magnetic field.

inertial navigation. Dead reckoning performed automatically by a device which
gives a continuous indication of position by double integration of accelerations since
leaving a starting point.

infrared. Having a frequency immediately beyond the red end of the visible
spectrum.

initial great-circle course. The great-circle course at the point of departure.

inshore. In or near the shore.

installation error. That error of an instrument reading due to incorrect installa-
tion of the instrument.

instrument error. The inaccuracy of an instrument due to imperfections within
the instrument.

instrument shelter. A cage or screen in which a thermometer and sometimes
other instruments are placed to shield them from conditions that would interfere with
registration of true conditions.

intercardinal point. Northeast, southeast, southwest, or northwest.

intercardinal rolling error. Quadrantal error of a gyro compass.

intercept. Altitude difference.

international nautical mile. The nautical mile, of 1,852 meters.

interpolation. The process of determining intermediate values between given
values in accordance with some known or assumed rate or system of change.

interrupted quick flashing light. A light showing quick flashes for several seconds,
followed by a period of darkness.

inverse Mercator projection. Transverse Mercator projection.

inversion. A condition of the atmosphere in which temperature increases with
height.

ionosphere. That part of the earth’s atmosphere composed of several layers of
ionized gas, at a height of about 50 to 250 miles, which bend certain radio waves back
toward the surface of the earth.

932 APPENDIX C: GLOSSARY

irradiation. The apparent enlargement of a bright surface against a darker
background.

isobar. A line connecting points having the same atmospheric pressure reduced
to a common datum.

isoclinal. A line connecting points of equal magnetic dip.

isoclinal chart. A chart showing isoclinals.

isogonic. A line connecting points of equal magnetic variation.

isogonic chart. A chart showing isogonics.

isogriv. A line connecting points of equal grid variation.

isogriv chart. A chart showing isogrivs.

isomagnetic. A line connecting points of equality in some magnetic element.

isomagnetic chart. A chart showing isomagnetics.

isopor. A line connecting points of equal rate of change of any magnetic element.

isoporic chart. A chart showing isopors.

isotherm. A line connecting points of equal temperature.

junction buoy. A buoy marking the junction of two channels or two parts of a `
channel, when proceeding from seaward.

K-band. A radio-frequency band of 10,900 to 36,000 megacycles.

Kelvin temperature. Temperature based upon a scale starting at absolute zero
(—273°15 C) and using Celsius degrees.

kilocycle. One thousand cycles.

kilometer. One thousand meters (about 0.54 nautical mile).

knot. A unit of speed equal to one nautical mile per hour.

Lambert conformal projection. A conformal conic map projection in which the
surface of a sphere or spheroid, such as the earth, is conceived as developed on a cone
which intersects the sphere or spheroid at two standard parallels.

land effect. Coastal refraction.

landfall. The first sighting of land when approached from seaward.

land ice. All ice formed on land.

landmark. A conspicuous object on land, serving as an indicator for guidance or
warning.

land mile. Statute mile.

land navigation. Navigation across the surface of land or ice.

lane. 1. An established route. 2. One of the sections of the coverage area for a
phase comparison system, such as Decca, in which every phase relationship may be
measured.

lapse rate. The rate of decrease of temperature in the atmosphere with height.

large scale. A scale involving a relatively small reduction in size.

latitude. Angular distance north or south of the equator; the arc of a meridian
between the equator and a point on the surface of the earth, measured northward or
southward from the equator through 90°, and labeled N or S to indicate the direction
of measurement.

latitude factor. The change in latitude along a celestial line of position for a 1’
change in longitude.

latitude line. A line of position extending in a generally east-west direction.

lattice. A pattern formed by two or more families of intersecting lines, such as
loran lines of two or more rates of overlapping coverage.

L-band. A radio-frequency band of 390 to 1,550 megacycles.

lead (léd). A weight attached to a line.

lead (led). A long, narrow, navigable passage through pack ice, between rocks
or shoals, etc.

APPENDIX C: GLOSSARY 933

| leader cable. A cable carrying an electric current, signals from or the magnetic
influence of which indicate the path to be followed by a craft equipped with suitable
Instruments.

leading light(s). A light or lights arranged to indicate the path to be followed.

lead line. The line attached to a sounding lead.

lee. That side toward which the wind blows.

leeway. The leeward motion of a vessel, due to wind, expressed as distance,
speed, or an angle.

leg. One part of a track, consisting of a single course line.

legend. A title or explanation on a chart, diagram, illustration, etc.

lesser ebb. The weaker of two ebb currents occurring during a tidal day.

lesser flood. The weaker of two flood currents occurring during a tidal day.

light. A lighted aid to navigation, or its luminous energy.

lighthouse. A distinctive structure exhibiting a major navigational light.

light list. A publication tabulating navigational lights and related information.

light sector. A sector in which a navigational light is visible or has a distinctive
color.

lightship. A distinctively marked vessel anchored or moored at a charted point,
to serve as an aid to navigation. It has a characteristic light or lights, and usually
other aids.

light vessel. Lightship.

limb. 1. The graduated curved part of an instrument for measuring angles. 2.
The circular outer edge of a celestial body, particularly with respect to the top (upper
limb) or bottom (lower limb).

line of position. A line on some point of which a vessel may be presumed to be
located, as a result of observation or measurement.

line of soundings. A series of soundings obtained by a vessel underway, usually
at regular intervals.

liquid compass. A compass having a bowl completely filled with liquid in which
the compass card is mounted.

local apparent noon. The instant at which the apparent (true) sun is over the
upper branch of the local meridian.

local apparent time. The arc of the celestial equator, or the angle at the celestial
pole, between the lower branch of the local celestial meridian and the hour circle of the
apparent (true) sun, measured westward from the lower branch of the local celestial
meridian through 24 hours; local hour angle of the apparent (true) sun, expressed in
time units, plus 12 hours.

local attraction. Local magnetic disturbance.

local civil time. Local mean time.

local hour angle. Angular distance west of the local celestial meridian; the arc of
the celestial equator, or the angle at the celestial pole, between the upper branch of
the local celestial meridian and the hour circle of a point on the celestial sphere, meas-
ured westward from the local celestial meridian through 360°.

local magnetic disturbance. An anomaly of the magnetic field of the earth,
extending over a relatively small area, due to local magnetic influences.

local mean time. The arc of the celestial equator, or the angle at the celestial
pole, between the lower branch of the local celestial meridian and the hour circle of
the mean sun, measured westward from the lower branch of the local celestial meridian
through 24 hours; local hour angle of the mean sun, expressed in time units, plus 12
hours.

local meridian. The meridian through any particular place or observer.

934 APPENDIX C: GLOSSARY

local sidereal time. The arc of the celestial equator, or the angle at the celestial
pole, between the upper branch of the local celestial meridian and the hour circle of
the vernal equinox, measured westward from the upper branch of the local celestial
meridian through 24 hours; local hour angle of the vernal equinox, expressed in time
units.

log. 1. An instrument for measuring the speed or distance, or both, traveled by
a vessel. 2. Deck log.

long-distance navigation. 1. Navigation requiring only aids usable at long range,
relatively few of which could provide world coverage. 2. Navigation on a long trip, as
a voyage across an ocean.

longitude. Angular distance east or west of the prime meridian; the arc of a par-
allel, or the angle at the pole, between the prime meridian and the meridian of a point
on the earth, measured eastward or westward from the prime meridian through 180°,
and labeled E or W to indicate the direction of measurement.

longitude factor. The change in longitude along a celestial line of position for a
1’ change in latitude.

longitude line. A line of position extending in a generally north-south direction.

long-range navigation. Long-distance navigation, definition 1.

loom. The glow of a light which is below the horizon, caused by reflection by
solid particles in the air.

loran. An electronic navigational system by which hyperbolic lines of position
are determined by measuring the difference in the time of reception of synchronized
pulse signals.

loran rate. The frequency channel and pulse repetition rate by which a pair of
loran stations is identified.

loran tables. Publications containing tabular data for plotting loran lines of
position.

lower branch. That half of a meridian or celestial meridian from pole to pole
which passes through the antipode or nadir of a place.

lower high water. The lower of two high tides occurring during a tidal day.

lower limb. That half of the limb (of a celestial body) having the lesser altitude.

lower low water. The lower of two low tides occurring during a tidal day.

lower transit. Transit across the lower branch of the celestial meridian.

low frequency. Radio frequency of 30 to 300 kilocycles per second.

low tide. The minimum height reached by a falling tide.

low water. Low tide.

low water inequality. The difference between the heights of the two low tides
during a tidal day.

low water lunitidal interval. The interval of time between the transit (upper or
lower) of the moon and the next low water at a place.

loxodrome. Rhumb line.

lubber’s line. A reference line on any direction-indicating instrument, marking
the reading which coincides with the heading.

luminous range. The extreme distance at which a light can be seen when limited
only by the intensity of the light, clearness of the atmosphere, and sensitiveness of
the observer’s eyes.

lunar tide. That part of the tide due solely to the tide-producing force of the
moon.

lunitidal interval. The interval of time between the transit (upper or lower) of
the moon and the next high water or low water at a place.
magnetic amplitude. Amplitude relative to magnetic east or west.

APPENDIX C: GLOSSARY 935

magnetic azimuth. Azimuth relative to magnetic north.

magnetic bearing. Bearing relative to magnetic north.

magnetic chart. A chart showing magnetic information.

magnetic compass. A compass depending for its directive force upon the attraction
of the magnetism of the earth for a magnet free to turn in any horizontal direction.

magnetic compass table. Deviation table.

magnetic course. Course relative to magnetic north.

magnetic declination. Variation.

magnetic dip. The angle between the horizontal and lines of force of the earth’s
magnetic field.

magnetic equator. That line on the surface of the earth connecting all points at
which the magnetic dip is zero.

magnetic field. The space in which a magnetic influence exists.

magnetic heading. Heading relative to magnetic north.

magnetic latitude. The angle having a tangent equal to half that of the magnetic
dip at the place.

magnetic lines of force. Closed lines indicating by their direction the direction
of magnetic influence.

magnetic meridian. A line of horizontal magnetic force of the earth.

magnetic north. The direction north as indicated by the earth’s magnetic
lines of force.

magnetic pole. Either of the two places on the surface of the earth where the
magnetic dip is 90°.

magnetic storm. Violent, prolonged disturbance of the magnetic characteristics
of the earth.

magnetic track. The direction of the track relative to magnetic north.

magnetic variation. Variation.

magnitude. Relative brightness of a celestial body.

maneuvering board. A polar coordinate plotting sheet devised to facilitate solu-
tion of problems involving relative movement.

manual radio direction finder. A radio direction finder which requires manual
operation.

map. A representation, usually on a plane surface, of all or part of the surface of
the earth, celestial sphere, or other area; showing relative size and position, according to
a given projection, of the various features represented.

map projection. A representation or method of representing all or part of the
surface of a sphere or spheroid, such as the earth, upon a plane surface.

March equinox. Vernal equinox.

marine navigation. The navigation of water craft.

marine sextant. A sextant designed primarily for marine navigation.

master compass. That part of a remote-indicating compass system which deter-
mines direction for transmission to various repeaters.

master station. The governing station of two or more synchronized transmitting
stations.

maximum ebb. The greatest speed of an ebb current.

maximum flood. The greatest speed of a flood current.

mean sea level. The average height of the surface of the sea for all stages of
the tide, usually determined from hourly readings.

mean sun. A fictitious sun conceived to move eastward along the celestial equator
at a uniform rate equal to the average rate of the apparent sun along the ecliptic.

mean tide level. Half-tide level.

936 APPENDIX C: GLOSSARY

mean time. Time based upon rotation of the earth relative to the mean sun.

measured mile. A length of one nautical mile, the limits of which have been
accurately measured and are indicated by ranges ashore.

medium frequency. Radio frequency of 300 to 3,000 kilocycles per second.

megacycle. One million cycles.

Mercator projection. A conformal cylindrical map projection in which the surface
of a sphere or spheroid, such as the earth, is conceived as developed on a cylinder
tangent along the equator, with the expansion of the meridians being equal to that of the
parallels.

Mercator sailing. A method of solving the various problems involving course,
distance, difference of latitude, difference of longitude, and departure by considering
them in the relation in which they are plotted on a Mercator chart.

mercurial barometer. An instrument which determines atmospheric pressure
by measuring the height of a column of mercury which the atmosphere will support.

meridian. A great circle through the geographical poles of the earth or a similar
body.

meridian altitude. The altitude of a celestial body when it is on the celestial
meridian.

meridian angle. Angular distance east or west of the local celestial meridian; the
arc of the celestial equator, or the angle at the celestial pole, between the upper branch
of the local celestial meridian and the hour circle of a point on the celestial sphere,
measured eastward or westward from the local celestial meridian through 180%, and
labeled E or W to indicate the direction of measurement.

meridian observation. Measurement of meridian altitude, or the altitude so
measured.

meridian passage. Meridian transit.

meridian sailing. Following a true course of 000° or 180°.

meridian transit. The passage of a celestial body across a celestial meridian.

meridional difference. The difference between the meridional parts of any two
given parallels.

meridional parts. The length of the arc of a meridian between the equator and a
given parallel on a Mercator chart, expressed in units of 1’ of longitude at the equator.

meteorological tide. A change in water level due to meteorological conditions.

meteorology. The science of the atmosphere.

micrometer drum. A cylinder having a vernier for precise measurement, as on
certain type sextants.

micrometer drum sextant. A marine sextant providing a precise reading by means
of a micrometer drum attached to the index arm, and having an endless tangent screw
for controlling the position of the index arm.

microsecond. One-millionth of a second.

microwave. A very short radio wave, usually one shorter than one meter.

middle ground. A shoal with channels on both sides.

middle latitude. Half the arithmetical sum of the latitudes of two places on the
same side of the equator.

middle-latitude sailing. A method of converting departure into difference of
longitude, or vice versa, when the course is not 090° or 270°, by assuming that such a
course is steered at the middle latitude.

mid latitude. Middle latitude.

millibar. A unit of pressure equal to 1,000 dynes per square centimeter.

millisecond. One-thousandth of a second.

mist. Thin fog of relatively large particles, or very fine rain.

APPENDIX C: GLOSSARY 937

Å mixed current. A type of tidal current characterized by a conspicuous difference
E speed between the two flood currents or two ebb currents usually occurring each tidal
ay.

mixed tide. A type of tide having a large inequality in the heights of either the
two high tides or the two low tides usually occurring each tidal day.

modified Lambert conformal projection. A modification of the Lambert con-
formal projection for use in polar regions, the higher standard parallel being almost
at the pole, and the parallels being expanded slightly to form complete concentric
circles.

modulation. Variation of some characteristic of a wave, called the carrier wave, in
accordance with instantaneous values of another wave, called the modulating wave.

most probable position. That position of a craft judged to be most accurate when
the exact position is not known.

Mumetal. The trade name for an alloy of nickel and iron used for temporary
magnets.

nadir. That point on the celestial sphere vertically below the observer, or 180°
from the zenith.

name. The label of a numerical value, particularly the N (north) or S (south)
label of latitude and declination.

natural scale. The ratio between the linear dimensions of a chart, drawing, etc.,
and the actual dimensions represented, expressed as a proportion.

nautical almanac. A periodical publication of astronomical data designed pri-
marily for marine navigation.

nautical astronomy. Navigational astronomy.

nautical chart. A chart intended primarily for marine navigation.

nautical mile. A unit of distance equal to 1,852 meters (6,076.11549 U. S. feet,
approximately). This is equal approximately to the length of 1” of latitude.

nautical twilight. The period of incomplete darkness when the upper limb of the
sun is below the visible horizon, and the center of the sun is not more than 12° below
the celestial horizon.

naveam. An urgent notice of dangers to navigation in Eastern Atlantic or
Mediterranean waters.

navigable semicircle. That half of a cyclonic storm area to the left of the storm
track in the northern hemisphere, and to the right of the storm track in the southern
hemisphere. In this semicircle the winds are weaker and tend to blow a vessel away
from the path of the storm.

navigation. The process of directing the movement of a craft from one point to
another.

navigational aid. An instrument, device, chart, method, ete., intended to assist
in the navigation of a craft. |

navigational astronomy. That part of astronomy of direct use to a navigator,
comprising principally celestial coordinates, time, and the apparent motions of celestial
bodies.

navigational planets. The four planets commonly observed in celestial navigation;
Venus, Mars, Jupiter, and Saturn.

navigational triangle. The spherical triangle solved in computing altitude and
azimuth and great-circle sailing problems.

neap tides. The tides occurring near the times of first and last quarter of the
moon, when the range of tide tends to decrease.

Ney’s projection. Modified Lambert conformal projection.

night effect. A radio bearing error occurring chiefly at night.

938 APPENDIX C: GLOSSARY

nightmark. An object of distinctive characteristics serving as an aid to navigation
during darkness.

night order book. A notebook in which the commanding officer of a vessel writes,
as a guide to deck watch officers, various memoranda and orders relating to the naviga-
tion of the vessel during the night.

nimbostratus. A dark, low, shapeless cloud layer (mean upper level below 6,500
ft.) usually nearly uniform; the typical rain cloud.

nimbus. A characteristic rain cloud.

noise. Random interference which appears as extraneous signals in radio receivers
or on the scope of electronic instruments.

noon constant. A predetermined value added to a meridian or ex-meridian sextant
altitude to determine the latitude.

noon sight. Measurement of the altitude of the sun at local apparent noon, or
the altitude so measured.

northing. The distance a craft makes good to the north.

north-upward plan position indicator. A plan position indicator with north at the
top of the indicator regardless of heading.

null. Minimum or zero signal.

nun buoy. A buoy the above water part of which is in the shape of a cone or a
truncated cone.

nutation. Irregularities in the precessional motion of the equinoxes.

oblique Mercator projection. A conformal cylindrical map projection in which
points on the surface of a sphere or spheroid, such as the earth, are conceived as devel-
oped by Mercator principles on a cylinder tangent along an oblique great circle.

observed altitude. Corrected sextant altitude.

observed latitude. Latitude determined by means of an observation.

observed longitude. Longitude determined by means of an observation.

occluded front. The front formed when a cold front overtakes a warm front.

occulting light. A light totally eclipsed at intervals, the duration of light being
equal to or greater than that of darkness.

oceanography. The application of the sciences to the phenomena of the oceans.

ocean station vessel. A ship which remains close to an assigned position at sea
to take weather observations, assist aircraft, etc.

oersted. The centimeter-gram-second electromagnetic unit of magnetic intensity.

offshore. Away from the shore.

off soundings. In an area where the depth of water cannot be measured by an
ordinary sounding lead, generally considered to be beyond the 100-fathom line.

omnidirectional. In all directions.

on soundings. In an area where the depth of water can be measured by an
ordinary sounding lead, generally considered to be within the 100-fathom line.

on the beam. Bearing approximately 090° relative (“on the starboard beam”) or
270° relative (“on the port beam").

on the bow. Bearing approximately 045° relative (“on the starboard bow”) or
315? relative (“on the port bow").

on the quarter. Bearing approximately 135° relative (“on the starboard quarter”)
or 225° relative (“on the port quarter”)

opposition. The situation of two celestial bodies having either celestial longitudes
or sidereal hour angles differing by 180°.

ordinate. The vertical coordinate of a set of rectangular coordinates.
orthographic projection. A perspective azimuthal projection in which the project-
ing lines, emanating from a point at infinity, are perpendicular to a tangent plane.

APPENDIX C: GLOSSARY 939

orthomorphic projection. A projection in which very small shapes are correctly
represented.

overfalls. Short, breaking waves occurring when a current passes over a shoal or
other submarine obstruction or meets a contrary current or wind.

pack. A large field of floating pieces of sea ice which have drifted together.

parallactic angle. That angle of the navigational triangle at the celestial body.

parallax. The difference in the apparent direction or position of an object when
viewed from different points.

parallax in altitude. Geocentric parallax of a celestial body at any given altitude.

parallel. A circle on the surface of the earth, or a similar body, parallel to the
plane of the equator and connecting all points of equal latitude, or a closed curve
resembling or approximating such a circle.

parallel of altitude. A circle of the celestial sphere parallel to the horizon, con-
necting all points of equal altitude.

parallel of declination. A circle of the celestial sphere parallel to the celestial
equator.

parallel of latitude. 1. Parallel. 2. A circle of the celestial sphere, parallel to
the ecliptic, and connecting points of equal celestial latitude.

parallel rulers. An instrument for transferring a line parallel to itself.

parallel sailing. A method of converting departure into difference of longitude,
or vice versa, when the true course is 090° or 270°.

patent log. Any mechanical log, particularly a taffrail log.

P-band. A radio-frequency band of 225 to 390 megacycles.

pelorus. A dumb compass, or a compass card without a directive element,
suitably mounted to provide means for measuring bearings.

per gyro compass. Relating to the gyro compass.

perigean tides. Tides of increased range occurring when the moon is near perigee.

perigee. That orbital point nearest the earth when the earth is the center of
attraction (as in the case of the moon).

perihelion. That orbital point nearest the sun when the sun is the center of
attraction (as in the case of a planet).

Permalloy. The trade name for an alloy of nickel and iron, which is easily
magnetized and demagnetized.

permanent magnetism. Magnetism which is retained for long periods without
appreciable reduction, unless the magnet is subjected to a demagnetizing force.

personal error. A systematic error in observations due to the characteristics of
the observer.

perspective projection. The representation of a figure on a surface by means of
projecting lines emanating from a single point.

per standard compass. Relating to the standard magnetic compass.

per steering compass. Relating to the magnetic steering compass.

phase correction. That correction to sextant altitude due to offset of the apparent
center of a body because of its phase.

photogrammetry. The art or science of surveying by photography.

pilot chart. A chart giving information on ocean currents, weather, and other
items of interest to a navigator. »

piloting. Navigation involving frequent or continuous determination of position
or a line of position relative to geographical points, to a high order of accuracy.

pilot station. The place where the services of a pilot may be obtained.

pilot waters. 1. Areas in which the services of a pilot are desirable. 2. Waters
in which navigation is by piloting.

940 APPENDIX C: GLOSSARY

Pitot tube. A tube with an open end pointed toward a moving stream of fluid.
It is usually associated with a coaxial or nearly parallel tube having holes in its side to
permit measurement of static pressure. l ;

plane sailing. A method of solving the various problems involving course, dis-
tance, difference of latitude, and departure, in which the earth or a small part of it is
considered a plane. j

plan position indicator. A radar scope which provides a maplike presentation
of the surrounding area. i

plot. A drawing consisting of lines and points graphically representing certain
conditions, as the progress of a craft.

plotter. An instrument for plotting lines and measuring angles on a chart or plot-
ting sheet.

plotting chart. A chart designed primarily for plotting dead reckoning, lines of
position from celestial observations, or radio aids, etc.

plotting sheet. A blank chart showing only the graticule and one or more compass
roses, so that the plotting sheet can be used for any longitude.

point of arrival. The position a craft is assumed to have reached or will reach after
following specified courses for specified distances from a specified point.

point of departure. The point from which the initial course to reach the destina-
tion begins.

point of destination. The point at which the final course from the point of de-
parture ends, exclusive of the courses needed to reach a berth.

polar distance. Angular distance from a celestial pole, usually the elevated
pole.

Polaris correction. A correction to be applied to the observed altitude of Polaris
to obtain the latitude.

polarization error. That radio bearing error due to horizontally polarized com-
ponents of the electric field under certain transmission conditions.

polar navigation. Navigation in polar regions.

polar projection. A map projection centered on a pole.

pole. 1. Either of the two points of intersection of the surface of the earth or
similar body and its axis. 2. A magnetic pole.

polyconic projection. A conic map projection in which the surface of a sphere or
spheroid, such as the earth, is conceived as developed on a series of tangent cones,
which are then spread out to form a plane.

position. A point defined by stated or implied coordinates, particularly one on
the surface of the earth.

position angle. Parallactic angle.

post meridian. After noon.

precession. Change in the direction of the axis of rotation of a spinning body,
as a gyroscope, when acted upon by a torque.

precession of the equinoxes. The conical motion of the earth’s axis about the
vertical to the plane of the ecliptic, caused by the attractive force of the sun, moon,
and other planets on the equatorial protuberance of the earth. It produces a slow
change in declination and sidereal hour angle of stars.

precomputed altitude. The altitude of a celestial body computed before observa-
tion, and with the sextant altitude corrections applied with reversed sign.

pressure ice. Sea ice having any readily observed roughness of the surface.

primary radar. Radar using only reflection for indication of targets.

primary tide station. A place at which continuous tide observations are made over
a number of years to obtain basic tidal data for the locality.

APPENDIX C! GLOSSARY 941

prime meridian. The meridian of longitude 0?, used as the origin for the measure-
ment of longitude.

prime vertical. Prime vertical circle.

prime vertical circle. That vertical circle through the east and west points of the
horizon.

principal vertical circle. That vertical circle through the north and south points
of the horizon, coinciding with the celestial meridian.

prismatic error. That error due to lack of parallelism of the two faces of an
optical element, such as a mirror or a shade glass.

profile. A graph showing elevation or distribution of some property along a line;
as the graphic record made by a recording echo sounder while a vessel is underway.

proper motion. That component of the space motion of a celestial body per-
pendicular to the line of sight, resulting in the change of a stars apparent position
relative to other stars.

proportional parts. Numbers in the same proportion as a set of given numbers,
used as an aid to interpolation.

protractor. An instrument for measuring angles on a surface; an angular scale.

psychrometer. An instrument consisting of suitably mounted dry-bulb and
wet-bulb thermometers for determining relative humidity and dew point.

pulse. A very short burst of electromagnetic energy.

pulse duration. The time interval during which the amplitude of a pulse is at or
greater than a specified fraction of the maximum value.

pulse interval. The time interval between corresponding parts of successive
pulses in a sequence characterized by uniform spacing.

pulse length. Pulse duration.

pulse modulation. The process of forming very short bursts of a carrier wave,
separated by relatively long periods during which no carrier wave is transmitted.

pulse recurrence rate. Pulse repetition rate.

pulse repetition rate. The rate at which recurrent pulses are transmitted, usually
expressed in pulses per second.

pulse separation. The time interval between the trailing edge of one pulse and
the leading edge of the next pulse.

pulse train. A group of related pulses, constituting a series.

pulse width. Pulse duration.

pumping. Unsteadiness in the height of the mercury column of a barometer.

Q-band. A radio-frequency band of 36,000 to 46,000 megacycles.

quadrant. An instrument similar to a sextant but having a range of 180°. Usually
called a “sextant.”

quadrantal correctors. Masses of soft iron placed near a magnetic compass to
correct for quadrantal deviation.

quadrantal deviation. Deviation which changes its sign (E or W) approximately
each 90° change of heading.

quadrantal error. An error which changes sign (plus or minus) each 90°.

quadrantal spheres. Spherical quadrantal correctors.

quick flashing light. A light showing short flashes at the rate of not less than
60 per minute.

quintant. An instrument similar to a sextant but having a range of 144°. Usually
called a “sextant.”

race. A rapid current or a constricted channel in which such a current flows.

racon. A nondirectional radar beacon which returns a coded signal when triggered
by a radar signal.

942 APPENDIX C: GLOSSARY

radar. A system of determining distance of an object by measuring the time
interval between transmission of a pulse signal and reception of a signal returned as
an echo or by a transmitter triggered by the outgoing signal. The bearing of the
object can be determined by noting the orientation of the directional antenna.

radar beacon. A radiobeacon transmitting a characteristic signal on radar fre-
quency, permitting a craft to determine the bearing and with some types the distance
of the beacon.

radar bearing. A bearing obtained by radar.

radar conspicuous object. An object which returns a strong radar echo.

radar horizon. The radio horizon of a radar antenna.

radar reflector. A device capable of or intended for reflecting radar signals.

radar shadow. A condition in which radar signals do not reach a region because
of an intervening obstruction.

radar target. An object which reflects a sufficient amount of a radar signal to
produce an echo signal on the radar screen.

radian. The angle subtended at the center of a circle by an arc equal in length
to a radius of the circle. It is equal to 180°--7, or approximately 57?17'44*8.

radiant energy. Energy transmitted by radiation, as sound, heat, light, etc.

radiation. The emission, transmission, and absorption of radiant energy by
emanation through space.

radio. Communication by electromagnetic waves, without a connecting wire.

radio acoustic ranging. Determining distance by a combination of radio and
sound, the radio being used to indicate the instant of transmission or reception of the
sound, and distance being determined by the time of transit of sound, usually in water.

radio aid to navigation. An aid to navigation transmitting information by radio
waves.

radio astronomy. The science which deals with radio and thermal radiation from
extraterrestrial sources.

radiobeacon. A radio transmitter emitting a characteristic signal to permit a
craft with suitable equipment to determine its direction, distance, or position relative
to the beacon.

radio bearing. The bearing of a radio transmitter from a receiver, as determined
by a radio direction finder.

radio compass. Obsolete expression for radio direction finder.

radio direction finder. Radio receiving equipment which determines the direction
of arrival of a signal by measuring the orientation of the wave front, using a loop
antenna.

radio direction finder station. A radio station provided with equipment for obtain-
ing radio bearings, particularly such a station on the shore.

radio frequency. Any frequency at which electromagnetic radiation of energy
is useful for communication. j

radio horizon. The line at which direct rays from a transmitting antenna become
tangent to the earth’s surface.

radio navigation. Navigation by means of radio.

radio range. A radio station providing course guidance, or the courses so provided.

radiosonde. An instrument carried aloft by a free, unmanned balloon and equipped

with elements for determining temperature, pressure, and relative humidity and
automatically transmitting the measurements by radio.

radio time signal. A time signal sent by radio.

radio waves. Waves produced by oscillation of an electric charge at a frequency
useful for radio communication.

APPENDIX C: GLOSSARY i 943

radius of visibility. The radius of a circle limiting the area in which an objective
can be seen under specified conditions.

radome. A radio-transparent housing for a radar antenna assembly.

ramark. A radar beacon which continuously transmits a signal appearing as a
radial line on the PPI, the line indicating the direction of the beacon.

random error. A chance error, unpredictable in magnitude or sign.

range. 1. Two or more objects in line. 2. Distance in a single direction or along
a great circle. 3. The extreme distance at which an object or light can be seen, or a
radio signal can be used. 4. A radio station providing course guidance, or the courses
so provided. 5. A predetermined line along which a craft moves while certain data are
recorded, or the station at which this takes place.

range finder. An optical instrument for measuring the distance to an object.

range lights. Two or more lights in the same horizontal direction, particularly
those lights so placed as navigational aids to mark any line of importance to vessels,
as a Channel.

range of tide. The difference in height between consecutive high and low tides
at a place.

range of visibility. The extreme distance at which an object or light can be
seen.

Rankine temperature. Temperature based upon a scale starting at absolute zero
(—459°67 F) and using Fahrenheit degrees.

rational horizon. Celestial horizon.

ratio of ranges. The ratio of the ranges of tide at two places.

ratio of rise. The ratio of the height of tide at two places.

Réaumur temperature. Temperature based upon a scale in which, under standard
atmospheric pressure, water freezes at 0° and boils at 80° above zero.

rectangular projection. A cylindrical map projection with uniform spacing of
the parallels.

rectified altitude. Sextant altitude corrected for inaccuracies in the reading
(instrument, index, and personal errors, as applicable) and inaccuracies in the reference
level (principally dip or Coriolis), but not for other errors. This is the altitude a
celestial body appears to be above the celestial horizon, the value measured at an ob-
servatory, and for this reason is called “apparent altitude” by astronomers.

red azimuth tables. H.O. Pub. No. 260, Azimuths of the Sun.

red magnetism. The magnetism of the north-seeking end of a freely suspended
magnet.

red sector. A sector of the circle of visibility of a navigational light in which a
red light is exhibited.

reduction. The process of substituting for an observed value one derived there-
from.

reduction to the meridian. The process of applying a correction to an altitude
observed when a celestial body is near the celestial meridian, to find the equivalent
meridian altitude.

reference station. A place for which independent daily predictions are given in
the tide or tidal current tables, from which corresponding predictions are obtained
for other stations by means of differences or factors. |

refraction. The change in direction of motion of a ray of radiani energy as it
passes obliquely from one medium into another in which the speed of propagation 1s
different.

relative azimuth. Azimuth relative to heading.

relative bearing. Bearing relative to heading or to the craft.

944 APPENDIX C: GLOSSARY

relative humidity. The percentage of saturation of the air.

relative movement. Motion of one object or body relative to another.

relief. Inequalities in the elevations of the terrain, or their representation on a
chart. pia h

remote-indicating compass. A compass equipped with one or more indicators
to repeat at a distance the readings of the master compass.

repeater. A device for repeating at a distance the indications of an instrument
or device.

residual deviation. Deviation of a magnetic compass after adjustment or com-
pensation.

resolution. The separation, by a radar or optical system, of parts of an object
or of two or more objects close together, or the degree of ability to make such a separa-
tion.

retired line of position. A line of position which has been moved backward to
correspond with a time previous to that for which the line was established.

retrace. The path of the visible dot from the end of one sweep to the start of the
next sweep across the face of a cathode ray tube.

retrograde motion. The apparent motion of a planet westward among the stars.

rhumb bearing. The direction of a rhumb line through two terrestrial points.

rhumb course. The direction of the rhumb line from the point of departure to
the destination.

rhumb line. A line on the surface of the earth making the same oblique angle with
all meridians.

rhumb line distance. Distance along a rhumb line.

right ascension. Angular distance east of the vernal equinox; the are of the
celestial equator, or the angle at the celestial pole, between the hour circle of the vernal
equinox and the hour circle of a point on the celestial sphere, measured eastward from
the hour circle of the vernal equinox through 24^.

rise of tide. Vertical distance from the chart datum to a high water datum,
such as mean high water.

rocking the sextant. Swinging the arc.

rotary current. A tidal current which changes direction progressively through
360° during a tidal-day cycle, without coming to slack water.

round of sights. A group of sights made over a short period of time.

running fix. A position determined by crossing lines of position with an appreciable
time difference between them and advanced or retired to a common time.

sailing. A method of solving the various problems involving course, distance,
difference of latitude, difference of longitude, and departure.

sailing chart. A small-scale nautical chart for offshore navigation.

sailing directions. A descriptive book for the use of mariners, containing detailed
information of coastal waters, harbor facilities, etc., of an area, particularly along
coasts other than those of the United States.

St.-Hilaire method. The establishing of a line of position from the observation
of the altitude of a celestial body by the use of an altitude difference and azimuth.

same name. A name (such as north or south) the same as that of something else.
Usually used in connection with declination and latitude.

S-band. A radio-frequency band of 1,550 to 5,200 megacycles.

scalar. A quantity having magnitude only.

scale. 1. A series of marks or graduations at definite intervals. 2. The ratio

between the linear dimensions of a chart, map, drawing, etc., and the actual dimensions
represented.

APPENDIX C: GLOSSARY 945

\

scope. The face of a cathode ray tube.

sea-air temperature difference correction. That sextant altitude correction
resulting from abnormal refraction occurring when there is a difference in the tempera-
ture of the water and air at the surface.

sea anchor. An object towed by a vessel to keep it end-on to a heavy sea or surf
or to reduce the drift.

sea buoy. The outermost buoy marking the entrance to a channel or harbor.

sea ice. Ice formed by the freezing of sea water.

sea level. The height of the surface of the sea.

seamark. A conspicuous object in the water, serving as an indicator for guidance
or warning of a craft.

sea mile. Nautical mile.

seamount. An elevation of relatively small horizontal extent rising from the
bottom of the sea.

sea return. Radar echoes reflected from the sea.

sea room. Space in which to maneuver without grounding or colliding.

sea tilt correction. That altitude correction due to tilting of the surface of the sea.

seaway. A moderately rough sea.

secondary radar. Radar using automatic retransmission when triggered by a
radar signal.

secondary tide station. A place at which tide observations are made over a short
period to obtain data for a specific purpose.

sector. Part of a circle bounded by two radii and an arc.

sectored light. A light having sectors of different colors or the same color in
specific sectors separated by dark sectors.

secular. Of or pertaining to a long period of time.

seismic sea wave. One of a series of ocean waves propagated outward from the
epicenter of a submarine earthquake.

semicircular deviation. Deviation which changes sign (E or W) approximately
each 180° change of heading.

semidiurnal. Having a period of, occurring in, or related to approximately
half a day.

semidiurnal current. Tidal current having two flood currents and two ebb cur-
rents each tidal day.

semidiurnal tide. Tide having two high tides and two low tides each tidal day.

sense. The general direction from which a radio signal arrives.

sense antenna. An antenna used to resolve a 180° ambiguity in a directional
antenna.

sensible horizon. That circle of the celestial sphere formed by the intersection
of the celestial sphere and a plane through the eye of the observer and perpendicular to
the zenith-nadir line.

set. The direction toward which a current flows.

seven-eighths rule. A rule of thumb which states that the approximate distance
to an object broad on the beam equals % of the distance traveled while the relative
bearing (right or left) changes from 30° to 60° or from 120° to 150°.

seven-tenths rule. A rule of thumb which states that the approximate distance
to an object broad on the beam equals %o of the distance traveled while the relative
bearing (right or left) changes from 22°5 to 45° or from 135° to 157.5. |

seven-thirds rule. A rule of thumb which states that the approximate distance to
an object broad on the beam equals % of the distance traveled while the relative bearing
(right or left) changes from 22°5 to 26°5, 67°5 to 90°, 90° to 112.5, or 153°5 to 15725.

946 APPENDIX C: GLOSSARY

sextant. A double-reflecting instrument for measuring angles, primarily altitudes
of celestial bodies. Originally, the term was applied only to such instruments having
an arc of 60%, but the term is now generally applied to all such instruments regardless
of the length of arc. l

sextant adjustment. The process of checking the accuracy of a sextant and re-
moving or reducing its error.

sextant altitude. Altitude as indicated by sextant, before corrections are applied.

sextant altitude correction. Any of several corrections applied to a sextant
altitude in the process of converting it to observed altitude.

sextant error. The error in the reading of a sextant, due either to lack of proper
adjustment or imperfection of manufacture.

shade. Shade glass.

shade error. That error of an optical instrument due to refraction in the shade
glasses.

shade glass. A darkened transparency that can be moved into the line of sight
of an optical instrument, such as a sextant, to reduce the intensity of light reaching
the eye.

shielding factor. The ratio of the strength of the magnetic field at a compass to
the strength if there were no disturbing material nearby.

ship heading marker. A mark indicating the position or direction of the ship’s
head.

ship’s head. Heading of a vessel.

shoran. A precision electronic position fixing system using a pulse transmitter
and receiver and two transponder beacons at fixed points.

short-distance navigation. 1. Navigation employing aids usable at short ranges
only. 2. Navigation on a short trip.

short-long flashing light. A light showing a short flash of about 0.4 second, and a
long flash of four times that duration, this combination recurring about six to eight
times per minute.

short-range navigation. Short-distance navigation, definition 1.

side error. That error in the reading of a marine sextant due to nonperpendicular-
ity of the horizon glass to the frame.

sidereal. Of or pertaining to the stars.

sidereal day. The duration of one rotation of the earth on its axis, with respect
to the vernal equinox.

sidereal hour angle. Angular distance west of the vernal equinox; the arc of the
celestial equator, or the angle at the celestial pole, between the hour circle of the vernal
equinox and the hour circle of a point on the celestial sphere, measured westward from
the hour circle of the vernal equinox through 360°.

sidereal time. Time based upon the rotation of the earth relative to the vernal
equinox.

sight. Observation of the altitude, and sometimes also the azimuth, of a celestial
body for a line of position; or the data obtained by such an observation.

sight reduction. The process of deriving from a sight the information needed for
establishing a line of position.

sight reduction tables. Tables for performing sight reduction, particularly those
for determining computed altitude.

signal-to-noise ratio. The ratio of the amplitude of a desired radio signal at any

point to the amplitude of noise at the same point.

signature. The graphic record of the magnetic properties of a vessel traced as
the vessel passes over a recording instrument.

APPENDIX C: GLOSSARY 947

skip distance. The least distance from a transmitting antenna at which a sky
wave can normally be received.

skip zone. The area between the outer limit of reception of ground waves and
the inner limit of reception of sky waves, where no signal is received.

sky compass. An instrument for determining azimuth of the sun by utilizing the
polarization of sunlight in the sky.

sky wave. An indirect radio wave which travels from the transmitting antenna
into the sky, where the ionosphere bends it back toward the earth.

sky-wave correction. A correction to be applied to the reading of the indicator
of an electronic instrument when sky waves are used, to obtain the equivalent ground-
wave reading.

slack water. The condition when the speed of a tidal current is zero.

slave station. A transmitting station the emissions of which are controlled by a
master station.

small circle. The intersection of a sphere and a plane which does not pass
through its center.

small scale. A scale involving a relatively large reduction in size.

smog. A mixture of smoke and fog.

sofar. A navigational system by which hyperbolic lines of position are deter-
mined by measuring, at shore listening stations, the difference in the time of recep-
tion of sound signals produced in a sound channel in the sea, under the vessel.

soft iron. Iron or steel which is easily magnetized by induction, but loses its
magnetism when the magnetic field is removed.

solar day. The duration of one rotation of the earth on its axis, with respect to
the sun.

solar tide. That part of the tide due solely to the tide-producing force of the sun.

solar time. Time based upon the rotation of the earth relative to the sun.

solstice. One of the two points of the ecliptic farthest from the celestial equator,
or the instant the sun occupies one of these points, when its declination is maximum.

solstitial tides. Tides occurring near the times of the solstices, when the tropic
range is especially large.

sonar. A system of determining distance of an underwater object by measuring
the interval of time between transmission of an underwater sonic or ultrasonic signal
and return of its echo.

sonic depth finder. An echo sounder operating in the audible range of signals.

sonic navigation. Navigation by means of sound waves whether or not they are
within the audible range.

sonne. A German forerunner of the British consol.

sonobuoy. A buoy with equipment for automatically transmitting a radio signal
when triggered by an underwater sound signal.

sound buoy. A buoy equipped with a characteristic sound signal.

sounding. Measured or charted depth of water, or the measurement of such
depth.

sounding lead (léd). A lead used for determining depth of water.

sounding line. The line attached to a sounding lead.

sounding machine. An instrument for measuring depth of water by lowering a
recording device.

sounding wire. The wire attached to the recording device of a sounding machine.

sound wave. An audible disturbance in any material medium or, by extension,
a similar disturbance outside the audible range.

southing. The distance a craft makes good to the south.

948 APPENDIX C: GLOSSARY

space motion. Motion of a celestial body through space.

spar buoy. A buoy made of a tapered log or of metal similarly shaped.

specific pulse repetition rate. The pulse repetition rate of a pair of transmitting
stations using a group of rates differing only slightly from each other.

speed error. That error introduced in a gyro compass by the north- south com-
ponent of the craft’s motion.

speed line. A line of position approximately perpendicular to the course.

speed of advance. The speed expected to be made good over the ground.

speed over the ground. The speed actually made good over the ground.

spherical sailing. Any of the sailings that takes into account the spherical or
spheroidal shape of the earth.

spherical triangle. A closed figure having arcs of three great circles as sides.

spheroid. An ellipsoid.

spillover. The receiving of a radio signal of a frequency differing from that to
which the receiver is tuned.

splitting. The dividing of a sky-wave signal into two or more peaks.

spring range. The mean semidiurnal range of tide when spring tides are occurring.

spring tides. The tides occurring near the times of full moon and new moon,
when the range of tide tends to increase.

SS loran. Sky-wave synchronized loran.

stadimeter. An instrument for determining the distance to an object of known
height by measuring the angle subtended at the observer by the object.

stand. The condition at high tide or low tide when there is no change in the
height of the water.

standard compass. A compass designated as the standard for a vessel.

standard parallel. A parallel on a map projection, along which the scale is as
stated.

standard time. A variation of zone time used on or near land, with somewhat
irregular but defined zone limits.

star finder. A device to facilitate the recognition of stars.

star globe. A globe representing the celestial sphere, on which the apparent posi-
tions of the stars are indicated.

static. Radio noise caused by natural electrical discharges in the atmosphere.

station buoy. A buoy used to mark the approximate station of an important buoy
or a lightship.

station error. The difference between the direction of gravity and the perpen-
dicular (normal) to the reference spheroid representing the ees.

station pointer. Three-arm protractor.

statute mile. A unit of distance equal to 5,280 feet in the United States.

steam fog. Frost smoke.

steering compass. A compass by which a craft is steered.

steering repeater. A compass repeater by which a craft is steered.

stereographic projection. A perspective, conformal, azimuthal map projection
in which points on the surface of a sphere or spheroid, SEN as the earth, are conceived
as projected by radial lines from any point on the surface to a plane tangent to that
point opposite the point of projection.

storm tide. Increased water level due to a storm.

storm wave. A high tide caused by wind.

stranding. A serious grounding.

stratocumulus. Low clouds (mean upper level below 6,500 ft.) composed of a
layer or patches of globular masses or rolls.

APPENDIX C: GLOSSARY 949

stratus. A low cloud (mean upper level below 6,500 ft.) in a uniform layer, re-
sembling fog but not resting on the surface.

stream current. A relatively narrow, deep, fast-moving ocean current.

strength of current. The phase of a tidal current at which the speed is a maxi-
mum, or the speed at this time.

submarine bell. A bell whose signal is transmitted through the water.

submarine navigation. 1. Navigation of a submarine, whether or not sub-
merged. 2. Underwater navigation.

submarine oscillator. A large, electrically operated diaphragm horn which pro-
duces a powerful sound for transmission through water.

submarine sound signal. A sound signal transmitted through water.

subordinate station. A place for which tide or tidal current predictions are deter-
mined by applying a correction to the predictions of a reference station.

summer solstice. That point on the ecliptic occupied by the sun at maximum
northerly declination, or the instant the sun occupies this position, about June 21.

Sumner line. A celestial line of position, particularly one established by the
Sumner method.

Sumner method. The establishing of a celestial line of position by computing
two points on the line and connecting these with a straight line.

super high frequency. Radio frequency of 3,000 to 30,000 megacycles per second.

supplement. An angle equal to 180° minus the given angle.

surface navigation. Navigation of a vessel on the surface of the earth.

surveying sextant. A sextant intended primarily for use in hydrographic surveying.

sweep. The motion of the visible dot across the face of a cathode ray tube, as a
result of deflections of the electron beam.

sweeping. The process of towing a submerged line or object to locate any sub-
merged dangers or determine the least depth of an area; or the process of clearing an
area of such dangers.

swell. A relatively long wind wave, or series of waves, that have traveled a
considerable distance from the generating area.

swell direction. The direction from which swell is moving.

swinging ship. Placing a vessel on various headings to determine deviation.

swinging the arc. The process of rotating a sextant during observation, to deter-
mine the foot of the vertical circle through the body being observed.

swirl error. The additional error in the reading of a magnetic compass during a
turn, due to friction in the compass liquid.

synoptic chart. A chart showing the distribution of meteorological conditions
over an area at a given time. Popularly called a “weather map.”

systematic error. An error due to some law by which it might be predicted.

tabulated altitude. Altitude taken directly from a table, before interpolation.

taffrail log. A log consisting essentially of a rotor towed through the water by a
line attached to a distance-registering device secured at the taffrail.

tangent screw. A screw providing tangential movement along an arc, as that of
a marine sextant.

telegraph buoy. A buoy used to mark the position of a submarine telegraph cable.

telemeter. The equipment for measuring any quantity, transmitting the results
electrically to a distant point, and there recording the values measured.

temperature error. That instrument error due to nonstandard temperature.

terrestrial refraction. Atmospheric refraction of a ray of radiant energy from a
point on or near the surface of the earth.

950 APPENDIX C: GLOSSARY

terrestrial triangle. A triangle on the surface of the earth, especially the naviga-

tional triangle. k

theodolite. An optical surveying instrument for accurately measuring horizontal
and vertical angles.

thermometer. An instrument for measuring temperature.

three-arm protractor. An instrument consisting of a circle graduated in degrees,
to which is attached one fixed arm and two movable arms which can be clamped at
any angle to the fixed arm, within the limits of the instrument.

tidal current. Current due to tidal action.

tidal current tables. Tables listing predictions of the times and speeds of tidal
currents at various places, and other pertinent information.

tidal datum. A level of the sea, defined by some phase of the tide, from which
water depths and heights of tide are reckoned.

tidal day. The period of the daily cycle of the tides, averaging about 24°50" in
length.

tidal difference. The difference between the time or height of tides at a subordi-
nate station and its reference station.

tidal wave. The ridge of water raised by tidal action, resulting in tides at various
places. The expression is popularly but incorrectly used to refer to a tsunami or storm
wave which overflows the land.

tide. The periodic rise and fall of the water surfaces of the earth due principally
to the gravitational attraction of the moon and sun.

tide correction. That altitude correction due to tilting of the surface of the sea,
as by a tide wave.

tide gage. An instrument for measuring the height of tide.

tide rips. Small waves formed by the meeting of opposing tidal currents or by a
tidal current crossing an irregular bottom.

tide station. A place at which tide observations are made.

tide tables. Tables listing predictions of the times and heights of tides.

tide wave. The ridge of water raised by tidal action.

tilt error. That error introduced in the reading of an instrument due to tilt.

time. 1. The hour of the day reckoned by the position of a celestial reference
point relative to a reference celestial meridian. 2. An elapsed interval.

time and altitude azimuth. An azimuth determined when meridian angle, decli-
nation, and altitude are known.

time azimuth. An azimuth determined when meridian angle, polar distance (or
declination), and latitude are known.

time base. The sweep of a cathode ray tube, used for measuring time intervals.

time diagram. A diagram in which the celestial equator appears as a circle, and
celestial meridians and hour circles appear as radial lines.

time meridian. Any meridian used as a reference for reckoning time, particularly
zone time.

time sight. An observation of the altitude of a celestial body, made for the
purpose of determining longitude, or the method of reducing such an observation.

time signal. A signal marking a specified time.

time tick. A time signal consisting of one or more short audible sounds.

time zone. An area in all parts of which the same time is kept.
| topmark. A characteristic shape secured at the top of a buoy or beacon to aid
in its identification.

trace. The tine appearing on the face of a cathode ray tube when the visible dot
repeatedly sweeps across the face of the tube.

APPENDIX C: GLOSSARY 951

track. The horizontal component of the path followed or expected to be followed
by a vessel or a storm center.

track chart. A chart showing recommended, required, or established tracks,
and usually indicating turning points, courses, and distances.

tracking. The process of following the movements of an object.

transfer. The distance a vessel moves perpendicular to its initial direction of
motion in making a turn.

transit. 1. Meridian transit. 2. A theodolite that can be reversed in its supports
without being lifted from them.

transponder. A combined receiver and transmitter which transmits signals
automatically when triggered by an incoming signal.

transverse Mercator projection. A map projection similar to a Mercator projection
but with the cylinder rotated through 90°, so that it is tangent along a meridian.

traverse. A series of directions and distances, as the courses and speeds of a
vessel zigzagging.

traverse sailing. A method of determining the equivalent course and distance
made good by a vessel following a track consisting of a series of rhumb lines.

traverse table. A table giving relative values of various parts of plane right
triangles, for use in solving such triangles.

tropical cyclone. A violent cyclone originating in the tropics.

tropicrange. The difference in height between tropic higher high water and tropic
lower low water.

tropic tides. The tides that occur when the moon is near its maximum declina-
tion, when the diurnal range tends to increase.

true amplitude. Amplitude relative to true east or west.

true azimuth. Azimuth relative to true north.

true bearing. Bearing relative to true north.

true course. Course relative to true north.

true heading. Heading relative to true north.

true north. The direction of the north geographical pole.

true wind. Wind relative to a fixed point on the earth.

tsunami. An ocean wave produced by a submarine earthquake, landslide, or
volcanic action. Popularly called a “tidal wave” when it overflows the land.

turning buoy. A buoy marking a turn, as in a channel.

twilight. The periods of incomplete darkness following sunset or preceding
sunrise.

twilight compass. A compass for indicating direction during twilight, particularly
a sky compass.

ultra high frequency. Radio frequency of 300 to 3,000 megacycles per second.

ultrasonic depth finder. An echo sounder operating at a frequency above the
audible range.

ultraviolet. Having a frequency immediately beyond the violet end of the
visible spectrum.

uncorrecting. The process of converting true direction to magnetic, compass, or
gyro direction, or magnetic direction to compass direction.

undercurrent. A current below the surface.

underwater navigation. Navigation of a submerged vessel.

unfavorable current. A current which decreases the speed of a vessel over the

ground. b
unfavorable wind. A wind which delays the progress of a craft in a desired

direction.

952 APPENDIX C: GLOSSARY

unidirectional. In one direction only.

universal plotting sheet. A plotting sheet that can be used at various latitudes
and any longitude.

universal time. Greenwich mean time.

upper air sounding. Determination of the characteristics of the upper alr.

upper branch. That half of a meridian or celestial meridian from pole to pole
which passes through a place or its zenith.

upper limb. That half of the limb (of a celestial body) having the greatest
altitude.

upper transit. Transit across the upper branch of the celestial meridian.

variation. The angle between the magnetic and geographical meridians.

V-band. A radio-frequency band of 46,000 to 56,000 megacycles.

vector. A straight line representing both direction and magnitude.

vector diagram. A diagram of more than one vector drawn to the same scale and
reference direction, and in correct position relative to each other.

vector quantity. A quantity having both magnitude and direction.

veer. Of the wind, (a) to change direction clockwise in the northern hemisphere
and counterclockwise in the southern hemisphere, or (b) to shift aft.

velocity. Rate of motion in a given direction.

velocity ratio. The ratio of the speed of tidal currents at a subordinate station
and its reference station.

vernal equinox. That point of intersection of the ecliptic and the celestial equator,
occupied by the sun as it changes from south to north declination, on or about March 21,
or the instant this occurs.

vernier. A scale or control used for interpolation in the reading of an instrument
or for closer adjustment of any equipment.

vernier sextant. A marine sextant having a vernier used directly with the arc.

versine. One minus the cosine (1—cos).

vertical circle. A great circle of the celestial sphere, through the zenith and nadir,
and hence perpendicular to the horizon.

very high frequency. Radio frequency of 30 to 300 megacycles per second.

very low frequency. Radio frequency of less than 30 kilocycles per second.

vigia. A rock or shoal the existence or position of which is doubtful.

visibility. The extreme horizontal distance at which prominent objects can be
seen and identified by the unaided eye.

visible horizon. That line where earth and sky appear to meet.

vulgar establishment. The average interval of time between the transit (upper
or lower) of the full or new moon and the next high water.

warm air mass. An air mass that is warmer than surrounding air, and usually
warmer than the surface over which it is moving.

warm front. That line of discontinuity, at the earth’s surface or at a horizontal
plane aloft, where the forward edge of an advancing warm air mass is replacing a colder
air mass.

warm sector. An area at the earth's surface bounded by the warm and cold fronts
of a cyclone.

war time. Daylight saving time kept throughout the year during a war.

watch buoy. Station buoy.

watch error. The amount by which watch time differs from the correct time.

watch rate. The amount gained or lost by a watch or clock in unit time, usually
seconds per day. d

watch time. The hour of the day as indicated by a watch or clock.

APPENDIX C: GLOSSARY 953

wave. 1. An undulation or ridge on the surface of a liquid, or anything resembling
this. k 2. A disturbance propagated in such a manner that it may progress from point
to point.

wave crest. The highest part of a wave.

wave direction. The direction from which waves are moving.

wave height. The distance from the trough to the crest of a wave, measured
perpendicular to the direction of advance. i

wave height correction. That altitude correction due to elevation of the visible
horizon by waves.

wave length. The distance in the direction of advance between the same phase of
consecutive waves.

wave period. The time interval between passage of successive wave crests at a
fixed point.

wave train. A group of related waves, constituting a series.

wave trough. The lowest part of a wave, between two crests.

weather map. Synoptic chart.

weather signal. A visual signal displayed to indicate a weather forecast.

weather vane. A device to indicate the direction from which the wind blows.

westing. The distance a craft makes good to the west.

wind. Moving air, especially a mass of air having a common direction of motion.

wind current. A current created by the action of wind.

wind direction. The direction from which wind blows.

wind rose. A diagram showing the relative frequency and sometimes the average
speed of the winds blowing from different directions in a specified region.

wind vane. A device to indicate wind direction.

wind wave. A wave generated by friction between wind and a fluid surface.

winter solstice. That point on the ecliptic occupied by the sun at maximum
southerly declination, or the instant the sun occupies this position, about December 22.

wiping. The process of reducing the amount of permanent magnetism in a vessel
by placing a single coil horizontally around the vessel and moving it, while energized, up
and down along the sides of the vessel.

wire drag. A buoyed wire towed at a given depth to determine whether any
isolated rocks, small shoals, etc., extend above that depth, or for determining the least
depth of an area.

X-band. A radio-frequency band of 5,200 to 10,900 megacycles.

young ice. Newly formed ice.

zenith. That point of the celestial sphere vertically overhead.

zenithal projection. Azimuthal projection.

zenith distance. Angular distance from the zenith.

zodiac. That band of the sky extending 8° either side of the ecliptic.

zone description. The number, with its sign, that must be added to or subtracted
from zone time to obtain Greenwich mean time.

zone time. The local mean time of a reference or zone meridian whose time is kept
throughout a designated zone.

APPENDIX D
MISCELLANEOUS DATA

Exact relationships shown by asterisk (*). See footnote on page 962.

Area

square inch- 2 2-0 = eee RENI = 6.4516 square centimeters*

disquarefooter 3 Ut E =144 square inches*
=0.09290304 square meter?
=0.00002296 acre

Lisquare yard tanta. ip A, S S =9 square feet*
= 0.83612736 square meter

Msquares(statute)y milo = 27,878,400 square feet*
= 640 acres*
= 2.589988110336 square kilometers*

l sduare centimeters d E =0.15500031 square inch
= ().00107639 square foot

square meter A = 10.76391045 square feet
=1.19599005 square yards

square kilometer kerro EE = 247.1053815 acres
=0.38610216 square statute mile
=0.29155335 square nautical mile
Astronomy

lBímean“solar unit c =1.00273791 sidereal units

ló siderealkunits ee E =0.99726957 mean solar unit

JEmicrose Cond a TE S =0.000001 second*

Tee ol e e at =1,000,000 microseconds*
=0.01666667 minute
=0.00027778 hour
=0.00001157 day

AST INU NR S y AAA =60 seconds*
=0.01666667 hour
=0.00069444 day

D Du Jace ce). d ee eee = 3,600 seconds*

=60 minutes*
= 0.04166667 day
EE e a c =24'03m56:55536 of mean sidereal time
=1 rotation of earth with respect to sun (mean) *
= 1.00273791 rotations of earth with respect to
vernal equinox (mean)
= 1.0027378118868 rotations of earth with respect
to stars (mean)
meanisiderealiday == ae RI EE = 23556™04:09054 of mean solar time
sidereal mont hes ee = 27.321661 days
= 27107543™1185
SALE O ee = 29.530588 days
= 29412544m0288
en eee In = 31,556,925.975 seconds
= 525,948.766 minutes
= 8,765.8128 hours
= 365424219879 — 040000000614 (t— 1900), where t
=the year (date)
= 365405»48m46s
sidereal ¡year £ ot NM =865425636042+ 0.0000000011(t—1900), where t
=the year (date)
= 365406509™0985

5
e
©
|5)
[^n
e
£5
H
a
y
<

Ra a

pæ
un
<
=
o
[oh
[em
Q
S
E
H
=)
=
=
E

=
et
O
E
e
E
ES
Ø
o
5
ES
=
D
H
<
=
<
o
E
H

—

APPENDIX D: MISCELLANEOUS DATA 955

Astronomy—Continued

1 calendar year (common)-__________________ = 31,536,000 seconds*
= 525,600 minutes*
=8,760 hours *
= 365 days *
Kë fk apt Za = 31,622,400 seconds*
= 527,040 minutes*
=8,784 hours*
=366 days*
A cec e ee = 9,460,000,000,000 kilometers
— 5,880,000,000,000 statute miles
= 5,110,000,000,000 nautical miles
= 63,300 astronomical units
IBD ATSCC heen Lu SE S ee E = 31,000,000,000,000 kilometers
= 19,300,000,000,000 statute miles
= 16,700,000,000,000 nautical miles
= 206,265 astronomical units
= 3.26 light years
BMastronomicalun m T = 149,500,000 kilometers
= 92,900,000 statute miles
=80,700,000 nautical miles
=mean distance, earth to sun
Mean distance, earth to moon_______________ =384,411 kilometers
= 238,862 statute miles
= 207,565 nautical miles
Mean distance, earth to sun_________________ = 149,500,000 kilometers
= 92,900,000 statute miles
= 80,700,000 nautical miles
= 1 astronomical unit
Sun diameter A mee ee tee AT = 1,393,000 kilometers
= 866,000 statute miles
= 752,000 nautical miles
SUES SIN ASS ee EE aE = 1,987,000,000,000,000,000,000,000,000,000,000
grams
= 2,200,000,000,000,000,000,000,000,000 short tons
= 2,000,000,000,000,000,000,000,000,000 long tons
Speed of sun relative to neighboring stars... — 19.6 kilometers per second
= 12.2 statute miles per second
= 10.6 nautical miles per second
Orbitalspeedsofiearuhmeec m e — 29.8 kilometers per second
—18.5 statute miles per second
=16.1 nautical miles per second

1 calendar year (leap)

Oblicuityeotsthe ecliptic sess e e eee =2327'08"26 — 074684 (t — 1900), where t= the year
(date)
General precession of the equinoxes.........- = 5072564. 4- 07000222 (t — 1900) per year, where t=

the year (date)
Precession of the equinoxes in right ascension. = 4670850 + 07000279 (t— 1900) per year, where t=
the year (date)

Precession of the equinoxes in declination.... = 2070468 — 07000085 (t— 1900) per year, where t=
the year (date)
EE =2.512
SON
Charts
Nautical miles per inch_----. as ee =reciprocal of natural scale-- 72,913.39
Statutermiles perunchs = oe = eee e =reciprocal of natural scale= 63,360*
Inchesimernautical mc e koe see =72.913.39 X natural scale
inches) peristatute mile- < c = 63,360 X natural scale*

=1:72,913.39X nautical miles per inch
= 1:63,360 X statute miles per inch*

Natura ee ee K d

956 APPENDIX D: MISCELLANEOUS DATA

Earth

Acceleration due to gravity (standard)------- =980.665 centimeters per second per second
=32.1740 feet per second per second

Mass: = 22 22023226 2022 A = 5,980,000,000,000,000,000,000,000,000 grams
= 6,600,000,000,000,000,000,000 short tons
= 5,900,000,000,000,000,000,000 long tons

Meantdensity-" 5022 2 Sraa E = 5.517 grams per cubic centimeter

Velocity rol escaner AA =6.94 statute miles per second

Curvature Of surfaces. "m =0.8 foot per nautical mile

Clarke spheroid of 1866
Equatorakradius (OE eee = 20,925,874.05 feet

=6,975,291.35 yards
= 6,378,206.4 meters
=3,963.234 statute miles
=3,443.957 nautical miles
Bolartadils(0) Seen se m < Ee = 20,854,933.76 feet
=6,951,644.59 yards
= 6,356,583.8 meters
=3,949.798 statute miles
28-18 =3,432.282 nautical miles
Mean radius (<= AO R ee =20,902,227.28 feet
=6,967,409.09 yards
= 6,370,998.9 meters
=3,958.755 statute miles
=3,440.065 nautical miles
Lote quators.-.. 5. 25428 c Se AE = 6,087.090 feet
= 2,029.030 yards
=1,855.345 meters
=1.153 statute miles
=1.002 nautical miles
I” of latitude at equator 2-1 T = 6,045,889 feet
=2,015.296 yards
=1,842.787 meters
=1.145 statute miles
=0.995 nautical mile
E e dete ae =6,107.795 feet
= 2,035.932 yards
=1,861.656 meters
=1.157 statute miles
=1.005 nautical miles
1

1’ of latitude at pole

Flattening or ellipticit wit ——— —

> D D Lay bli aed io 294.98
=0.00339007530

Eccentricity (e=/2f—f2)___._.___ n = 0.08227185422

Eccentricity squared (2)... =0.00676865800

Clarke spheroid of 1880

HģuatoriaKradigs (a) eee =20,926,014.29 feet
= 6,975,338.10 yards
=6,378,249,145 meters
=3,963.260 statute miles
= 3,443.980 nautical miles

Polanradius DE = Tr Dn =20,854,707.61 feet
—6,951,569.20 yards
—6,356,514.870 meters
=3,949.755 statute miles
=3,432,245 nautical miles

APPENDIX D: MISCELLANEOUS DATA 957

Earth— Continued
Clarke spheroid of 1880— Continued

Mean radius (=P) sk oe e, — 20,902,245.39 feet
= 6,967,415.13 yards
= 6,371,004.387 meters
=3,958.759 statute miles
=3,440.068 nautical miles
MEOhequatore co ek ak ass = 6,087.129 feet
=2,029.043 yards
=1,855.357 meters
=1.153 statute miles
=1.002 nautical miles
ivoflatitude at equator. ce EE =6,045.719 feet
= 2,015.240 yards
=1,842.735 meters
= 1.145 statute miles
=0.995 nautical mile
iMorlatitudesatipole (24425224 sepa =6,107.943 feet
j =2,035.981 yards
=1,861.701 meters
=1.157 statute miles
=1.005 nautical miles

S T et a—b 1
Flattening or ellipticity (7 = ) ker Lies oe = 993 465
= ().00340756138
Hecentricity O VE tos =0.08248339904
Hegentricity, squared, (62) eg 2 =. =0.00680351112
International spheroid
SGOT) | TAUS (OO) c Ss SE EE = = 20,926,469.85 feet

=6,975,489.95 yards
— 6,878,388 meters
=3,963.347 statute miles
=3,444.055 nautical miles
BoJartradiusi(0) mec e Sa ere ceu 3 =20,856,010.35 feet
—6,952,003.45 yards
=6,356,911.946 meters
=3,950.002 statute miles
' aa =3,432.459 nautical miles
Mean radius ( 3 ) En NN 8 =20,902,983.35 feet
—6,967,661.12 yards
=6,371,229.315 meters
= 3,958.8987 statute miles
=3,440.190 nautical miles
MOLE CUAL OTs EO ECCO SC =6,087.264 feet
=2,029.088 yards
=1,855.398 meters
=1.153 statute miles
=1.002 nautical miles
Kots atitutelatieduator Seces SES E =6,046.342 feet
=2,015.447 yards
=1,842.925 meters
= 1.145 statute miles
=0.995 nautical mile
t of latitude at polea al e SEO DS = 6,107.828 feet
= 2,035.943 yards
= 1,861.666 meters
=1.157 statute miles
=1.005 nautical miles

958 Å APPENDIX D: MISCELLANEOUS DATA

Earth—Continued

International spheroid—Continued

i ER a—b dal

Flattening or ellipticity ( f= z ) Jc qus —397
—0.00336700337

Eccentricity Lee SE —0.08199188997

Eccentricity squared (6) EC C = ().00672267002

Length

Tintin E PERA =25.4 millimeters*
— 2.54 centimeters*

1 foot (U.S) cc LA S = 12 inches*
=1 British foot
= yard*

=0.3048 meter?
=% fathom*

1 foot (U.S. ENEE =0.30480061 meter
1 yardz.--- 2---: E IMA SS — 86 inches *

=3 feet *

=0.9144 meter*
liathoms.....-.-:c5—-.. RPM AMA ES —6 feet *

—2 yards*

= 1.8288 meters *
cable. ¡li cw es =720 feet*

—240 yards*

—219.4560 meters *
ldcableš(British) = O YO =0.1 nautical mile
ltstatutēemilēt An = 5,280 feet*

=1,760 yards*

=1,609.344 meters*

=1.609344 kilometers*

=0.86897624 nautical mile
Eu ee =6,076.11548556 feet

=2,025.37182852 yards

=1,852 meters*

=1.852 kilometers*

=1.150779448 statute miles
A n N EET =100 centimeters*

=39.370079 inches

= 8.28083990 feet

= 1.09361330 yards

=0.54680665 fathom

= 0.00062137 statute mile

= 0.00053996 nautical mile
1 kilometero a 39 PAB = 8,280.83990 feet

—1,093.61330 yards

— 1,000 meters *

—0.62137119 statute mile

=0.53995680 nautical mile

Mass
1 ounee ccoo t... AINĀS =437.5 grains*
=28.349523125 grams*
=0.0625 pound*
= 0.028349523125 kilogram*
lpound........ == cc ISS = 7,000 grains*
— 16 ounces*
=0.45359237 kilogram*
Pshortión... ob. _ .. bm INDEM — 2,000 pounds*

= 907.18474 kilograms*
=0.90718474 metric ton*
=0.89285714 long ton

APPENDIX D: MISCELLANEOUS DATA 959

Mass— Continued

Mone ton e ua Baier BON fta = 2,240 pounds*
=1,016.0469088 kilograms*
=1.12 short tons*

i = 1.0160469088 metric tons*
kilogram A CAS a ra E = 2.204622622 pounds
= 0.00110231 short ton
| =0.00098421 long ton

CO A ITV = 2,204.6226218 pounds
= 1,000 kilograms*
= 1.10231131 short tons
= 0.98420653 long ton

Mathematics
Tor al ASS eee Soe Se ee ee e = 3.1415926535897932384626433832795028841971
a. A a coria EE — 9.8696044011
EE eos PURA 199 houoq 318080 (orto = 1.7724538509
Base of Naperian logarithms (e)-----------_- = 2.718281828459
Modulus of common logarithms (logie)... = 0.43429448 19032518
1 CECEN A A SVA =206,264"80625
= 3,437! 7467707849
= 5722957795131
=57°17'44"80625
¡ro A ND T =1,296,000"* |
—21,600'*
=360°*
—2m radians*
ISO PR T" — ——— eec = radians*
IIS. se se rmn tat pā it ene o t =3600"*
=O".
=0.0174532925199432957666 radian
1⁄ MM = 60"*
= 0.000290888208665721596 radian
pe In PAC cm ape vg enm Te =0.000004848136811095359933 radian
Sine agg AAA sod Me TRONS IP =0.00029088820456342460
Se o e Toq ni MOLS MU w =0.00000484813681107637
Meteorology
Atmosphere (dry air)
Nitrogen SOMU AICA TT $TVOC E vv ese =78.08%
Oxygen 2 Æ EE =20.95%
e dā: (ADM 30309) Nis tol edd ee = 0.93% 99.99 7
Garbontdioxides3AMDM WI ema germ AA = 0.083%
Neon ANER 36 fil LIO. GS = 0.0018%
Heliumo- a de adim TAVA SI = 0.000524%
Krypton nat 10 E LJ = 0.0001%
Hydrogen dura Jo Sastre tøð sem En = 0.00005%
Xenon e DEER 30 Im DADO E = 0.0000087 %
Ozonesece Vites Jo Bl nt POOL = 0 to 0.000007 % (increasing with altitude)
Radon A rene OR ONRAT UU eS = 0. 000000000000000006 % (decreasing with al-
titude)
Standard atmospheric pressure at sea level... =1,013.250 dynes per square centimeter*

=1,033.227 grams per square centimeter
=1,033.227 centimeters of water

= 1,013.250 millibars*

= 760 millimeters of mercury

=76 centimeters of mercury

= 33.8985 feet of water

= 29.92126 inches of mercury

= 14.6960 pounds per square inch

= 1.033227 kilograms per square centimeter
= 1.013250 bars*

Absolute zero ee eee EET e =(—) 273:15 C
=(—) 459°67 F

960 | APPENDIX D: MISCELLANEOUS DATA
Pressure
1 dene per square centimeter_-------------- —0.001 millibar*
=0.000001 bar*
1 gram per square centimeter___------------ =1 centimeter of water

= (0.980665 millibar*
=0.07355592 centimeter of mercury
=0.0289590 inch of mercury
=0.0142233 pound per square inch
=0.001 kilogram per square centimeter*
=0.000967841 atmosphere
]amilibarzs-...--..- PRE Ret HTA RT =1,000 dynes per square centimeter*
=1.01971621 grams per square centimeter
=0.7500617 millimeter of mercury
=0.03345526 foot of water
= 0.02952998 inch of mercury
=0.01450377 pound per square inch
— 0.001 bar*
= ().00098692 atmosphere
1 milimeter of mercury- <- AS a = 1.35951 grams per square centimeter
= 1.3332237 millibars
=0.1 centimeter of mercury*
=0.04460334 foot of water
=0.039370079 inch of mercury
—0.01933677 pound per square inch
=0.001315790 atmosphere
Iecentimeterolsmer curry === =10 millimeters of mercury*
LEE EE =34.53155 grams per square centimeter
=33.86389 millibars
— 25.4 millimeters of mercury *
=1.132925 feet of water
—0.4911541 pound per square inch
=0.03342106 atmosphere

centimeter OM UE =1 gram per square centimeter
=0.001 kilogram per square centimeter
1 foot of Water: ee =30.48000 grams per square centimeter

= 29.89067 millibars
= 2.241985 centimeters of mercury
= 0.882671 inch of mercury
= 0.4335275 pound per square inch
= 0.02949980 atmosphere

pound persqguare inmemor. ene = 68,947.57 dynes per square centimeter
=70.30696 grams per square centimeter
="70.30696 centimeters of water
—68.94757 millibars
=51.71493 millimeters of mercury
— 5.171493 centimeters of mercury
= 2.306659 feet of water
— 2.036021 inches of mercury
=0.07030696 kilogram per square centimeter
= 0.06894757 bar
=0.06804596 atmosphere

1 kilogram per square centimeter____________ = 1,000 grams per square centimeter*
= 1,000 centimeters of water
1 baron 2 des Man EECH =1,000,000 dynes per square centimeter*
=1,000 millibars*
Speed
I foot per-minutes cum le la A =0.01666667 foot per second

=0.00508 meter per second*

m T

APPENDIX D: MISCELLANEOUS DATA 961

Speed—Continued

yard per minutes --- Eden aktii RODNE ca =3 feet per minute*
=0.05 foot per second*
=0.03409091 statute mile per hour
=0.02962419 knot
=0.01524 meter per second*

4000 Per second er 9009 EROS, Aha — 60 feet per minute*
—20 yards per minute*
— 1.09728 kilometers per hour*
—0.68181818 statute mile per hour
=0.59248380 knot
— 0.3048 meter per second*

Mstauute mile pen hours: mw imr EMS de —88 feet per minute*
—29.33333333 yards per minute
— 1.609344 kilometers per hour*
=1.46666667 feet per second
=0.86897624 knot
— 0.44704 meter per second*

il immotus te dero cn mec AN AR bem —101.26859143 feet per minute
=33.75619714 yards per minute
— 1.852 kilometers per hour*
=1.68780986 feet per second
—1.15077945 statute miles per hour
—0.51444444 meter per second

iSklometerr per hours: Se ees. AU 35 8852 Dee =0.62137119 statute mile per hour
=0.53995680 knot
T meter per second seo: "dus AOL Lite =196.85039340 feet per minute

—65.6167978 yards per minute
=3.6 kilometers per hour*
=3.28083990 feet per second
=2.23693632 statute miles per hour
=1.94384449 knots

Iūehtiunšvacuo ee e Ee TU — 299,792 kilometers per second
= 186,282 statute miles per second
= 161,875 nautical miles per second
— 983.570 feet per microsecond

Ment In air ee SEE 1 et Sen = 299,708 kilometers per second
= 186,230 statute miles per second
— 161,829 nautical miles per second
— 983.294 feet per microsecond

Sound in dry air at 60? F and standard sea =1,116.99 feet per second

level pressure

=761.59 statute miles per hour
—661.80 knots
— 340.46 meters per second

Sound in 3.485 percent salt water at 60° F__.=—4,945.37 feet per second
— 3,371.85 statute miles per hour
—2,930.05 knots
=1,507.35 meters per second

Volume

[Ncubrenncheeme A S mes — 16.387064 cubic centimeters*
=0.01638661 liter
=0.00432900 gallon

ECHO CHLOO Ue ee eee EE = 1,728 cubic inches*
= 28.31605503 liters
=7.48051946 U.S. gallons
= 6.22883522 imperial (British) gallons
= 0.028316846592 cubic meter*

962 APPENDIX D: MISCELLANEOUS DATA

Volume—Continued
1 cubic ges =46,656 cubic inches*
= 764.53367616 liters
= 201.974010624 U.S. gallons
= 168.17859283 imperial (British) gallons
=27 cubic feet*
=0.764554857984 cubic meter*
1 cubic centimeters. MAN EE EE =0.06102374 cubic inch
=0.00026417 U.S. gallon
=0.00021997 imperial (British) gallon
T cubic meter: eseru = 264.17203187 U.S. gallons
=219.96923879 imperial (British) gallons
= 35.31466655 cubic feet
= 1.30795059 cubic yards
1 quart. (U:S Jamal «ce to eS dE Rue =57.75 cubic inches*
= 32 fluid ounces*
=2 pints*
= 0.94632645 liter
—0.25 gallon*
1 gallon.(U:S.) 4" = ee ASS IA = 3,785.3984784 cubic centimeters*
= 231 cubic inches*
=0.13368056 cubic foot
=4 quarts*
=3.7853058 liters
=0.83267412 imperial (British) gallon
1 Her ATA IL e E =1,000.028 cubic centimeters
=61.02545 cubic inches
=1.05671780 quarts
=0.26417945 gallon

l register tons. Jesse POE E =100 cubic feet*
=2.8316846592 cubic meters*
imeasurementiton = MEM Fu =40 cubic feet*
=1 freight ton*
t freight totie= sae see. Ta or EE ee =40 cubic feet*
=1 measurement ton*
Volume-mass
1⁄eubic-foot;rof.sea mater = 64 pounds
1 cubic'footiof freshuwaters EE =62.428 pounds at temperature of maximum
density (4° C=39°2 F)
licubicifootxof EE =56 pounds
i displacement io =35 cubic feet of sea water*
=1 long ton

NOTE:-AIl values in this appendix are based on the following relationships:
1 inch 22.54 centimeters*
1 yard —0.9144 meter*
] pound (avoirdupois) —0.45359237 kilogram*
1 nautical mile— 1852 meters*
Absolute zero=(—) 273715 C 2 (—) 459267 F.

Coordinate

Symbol

Measured from

APPENDIX E
NAVIGATIONAL COORDINATES

Measured along

Measured to

Maximum
value

963

Labels

latitude

colatitude

L, lat.

colat.

equator

poles

meridian

meridian

parallel

parallel

902
90°

longitude

declination

A, long.

d, dec.

prime merid-
ian

parallel

celestial equa-
tor

polar
distance

altitude

zenith dis-

tance
azimuth

azimuth
angle

amplitude

p

h

Greenwich
hour angle

local hour
angle

hour circle

local meridian

parallel of
declination

elevated pole
horizon

zenith

hour circle

parallel of
declination

vertical circle

vertical circle

north

north, south

horizon

horizon

parallel of
altitude

parallel of

altitude

vertical circle

360?

vertical circle

180? or 90°

east, west

horizon

body

90?

Greenwich
celestial
meridian

local celestial

meridian

meridian
angle

sidereal
hour
angle

right ` `
ascension

Greenwich
mean
time

local mean
time

zone time

Greenwich
apparent
time

local
apparent
time

Greenwich
sidereal
time

local celestial
meridian

parallel of
declination

parallel of
declination

hour circle

hour circle

parallel of
declination

hour circle

hour circle of
vernal equi-
nox

parallel of
declination

lower branch

hour circle of
vernal equi-
nox

parallel of
declination

hour circle

hour circle

lower branch
Greenwich
celestial
meridian

parallel of
declination

hour circle
mean sun

local
celestial
meridian

lower branch

zone `
celestial
meridian

parallel of
declination

hour circle
mean sun

parallel of
declination

hour circle
mean sun

lower branch
Greenwich
celestial
meridian

parallel of,
declination

hour circle
apparent
sun

lower branch
local
celestial
meridian

parallel of
declination

hour circle
apparent
sun

Greenwich
celestial
meridian

parallel of
declination

hour circle
vernal
equinox

local
sidereal
time

local
celestial
meridian

*When measured from celestial horizon.

parallel of
declination

hour circle
vernal
equinox

964

Known satel-
lites

Mercury| Venus

Mean distance
from sun in
astronomical
units

from sun in
millions of
miles (stat-
ute)

in miles (stat-
ute)

Mean distance

Mean diameter

APPENDIX F

PLANETS

Jupiter Saturn

Uranus

483. 3 | 886. 2

Volume
(earth=1)

Mass (earth= 1)

Density
(water=1)

86, 740 | 71, 500

1, 318

316. 94

1. 38

Mean surface
gravity
(earth — 1)

2. 64

Oblateness

297

BH
15. 4

Period of axial
rotation

23556™

9502

Mean orbital
velocity in
statute miles
per second

Sidereal period
of revolution

36542

Eccentricity of
orbit

0. 017

Inclination of
equator to
orbit

23°27’

Inclination of
orbit to eclip-
tic

Stellar
magnitude

17°09’

APPENDIX G
IDENTIFICATION OF NAVIGATIONAL STARS

Introduction.—The following summary is not intended as a substitute for a star
finder such as H.O. 2102-D, or of a knowledge of the heavens, but is given as a supple-
mentary reference to assist in locating the 57 stars included in the main listing in the
Nautical Almanac, plus Polaris. The observer is assumed to be at about the average
latitude of the United States, unless another latitude is indicated. If a celestial body
is said to be east of another, it is lower in the sky if both are rising and higher if both are
setting. A body north of another is nearer the north celestial pole. Directions refer
to great circles on the celestial sphere. Figures referred to are the star charts of
chapter XXII, which should be of assistance in interpreting the descriptions given. It
is assumed the reader is familiar with such well-known configurations as the big dipper
and Orion. Constellation names are given in italics.

Acamar crosses the celestial meridian near the southern horizon during evening
twilight in February, and during morning twilight in August. It is part of the con-
stellation Eridanus, the river, which is not a striking configuration. It is the faintest
star listed among the 57 in the almanac, but is the brightest in its immediate vicinity.
The nearest bright star is Achernar, about 20? away in a generally southwesterly
direction. Dec. 40°S, SHA 316°, mag. 3.1. Fig. 2205.

Achernar, at the southern end of the inconspicuous constellation Eridanus, the
river, is one of the brightest stars of the southern hemisphere. It is not visible north
of latitude 33? N. It crosses the celestial meridian during evening twilight in January,
and during morning twilight in early August. Nearly a straight line is formed by
Fomalhaut, about 40° WNW; Achernar; and Canopus, about the same distance in the
opposite direction. However, since these stars are widely separated, the relationship
is not striking. Achernar forms large triangles with Acamar and Ankaa, Ankaa and
Al Na'ir, and with Al Na'ir and Peacock. Dec. 57°S, SHA 336°, mag. 0.6. Fig. 2205.

Acrux is the brightest and most southerly star in the famed southern cross. It is
not visible north of latitude 27? N. It crosses the celestial meridian during evening
twilight in early June and during morning twilight in January. It is about 15° WSW
of first magnitude Hadar and Rigil Kentaurus. Dec. 63°S, SHA 174°, mag. 1.1.
Fig. 2207.

Adhara. About 10?S and a little to the east of Sirius is a small, approximately
equilateral triangle of three second magnitude stars. Adhara is the westernmost and
brightest of the three. It crosses the celestial meridian to the south during evening
twilight in March, and during morning twilight in October. Dec. 295, SHA 256°,
mag. 1.6. Fig. 2206.

Aldebaran. If the line formed by the belt of Orion, the hunter, is extended about
20° to the northwestward, and curved somewhat toward the north, it leads to first
magnitude Aldebaran in Taurus, the bull. This is a group of stars forming a V. A long,
curving line starting at Sirius extends through Procyon, Pollux, Capella, and Aldebaran.

Dec. 16°N, SHA 292°, mag. 1.1. Fig. 2206.
965

966 APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS

Alioth is the third star from the outer end of the handle of the big dipper, and the
brightest star of the group. Dec. 56°N, SHA 167°, mag. 1.7. Fig. 2207.

Alkaid is the star at the outer end of the handle of the big dipper, farthest from the
bowl. It is the second brightest star of the group. Dec. 50°N, SHA 154°, mag. 1.9.
Fig. 2207.

Al Na'ir is the westernmost of two second magnitude stars of nearly equal bright-
ness about midway between first magnitude Fomalhaut, approximately 20° to the
northeast, and second magnitude Peacock, about the same distance in the opposite
direction. A curved line extending eastward from the southern cross passes through
Hadar and Rigil Kentaurus and, if extended with less curvature, leads first to Peacock
and then to Al Na’ir. This star forms triangles with Fomalhaut and Ankaa, Ankaa and
Achernar, and with Achernar and Peacock. It is not visible north of latitude 43°N.
It crosses the celestial meridian during evening twilight early in December, and during
morning twilight in June. Dec. 47°S, SHA 29°, mag. 2.2. Figs. 2205, 2208.

Alnilam is the middle star of the belt of Orion, the hunter. Dec. 195, SHA 277°,
mag. 1.8. Fig. 2206.

Alphard, a second magnitude star, is the brightest in the inconspicuous constella-
tion Hydra, the water monster. The nearest bright star is first magnitude Regulus,
about 20° NNE. It is about midway between the horizon and zenith when it crosses
the celestial meridian to the southward during evening twilight in late April, and during
morning twilight in November. Dec. 8°S, SHA 219°, mag. 2.2. Fig. 2207.

Alphecca is the brightest star of Corona Borealis, the northern crown, about
20°ENE of first magnitude Arcturus. It forms a triangle with Arcturus and Alkaid.
It crosses the celestial meridian near the zenith during evening twilight in July, and
during morning twilight in February. Dec. 27°N, SHA 127°, mag. 2.3. Figs. 2207,
2208.

Alpheratz, a second magnitude star, is at the northeast corner of the great square of
Pegasus, the winged horse, and is the brightest of the four stars forming the square.
It crosses the celestial meridian near the zenith during evening twilight early in January,
and during morning twilight in July. Dec. 29°N, SHA 359°, mag. 2.2. Fig. 2205.

Altair is at the southern vertex of a large, nearly right triangle which is a con-
spicuous feature of the evening sky in late summer and in autumn. The right angle is
at Vega and the northern vertex is at Deneb. All three are first magnitude stars.
Two fainter stars close to Altair, one on each side in a line through Vega, form a charac-
teristic pattern making Altair one of the easiest stars to identify. It crosses the
celestial meridian during evening twilight in October, and during morning twilight in
May. Dec. 9°N, SHA 63°, mag. 0.9. Fig. 2208.

Ankaa, a second magnitude star, is the brightest star in inconspicuous Phoeniz.
It is surrounded by and forms a series of triangles with Diphda, Fomalhaut, Al Na’ir,
Achernar, and Acamar. It crosses the celestial meridian low in the southern sky in
January, and during morning twilight in July. Dec. 42°S, SHA 354°, mag. 2.4.
Fig. 2205.

Antares is the brightest star in the conspicuous constellation Scorpio, the scorpion,
which is low in the southern sky during evening twilight in late July, and morning
twilight in late February. No other first magnitude star is within 40° of Antares and
none toward the north is within 60°. It has a noticeable reddish hue and in appear-
ance somewhat resembles Mars, which is occasionally near it in the sky. Dec. 26°S,
SHA 113°, mag. 1.2. Fig. 2208.

APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS 967

Arcturus. The curved line along the stars forming the handle of the big dipper,
if continued in a direction away from the bowl, passes through brilliant, first magni-
tude Arcturus. The distance from Alkaid, at the end of the big dipper, to Arcturus is
a little more than the length of the dipper. Arcturus forms a large triangle with
Alkaid and Alphecca. Dec. 19°N, SHA 147°, mag. 0.2. Figs. 2207, 2208. `

Atria is the brightest of three stars forming a small triangle called Triangulum
Australe, the southern triangle, not far from the south celestial pole. It is not seen
north of latitude 21°N. A line through the east-west arm of the southern cross, if
continued toward the east and curved somewhat toward the south, leads first to Hadar,
then to Rigil Kentaurus, then, by curving more sharply, to the northernmost star of
the triangle, and finally to Atria, only about 21° from the south celestial pole. Dec.
69°S, SHA 109°, mag. 1.9. Fig. 2207.

Avior is the westernmost star of Vela, the sails, or false southern cross, about 30°
WNW of the true southern cross, about 15° ESE of the brilliant Canopus, and nearly
enclosed within a large triangle formed by Canopus, Suhail, and Miaplacidus. It is
not visible north of latitude 31°N. Below this, it crosses the celestial meridian low
in the southern sky during evening twilight in April, and morning twilight in early
November. Dec. 59°S, SHA 235°, mag. 1.7. Figs. 2206, 2207.

Bellatrix is a second magnitude star north and a little west of the belt of Orion,
the hunter. It is about equidistant from the belt and first magnitude, red Betelgeuse.
Bellatrix is at the northwest corner of a box surrounding the belt of Orion. Dec. 6°N,
SHA 279°, mag. 1.7. Fig. 2206.

Betelgeuse is a conspicuous, reddish star of variable brightness about 10% north
and a little east of the belt of Orion, the hunter. A line through the center of the belt
and perpendicular to it passes close to red Betelgeuse to the north and blue Rigel about
the same distance south of the belt. Betelgeuse and Rigel are at opposite corners of
a box surrounding the belt of Orion. Dec. 7? N, SHA 272°, mag. 0.1-1.2 (variable).
Fig. 2206.

Canopus, second brightest star in the sky, is about 35% south of Sirius. A line
extending eastward through the belt of Orion and curving toward the south passes
first through Sirius, then through the small triangle of which Adhara is the brightest
star, and finally to Canopus, which forms a large, almost equilateral triangle with
Suhail and Miaplacidus. This triangle nearly encloses Vela, the sails or false southern
cross, about 20°ESE of Canopus. Canopus is not visible north of latitude 37°N.
It is on the edge of the Milky Way and while many relatively bright stars are nearby,
none in the immediate vicinity of Canopus approaches it in brightness. Dec. 5325,
SHA 264°, mag. (—)0.9. Fig. 2206.

Capella is a brilliant star about 45° north of the belt of Orion, the hunter. A
curved line starting at Sirius and extending through Procyon, Pollux, Capella, Alde-
baran, the belt of Orion, and back to Sirius forms an inverted tear-drop figure with
Capella at the top and the various parts being about equally spaced along the curve.
Capella crosses the celestial meridian near the zenith during evening twilight in early
March, and during morning twilight in late September. Dec. 46°N, SHA 282%,
mag. 0.2. Fig. 2206. à

Deneb is a bright star at the northeastern vertex of a large, nearly right triangle
formed by Altair, Vega, and Deneb, the right angle being at Vega. These three stars
are the brightest in the eastern sky during summer evenings. Deneb is not as bright
as the other two, but is the brightest star in the constellation Cygnus, the swan. It
crosses the celestial meridian near the zenith during evening twilight in November,
and during morning twilight in late May. Dec. 45? N, SHA 50°, mag. 1.3. Fig. 2208.

968 APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS

Denebola, in Leo, the lion, is a second magnitude star at the opposite end of the
constellation from Regulus. A straight line from Regulus, on the west, to Arcturus,.
on the east, passes close to Denebola, which is somewhat nearer Regulus. Denebola
crosses the celestial meridian to the south during evening twilight in May, and during
morning twilight in December. Dec. 15°N, SHA 183°, mag. 2.2. Fig. 2207.

Diphda. A line extending southward through the eastern side of the great square
of Pegasus, the winged horse, and curving slightly toward the east, leads to second
magnitude Diphda. The distance from the southern star of Pegasus to Diphda is about
twice the length of one side of the square. Diphda is part of the inconspicuous con-
stellation Cetus, the whale. The only nearby first magnitude star is Fomalhaut,
about 25° in a generally southwest direction. Diphda, Fomalhaut, and Ankaa form
a nearly equilateral triangle. Dec. 18°S, SHA 350%, mag. 2.2. Fig. 2205.

Dubhe forms the outer rim of the bowl of the big dipper. It and Merak (not one
of the 57 navigational stars) are the two “pointers”” used to locate Polaris, Dubhe
being the one nearer the pole star. Dec. 62°N, SHA 195°, mag. 2.0. Fig. 2207.

Elnath is a second magnitude star between Capella, about 15° to the north, and
Betelgeuse, about 20° to the south. It is a little north of a line connecting Aldebaran
and Pollux. It is at the end of the northern fork of V-shaped Taurus, the bull. Alde-
baran is the principal star at the closed end of the V. This constellation is approximately
25° NNW of Orion, the hunter. Dec. 29°N, SHA 279°, mag. 1.8. Fig. 2206.

Eltanin is the southernmost and brightest star in the inconspicuous constellation
Draco, the dragon, south and somewhat east of the little dipper. A straight line extend-
ing northwestward through Altair and its two fainter companions passes first through
brilliant Vega, and, about 15° beyond, to second magnitude Eltanin. Eltanin crosses
the celestial meridian high in the sky toward the north during evening twilight in early
September, and during morning twilight in late March. Dec. 51°N, SHA 91°, mag.
2.4. Fig. 2208.

Enif is a third magnitude star approximately midway between Altair, about 25°
west, and Markab, about 20% ENE. From Markab, at the southwestern corner of
the great square of Pegasus, the winged horse, a line extending in a generally west-
southwesterly direction passes through two almost equally spaced fourth magnitude
stars. From the second of these, a line about 5° long extending in a northwesterly
direction leads to Enif. Enif crosses the celestial meridian to the south during evening
twilight in November, and during morning twilight in June. Dec. 10°N, SHA 35°,
mag. 2.5. Figs. 2205, 2208.

Fomalhaut is a first magnitude star well separated from stars of comparable
brightness and from conspicuous configurations. A line through the western side of
the great square of Pegasus, the winged horse, and extended about 45° toward the
south passes close to Fomalhaut, which forms two large, nearly equilateral triangles
with Diphda and Ankaa and with Ankaa and Al Na'ir. Dec. 30°S, SHA 16°, mag.
1.3. Fig. 2205.

Gacrux is the northernmost star of the southern cross. It is bright for a second
magnitude star, but its brilliance is overshadowed by the brighter 8 Crucis (not listed
among the 57 navigational stars) and Acrux, the two brightest stars of the southern
cross, and by Hadar and Hiel Kentaurus, about 15° ESE. Gacrux crosses the celestial
meridian during evening twilight in early June, and during morning twilight in late
December, but is not visible north of latitude 33°N. Dec. 57°S, SHA 173°, mag.
1.6. Fig. 2207.

Gienah is a third magnitude star, the brightest in the constellation Corvus, the
crow. A long, sweeping arc starting with the handle of the big dipper and extending

APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS 969

successively through Arcturus and Spica leads to this relatively small, four-sided figure
made up of third magnitude stars. Gienah is at the northwest corner. It crosses the
celestial meridian during evening twilight in late May, and during morning twilight
in December. Dec. 17°S, SHA 177°, mag. 2.8. Fig. 2207.

Hadar is a first magnitude star about 10° east of the southern cross, and about
5° west of Rigil Kentaurus, the brightest of several bright stars in this part of the sky.
Dec. 60°S, SHA 150°, mag. 0.9. Fig. 2207.

Hamal is the brightest star of the inconspicuous constellation Aries, the ram. A
line through the center of the great square of Pegasus, the winged horse, extended
about 25° east, and curved slightly toward the north, leads to Hamal. It is over the
meridian to the south during evening twilight in January, and during morning twilight
in August. Dec. 23°N, SHA 329°, mag. 2.2. Fig. 2205.

Kaus Australis is near the southern end of a group of second and third magnitude
stars forming the constellation Sagittarius, the archer, about 25° ESE of Antares, in
Scorpio, the scorpion. It is about 10°SW of Nunki, also in Sagittarius, and about the
same distance ENE of Shaula, in Scorpio. With Antares, Sabik, and Nunki, it forms
a large, poorly defined box. It is over the meridian to the south during evening twilight
in September and during morning twilight in April. Dec. 34°S, SHA 85°, mag. 2.0.
Fig. 2208.

Kochab forms the outer rim of the bowl of the little dipper, at the opposite end
from Polaris, about 15° north. It is directly above the pole during evening twilight
in early July and during morning twilight in January; and directly below the pole,
low in the northern sky, during evening twilight of early February and morning twilight
of late August. Dec. 74°N, SHA 137°, mag. 2.2. Fig. 2208.

Markab is the star at the southwest corner of the great square of Pegasus, the
winged horse, at the opposite corner from Alpheratz. It is over the celestial meridian
to the south during evening twilight in December, and during morning twilight late
in June. Dec. 15°N, SHA 14°, mag. 2.6. Fig. 2205.

Menkar is a third magnitude star at the eastern end of the inconspicuous constel-
lation Cetus, the whale. No bright stars are nearby. A straight line from Aldebaran
extending about 25° in the direction indicated by the point of the V of Taurus, the bull,
leads to Menkar. A long, straight line from Fomalhaut east-northeastward through
Diphda, and extended about 40°, leads to Menkar. It crosses the celestial meridian
during evening twilight in February, and during morning twilight in August. Dec. 4°
N, SHA 315°, mag. 2.8. Figs. 2205, 2206.

Menkent is a second magnitude star about 25° north of Hadar and about 30°
northeast of the southern cross. A line from Gienah across the opposite corner of the
small, four-sided Corvus, the crow, and then curving a little toward the east, leads to
Menkent. A number of third magnitude stars are nearby, but they do not form a
conspicuous configuration. With Antares and Rigil Kentaurus, Menkent forms a large
triangle. It crosses the celestial meridian low in the southern sky during evening
twilight in late June and during morning twilight in early January. Dec. 36°S, SHA
149°, mag. 2.3. Figs. 2207, 2208.

Miaplacidus is a second magnitude star about 10° south of the false southern cross.
It is the nearest of the 57 navigational stars to the south celestial pole, about 20° away,
and is not visible north of latitude 20° N. With Suhail and brilliant Canopus it forms
a large, nearly equilateral triangle almost enclosing the false southern cross. South of
latitude 20°S, it does not set, but circles the south celestial pole in a clockwise direction,
reaching its maximum altitude above the pole during evening twilight in early May

970 APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS

and during morning twilight in November. Dec. 70°S, SHA 222°, mag. 1.8. Figs.
2206, 2207. E.

Mirfak is à second magnitude star at the northeastern end of a gently curving line
extending in a northeasterly direction from Alpheratz at the northeastern corner of the
great square of Pegasus, the winged horse, through two other second magnitude stars,
Mirach and Almach, not included among the 57 navigational stars. Mirfak is about
25? east and a little south of Cassiopeia, and about 20? WNW of Capella. A line from
Kochab through Polaris, and curved slightly toward the east, leads to Mirfak. Dec.
50 N, SHA 310°, mag. 1.9. Figs. 2205, 2206.

Nunki is the more northerly of the two brightest stars of a group of second and
third magnitude stars forming the constellation Sagittarius, the archer, about 30° E of
Antares. It is about 10? NE of Kaus Australis, also in Sagittarius. With Sabik,
Antares, and Kaus Australis, it forms a large, poorly defined box. It is over the
meridian to the south during evening twilight in early October and during morning
twilight in April. Dec. 26°S, SHA 77°, mag. 2.1. Fig. 2208.

Peacock, the brightest star in the southern constellation of the same name, is not &
part of a conspicuous configuration of stars. A curved line extending eastward from
the southern cross passes through Hadar and Rigil Kentaurus and, if extended with less
curvature, leads to Peacock, about 30? southeast of Scorpio, the scorpion, and about 20?
southwest of Al Na'ir. With Al Na'ir and Achernar it forms a large, poorly defined
triangle. It crosses the celestial meridian during evening twilight in early November,
and during morning twilight in late May, but is not visible north of latitude 339 N.
Dec. 57?8, SHA 54?, mag. 2.1. Figs. 2205, 2208.

Polaris is not listed among the 57 navigational stars, but is treated separately be-
cause it is less than 1? from the north celestial pole. It is about midway between the
big dipper and Cassiopeia. A line through Dubhe and Merak (not one of the 57
navigational stars), the pointers forming the outer side of the bowl of the big dipper, if
extended northward for about 30?, leads almost directly to Polaris. A line extending
north from Alpheratz at the northwest corner of the great square of Pegasus, the winged
horse, passes through Caph (not one of the 57 navigational stars) in Cassiopeia and then
Polaris at about equal intervals. Dec. 892 N, SHA 332°, mag. 2.1. Figs. 2205-2208.

Pollux is the brighter of the “twins of Gemini,” two relatively bright stars about
45° NE of Orion, the hunter, and about 459 ENE of Aldebaran. A curved line starting
at Sirius extends through Procyon, Pollux, and Capella, all first magnitude stars.
Dec. 282 N, SHA 244°, mag. 1.2. Fig. 2206.

Procyon is a bright star about 30° east of Orion, the hunter. A curved line starting
at Sirius extends through Procyon, Pollux, and Capella, all first magnitude stars.
Dec. 5? N, SHA 246°, mag. 0.5. Fig’ 2206.

Rasalhague forms a large, nearly equilateral triangle with Altair and Vega, Rasal-
hague being at the western vertex. Both of the other stars are considerably brighter
than Rasalhague. It crosses the celestial meridian to the south during evening twilight
in early September, and during morning twilight in late March. Dec. 13°N, SHA 97°,
mag. 2.1. Fig. 2208.

Regulus is at the opposite end of Leo, the lion, from Denebola, and is the brightest
star of the constellation. A line through Dubhe and Merak (not one of the 57 naviga-
tional stars), the pointers by which Polaris is usually identified, extended about 45°
southward, and curved slightly toward the west, leads to Regulus, which forms the

southern end of the handle of the sickle, part of Leo. Dec. 12° N, SHA 209°, mag. 1.3.
Fig. 2207.

APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS 971

; Rigel is a brilliant bluish star about 10°S and.a little to the west of the belt of
Orion, the hunter. A line through the center of the belt and perpendicular to it passes
close to blue Rigel to the south and red Betelgeuse about the same distance north of the
belt. Rigel and Betelgeuse are at opposite corners of a box surrounding the belt of
Orion. Dec. 825, SHA 282°, mag. 0.3. Fig. 2206.

Rigil Kentaurus is the brighter and more easterly of two first magnitude stars about
15° east of the southern cross. It is over the meridian during evening twilight in early
July, and during morning twilight in late January, but is not visible north of latitude
299 N. Dec. 61°S, SHA 141°, mag. 0.1. Figs. 2207, 2208.

Sabik is part of the inconspicuous constellation Ophiuchus, the serpent holder,
about 20° north of Scorpio, the scorpion. With Antares, Kaus Australis, and Nunki,
it forms a large, poorly defined box in the southern sky on summer evenings. Sabik
crosses the celestial meridian during evening twilight in August, and during morning
twilight in March. Dec. 16°S, SHA 103°, mag. 2.6. Fig. 2208.

Schedar is the southernmost star of the W (or M) of Cassiopeia, on the opposite
side of Polaris from the big dipper. It is the second star from the leading edge of this
configuration as it circles the north celestial pole. Dec. 56°N, SHA 351°, mag. 2.5.
Figs. 2205, 2206, 2208.

Shaula is a second magnitude star marking the end of the tail of Scorpio, the
scorpion, at the opposite end from Antares. This constellation is low in the southern
sky onsummer evenings. Shaula is about 15° southeast of Antares and about 10° WSW
of Kaus Australis. It crosses the celestial meridian during evening twilight in early
September, and during morning twilight in March. Dec. 37°S, SHA 97°, mag. 1.7.
Fig. 2208.

Sirius, the brightest star in the heavens, is in the constellation Canis Major, the
‘large dog” of Orion, the hunter. The line formed by the belt of Orion, if extended
about 20° to the eastward and curved toward the south, leads to Sirius. Dec. 17°S,
SHA 259°, mag. (—)1.6. Fig. 2206.

Spica is the brightest star of Virgo, the virgin, an inconspicuous constellation on the
celestial equator to the south during evening twilight in early summer. The curved
line along the stars forming the handle of the big dipper, if continued in a direction
away from the pointers, passes through Arcturus and then Spica. The distance between
Alkaid, at the end of the big dipper, and Arcturus is about the same as that between
Arcturus and Spica, and is a little more than the length of the big dipper. Spica
crosses the celestial meridian during evening twilight in June, and during morning
twilight late in December. Dec. 11°S, SHA 159°, mag. 1.2. Fig. 2207.

Suhail is one of a number of second magnitude stars extending along the Milky
Way between Sirius and the southern cross. Itis about 10° north of the false southern
cross, which is nearly enclosed by a large, nearly equilateral triangle formed by Suhail,
Canopus, and Miaplacidus. Canopus and Suhail are on opposite edges of the Milky
Way, with a number of second magnitude stars between them. A straight line extend-
ing eastward through the east-west arm of the southern cross leads to Suhail, about
35° away. In the southern United States, Suhail crosses the celestial meridian near the
southern horizon during evening twilight in April, and during morning twilight in
November. Dec. 43? 8, SHA 223°, mag. 2.2. Figs. 2206, 2207.

Vega is the brightest star north of the celestial equator, and the third brightest in
the entire sky. It is at the western vertex and the nearly-right angle of a large
triangle which is a conspicuous feature of the evening sky in late summer and in autumn.
The other two stars of the triangle are Altair and Deneb, both of the first magnitude.

972 APPENDIX G: IDENTIFICATION OF NAVIGATIONAL STARS
Vega passes through the zenith approximately at latitude 38°45’N during evening
twilight in September and during morning twilight in April. Dec. 39°N, SHA 81°,
mag. 0.1. Fig. 2208.

Zubenelgenubi, a third magnitude star, is the southern (or western) basket of
Libra, the balance. The boxlike Libra is about 25? WNW of Antares, in Scorpio, the
scorpion. A long line extending eastward from Alphard, between Gienah and Spica,
leads to Zubenelgenubi. Dec. 16°S, SHA 138°, mag. 2.9. Figs. 2207, 2208.

APPENDIX H

NAVIGATIONAL STARS AND THE PLANETS

973

RR ' Origin Á is-
Name Pronunciation Bayer name AL Meaning of name e
Acamar &'kd-mür 0 Eridani Arabic | another form of Achernar 120
Achernar ā'kēr.nār a Eridani Arabic end of the river (Eridanus) 72
Acrux á krüks a Crucis Modern | coined from Bayer name 220
Adhara ā:dā'rā , « Canis Majoris Arabic the virgin (s) 350
Aldebaran ál déb d-rān a Tauri Arabic follower (of the Pleiades) 64
Alioth āl'rēth € Ursa Majoris Arabic | another form of Capella 49
Alkaid ál-kåd' n Ursa Majoris Arabic leader of the daughters of the bier 190
Al Na'ir āl.nār a Gruis Arabic bright one (of the fish's tail) %
Alnilam Alni.lám e Orionis Arabic | string of pearls 410
Alphard ál fārd a Hydrae Arabic | solitary star of the serpent 200
Alphecca AL fék'à a Corona Borealis Arabic | feeble one (in the erown) 76
Alpheratz Āl.fē'rāts a Andromeda Arabic the horse's navel 120
Altair Al.tár' a Aquilae Arabic flying eagle or vulture 16
Ankaa ün'kà ` a Phoenicis Arabic coined name 93
Antares ān-tā'rēz a Scorpii Greek rival of Mars (in color) 250
Arcturus ürk-tü'rüs a Bootis Greek the bear’s guard 37
Atria Base: a Trianguli Australis | Modern | coined from Bayer name 130
Avior ` 4’vi-or e Carinae Modern | coined name 350
Bellatrix bé-1a’triks ; y Orionis Latin female warrior 250
Betelgeuse bēt'ēl:jūz a Orionis Arabic | the arm pit (of Orion) 300
Canopus kéng nis a Carinae Greek city of ancient Egypt 230
Capella ká-pél'á a Aurigae Latin little she-goat 46
Deneb ` dén'éb , a Cygni Arabic tail of the hen 600
Denebola dé-néb'0-lá B Leonis Arabic tail of the lion 42
Diphda dif'dá B Ceti Arabic paces frog (Fomalhaut was once 57
the first
Dubhe dūb'ē a Ursa Majoris Arabic the bear's back 100
Elnath ēl'nāth B Tauri Arabic one butting with horns 130
Eltanin ēl.tā'nīn y Draconis Arabic head of the dragon 150
Enif Cif: 5 e Pegasi Arabic nose of the horse 250
Fomalhaut fo'mdl.ot «a Piscis Austrini Arabic mouth of the southern fish 23
Gacrux gā'krūks y Crucis Modern | coined from Bayer name 72
Gienah jē'nd y Corvi Arabic right wing of the raven 136
Hadar hā'dār B Centauri Modern | leg of the centaur 200
Hamal hám'dl a Arietis Arabie | full-grown lamb 76
Kaus Australis kós Os-trà'lis e Sagittarii Ar., L. | southern part of the bow 163
Kochab ko'káb B Ursa Minoris Arabic shortened form of “north star” (named 100
when it was that, c. 1500 B C- A D 300)
Markab már'káb a Pegasi Arabic | saddle (of Pegasus) 100
Menkar mēn'kār a Ceti Arabic nose (of the whale) 1,100
Menkent mén'ként 9 Centauri Modern | shoulder of the centaur 55
Miaplacidus mī'd-plās'i.dūs B Carinae Ars Li guiet or still waters 86
Mirfak mir'fāk a Persei Arabic elbow of the Pleiades 130
Nunki nūn'kē c Sagittarii Bab. constellation of the holy city (Eridu) 150
Peacock pé'kók a Pavonis Modern nee from English name of con- 250
stellation
Polaris po-la’ris a Ursa Minoris Latin the pole (star) 450
Pollux pēl'ūks B Geminorum Latin Zeus' other twin son (Castor, « Gemi- 33
norum, is first twin)
Procyon pro’si-on a Canis Minoris Greek before the dog (rising before the dog 11
star, Sirius)
Rasalhague rās'āl.hā'gwē a Ophiuchi Arabic head of the serpent charmer 67
Regulus rég'u-lüs « Leonis Latin the prince ; 67
Rigel ri/jel B Orionis Arabic foot (left foot of Orion) 500
Rigil Kentaurus | rī'jil kén-tó'rüs a Centauri Arabic foot of the centaur 4.3
Sabik sā'bik n Ophiuchi Arabic second winner or conqueror 69
Schedar shéd'ár a Cassiopeiae Arabic the breast (of Cassiopeia) | 1 360
Shaula shô’lå A Scorpii Arabic | cocked-up part of the scorpion’s tail 200
Sirius sir’i-ŭs a Canis Majoris Greek SC SEH one (popularly, the dog 8.6
star
Spica spī'kd a Virginis Latin the ear of corn 155
Suhail SE hal’ A Velorum Arabic shortened form of Al Suhail, one 200
Arabic name for Canopus
Vega vé'gá a Lyrae Arabic the falling eagle or vulture ` 27
Zubenelgenubi z00-bén'é]-jé.nü^bé a Librae Arabic southern claw (of the scorpion) 66
PLANETS
M —— TL
Name Pronunciation Origin of name Meaning of name
Mercury mūr'kūrrī Latin god of commerce and gain
Venus vē'nūs Latin goddess of love
Earth ūrth Mig Eng. SS
S márz atin god ol war 3
een joo'pi-tér Latin god of the heavens, identified with the Greek Zeus, chief of the
Olympian gods
Saturn sát'érn Latin god of seed-sowing
Uranus ú'rá-nús Greek the Dee of heaven
Neptune nép'tun Latin. god of the sea
Pluto pido'£o Greek god of the lower world (Hades)

Guide to pronunciations:

fate, Add, final, last, bound, arm; bē, ēnd, camél, reader; ice, bit, animal; over, poetic, hót, lórd, moon; vúbe, únite, túb,

circús, arn
*Distances in light-years.

tances of the stars; the values given are representative.

One light-year equals approximately 63,300 AU, or 5,880,000,000,000 miles. Authorities differ on dis-

974

Name

Pronunciation

APPENDIX I
CONSTELLATIONS

Genitive

Pronunciation

Meaning

Navigational stars or
approximate position

Andromeda*

Antlia

Apus

Aquarius (=) *
Aquila*

Ara*

Aries (T)*
Auriga*
Bootes*
Caelum
Camelopardalis
Cancer (95)*
Canes Venatici

Canis Major*
Canis Minor*
Capricornus (Vj)
Carina**

Cassiopeia*
Centaurus*
Cepheus*

Cetus*
Chamaeleon
Circinus
Columba
Coma Berenices
Corona
Australis*
Corona
Borealis*
Corvus*
Crater*
Crux
Cygnus*
Delphinus*
Dorado
Draco*
Equuleus*
Eridanus*
Fornax
Gemini (II)*
Grus
Hercules*

Horologium
Hydra*
Hydrus
Indus

**Part of the single constellation Ar
{Parts within brackets are am
ftParts within parenthe

án-dróm' é-dá

ānt'li:d

ā'pūs

d:kwār'i.ūs
āk'wild

ā'rā

a'ri-é6z

Ó-ri'gå

bó-o'téz

sē'lūm
ka-mél’6-pir/dd-lis
k&n/sér

kā'nēz vé-nat’i-si

kà'nis mā'jēr
kā'nis mī/nēr
kāp'ri:kūr/nūs
ka@-ri/na

kās'i:0.pē”yd
sén-t0'rús
sē'fūs

sē'tūs

kd:mē'lē.ūn
sūr'si:nūs
kó-lúm/'bá

kē'mū bér-é-niséz
kó-r0'ná 6s-tra/lis

k-rü/nd bo’ré-a/
lís
kūr'vūs
krā'tēr
krūks
sig'nús
dél-fi'nús
dó-rá/dó
drà'ko
é-kwoo'lé-üs
é-rid/á-nús
fūr'nāks
jēm'i.nī
grūs
húr'kú-léz

hór'ó-15/j1-%m
hī'drā

hi'drús
In'düs

Zodiacal constellations are given in bold

Guide to pronunciations:

fate, cáre, hát, findl, abound, sofa, arm; be, créate, énd, reader; ice, bit; ov

tüb, circús, úrn.

Andromedae

Antliae

Apodis

A quarii

Aquilae

Arae

Arietis

Aurigae

Bootis

Caeli

Camelopardalis

Cancri

Canum Venati-
eorum

Canis Majoris

Canis Minoris

Capricorni

Carinae

Cassiopeiae
Centauri
Cephei

Ceti
Chamaeleontis
Circini

Columbae

Comae Berenices
Coronae Australis

Coronae Borealis

Corvi
Crateris
Crucis
Cygni
Delphini
Doradus
Draconis
Equulei
Eridani
Fornacis
Geminorum
Gruis
Hereulis

Horologii
Hydrae
Hydri
Indi

go Navis of Ptolemy.
plifications of the meanings of constellation names.
ses are the meanings of words deleted from former, more complete constellation names.

án-dróm'é-dé

Ant/li-é

áp'0-dís

d:kwār'Lī

āk'wi.lē

ā'rē

@-ri’é-tis

0-ri'jé

bó-0'tis

sē'lī

ká-mél/ó-pár/dà-lis

káng'kri

kā'nūm vé-nat’i-
ko'rúm

kā'nis má-jo'ris

ka/nis mi-nd’ris

kap’ri-k6r/ni

ká-ri'né

kd:mē'lē.on'tīs
sar’si-ni
kó-lúm'bé

kū'mē bēr'ē.nī'sēz
kó-r0'né 6s-tra’lis

kó-r0'né bū'rē.ā”
lis
kór'vi
krd-té'ris
kroo'sis
sig/ni
dēl.fī'nī
dó-rü'düs
drá-ko'nis
é-kwoo'lé-i
ē-rīd'd-nī
for-na/sis
jém’i-nd/rim
groo'is
hūr'kū.lis

hór'ó-lo/ji-i
hi'dré
hi'dri

in'dī

type, with their symbols.
"One of the original constellations of Ptolemy.

Andromeda [the

chained woman]t
(air) pumptt
bird of paradise
water carrier
eagle
altar
ram
charioteer
herdsman
graving tool
giraffe
crab
hunting dogs

larger dog
smaller dog
horned goat
keel

Cassiopeia [the lady

in the chair]t
centaur

Cepheus [the shep-

herd]t
whale
chameleon
pair of compasses
dove
Berenice's hair
southern crown

northern crown

crow

cup

Cross

swan

dolphin

dorado [a fish]t

dragon

colt

Eridanus [a river]t

furnace

twins

crane [a bird]t

Hercules
logical hero]t

clock

water monster

water snake

Indian

[mytho-

Alpheratz

d 35°S, SHA 210°
d 75°S, SHA 120°
d 5°S, SHA 25°
Altair

d 55°S, SHA 100°
Hamal

Capella

Arcturus

d 40°S, SHA 290°
d 70°N, SHA 275°
d 20°N, SHA 230°
d 40°N, SHA 165°

Adhara, Sirius

Procyon

d 20°S, SHA 45°

Avior, Canopus,
Miaplacidus

Schedar

Hadar, Menkent, Ri-
gil Kentaurus
d 75°N, SHA 15°

Diphda, Menkar
d 8098, SHA 200°
d 65°S, SHA 140°
d 35°S, SHA 275°
d 25°N, SHA 170°
d 40°S, SHA 80°

Alphecca

Gienah

d 1598, SHA 190°
Acrux, Gacrux
Deneb

d 15°N, SHA 50°
d 6098, SHA 285°
Eltanin

d 10°N, SHA 40°
Acamar, Achernar
d 30°S, SHA 320°
Pollux

Al Na'ir

d 30°N, SHA 100°

d 5098, SHA 310°
Alphard

d 70°S, SHA 320°
d 60°S, SHA 35°

er, poetic, hót, connect, lord, moon; tübe, únite,

APPENDIX I

CONSTELLATIONS

975

Navigational stars or

Name Pronunciati Genitive iati ;
J- nciation ienitive Pronunciation Meaning approximate position
Lacerta lūrsūr'tū Lacertae la-stir’té lizard d 45°N, SHA 25?
Leo (Dis lé'o Leonis lé-onis lion Denebola, Regul
Leo Minor lé'o mr'nér Leonis Minori Sai ar h EE
Sii OS 1ē-0'nis mi-nó'ris | smaller lion d 35°N, SHA 205°
Lepus* M BS Leporis lép'i-rls hare d 20°S, SH A 275°
= * =p n ; = pe ,
a s ) s Prá Librae li’bré balance [scales]t Zubenelgenubi
Ep Kg Lupl lü'pi wolf d 4598, SH A 130°
Lynx lingks Lyncis lin’sis lynx d 50°N, SHA 240°
Lyra* lī'rd Lyrae li’ré lyre Vega
AY SC
Mena — m Mensae mén'sé table (mountain){t | d 75%, SHA 275°
Microscopium mi kro-:skū'pl:ūm | Microscopii mi'kró-skó' pl-i microscope d 35°S, SHA 45°
Monoceros mo-nos’ér-ds Monocerotis mó-nós'ér-ó'tls unicorn d 0? SH A 2559
Musca mūs'kd Muscae mūs'sē fly d 70°S SHA 175°
ay ` H
Norma vides Normae nór'mé square (and rule) tt | d 50%S, SHA 120°
Octans e váð Octantis ók-tán'tís octant d 85°S, SHA 40°
Ophiuchus* ēf'frū'kūs Ophiuchi Of'i:ū'kī serpent holder Rasalhague, Sabik
n * ri 1 s A 2 ,
Orion O-rī' On Orionis O'ri:0/nis Orion [the hunter]t | Alnilam, Bellatrix,
icd i x Betelgeuse, Rigel
Pavo pā vē Pavonis pā-vū'nis peacock Peacock
Pegasus* pég'á-süs Pegasi pég’a-si Pegasus [winged Enif, Markab
d LS: b ^ horse]t
Perseus pür'süs Persei pür'sé-i Perseus [mytholog- | Mirfak
i N art ical character]f
Phoenix fe'niks Phoenicis fē.nī/sīs phoenix [the im- | Ankaa
k E» 4 L mortal bird]t
Pictor Du t Pictoris plk-tó'ris painter (easel of)tt | d 55%, SH A 275°
Pisces (X)* pis'éz Piscium pish'i:ūm fishes d 15°N, SHA 355°
Piscis Austrinus* | pis'is 0s-tri'nús Piscis Austrini pis'is ós-tri'ni southern fish Fomalhaut
Puppis** ponas | Aronu püp'is stern [of ship]t d 30°S, SHA 245°
Pyxis** pik'sis Pyxidis pik’si-dis mariner’s compass d 25°S, SHA 230°
Reticulum ré-tik'u-lám Reticuli ré-tík'ü-li net d 6098, SHA 300°
Sagitta* sā-jit'ā Sagittae sd-jit'ē arrow d 20%N, SHA 65°
Sagittarius (7)* | sāj'i:tā'rīcūs Sagittarii sáj'i-ta/ri-i archer Kaus Australis,
n "AM E Nunki
Scorpius (M)* skor’pi-ts Scorpii ` sk6r’pi-i scorpion Antares, Shaula
Sculptor skúlp'tér Sculptoris skülp-to'ris sculptor (workshop | d 3098, SH A 355?
` of) tt
Scutum skū'tūm Scuti skü'ti shield d 10%S, SHA 80°
Serpéns* sür'pénz Serpentis sér-pén'tis serpent d 10°N, SHA 125°
Sextans séks'tünz Sextantis sēks:tān'tīs sextant d 0°, SHA 205°
Taurus (8)* to'rús Tauri tó'ri bull Aldebaran, Elnath
Telescopium tél'é-sk0"] pi:ūm Telescopii tél'é-sko'pl-1 telescope d 5098, SHA 75?
Triangulum* titane guum abs tri-áng'gü-li triangle d 30°N, SHA 330°
Triangulum tri-dng’gu -lúm Trianguli tri-áng'gü.li southern triangle Atria
Australe 0s-trā'lē Australis 6s-tra/lis
Tucana tü-kà'nd Tucanae tü-kà'né toucan [a birdļt d 65%, SHA 5°

Ursa Major*

Ursa Minor*
Vela**

Virgo (m)*
Volans
Vulpecula

ür'sà må/'jër

úr/sá mi'nér
vē'ld

vúr'gó
vo'lánz
vül.pék'/ü-ld

Ursae Majoris

Ursae Minoris
Velorum
Virginis
Volantis
Vulpeculae

ūr'sē ma-jo’ris

ür'sé mi-n6’ris
vē.lē'rūm
vur’ji-nis

vo lán'tis
vúl-pék'ú-1é

Zodiacal constellations are given in bold type, with their symbols,
*One of the original constellations of Ptolemy.
**Part of the single constellation Argo Navis of Ptolemy.

tParts within brackets are amplifications of the meanings of constellation name

ttParts within parentheses are the meanings of words deleted from former, more complete constellation names.

Guide to pronunci

fate, cáre, hát, final, abound, sofa, arm; be, créate, énd, reader; ice, bit; over, po

tub, circús,

ations:

arn.

larger bear

smaller bear
sails

virgin

flying (fish) tt
little fox

S.

Alioth, Alkaid,
Dubhe

Kochab, Polaris

Suhail

Spica

d 70%S, SH A 240°

d 25°N, SHA 60°

etic, hēt, cónnect, lord, moon; tübe, ünite,

APPENDIX J
BUOYAGE SYSTEMS

With modifications, two systems of buoyage are in general use throughout the
world. These are the lateral system and the cardinal system.

The lateral system is best suited for well-defined channels. The location of each
buoy indicates the direction of the danger it marks relative to the course which should
normally be followed. "Thus, a buoy which should be kept on the port hand lies
between the vessel and the danger when the buoy is abeam to port, approximately.

In principle, the positions of marks in the lateral system are determined by the
general direction taken by the mariner when approaching a harbor, river, estuary, or
other waterway from seaward, and may also be determined with reference to the main
stream of flood current. The application of this principle is defined, as required, by
nautical documents such as sailing directions.

The cardinal system is best suited for coasts with numerous rocks, shoals, and
islands, and for dangers in the open sea. The location of each buoy indicates the
approximate true bearing of the danger it marks. Thus, an eastern quadrant buoy
marks a danger, such as a shoal, which lies to the west of the buoy, approximately.

Although almost all of the major maritime nations have used either the lateral or
the cardinal system for many years, details such as the shapes and colors of the buoys
and the characteristics and colors of lighted aids generally have varied from country
to country. With the passage of time and the increase in maritime communication
between countries, the desirability of a uniform system of buoyage has become increas-
ingly apparent. Consequently, over the past century a number of attempts have been
made to standardize the various systems of buoyage. International conferences have
been held on the subject and recommendations have been made. These recommenda-
tions have often been conflicting, however, and although the differences in the various
methods as applied to the cardinal system are comparatively slight, two distinct
methods of applying the lateral system have evolved. The major discrepancy has
been in the colors of the buoys and of their lights.

In 1889 the International Marine Conference held in Washington, D. C., recom-
mended that in the lateral system starboard hand buoys be painted red and port hand
buoys black. With the introduction of lighted aids to navigation, these recommenda-
tions logically led to the use, by nations which had accepted the recommendation, of
red or white lights on the starboard side and green or white lights on the port side.

In 1936 in the most recent international pronouncement on the subject, a League
of Nations subcommittee recommended a coloring system diametrically opposed to
the 1889 proposal. This is part of the Uniform System, and it provides for black
buoys with green or white lights on the starboard side and red buoys with red or white
lights on the port side.

Most maritime countries using the lateral system have adopted one of these two
systems, usually with small variations. It may be said that, very generally, European
countries follow the Uniform System of 1936 and most other countries follow the system
proposed in 1889. Special Publication No. 38 of the International Hydrographic
Bureau, Systems of Maritime Buoyage and Beaconage Adopted by Various Countries,
contains discussions and illustrations of the systems actually used by 39 maritime

976

APPENDIX J: BUOYAGE SYSTEMS 977

countries, as well as the Uniform System. When actually piloting, the navigator should
in every case consult the latest nautical literature of the country in question. The following
is an abridgement of parts of IHB Special Publication No. 38:

United States System

The waters of the United States are marked by the lateral system of buoyage
recommended by the International Marine Conference of 1889. As all channels do
not lead from seaward, arbitrary assumptions are at times made in order that the
system may be consistently applied. Along the sea coasts of the United States, the
characteristics are based upon the assumption that proceeding “from seaward” consti-
tutes a clockwise direction: a southerly direction along the Atlantic coast, a northerly
and westerly direction along the Gulf coast, and a northerly direction along the Pacific
coast. On the Great Lakes, a westerly and northerly direction is taken as being “from
seaward” (except on Lake Michigan, where a southerly direction is used). On the
Mississippi and Ohio Rivers and their tributaries, the characteristics of aids to naviga-
tion are determined as proceeding from sea toward the head of navigation. On the
Intracoastal Waterway, proceeding in a generally southerly direction along the Atlantic
coast and in a generally westerly direction along the Gulf coast is considered as pro-
ceeding ‘‘from seaward.”’

The continuation of the lateral system along the coasts in the order indicated
refers only to the side of the vessel on which buoys are to be kept, as indicated by
color, shape, and light, if any; there is no numerical continuity between coast buoys.
In fairways and channels, however, buoys are numbered consecutively from seaward.

In the United States System, lighted buoys, bell buoys, whistle buoys, and combi-
nation buoys differ in shape (fig. 917) from the unlighted buoys shown in this appendix,
but not in color or marking.

In the Mississippi River, the numbering and lighting of buoys differ from that
shown under “Fairways and Channels."

Uniform System

As recommended by the League of Nations in 1936, a country uses the Uniform
Lateral System or the Uniform Cardinal System, or both, according to its requirements
or preference. When both are used, the transition from one to the other must be clearly
indicated in appropriate publications, such as sailing directions, or by suitable buoyage
marks.

Both the Uniform Lateral System and the Uniform Cardinal System employ
topmarks as an additional means of identification. Unless otherwise stated in this
appendix, a topmark is painted the darker of the colors used on the buoy. They are
optional in every case except on wreck buoys in the Uniform Cardinal System. Top-
marks are not used in the United States System.

In both the Uniform Lateral System and the Uniform Cardinal System, lighted
buoys have the same shape as the unlighted buoys shown. This differs from the United
States System, in which distinctively shaped buoys are used for lighted aids.

In both the Uniform Lateral System and the Uniform Cardinal System, a quick
flashing light is regarded as a single flashing light.

The numbering or lettering of fairway and channel buoys is an optional feature
of the Uniform Lateral System. In the United States System these buoys are always
numbered, commencing from seaward.

978 APPENDIX J: BUOYAGE SYSTEMS

UNITED STATES SYSTEM

Fairways and Channels

PorT HAND STARBOARD HAND
Buoy: | 4 |
MARKING: Odd numbers, commencing from Even numbers, commencing from
seaward. seaward.
LIGHTED Buoy: White or green, flashing or occulting; White or red, flashing or occulting; or,
or, when marking important turns, when marking important turns,
quick flashing. quick flashing.

Middle Grounds

MAIN CHANNEL To RIGHT MAIN CHANNEL To LEFT
B B | A
MARKING: May be lettered. May be lettered.

LIGHTED Buoy: White or green, interrupted quick flashing. White or red, interrupted quick flashing.

Where channels are of equal importance, either of the above buoys is used, without regard to the uppermost band.

Mid Channel

MARKING: May be lettered.

LIGHTED Buoy: White, short-long flashing.

Wrecks or Other Obstructions

To BE PasseD ON Port HAND To BE PASSED ON STARBOARD HAND
^. | | A
MARKING: Usually lettered “WR.” Usually lettered “WR.”

LIGHTED Buoy: White or green, quick flashing. White or red, quick flashing.

Where wrecks or other obstructions may be passed on either hand, either Middle Ground buoy is used, without
regard to the uppermost band.

SHAPE:

COLOR:

MARKING:

LIGHTED Buoy:

TOPMARK:

Buoy:

MARKING:

APPENDIX J: BUOYAGE SYSTEMS 979

UNITED STATES SYSTEM

Miscellaneous

Optional.

Quarantine — Yellow.

Anchorage —W hite.

Fish Nets —Black-and-white horizontal bands.

Dredging — White with green top.

Seadromes — Y ellow-and-black vertical stripes.

Special Purpose —W hite-and-international orange horizontal or vertical bands.

May be lettered.

Any color except red or green; fixed,occulting, or slow flashing.

UNIFORM LATERAL SYSTEM

Fairways and Channels

Port HAND STARBOARD HAND

B ww (Y a g A

"T'-shaped topmark Diamond-shaped top-
not used at channel mark not used at
entrance. channel entrance.

eel AAI

In secondary channels only, yellow may be substituted for white in checkered buoys.

Even numbers, commencing Odd numbers, commencing
from seaward. from seaward.

LIGHT: Red, single flashing or occulting or group White, single flashing or occulting, or

flashing or occulting, with a number of group flashing or occulting (3); or green,
flashes or occultations up to four; or of a different character from wreck
white, group flashing or occulting markings; or both white and green with

(2 or 4); both red and white with above the above characteristics.
characteristics.

980 APPENDIX J: BUOYAGE SYSTEMS
UNIFORM LATERAL SYSTEM
Middle Grounds

CHANNELS OF MAIN CHANNEL

MAIN CHANNEL
EQUAL IMPORTANCE To LEFT

To RIGHT
TOPMARK:

Bifurcation g A O

du

Distinctive where possible. Distinctive where possible. Distinctive where possible.

Junction ap

= 64 00
= E 0)

LIGHT:

Mid Channel

TOPMARK: Shape optional, but not conical, cylindrical, or spherical.
Buoy: Shape optional, but not conical, cylindrical, or spherical.

COLOR: Red-and-white or black-and-white vertical stripes; topmark red or black to conform with buoy.

LIGHT: Different from neighboring lights.

Marking of Wrecks
To BE PaássFD ON To BE PASSED ON To BE PASSED ON
Port HAND EITHER HAND STARBOARD HAND
By Buoys
TOPMARK: E 6 A
Buoy: |
MARKING: “W” in white. “W” in white. “W” in white.
LIGHT: Green, group flashing (2). Green, single occulting. Green, group flashing (8).
By Vessels
VESSEL:

MARKING: “W ”or“ WRECK ” in white. “W”or“ WRECK "in white. “W "or “WRECK ” in white.
LIGHT: Fixed green, corresponding in number and arrangement to shapes displayed by day.

BELL: Two strokes at intervals of Four strokes at intervals of Three strokes at intervals of
not more than 30 seconds. not more than 30 seconds. not more than 30 seconds.

APPENDIX J: BUOYAGE SYSTEMS 981

UNIFORM CARDINAL SYSTEM

Danger Markings

NW NE

TOPMARK: A

Buoy: x

LIGHT: White. Preferably flashing
or group flashing, with odd
number of flashes; or occulting
or group occulting, with odd
number of occultations.

S
TOPMARK: y

BuoY: A

LIGHT: Red, preferably, or white.
Flashing or group flashing, pref-
erably, with odd number of
flashes; or occulting or group
occulting with odd number of
occultations.

TOPMARK:

wv
A

Buoy:

LIGHT: White. Preferably group
flashing with even number of
flashes, or group occulting with
even number of occultations.

TOPMARK:

LIGHT: Red, preferably, or white.
Group flashing, preferably, with
even number of flashes; or group
occulting with even number of

SW occultations. SE
Variations in Danger Markings
Northern Eastern Southern Western Northern Eastern
Quadrant Quadrant Quadrant Quadrant Quadrant Quadrant

ei A il

Note: The number of characteristic shapes employed for the
buoy itself may be limited to two, the conical shape being
employed in the northern and eastern quadrants and the
cylindrical shape in the southern and western quadrants, as

shown above.

Note: When spars only are used, it
may be advantageous in the
northern and eastern quadrants to
reverse the positions of the dark
colors, as shown above.

982 APPENDIX J: BUOYAGE SYSTEMS

UNIFORM CARDINAL SYSTEM

Marking of Wrecks
WESTERN QUADRANT EASTERN QUADRANT
TOPMARK: v A
A v
MARKING: “W” in white, if possible. “W” in white, if possible.
LIGHT: Green, quick flashing. Green, interrupted quick flashing.

In the Uniform Cardinal System, wreck buoys are not used in the northern or southern quadrants.

UNIFORM SYSTEM—LATERAL AND CARDINAL
(Common To Both)

Isolated Dangers

TOPMARK: e O =
Buoy:
LIGHT: White or red, rhythmic.
Miscellaneous

TOPMARK: Landfall— Shape optional, but not misleading.
Transition — Shape optional, but not misleading.
Others — None.

Buoy: Shape optional, but not misleading.

COLOR: Landfall —Black-and-white or red-and-white vertical stripes.
Transition —Red-and-white or black-and-white spiral bands.
Quarantine — Y ellow.
Outfall —Y ellow above and black below.
Military Practice Area —White, with two blue stripes rising from the waterline and
intersecting at right angles on top of the buoy, and, optionally, lettering in the
national language indicating a danger area (e.g., in English, “D.A.”).

LIGHT: Landfall —Rhythmic.

Outfall —Optional, with due regard to other lights in the area.
Others —None.

APPENDIX K
CHART SYMBOLS
(Extracts from Chart No. 1, September 1963)

GENERAL REMARKS

Chart No. 1 contains the standard symbols and abbreviations which have been approved for
use of nautical charts published by the United States of America.

Symbols and abbreviations shown on Chart No. 1 apply to the regular nautical charts and may
differ from those shown on certain reproductions and special charts.

Terms, symbols and abbreviations are numbered in accordance with a standard form approved
by a Resolution of the Sixth International Hydrographic Conference, 1952.

Vertical figures indicate those items where the symbol and abbreviation are in accordance with
the Resolutions of the International Hydrographic Conferences.

Slanting figures indicate those items where the symbol and/or abbreviation differ from the Resolu-
tions of the Conferences, or for which Resolutions do not yet exist.

(Those items which differ from the Resolutions are underlined.)

Slanting letters in parentheses indicate that the items are in addition to those shown on the approved
standard form.

Colors are optional for characterizing various features and areas on the charts.

Lettering styles and capitalization as used on Chart No. 1 are not always rigidly adhered to on
the charts.

Longitudes are referred to the Meridian of Greenwich.

Scales are computed on the middle latitude of each chart, or on the middle latitude of a series
of charts. j

Buildings—A conspicuous feature on a building may be shown by a landmark symbol with
descriptive note (See L-63 € I-n). Prominent buildings that are of assistance to the mariner are
crosshatched (See I-8a, 5, 47 & 66).

Shoreline is the line of Mean High Water, except in marsh or mangrove areas, where the outer
edge of vegetation (berm line) is used. A heavy line (A-9) is used to represent a firm shoreline. A
light line (A—7) represents a berm line.

Heights of land and conspicuous objects are given in feet above Mean High Water, unless other-
wise stated in the title of the chart. :

Depth Contours and Soundings may be shown in meters on charts of foreign waters.

Visibility of a light is in nautical miles for an observer’s eye 15 feet above water level.

Buoys and Beacons—On entering a channel from seaward, buoys on starboard side are red with
even numbers, on port side black with odd numbers. Lights on buoys on starboard side of channel
are red or white, on port side white or green. Mid-channel buoys have black-and-white vertical
stripes. Junction or obstruction buoys, which may be passed on either side, have red-and-black
horizontal bands. This system does not always apply to foreign waters. The dot of the buoy
symbol, the small circle of the light vessel and mooring buoy symbols, and the center of the beacon
symbol indicate their positions.

Improved channels are shown by limiting dashed lines, the depth, month, and the year of latest
examination being placed adjacent to the channel, except when tabulated.

U.S. Coast Pilots, Sailing Directions, Light Lists, Radio Aids, and related publications furnish
information required by the navigator that cannot be shown conveniently on the nautical chart.

U.S. Nautical Chart Catalogs and Indexes list nautical charts, auxiliary maps, and related publi-
cations, and include general information (marginal notes, etc.) relative to the charts.

A glossary of foreign terms and abbreviations is generally given on the charts on which they
are used, as well as in the Sailing Directions.

Charts already on issue will be brought into conformity as soon as opportunity affords.

983

984 APPENDIX K: CHART SYMBOLS S Å >

The Coastline (Nature of the Coast)

11e Sand and mud

2 Steep coast (Bluff)

Bac =
vēri $

11g Coral, uncovers at sounding
datum (See O-/O,

2a Flat coast

fif extensive )

Å li 12 Breakers along a shore
3 Cliffy coast 10 Low waterline (See 0-25)

11 Foreshore
(Strand in general)

3a Rocky coast

Sandhills; Dunes

Stony or Shingly shore

(Aa) Rubble

11c Stones; Shingle; or Gravel

€ — ES
GP. APS)
T, Oc ¡ud
Gr iyo
UNA ga

(Ab) Shoreline from older surveys or
small-scale charts

Sandy shore

11d Fock, uncovers at sounding
datum (See A-Ilg)

Gulf
Bay
Bayou
Fjord
Loch; Lough;
Lake
Creek
Cove
Inlet
Strait
Sound
Passage; Pass
Thorofare
Channel
Narrows
Entrance
Estuary
Delta
Mouth
Road; Roadstead
Anchorage
Harbor
Haven
Port
Pond
Island
/s/et
Archipelago
Peninsula
Cape
Promontory
Head; Headland
Point
Mountain;
Mount
Range
Valley
Summit
Peak
Volcano
Hill
Boulder
Landing
Table-land
(Plateau)
Rock
/solated rock
Stream
River
Slough
Lagoon
Approaches
Rocky

APPENDIX K: CHART SYMBOLS

Y y Y

5d Nipa palm

1 Contour lines Lengt 5e Filao

Lut

5f Casuarina

1 Coen pem
approximate

"NS6/0 HU S.
fe AS E e

6a Grass fields

Rice ES

7 Paddy (rice) fields

7a Park; Garden

Bushes

Form „` no dennie 8 Bushes

2a interval

2b Shading

~ PATTI

I

\ ES

3 Glacier

4 Saltpans
(QTREE

5 /solated trees

Deciduous or of unknown
5a or unspecified type

14 /ntermittent stream
5b Coniferous

SS

5c Palm tree 15 Lake; Pond

985

Symbol used
in small areas

APPENDIX K: CHART SYMBOLS

Control Points

[OPE

ER

AN 256

'O 256.

e Obs Spot
BM

See View

Triangulation point (station)

Fixed point (landmark) (See L-63)

Summit of height (Peak)
(when not a landmark)

Peak, accentuated by contours
Peak, accentuated by hachures
Peak, elevation not determined
Peak, when a landmark
Observation spot

Bench mark

View point

Datum point for grid of a plan
Graphical triangulation point
Astronomical

Triangulation

Corps of Engineers

Great trigonometrical survey station
Traverse station

Boundary monument

International boundary monument

Hour

Meter
Decimeter

Centimeter

Millimeter

Kilometer
Inch
Foot
Yard
Fathom

Knot

Ton

Minute (of time)

3 sec Second (of time)

Square meter

Cubic meter

Cable length

Nautical mile

Candela
(new candle)

Latitude

14 long Longitude
15 pub Publication
16 Ed Edition

17 corr Correction
18 alt Altitude

19 ht; elev Height; Elevation

20 o Degree
212 Minute (of arc)
22 " Second (of arc)
23 No Number

(Ea) St. M Statute mile
(Eb) Msec Microsecond

F

W MAN DAA KR WH Fa

M kat N NON oM NN ON
DN eats ey RR

18a

w w N ka ba bah N N h
WM B mus RERUM MEE

(Fa)
(Fb)

(Fc)
(Fd)

(Fe)
(Ff)
(Fg)
(Fh)
(Fi)
(Ej)
(Fk)

(Fl)
(Fm)
(Fn)

Adjectives, Adverbs |

e and other abbreviations

gt
lit
Irg
sml

mid
anc

St
conspic

D., Destr

dist
abt

sub
AERO

exper
discontd
prohib
explos
estab
elec
priv
prom
std
subm
approx
unverd
AUTH

CL
maintd
aband
cor
concr
fl

extr
mod
bet

Ist
2nd
3rd

Great

Little

Large
Small
Outer

Inner
Middle

Old

Ancient
New

Saint
Conspicuous
Remarkable
Destroyed

Projectec'

Distant

About

See chart

See plan

Lighted; Luminous

Submarine
Eventual
Aeronautical
Higher
Experimental
Discontinued
Prohibited
Explosive
Established
Electric
Private, Privately
Prominent
Standard
Submerged
Approximate
Unverified
Authorized
Clearance
Maintained
Abandoned
Corner
Concrete
Flood
Extreme
Moderate
Between

First
Second
Third

Fourth

APPENDIX K: CHART SYMBOLS

Anchorage (large vessels)'

Anchorage (small vessels)

Harbor

Haven
F Port

Breakwater
6a Dike
Z Mole
^ dl ra Jetty (partly below

MHW)

8a nd Submerged Jetty

Jetty (small scale)

Pier
10 A

Spit

Groin (partly below

MHW)
12 l ANCHORAGE | ANCH Anchorage prohibited
ES | PROHIBITED | PROHIB (See P-25)
13 1 Spoil Area | Spoil ground

Dumping ground

l 83 !
| Disposal Area |
IDepths from survey!

, of June 1963 i

(Gc) Disposal area

95 |
B ae we
Fsh :
14 WILL y S Fisheries; Fishing stakes

Fish trap; Fish weirs
[actual shape charted)

Duck blind

14a

14b

Tunny nets (See G-/4a)

Oyster bed

== Ano

Landing place

Watering place

Wharf

Quay

Ports and Harbors

204

20b

25a

o Dol

Quar

Harbor Master
Cus Ho

B Hbr

D2777777727
E EE.

| PROHIBITED. | PROHIB

AREA AREA

Under
L construction

987

Berth
Anchoring berth

Berth number

Dolohin
Bollard
Mooring ring
Crane

Landing stage
Landing stairs
Quarantine
Lazaret
Harbor master's office
Customhouse
Fishing harbor
Winter harbor
Refuge harbor

Boat harbor

Stranding harbor
uncovers at LW)

Dock

Dry dock (actual shape
on large-scale charts)

Floating dock(actualshape
on large-scale charts)

Gridiron; Careening grid

Patent slip; Slipway;
Marine railway

Ramp

Lock (point upstream)
Ge H-I3)

Wet dock
Shipyard

Lumber yard
Health officer's office

Hulk (actual shape on frg.
scale charts) (See O-//)

Prohibited area
Anchorage for seaplanes
Seaplane landing area

Work in progress

Under construction

Submerged ruins

ee

988 APPENDIX K:

Topography

== See Small-scale chart
1 Road (Rd) or r Highwey (Hy /)

2 Track, Footpath, or Trait

M&LS RR

=

= ge 2
—4— oom
TË

Same grade

Ry. above Ry. below

3 Rarlway(Ry) (single or double track); Railroad (RR) 77

tt _—
3a Tramway

A M TE A
3b Frai/way station

3c Tunnel (railroad or road)

CHART SYMBOLS

(Artificial Features)

Bridge BR) in general
Stone, concrete bridge (Same as H-/4)

Wooden bridge (Same as H-/4)

Iron bridge (Same as H-/4)

Suspension bridge (Same as H-/4)

Drawbridge (in general)

Swing bridge (Same as H-/5)

ABA AAA ba dk AA AAA AAA A A AA LAA a LLLLLU ALA UL kadi) UU VALDI
AAA DA LAL AAA TI AAA O FTT) (TTD mm

.3d Embankment, Levee

PYYYYYYTYTYTTYTTTYTTYYYTTYUVIUY
AÀ AAA AAA AAA AAA AAA AAA AAA AAA AA

3e Cutting

OVERHEAD POWER CABLE
206 CL. 140 FT

aa OMS
Overhead power cable (OVHD. PWR. CAB:)

—-—-e---e-—-e-—-—e—-——e—-——e—-——e—

Power transmission line

Power transmission mast

=0---e--- e-e- >o ————— Sh —— m

Prominent telegraph or telephone line

7 Aqueduct; Water pipe

Lift bridge

16b Werghbridge or Bascule bridge

17 Pontoon bridge

17a Footbridge -—--

VERT. CL. 6 FT
18a Bridge clearance, vertical

HOR CL. 28 FT

J L Viaduct
8 Viaduct T

m
8a Oil pipeline

18b Bridge clearance, horizontal

Ferry

EC TESTI

| 19 Ferry (Fy)

On small-scale chart

? Pile Piling ? Post

9 Pile; Piling; Post (above MHW) (See L-59, 0-30)

9a Mast Omast 9 Mast

20 Ford
|2 il Dam | |

10 Highway (See H-I)

22 Fence

| 23 Training wall

12 Culvert
m Cana OR

Ditch Sluice
(Tidegate, Floodgate)
Canal; Ditch; Lock, Sluice (point upstream)

Sr | (Ha) Log boom

a

APPENDIX K: CHART SYMBOLS 989

I. Buildings and Structures (see General Remarks)
City or Town (large scale) 26a As Ave Ave Avenue
City or Town (small scale) (le) SABLE Blvd Boulevard

2 Suburb 27 Tel Telegraph

3 Vil Village 28 Tel.Off Telegraph office

— 7

3a PS] Buildings in general 29 PO SOSA

4 Cas Castle 30 Govt. Ho Government house
Y,
5 a D House 31 Town hall
S A 32 Hosp Hospital
7 Farm
38 Slaughterhouse
s H. i Ch Church
34 Magz Magazine
8a + i Cath Cathedral "
so Ospire X SE 34a Warehouse; Storehouse
8c é Christian Shrine 35 Opon P Mon Monument
o Æ i Roman Catholic Church 36 "eve Ce Cupola
10 d i Temple 37 Ourv Elev. Elevator; Lift
T Chapel
de Se (1f) Elev Elevation; Elevated
12 ú Mosque; Minaret i
e 38 Shed
(1b) A Moslem Shrine j
13 U PPR 39 Zinc roof
pose
14 i Pag Pagoda ao ls JRuns| “Ru Ruins
15 " Buddhist Temple; Joss-House | 41 Orr 9, Tower
15a é Shinto Shrine 42 TS AK Ee ue Windmill
16 Monastery; Convent 43 Ð arem
17 Calvary; Cross
; x é
ED 7 43a 10% SAN Windmotor
Iza WB l Cemetery, Non-Christian
Ü 1
VC 1 o > Y
" | em | os 44 Ocny Chy Chimney; Stack
t=-
18a Tomb 45 'Os'PiPe “Sipe Water tower: Standpipe
19 "P E Fort (actual shape charted) 46 Ð Q Oil tank
20 Battery (Same as 1-19) 47 h E D Facty Factory
21 Barracks 48 Saw mill
22 Powder magazine 49 Brick kiln
23 INA Airplane landing field 50 x Mine ; Quarry
] i
24 KA Ni Airport, large scale (See P-/3)| 51 4° Well Well
= ¡PA
(Ic) Q Airport, military (small scale)| 52 Cistern
(Id) o Airport, civil (small scale) 53 Ð Orank STk Tank
25 Za Mooring mast 54 Noria

26 King St St Street 55 Fountain

990 APPENDIX K: CHART SYMBOLS

Buildings and Structures (continued)

71 EI $ Gas tank; Gasometer
Institute 72 Osas Kä Gable
Establishment 73 Wall
Bathing establishment Limited
Courthouse Apartment
School Capitol
High school Company
University Corp Corporation
Building Landmark (conspicuous object)
Pavilion Landmark (position approx.)
Hut

Stadium

Telephone

Miscellaneous Stations

Any kind of station 13 Tide signal station
2 Sta Station 14 Stream signal station
3 Coe Coast Guard station 15 Ice signal station

(Similar to LS. S.)

16 Time signal station

(Ja) orn sanos Coast Guard station 17 Time ball
(when landmark)
18 Signal mast
EX y
S FP
4 OLook.TR Lookout station; Watch tower | 19 E e e Flagstaff; Flagpole
FS FP
5 Lifeboat station Jc) HORES ERN Flag tower
6 Lifesaving station 20 Signal
vss (See J-3)
21 Obsy Observatory
7 Rkt. Sta /rocket station 22 Off Office

o
8 O) OPIL. sta Pilot station (Jd) BELL Bell (on land)

9 Sig. Sta Signal station (Je) HECP Harbor entrance control post
10 Sem Semaphore

11 S. Sig Sta Storm signal station
12 Weather signal station

(Jb) © w.B. SIG. STA Weather Bureau signal station

1 0

2 Lt
(Ka) dis

3 Lt Ho
4 Quero

4a

3 & O...

8

9

10 REF
n ¡Sie ut
12
13

14

135

16

a o, maintd
21 F

22 Occ
23 Fl

24 Qk Fl
m
(Kb) E Int
25a SEI
26 Alt

27 Gp Occ
28 Gp Fl
28a Sl
28b

APPENDIX K:

Position of light

Light

Riprap surrounding light
Lighthouse

Aeronautical light (See F-22)
Marine and air navigation light
Light beacon

Light vessel, Lightship

Lantern

Street lamp

Reflector

Leading light

Sector light

Harbor light

Fishing light

Tidal light

Private light (maintained by
private interests; to be
used with caution)

Fixed light

Occulting light

Flashing light

Quick flashing (scintillating) light
Interrupted quick flashing light
Equal interval (/sophase) light
Short flashing light

Alternating light

Group occulting light

Group flashing light

Short-long flashing light

CHART SYMBOLS

(Khb)

(Kc)

(Kd)

(Ke)

45

46

46a

47

48

49

50

51

52

61

62

63

64

65

66

67

67a

68

Group short flashing light (Kf)

sec

SEC

Aux

Vi

Am
OBSC

Fog Det Lt

991

Fixed and flashing light

Fixed and group flashing light
Revolving or Rotating light
Morse code

Period

Every

With

Visible (range)

Nautical mile

(See E-//)

Minutes
(See E-2)

Seconds

(See E-3)

Flash
Occultation
Eclipse

Group
Intermittent light
Sector

Color of sector

Auxiliary light

Varied

Violet

Purple

Blue

Green

Orange

Red

White

Amber
Obscured light

Fog detector light (See Nb)

992

1 E

2 d

3 Pec
3a Pconc
4 Pus
s ME
e Ln

7 MES
8 fs
ga Pp

d

10 BR
(La) P

(Lb) 2 FLOAT

12 d or

13
14 Pew
14a Ja W

APPENDIX K: CHART SYMBOLS

(continued)

Lights

Unwatched light
Occasional light
Irregular light
Provisional light
Temporary light
Destroyed
Extinguished light
Faint light
Upper light
Lower light
Rear light

Position of buoy 16 [4 dab
Light buoy LG Ze pre
Bell buoy 18 ye pre
Gong buoy 19 pre pre
Whistle buoy 20 Gre De
Can or Cylindrical buoy 20a Pre Po
Nun or Conical buoy 21 2 Tel
Spherical buoy 22 v $
Spar buoy 22a
Pillar buoy 22p "Tel
pue R EE (ball) 22 wr
Barrel or Ton buoy 23 0

aa Er
Color unknown 25 PE
Float 25a Lacro
Lightfloat 26 «Deviation
Outer or Landfall buoy 27 pew
Fairway buoy (BWVS) 27a H
Mid-channel buoy (BWVS) 28 2

Starboard-hand buoy (entering

from seaward) 29 H Priv maintd

Front light

Vertical lights
Horizontal lights
Vertical beam

Range

Experimental light
Temporarily replaced by

lighted buoy showing the
same characteristics

Temporarily replaced by
unlighted buoy

Temporary lighted buoy
Temporary unlighted buoy

Buoys and Beacons (see General Remarks)

Port-hand buoy (entering from
séaward)

Bifurcation buoy (RBHB)

Junction buoy (RBHB)

Isolated danger buoy (RBHB)

Wreck buoy (RBHB or G)

Obstruction buoy (RBHB or G)

Telegraph-cable buoy

Mooring buoy (colors of moor-

ing buoys never carried)

Mooring

Mooring buoy with telegraphic

communications

Mooring buoy with telephonic
communications

Warping buoy

Quarantine, buoy

Explosive anchorage buoy

Aeronautical anchorage buoy

Compass adjustment buoy

Fish trap buoy (BWHB)

Spoil ground buoy

Anchorage buoy (marks limits)

Private buoy (maintained by pri-
vate interests, use with caution)

30
30a
an m HB
32 D vs
33 E Chec
(Lc) Ë Diag
41 C] W
42 Ý B
43 R
44 Y
45 S G
46 Br
47 Gy
48 = Bu
(Ld) Am
(Le) Or
51 H
Ag AY, a,
524 ABn

A Bn

(Lf) OMARKER
53 Bn

54

APPENDIX K: CHART SYMBOLS

Buoys and Beacons (continued)

Temporary buoy
(See Kk, 1, m,n)

Winter buoy

Horizontal stripes or bands

Vertical stripes

Checkered

Diagonal buoy

White

Black

Red

Yellow

Green

Brown

Gri ay

Blue

Amber

Orange

Floating beacon

Fixed beacon (unlighted or
daybeacon)
Black beacon

Color unknown

Private aid to navigation

Beacon, in general (See L-52)

Tower beacon

55

56 A Ti

57
58
" Piles
did
59
“Stumps
Sh AL

Å o
61 Ocairn Cairn

62

es Q

(Lg) o

64 REF

65 Omar ER

WO WO
«en |^

70 Note:

993

Cardinal marking system

Compass adjustment beacon

Topmarks (See L-9, 70)

Telegraph-cable (landing)
beacon

Piles (See 0-30, H-9)

Stakes

Stumps (See 0-30)

Perches

Ca/rn
Painted patches
Landmark (conspicuous object)

(See D-2)
Landmark (position

approximate)
Reflector

Range targets, markers

Special-purpose buoys

TOPMARKS on buoys and beacons may

be shown on charts of foreign waters.
The abbreviation for black 1s not
shown adjacent to buoys or beacons.

(Li) X Rakef

Radar reflector (See M-/3)

994 APPENDIX K: CHART SYMBOLS

Radio and Radar Stations

Radio telegraph station 12 (©) recon Radar responder beacon

Radio telephone station 13 = Ra Ref Radar reflector (See Li)

Radiobeacon Ra (conspic) Radar conspicuous object

Circular radiobeacon Ramark

Distance finding station
Directional radiobeacon; sb. (synchronized signals)
Radio range = :

Rotating loop radiobeacon Aeronautical radiobeacon

Radio direction finding station , ) II. Aeronautical radio range

Telemetry antenna O Jc Bn Fadar calibration beacon

Radio mast BR
Radio tower 20 Conso! (Consolan) station

Television fower j Å
Loran station (name)

Radio broadcasting station Å Å
(commercial) ~ LORAN Loran tower (name)

Q.7.G. Radio station H R >
Radio calling-in point

for traffic contro/
Radar station

Ë
|

Fog-signal station Fog trumpet
Radio fog-signal station Fog horn
Explosive fog signal Fog bell

Submarine fog signal Fog whistle

SUB-BELL Submarine fog bell Reed horn
(action of waves)

SUB-BELL Submarine fog bell
(mechanical)

SUB-OSC Submarine oscillator

Fog gong

Submarine sound signal not
connected to the shore
NAUTO Nautophone (See N SA

Submarine sound signal
i n
Diaphone connected to, the shore

(See N-5, 6,7)

Fog gun HORN Typhon

Foo siren Fog Det Lt Fog detector light (See Kf)

APPENDIX K: CHART SYMBOLS 995

Dangers

DI D

Wreck showing any portion of hull or
superstructure above sounding datum

Í (25)

Rock which does not cover
(elevation above MHW)
(See general remarks)

154 Obstr
27 Obstruction

=

Wreck (See O-// to 16)

E

* Uncov 2 ft ES Uncov 2 ft E

12 Wreck with only masts visible d
above sounding datum

*
(2) & (2) Wreckage

29a Wreck remains (dangerous
only for anchoring)

Rock which covers and uncovers,
with height in feet above chart
(sounding) datum

13 Old symbols for wrecks

ve
Subm pil
13a Wreck always partially submerged vui

30 Submerged piling
(See H-9, L-59)

3 Rock awash at the level of chart
: (sounding) datum

14
Sunken wreck which may be dangerous
to surface navigation (See O-6a)

* Snags * Stumps

ae ae

When rock of O-2or O-3 is con- 30a Snags. Submerged stumps

sidered a danger to navigation eu Wk (See L-59)
15 Wreck over which depth is known | 31 Lesser depth, possible
4 Sunken rock with less than 6
qol SEU it 32 Uncov Dries(See A-/O; 0-2, /0)
SÐ EES 33 Cov Covers (See 0-2, /O)
34 Uncov Uncovers
Sunken rock with between 6 and| 16 Sunken wreck, not dangerous to :
MUN (See A-/O; O-2, /O)
33 ft. of water over it surface navigation
(Same as O-26) m
13; Rep (1958)
EH
Reported (with date)
5a Shoa/ sounding on isolated rock
(replaces symbol) 17 Foul ground ae Eagle Rk
geg (rep 1958)
iw ee with more than Tide Rips 5 = ye 35 Reported (with name and date)
eet of wafer over if
18 Overfalls or Symbol used only à
(Same as O-26) Tide Ties E sre areas ú 36 Disco! | Discolored (See O-9)
es /solated danger
21 21 21 E
2h Rk 2LWk = 24 0bs¢r Edies pura e

6a Sunken danger with depth cleared Eesen T 3
by wire drag (in feet or-fathoms) 19 Eddies in small areas 4

38 = Limiting danger line

Reef Kelp S
Symbol used onl A phy. ši
7 Reefof unknown extent 20 Kelp, Seaweed “a small areas. Se ie

39 Limit of rocky area

(Sub Vol 21 Bk Bank AVISA Position approximate
2 Positi tful
8 Submarine volcano 22 Sh/ Shoal 5 (21 Gre doub E j
23 RF Reef (See A-lld,/lg;0-/0)| 43 ED Existence doubttu

44 P Pos Position

23a Ridge
D Doubtful

© 7 Disco! Water
24 Le Ledge

9 Discolored water

LI Subm melo
¿e z E Crib (above water)
Coral” Co :x:Co
ey u Makar? r KÉ (Oa) Crib

10 Coral reef, detached (uncovers af

25 Breakers (See A-/2)
sounding datum)

m Platform (lighted)
HORN

(Ob) Offshore platform (unnamed)

+

26 Sunken rock (depth unknown)
Se En m Hazel (lighted)
nnd HORN

Coral or Rocky reef, covered af

When rock 1s considered a
sounding datum (See A-/Id, //g)

danger to navigation Offshore platform (named)

(Oc)

996

25

AI

| COURSE 053*00 ^1

P

|». MARKERS
MARKERS (6)

ROHIBITED AREA;

APPENDIX K:

CHART SYMBOLS

Leading line; Range line

Transit

In line with

Limit of sector

Channel, Course, Track
recommended (marked b
buoys or beacons)(See P-2/,

Alternate course

Leader cable

Submarine cable (power,
telegraph, telephone, etc.)

Submarine cable area
Submarine pipeline

Submarine pipeline area

Maritime limit in general
Limit of restricted area

Limit of fishing zone
(fish trap areas)

Limit of dumping ground,
spoil ground (See P-9, G-/3)

Ancnorage limit

Limit of airport
(See /-23, 24)

Limit of sovereignty
(Territorial waters)

Customs boundary

International boundary
(also State boundary)

Stream limit

Ice limit

Limit of tide

Limit of navigation

Course recommended (not
marked by buoys or
beacons)(See P-5)

District or province limit

Reservation line
Measured distance

Prohibited area (See G-/2)

¡A

10

13

14

15

16

17

18

(Qa)

| 24 FEE

Soundings

==

[I
Æ

—-—4 MAY /958——

82

zo:
Ex 125)

(ANNO
er po -
LT I IJI

32

emm bech

/9

I9

"Zo

6;

2ft

ee
——

Doubtful sounding

No bottom found

Out of position

Least depth in narrow
channel

Dredged channel (with .
Controlling pat indicated)

Dredged area

Swept channel (See Q-9)

Drying or uncovering height
in feet above chart
(sounding) datum

Swept area, not adequately
sounded (shown by
greer tint)

Swept area adequately
sounded (swept by wire
drag to depth indicated)

Hair-line depths

Figures for ordinary
soundings

Soundings taken from
foreign charts

Soundings taken from older
surveys or smaller
scale charts

Soundings taken by echo

Sloping figures
(See Q-/2)

Upright figures (See Q-/0a)

Bracketed figures
(See O-/, 2)

Underlined sounding figures
ee Q-8) E

Soundings expressed in
fathoms and feet

Stream

APPENDIX K: CHART SYMBOLS 997

| R. Depth Contours and Tints (see General Remarks)

| feet | Fathoms |

300 50

Or continuous lines,
with values

Mussels 50 spk Speckled

Ground

Sand Sponge Gu ^ qu Gritty `
Mud; Muddy Kelp 52 Decayed
Ooze Seaweed EY Ty, Flinty
Marl Grass 54 glac Glacial
Clay 29 Seatangle 55 Tenacious
7 G Grave/ 56 wh White
8 Sn Shingle EN Spicules 57 bk Black
9 P Pebbles 32 [Fp Foraminifera 58 ví Violet
ES, Stones 33 GI Globigerina 59 bu Blue
11 Rk; rky Rock; Rocky 34 Di Diatoms 60 gn Green
lla Bids Boulders 35 Fed Radiolaria 61 yl Yellow
12) Ck Chalk 36 Pt Pteropods 62 or Orange
12a Ca Calcareous 37 Po Polyzoa 630 Red
13 Oz Quartz 38 Cirripeda 64 br Brown
13a Schist 38a Fucus GO Chocolate
TACO Coral 38b Mattes 66 QY Gray
(Sa) Co Hd Coral head 39 fne Fine 67 /t Light
15 Mads Madrepores 40 crs Coarse 68 dk Dark
16 Vol Volcanic 4l sf Soft
(Sb) Vol Ash Volcanic ash 42 hrd Hard 70 Varied
17 La Lava 43 stf Stiff 71 Uneven
18 Pm Pumice 44 sm/ Small
1990 7. Tufa 45 Irg Large
208856 Scoriae 46 stk Sticky
El en QUSS Sé dis SE DUM Fresh water
22 Mn Manganese 47a grd Ground 76 diss springs in

sea-bed
Shells

48 Rotten

Oysters 49 Streaky

998

la HHW

2 LW
(Ta) LWD

2a LEW

ST EE

4 MSL
4a

5

CASE

7 Np

8 MHWS
Sa MHWN
8b MHHW
(Tb) MHW

9 MLWS
9a MLWN
9b MLLW
(Tc) MLW
10 /SLW
11

12

ES)

13a

14

15

16

I7 She

18 P» Ek
19 VS
20 ES

EHE on

21 O Tide gauge

23 vel.
EEL Jam
25 hf.

APPENDIX K: CHART SYMBOLS

High water
Higher. high water
Low water

Low water datum
Lower low wafer
Mean tide level

Mean sea level

Elevation of mean sea level
above chart (sounding) datum

Chart datum (datum for
sounding reduction)

Spring tide

Neap tide

Mean high water springs

Mean high water neaps

Mean higher. high water

Mean high water

Mean low water springs

Mean low water neaps

Mean lower low water

Mean low water

Indian spring low water

High water full and change (vul-
gar establishment of the port)

Low water full and change

Mean establishment of the port

Establishment of the port
Unit of height
Equinoctial

Quarter; Quadrature

Stream

Current, general, with rate
Flood stream (current) with rate

Ebb stream (current) with rate
Tide gauge; Tidepole;
Automatic tide gauge

Velocity; Rate
Knots

Height

Tide

New moon
Full moon
Ordinary
Syayay
Flood

Ebb

Tidal stream diagram

Place for which tabulated tidal
stream data are given

Range (of tide)
Phase lag

Current diagram, with
explanatory note

The outer circle is in degrees with zero at true
north. The inner circles are in points and degrees with
the arrow indicating magnetic north.

S BND A F&F WD ra

MM
M S

hu
N

21
22
23
24
25
25a
26

E
28

4 E
NS sten lua;

SINS TT TOTNM C
AR SN ECLI

FR C7)

5 van t+ 53
ave EET MUS
c =
SE
DA
AV Gt S
Ke O, 7, i hf, | Ae SS. SOM
ON GG, N age es
Z, Pepo SS
Sru, Ole EN
DA Pp] qu ie

(“ey Apall Z

deg

dev

Ze
se te,

Compass Rose

North
East
South
West
Northeast
Southeast
Southwest
Northwest
Northern
Eastern
Southern

Western

Bearing

True

Magnetic
Variation
Annual change

Annual change nil

Abnormal variation;
Magnetic attraction

Degrees (See E-20)

Deviation

Nation

Argentina
Australia
Belgium
Brazil
Canada

Chile
Denmark

Finland
France

Germany
Great Britain
Greece

Italy

Japan

Netherlands
Norway

Portugal
Russia (USSR)

Thailand
Spain
Sweden

Turkey
Uruguay
Yugoslavia

APPENDIX L

UNITS OF DEPTH MEASUREMENT ON CHARTS
OF VARIOUS NATIONS

Unit of depth measurement

Braza
Fathom
Metre
Metro
Fathom

Metro
Favn

Meter
Metre
Metre

Meter

Fathom

Metre (Metpa)
Metre

Metre

Vadem
Meter
Favn
Meter
Metro

Sazhen'
Metre
Metre
Metro
Famn
Meter

Fathom (Kulac)
Metro
Metar

999

Equivalent in United States

Feet Fathoms

6.000

1000

APPENDIX M
TIDAL DATUMS IN USE IN VARIOUS AREAS

Area Datum Area
Admiralty Islands Lowest normal LW Egypt (Mediterra-
Alaska Mean lower LW nean)

Algeria Lowest LW El Salvador
Angola Lowest normal LW Estonia
Argentina Lowest normal LW Ethiopia
Australia Lowest normal Finland
Wt France
Azores Lowest normal LW French Guiana
Bahama Islands Mean lower LW French Somaliland
PRIMES Gabon
Belgium Mean lower LW Gambia
springs
Bermuda Mean lower LW Germany (Baltic)
springs G North
Bismarck Archipel- | Lowest normal LW e (Ns
ago
Brazil Indian spring LW* Ghani

British Guiana

British Honduras

Bulgaria

Burma

Cambodia

Cameroon

Canada

Canal Zone (Atlan-
tic)

Canal Zone (Pacific)

Canary Islands

Caroline Islands

Chile

China

Colombia (Atlantic)

Colombia (Pacific)

Congo

Costa Rica (Atlantic)

Costa Rica (Pacific)

Cuba

Denmark (Baltic)

Denmark (North
Sea)

Dominican Republic

Ecuador

Egypt (Red Sea)

Lowest normal LW
Mean LW springs
Mean sea level
Lowest normal LW
Lowest LW
Lowest LW
Lowest normal LW
Mean LW

Mean LW springs
Lowest normal LW
Lowest normal LW
Lowest normal LW
Lowest normal LW
Mean LW

Mean LW springs
Lowest LW

Mean LW

Mean LW springs
Mean LW

Mean sea level
Mean LW springs

Mean LW
Mean LW springs
Indian spring LW*

Gilbert Islands
Great Britain
Greece
Greenland
Guadeloupe
Guam
Guatemala
Guinea

Haiti

Hawaiian Islands
Honduras (Atlantic)
Honduras (Pacific)
Iceland

India

Indonesia

Iran

Iraq

Israel

Italy

Ivory Coast
Jamaica

Japan
Kenya

*The chart datum is somewhat lower than the datum indicated.

**A chart datum approximating mean LW springs or Indian spring LW is used for a number of

places on the north and northwest coasts of Australia.

Datum

Mean LW springs

Mean LW springs

Mean sea level

Indian spring LW*

Mean sea level

Lowest LW

Lowest LW

Mean LW springs*

Lowest LW

Mean lower LW
springs

Mean sea level

Mean LW springs

Mean lower LW
springs
Mean LW springs
Mean LW springs*
Mean LW springs*
Mean LW springs
Lowest LW
Mean lower LW
Mean LW springs
Lowest LW
Mean LW
Mean lower LW
Mean lower LW
Mean LW springs
Mean LW springs
Indian spring LW*
Lowest normal LW
Indian spring LW
Indian spring LW
Mean LW springs
Mean LW springs
Lowest LW
Mean lower LW
springs
Indian spring LW
Indian spring LW

Area

Korea
Latvia
Liberia

Libya

Lithuania
Loyalty Islands
Madagascar
Madeira Islands
Malaya
Mariana Islands

Marshall Islands

Martinique

Mauritania

Mexico (part of
Atlantic)

Mexico (Pacific and
part of Atlantic)

Morocco

Mozambique

Netherlands

New Caledonia
New Hebrides
New Zealand
Nicaragua
Nigeria
Norway

Pakistan

Panama (Atlantic)
Panama (Pacific)
Papua

Peru

Philippines
Poland

Portugal
Portuguese Guinea
Puerto Rico

Rio Muni
Rumania

Saipan

Samoa

APPENDIX M

TIDAL DATUMS IN USE IN VARIOUS AREAS

Datum

Area

1001

Datum

Indian spring LW
Mean sea level
Mean lower LW
springs
Mean LW springs
Mean sea level
Lowest normal LW
Lowest LW
Lowest normal LW
Lowest normal LW
Lowest normal
LW **
Lowest normal LW
Lowest LW
Lowest LW
Mean LW

Mean lower LW

Lowest LW

Lowest LW

Mean lower LW
springs

Lowest LW

Lowest normal LW

Lowest normal LW

Mean LW springs

Mean LW springs

Equatorial spring
LW

Lowest normal LW
Mean LW

Mean LW springs
Lowest LW

Mean LW springs
Mean lower LW
Mean sea level
Lowest normal LW
Lowest normal LW
Mean LW

Lowest normal LW
Mean sea level
Mean lower LW
Mean LW springs

Saudi Arabia
Senegal
Sierra Leone

Solomon Islands
Somali Republic
South Africa
South-West Africa
Spain

Spanish Sahara
Sudan

Surinam

Sweden
Syria
Tanganyika
Thailand
Tinian
Togo
Trinidad

Tuamoto Archipel-
ago

Tunisia

Turkey (Black Sea)

Turkey (Mediter-
ranean)

United Arab Repub-
lic (Egypt) (Medi-
terranean)

United Arab Repub-
lie (Egypt) (Red

ea
USA (Atlantic)
USA (Pacific)
USSR (Baltic and
Black Sea)
USSR (Arctic and
Pacific)
Uruguay
Venezuela
Vietnam
Virgin Islands
Yugoslavia

*The chart datum is somewhat lower than the datum indicated.
** At Guam, Saipan, and Tinian the chart datum is mean lower LW.

Indian spring LW*
Lowest LW

Mean lower LW
springs

Lowest normal LW
Mean LW springs*
Mean LW springs
Mean LW springs*
Lowest normal LW
Lowest normal LW
Indian spring LW*
Mean lower LW
springs

Mean sea level
Mean LW springs*
Mean LW springs
Lowest normal LW
Mean lower LW
Lowest LW

Mean lower LW
springs

Mean LW springs

Lowest LW
Mean sea level
Mean LW springs

Mean LW springs
Indian spring LW *

Mean LW
Mean lower LW
Mean sea level

Lowest normal LW

Lowest normal LW

Mean LW springs

Lowest LW

Mean LW

Mean lower LW
springs

APPENDIX N
SOURCES OF CHARTS AND PUBLICATIONS

Certain types of charts and publications, listed below, can be purchased from the places indicated.
Many of the publications listed are also available from the Superintendent of Documents, U.S. Govern-
ment Printing Office, Washington, D.C. 20402.

Orders for charts or publications, when addressed to Government agencies, should be accompanied
by a check or post office money order made payable to the Treasurer of the United States. Postage
stamps are not accepted, and cash is sent at the sender’s risk of loss.

Government agencies make no charge for postage to addresses in the United States and posses-
sions, and none to Canada, Cuba, Mexico, and Panama if the total weight of the shipment does not
exceed four pounds. In all other cases, postage is required at the rates for printed matter. Remit-
tance should accompany the order.

Orders for charts and publications should be as specific as possible, citing the numbers assigned
by the publishing agency as identification of the items desired. To facilitate selection, the U.S. Navy
Hydrographic Office, Washington, D.C. 20390 and U.S. Coast and Geodetic Survey, Washington, D.C.
20230, distribute free of charge, catalogs of salable material. More detailed information on U.S.
Navy Hydrographic Office nautical charts and publications is given in Pub. No. 1-N, Introduction
Part I. Aeronautical charts and publications are listed in the Catalog of U.S. Navy Aeronautical
Charts and Related Publications, the Coast and Geodetic Survey Catalog of Aeronautical Charts and
Related Publications and the DOD Catalog of Acronautical Charts and Flight Information Publications.
The DOD catalog is available only to military users.

Nautical Charts

Coasts of the United States and its territories
and possessions.

U.S. Coast and Geodetic Survey and sales agents.

Mississippi River from the Head of Passes to
Cairo, Ill.

Illinois waterway system (Great Lakes to Gulf
of Mexico).

Various United States rivers.

Great Lakes, Lake Champlain, and the St. Law-
rence River above St. Legis and Cornwall,
Canada.

New York State canals.

Coasts of foreign countries.

Mississippi River Commission, Vicksburg, Miss.

Distriet Engineer, Chicago District, Chicago, Ill.

District Engineer Offices.

U.S. Lake Survey, Detroit, Mich., and District
Engineer, Buffalo District, Buffalo, N.Y.

U.S. Lake Survey, Detroit, Mich.; Superintend-
ent of Publie Works, Albany, N.Y.; and Dis-
triet Engineer, Buffalo Distriet, Buffalo, N.Y.

U.S. Navy Hydrographic Office sales agents.

Oceanographic Charts and Publications

'Tide and tidal current tables.

Tidal current charts, certain United States harbors.

Current charts of the oceans.

Pilot charts.

Bottom sediment charts.

Surface temperature charts.

Sea and swell charts.

Water temperature and density tables.

Oceanographic Atlas of the Polar Seas (Pub. No.
705).

Sonic Soundings (H.O. Pub. No. 606-b).

Bathythermograph Observations (H.O. Pub. No.
606—c).

Ice Observations (H.O. Pub. No. 606-d).

Sea and Swell Observations (H.O. Pub. No. 606-e).

Miscellaneous oceanographic publications.

1002

U.S. Coast and Geodetic Survey and sales agents.
U.S. Coast and Geodetic Survey and sales agents.

S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.

8. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.

S. Navy Hydrographic Office sales agents.
U.S. Coast and Geodetic Survey and sales agents.
S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.
S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents and
U.S. Coast and Geodetic Survey and sales agents.

APPENDIX N: SOURCES OF CHARTS AND PUBLICATIONS

1003

Electronic Navigation

Loran charts.

Loran tables (H.O. Pub. No. 221, various rates).
Radio Navigational Aids (H.O. Pub. No. 117).
Radio Weather Aids (H.O. Pub. No. 118).
Weather Station Index (H.O. Pub. No. 119).
Radio circulars giving schedules, frequencies, and
data included in weather broadcasts.
International Code of Signals, Vol. 11, radio (H.O.
Pub. No. 104).
Federal Communications Commission Rules and
Regulations, Vol. IV, July 1964.
Communications Act of 1934, Revised 1960.
International Convention for the Safety of Life at
Sea, 1960.
International Publications:
List of Frequencies.
List of Coast Stations.
List of Ship Stations.
List of Broadcasting Stations.
List of Radio Determination and Special Service
Stations.
List of Call Signs of Stations Used by the Mari-
time Mobile Service.
List of Fixed Stations Operating International
Circuits.
Radio Aids to Maritime Navigation and Hydrog-
raphy. (IHB Special Pub. No. 39).

U.S. Navy Hydrographie Office sales agents;
U.S. Coast and Geodetic Survey and sales
agents; and U.S. Air Force Aeronautical Chart
and Information Center.

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.

Chief, U.S. Weather Bureau. (Also in H.O.
Pub. No. 117).

U.S. Navy Hydrographic Office sales agents.

Superintendent of Documents.

Superintendent of Documents.

Intergovernmental Maritime Consultative Or-
ganization, London, England.

International Telecommunication Union, Geneva,
Switzerland.

International Hydrographic Bureau, Monaco.

Navigational Publications

Coast pilots (sailing directions), coasts of the
United States and its territories and posses-
sions.

Sailing directions (coast pilots), foreign coasts.

Light lists, United States waters.

Light lists, foreign coasts.
Navigational tables:
Table of Distances Between Ports (H.O. Pub.
No. 151).
Tables of Computed Altitude and Azimuth (H.O.
Pub. No. 214, nine vols.).
Sight Reduction Tables for Air Navigation (H.O.
Pub. No. 249, three vols.).
Various sight reduction tables (H.O. Pubs.
Nos. 208, 211, 218).
Azimuths of the Sun (H.O. Pub. No. 260).
Azimuths of Celestial Bodies (H.O. Pub. No.
261).
Distances Between United States Ports.
Almanacs:
The Air Almanac.
The American Ephemeris and Nautical Al-
manac.
The Nautical Almanac.

U.S. Coast and Geodetic Survey and sales agents.

U.S. Navy Hydrographic Office sales agents.
Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.
U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.

U.S. Coast and Geodetic Survey and sales agents.

Published by U.S. Naval Observatory, distrib-
uted by Superintendent of Documents and
sales agents.

1004

APPENDIX N: SOURCES OF CHARTS AND PUBLICATIONS

Periodical Publications

Notice to Mariners.
Daily Memorandum.

U.S. Navy Hydrographic Office and branches.
U.S. Navy Hydrographic Office and branches.

Miscellaneous

Isomagnetic charts.

Magnetic variation charts of the United States,
Caribbean, and Alaska.

Great-circle charts.

Charts of polar regions.

Aeronautical charts, United States.
Aeronautical charts, world coverage.

Aeronautical publications.

Plotting charts and plotting sheets.
Special charts.

International Code of Signals, Vol. I, visual (H.O.
Pub. No. 103).

Merchant Marine House Flags and Stack Insignia
(H.O. Pub. No. 100).

Navigational Observations (H.O. Pub. No. 606-a).

Shipboard Wind Plotter.

Weather maps and reports.

Mariners Weather Log.

World Port Index (H.O. Pub. No. 150).

Eskimo Place Names and Aids to Conversation
(H.O. Misc. 10578).

Star Finder and Identifier (H.O. 2102-D).

Rules of the Road—International—Inland (CG—
169).

Rules of the Road—Great Lakes (CG-172).

Rules of the Road— Western Rivers (OG-184).

Systems of Maritime Buoyage and Beaconage
Adopted by Various Countries. (IHB Special
Pub. No. 38).

Aids to Marine Navigation of the United States
(CG-193).

Radar Plotting Manual (H.O. Pub. No. 257).

Maneuvering Board Manual (H.O. Pub. No. 217).

Navigation Dictionary (H.O. Pub. No. 220).

Handbook of Magnetic Compass Adjustment and
Compensation (H.O. Pub. No. 226).

Laws Governing Marine Inspection (CG-227).

Instrument instruction pamphlets.
Great Lakes Pilot.

U.S. Navy Hydrographic Office sales agents.
U.S. Coast and Geodetic Survey and sales agents.

.S. Navy Hydrographic Office sales agents.

S. Navy Hydrographic Office sales agents and
U.S. Air Force Aeronautical Chart and Infor-
mation Center.

.S. Coast and Geodetic Survey and sales agents.
S. Hydrographic Office sales agents and U.S.
Air Force Aeronautical Chart and Information
Center.

U.S. Navy Hydrographic Office sales agents and
Federal Aviation Agency.

.S. Navy Hydrographic Office sales agents.

.S. Navy Hydrographic Office sales agents and
U.S. Coast and Geodetic Survey and sales
agents.

U.S. Navy Hydrographic Office sales agents.

aq

ee)

ara

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.

U.S. Weather Bureau.

U.S. Weather Bureau.

Published by U.S. Weather Bureau, distributed
by Superintendent of Documents.

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.

U.S. Navy Hydrographic Office sales agents.
Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.
Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.
Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.
International Hydrographic Bureau, Monaco.

Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.
U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.
U.S. Navy Hydrographic Office sales agents.

Published by U.S. Coast Guard, distributed by
Superintendent of Documents and sales agents.

Manufacturer of equipment.

U.S. Lake Survey, Detroit, Michigan.

APPENDIX O
MATHEMATICS

Arithmetic

01. Definitions.—Arithmetic is that branch of mathematics dealing with compu-
tation by numbers. The principal processes involved are addition, subtraction,
multiplication, and division. A number consisting of a single symbol (1, 2, 3, etc.)
is a digit. Any number that can be stated or indicated, however large or small, is
called a finite number; one too large to be stated or indicated is called an infinite
number; and one too small to be stated or indicated is called an infinitesimal number.

The sign of a number is the indication of whether it is positive (+) or negative (—).
This may sometimes be indicated in another way. Thus, latitude is usually indi-
cated as north (N) or south (S), but if north is considered positive, south is then nega-
tive with respect to north. In navigation, the north or south designation of latitude
and declination is often called the “name” of the latitude or declination. A positive
number is one having a positive sign (+); a negative number is one having a negative
sign (—). The absolute value of a number is that number without regard to sign.
Thus, the absolute value of both (+)8 and (—)8 is 8. Generally, a number without
a sign can be considered positive.

O2. Expressing numbers.—In navigation, fractions are usually expressed as
decimals. Thus, Mis expressed as 0.25 and 4 as 0.33. To determine the decimal equiva-
lent of a fraction, divide the numerator (the number above the line) by the denominator
(the number below the line). When a decimal is less than 1, as in the examples above,
it is good practice to show the zero at the left of the decimal point (0.25, not .25).

A number should not be expressed to a greater precision than justified. The
precision of a decimal is indicated by the number of digits shown to the right of the
decimal point. Thus, the expression “14 miles” indicates a precision to the nearest
whole mile, or any value between 13.5 and 14.5 miles. The expression “14.0 miles"
indicates a precision of a tenth of a mile, or any value between 13.95 and 14.05 miles.

In a number without a decimal there is sometimes doubt as to the degree of pre-
cision indicated. For example, the number 186,000 may indicate a precision to three,
four, five, or six places. This ambiguity is sometimes avoided by expressing numbers
as powers of 10 (art. OS). Thus, 18.6X10* (18.6X10,000) indicates a precision to
the nearest thousand (three places), 18.60X10* to the nearest hundred (four places),
18.600 10* to the nearest ten (five places), and 18.6000X10* to the nearest unit (six
places). The position of the decimal is not important if the correct power of 10 is
given. For example, 18.610‘ is the same as 1.86 10°, 18610”, etc.

The small number above and to the right of 10 (the exponent) indicates the number
of places the decimal point is to be moved to the right. If the exponent is negative,
it indicates a reciprocal, and the decimal point is moved to the left. Thus, 1.86 X 107° =
0.00000186. This system is sometimes used to avoid long numbers.

Another way of indicating degree of precision is to state the number of significant
digits. These are the digits in a number, excluding zeros at the left and sometimes
those at the right. Thus, 1,325, 1,001, 1.408, 0.00005926, 625.0, and 0.04000 have
four significant digits each. But in the number 312,600 there may be four, five, or six

1005

1006 APPENDIX O: MATHEMATICS

significant digits. Any doubt may be removed by expressing the number times a
power of 10, as explained above. m

If there are no more significant digits, regardless of how far a computation is
carried, this may be indicated by use of the word “exactly.” Thus, 12=-4=3 exactly,
and one nautical mile— 1,852 meters exactly; but 122-7 —1.7 approximately, the word
"approximately" indicating that additional decimal places might be computed. Another
way of indicating an approximate relationship is by placing a positive or negative sign
after the number. Thus, 12+7=1.7+, and 11+7=1.6—. This system has the
advantage of showing whether the approximation is too great or too small.

In any arithmetical computation the answer is no more accurate than the least
precise value used. Thus, if it is desired to add 16.4 and 1.88, the answer might be
given as 18.28, but since the first term might be anything from 16.35 to 16.45, the
answer is anything from 18.23 to 18.33. Hence, to retain the second decimal place in
the answer is to give a false indication of accuracy, for the number 18.28 indicates a
value between 18.275 and 18.285. However, additional places are sometimes re-
tained until the end of a computation to avoid an accumulation of small errors due
to rounding off (art. O4). In marine navigation it is customary to give most values
to a precision of 0.1, even though some uncertainty may exist as to the accuracy of the
last place. Examples are the dip and refraction corrections of sextant altitudes (arts.
1606, 1613).

In general, a value obtained by interpolation in a table should not be expressed
to more decimal places than given in the table.

O3. Precision and accuracy.— The word ''precision" as used above is not the
same as “accuracy,” although the two are sometimes confused. A quantity may be
expressed to a greater precision than is justified by the accuracy of the information
from which the quantity is derived. For instance, if a ship steams one mile in 39215, its
speed is 60?—-37215—60—-3.35 —17.910447761194 knots, approximately. The division
can be carried to as many places as desired, but if the time is measured only to the
nearest second, the speed is accurate only to one decimal place in this example,
because an error of 0.5 second introduces an error of more than 0.05 knot in the speed.
Hence, the additional places are meaningless and possibly misleading, unless more
accurate time is available. In general, it is not good practice to state a quantity to
greater precision than justified by its accuracy. However, in marine navigation the accu-
racy of information is often unknown, and it is customary to give positions to a precision
of 0:1 of latitude and longitude, although they may not be accurate even to the
nearest whole minute.

The absolute precision of a number is indicated by its number of decimal places;
its relative precision by its number of significant digits. Although this is an indica-
tion of precision, it may also be a measure of accuracy, and the expressions absolute
accuracy and relative accuracy used. However, the term “accuracy” should not be
used when “precision” only is intended. Thus, the values 186,000 and 0.00000186
may each have three significant digits, or “be correct to three digits," although the
first value may be accurate (absolute accuracy") only to- the nearest 1,000, and the
second to the nearest 0.00000001. If the numbers are accurate to the number of signifi-
cant digits shown, each has an error ("relative accuracy”) of less than “one part in 186."

Unless all numbers are exact, doubt exists as to the accuracy of the last digit in
a computation. Thus, 12.34-9.4--4.6—26.3. But if the three terms to be added
have been rounded off from 12.26, 9.38, and 4.57, the correct answer is 26.2, obtained
by rounding off the answer of 26.21 found by retaining the second decimal place until
the end. It is good practice to work with one more place than needed in the answer,

APPENDIX 0: MATHEMATICS 1007

when the information is available. In computations involving a large number of terms,
or if great accuracy is desired, it is sometimes advisable to retain two or more additional
places until the end.

04. Rounding off.—In rounding off numbers to the number of places desired, one
should take the nearest value. Thus, the number 6.5049 is rounded to 6.505, 6.50,
6.5, or 7, depending upon the number of places desired. If the number to be rounded

off ends in 5, the nearer even number is taken. Thus, 1.55 and 1.65 are both rounded
to 1.6. Likewise, 12.750 is rounded to 12.8 if only one decimal place is desired. How-

ever, 12.749 is rounded to 12.7. That is, 12.749 is not first rounded to 12.75 and then
to 12.8, but the entire number is rounded in one operation. When a number ends in
5, the computation can sometimes be carried to additional places to determine whether
the correct value is more or less than 5.

O5. Reciprocals.— The reciprocal of a number is 1 divided by that number. The
reciprocal of a fraction is obtained by interchanging the numerator and denominator.
Thus, the reciprocal of % is %. A whole number may be considered a fraction with 1
as the denominator. Thus, 54 is the same as 5%, and its reciprocal is X4. Division
by a number produces the same result as multiplying by its reciprocal, or vice versa.
Thus, 122-2—12X X—6, and 12x 2—12--X— 24.

O6. Addition.—When two or more numbers are to be added, it is generally most
convenient to write them in a column, with the decimal points in line. Thus, if 31.2,
0.8874, and 168.14 are to be added, this may be indicated by means of the addition
sign (+): 31.22-0.8874--168.14— 200.2. But the addition can be performed more
conveniently by arranging the numbers as follows:

31.2
0. 8874
168. 14
200. 2.

The answer is given only to the first decimal pláce, because the answer is no more
accurate than the least precise number among those to be added, as indicated previously.
Often it is preferable to state all numbers in a problem to the same precision before
starting the addition, although this may introduce a small error, as indicated in article

03:

If there are no decimals, the last digit to the right is aligned:

166

2
96,758
96,926.

Numbers to be added should be given to the same absolute accuracy, when available,
to avoid a false impression of accuracy in the result. Consider the following:

186,000
71,832
9,614
728
268,174.

1008 APPENDIX O: MATHEMATICS

The answer would imply an accuracy to six places. If the first number given is accurate
to only three places, or to the nearest 1,000, the answer is not more accurate, and
hence the answer should be given as 268,000. Approximately the same answer would
be obtained by rounding off at the start:

186,000
72,000
10,000

1,000

269,000.

If numbers are added arithmetically, their absolute values are added without
regard to signs; but if they are added algebraically, due regard is given to signs. If
two numbers to be added algebraically have the same sign, their absolute values are
added and given their common sign. If two numbers to be added algebraically have
unlike signs, the smaller absolute value is subtracted from the larger, and the sign of
the value having the larger absolute value is given to the result. Thus, if +8 and —7
are added arithmetically, the answer is 15, but if they are added algebraically, the
answer is 4-1.

An answer obtained by addition is called à sum.

O7. Subtraction is the inverse of addition. Stated differently, the addition of a
negative number is the same as the subtraction of a positive number. That is, if a
number is to be subtracted from another, the sign (+ or —) of the subtrahend (the
number to be subtracted) is reversed and the result added algebraically to the minuend
(the number from which the subtrahend is to be subtracted). Thus, 6—4—2. This
may be written +6—(+4)=+2, which yields the same result as +6 + (—4). For
solution, larger numbers are often conveniently arranged in a column with decimal
points in a vertical column, as in addition. Thus, 3,728.41— 1,861.16 may be written

(+)3,728.41
(+)1,861.16 (subtract)
(+)1,867.25

This is the same as
(+)3,728.41
(—)1,861.16 (add algebraically)
(+)1,867.25

The rule of sign reversal applies likewise to negative numbers. Thus, if —3 is
to be subtracted from +5, this may be written +5— (—3)—5--3—8.

In the algebraic addition of two numbers of opposite sign (numerical subtraction),
the smaller number is subtracted from the larger and the result is given the sign of
the larger number. Thus, +7—4=+3, and —7+4=-—3, which is the same as
+4—7=—53.

In navigation, numbers to be numerically subtracted are usually marked (—),
and those to be numerically added are marked (+) or the sign is not indicated. However,
when a sign is part of a designation, and the reverse process is to be used, the word
“reversed” (rev.) is written after the number. Thus, if GMT is known and ZT in the
(+)5 zone is to be found (by subtraction), the problem may be written:

APPENDIX 0: MATHEMATICS 1009

GMT 1754
ZD (+)5 _ (rev.)
ZT 1254

The symbol ~ indicates that an absolute difference is required without regard
to sign of the answer. Thus, 28—13—15, and 13~28=15. In both of these solutions
13 and 28 are positive and 15 is an absolute value without sign. If the signs or names
of both numbers are the same, either positive or negative, the smaller is subtracted
from the larger, but if they are of opposite sign or name, they are numerically added.
Thus, (+)16~(+)21=5 and (—)16~(—)21=5, but (+)16~(—)21=37 and (—)16~
(+)21=37. Similarly, the difference of latitude between 15°N and 20°N, or be-
tween 15°S and 20°S, is 5°, but the difference of latitude between 15°N and
20°S, or between 15°S and 20°N, is 35°. If motion from one latitude to another is
involved, the difference may be given a sign to indicate the direction of travel, or the
location of one place with respect to another. Thus, if B is 50 miles west of A, and C
is 125 miles west of A, B and C are 75 miles apart regardless of the direction of travel.
However, B is 75 miles east of C, and Cis 75 miles west of B. When direction is indicated,
an algebraic difference is given, rather than an absolute difference, and the symbol ~
is not appropriate.

It is sometimes desirable to consider all addition and subtraction problems as
addition, with negative signs (—) given before those numbers to be subtracted, so
that there can be no question of which process is intended. The words “add” and
“subtract” may be used instead of signs. In navigation, “names” (usually north,
south, east, and west) are often used, and the relationship involved in a certain problem
may need to be understood to determine whether to add or subtract. Thus, LHA=
GHA — (west) and LAA=GHA>+A(east). This is the same as saying LHA=GHA—A
if west longitude is considered positive, for in this case, LAA=GHA—(—A) or LHA =
GHA +1 in east longitude, the same as before.

Tf numbers are subtracted arithmetically, they are subtracted without regard to
sign; but if they are subtracted algebraically, positive (+) numbers are subtracted
and negative (—) numbers are added.

An answer obtained by subtraction is called a difference.

OS. Multiplication may be indicated by the multiplication sign (X), as 154. 28—
4,312. For solution, the problem is conveniently arranged thus:

154
CX) 28
1232
308
4312.

Either number may be given first, but it is generally more convenient to perform the
multiplication if the larger number is placed on top, as shown. In this problem, 154 is
first multiplied by 8 and then by 2. The second answer is placed under the first, but
set one place to the left, so that the right-hand digit is directly below the 2. These
steps might be reversed, multiplication by 2 being performed first. This procedure is
sometimes used in estimating.
When one number is placed below another for multiplication, as shown above, it
is usually best to align the right-hand digits without regard for the position of the

1010 APPENDIX 0: MATHEMATICS i
decimal point. The number of decimal places in the answer is the sum of the decimal
places in the multiplicand (the number to be multiplied) and the multiplier (the second

number): ter
(X) 263.9
146943
48981
97962
32654

43086.953.

However, when a number ends in one or more zeros, these may be ignored until the
end and then added on to the number:

1924
(X) 1800
15392
1924

3463200.

This is also true if both multiplicand and multiplier end in zeros:

1924000
(X) 1800
15392
1924

3463200000.

When negative valves are to be multiplied, the sign of the answer is positive if an
even number of negative signs appear, and negative if there are an odd number. Thus,
2X3=6, 2xX(-3)=-—6, —2X3=—6, —2X(—3)=(+)6. Also,2X3X8X(—2) X5=
—480, 2X(—3)X8X(—2)X5=480, 2X(—3)X(—8)X(—2)X5= —480, 2X(—3) X
(—8)X(—2)X(—5)=480, and (—2)X(—3)X(—8)X(—2)X(—5) = —480.

An answer obtained by multiplication is called a product. Any number multiplied
by 1 is the number itself. Thus, 125X1=125. Any number multiplied by 0 is 0. Thus,
125X0=0 and 1X0=0.

To multiply a number by itself is to square the number. This may be indicated
by the exponent 2 placed to the right of the number and above the line as a superior.
Thus, 15X15 may be written 15?. Similarly, 15x 15x 15—15?, and 15X15X15X15=
15%, etc. The exponent (2, 3, 4, etc.) indicates the power to which a number is to be
raised, or how many times the number is to be used in multiplicat:;n. The expression
15? is usually read “15 squared," 15? is read “15 cubed” or “15 to the third power,”
15* (or higher power) is read “15 to the fourth (or higher) power.” The answer obtained
by raising to a power is called the “square,” “cube,” etc., or the “ . . . power” of the
number. Thus, 225 is the “square of 15,” 3,375 is the “cube of 15” or the “third power
of 15,” etc. The zero power of any number except zero (if zero is considered a number)
is 1. The zero power of zero is zero. Thus, 15°=1 and 0°=0.

Parentheses may be used to eliminate doubt as to what part of an expression is
to be raised to a power. Thus, —3? may mean either—(3X3)= —9 or—3X —3=
(+)9. To remove the ambiguity, the expression may be written— (3)? if the first
meaning is intended, and (—3)? if the second meaning is intended.

APPENDIX 0: MATHEMATICS 1011

09. Division is the inverse of multiplication. It may be indicated by the division
sign (+), as 376+21=18 approximately; or by placing the number to be divided,

called the dividend (376), over the other number, called the divisor (21), as 9-18

Í ETES : ^
approximately. The expression p May be written 376/21 with the same meaning.

Such a problem is conveniently arranged for solution as follows:

17
211376
21
166
147
` 19.

Since the remainder is 19, or more than half of the divisor (21), the answer is 18 to
the nearest whole number.

An answer obtained by division is called a quotient. Any number divided by 1 is
the number itself. Thus, 65=1=65. A number cannot be divided by 0.

If the numbers involved are accurate only to the number of places given, the
answer should not be carried to additional places. However, if the numbers are
exact, the answer might be carried to as many decimal places as desired. Thus,
374-21 =17.809523809523809523809523809523809523 . . . . When a series of digits
repeat themselves with the same remainder, as 809523 (with remainder 17) in the
example given above, an exact answer will not be obtained regardless of the number of
places to which the division is carried. The series of dots ( . . . ) indicates a repeating
decimal. In a nonrepeating decimal, a plus sign (+) may be given to indicate a
remainder, and a minus sign (—) to indicate that the last digit has been rounded to
the next higher value. Thus, 18.68761 may be written 18.6876+ or 18.688—. If the
last digit given is rounded off, the word “approximately” may be used instead of dots
or a plus or minus sign.

If the divisor is a whole number, the decimal point in the quotient is directly
above that of the dividend when the work form shown above is used. Thus, in the
example given above, if the dividend had been 37.6 instead of 376, the quotient would
have been 1.8 approximately. If the divisor is a decimal, both it and the dividend
are multiplied by the power of 10 having an exponent equal to the number of decimal
places in the divisor, and the division is then carried out as explained above. Thus, if
there are two decimal places in the divisor, both divisor and dividend are multiplied
by 10?=100. This is done by moving the decimal to the right until the divisor is a
whole number. If necessary, zeros are added to the dividend. Thus, if 3.7 is to be
divided by 2.11, both quantities are first multiplied by 10’, and 370 is divided by 211.
This is usually performed as follows:

1.75
2/11 | 3/70.00
211

1590
1477).
1130
1055
75.

1012 APPENDIX O: MATHEMATICS

If both the dividend and divisor are positive, or if both are negative, the quotient
is positive; but if either is negative, the quotient is negative. Thus, 6+3=2,
(—6)+(—3)=+2, (—6)2-3— —2, and 6+(—3)=—2.

The square root of a number is that number which, multiplied by itself, equals
the given number. Thus, 15X15=15*%=225, and y225=225'*=15. Either the
symbol v, called the radical sign, or the exponent X indicates square root. Also,
Ar, or 4 as an exponent, indicates cube root. Fourth, fifth, or any root is indicated
similarly, using the appropriate number. Nearly any arithmetic book explains the
process of extracting roots, but this process is most easily performed by table, loga-
rithms (art. O12), or slide rule (art. O15). If no other means are available, it can be
done by trial and error. The process of finding a root of a number is called extracting
a root.

010. Logarithms (“logs”) provide an easy way to multiply, divide, raise numbers
to powers, and extract roots. The logarithm of a number is the power to which a fixed
number, called the base, must be raised to produce the value to which the logarithm
corresponds. The base of common logarithms, (given in tables 32 and 33) is 10.
Hence, since 10!8=63 approximately, 1.8 is the logarithm, approximately, of 63 to
the base 10. In table 32 logarithms of numbers are given to five decimal places.
This is sufficient for most purposes of the navigator. For greater precision, a table
having additional places should be used. In general, the number of significant digits
which are correct in an answer obtained by logarithms is the same as the number of
places in the logarithms used.

A logarithm is composed of two parts. That part to the left of the decimal point
is called the characteristic. That part to the right of the decimal point is called the
mantissa. The principal advantage of using 10 as the base is that any given combina-
tion of digits has the same mantissa regardless of the position of the decimal point.
Hence, only the mantissa is given in the main tabulation of table 32. Thus, the logarithm
(mantissa) of 2,374 is given as 37548. This is correct for 2,374,000,000; 2,374; 23.74;
2.374; 0.2374; 0.000002374; or for any other position of the decimal point.

The position of the decimal point determines the characteristic, which is not
affected by the actual digits involved. The characteristic of a whole number is one
less than the number of digits. The characteristic of a mixed decimal (one greater
than 1) is one less than the number of digits to the left of the decimal point. Thus, in
the example given above, the characteristic of the logarithm of 2,374,000,000 is 9;
that of 2,374 is 3; that of 23.74 is 1; and that of 2.374 is 0. The complete logarithms
of these numbers are:

log 2,374,000,000=9.37548

log 2,374 =3.37548
log 23.74 = 1.37548
log 2.374 = 0.37548.

Since the mantissa of the logarithm of any multiple of ten is zero, the main table
starts with 1,000. This can be considered 100, 10, 1, etc. Since the mantissa of these
logarithms is zero, the logarithms consist of the characteristic only, and are whole
numbers. Hence, the logarithm of 1 is 0 (0.00000), that of 10 is 1 (1.00000), that of
100 is 2 (2.00000), that of 1,000 is 3 (3.00000), ete. |

The characteristie of the logarithm of a number less than 1 is negative. However,
it is usually more conveniently indicated in a positive form, as follows: the characteristic
1s found by subtracting the number of zeros immediately to the right of the decimal
point from 9 (or 19, 29, etc.) and following this by —10 (or —20, — 30, ete.). Thus, the

APPENDIX 0: MATHEMATICS 1013

characteristic of the logarithm of 0.2374 is 9—10; that of 0.000002374 is 4— 10; and that
of 0.000000000002374 is 8—20. "The complete logarithms of these numbers are:

log 0.2374 =9.37548—10
log 0.000002374 =4.37548—10
log 0.000000000002374=8.37548—20.

When there is no question of the meaning, the —10 may be omitted. This is usually
done when using logarithms of trigonometric functions, as shown in table 33. Thus,
if there is no reasonable possibility of confusion, the logarithm of 0.2374 may be
written 9.37548.

Occasionally, the logarithm of a number less than 1 is shown by giving the negative
characteristic with a minus sign above it (since only the characteristic is negative, the
mantissa being positive). Thus, the logarithms of the numbers given above might be
shown thus:

log 0.2374 adds
log 0.000002374 = 6.37548
log 0.000000000002374 = 12.37548.

In each case, the negative characteristic is one more than the number of zeros imme-
diately to the right of the decimal point.

There is no real logarithm of 0, since there is no finite power to which any number
can be raised to produce 0. As numbers approach 0, their logarithms approach
negative infinity.

To find the number corresponding to a given logarithm, called finding the anti-
logarithm (''antilog”), enter the table with the mantissa of the given logarithm and
determine the corresponding number, interpolating if necessary. Locate the position
of the decimal point by means of the characteristic of the logarithm, in accordance with
the rules given above.

O11. Multiplication by logarithms.—To multiply one number by another, add
their logarithms and find the antilogarithm of the sum. Thus, to multiply 1,635.8 by
0.0362 by logarithms:

log 1635.8 = 3.21373
log 0.0362 = 8.55871—10 (add)
log 59.216 —11.77244— 10 or 1.77244.

Thus, 1,635.8<0.0362=59.216. In navigation it is customary to use a slightly
modified form, and to omit the —10 where there is no reasonable possibility of confusion,

as follows:
1635.8 log 3.21373

0.0362 log 8.55871
59.216 log 1.77244.

To raise a number to a power, multiply the logarithm of that number by the power
indicated, and find the antilogarithm of the product. Thus, to find 1515059 DY:
logarithms, using the navigational form:

13.156 log 1.11913
x 3 (multiply)
2277.2 log 3.35739.

1014 APPENDIX O: MATHEMATICS

012. Division by logarithms.—To divide one number by another, subtract the
logarithm of the divisor from that of the dividend, and find the antilogarithm of the
remainder. Thus, to find 0.4637—-28.03 by logarithms, using the navigational form:

0.4637 log 9.66624
28.03 log (—) 1.44762 (subtract)
0.016543 log 8.21862.

It is sometimes necessary to modify the first logarithm before the subtraction can
be made. This would occur in the example given above, for instance, if the divisor
and dividend were reversed, so that the problem became 28.03--0.4637. In this case
10—10 would be added to the logarithm of the dividend, becoming 11.44762—10:

28.03 log 11.44762—10
0.4637 log (—) 9.66624—10
60.448 log 1.78138.

One experienced in the use of logarithms usually carries this change mentally, without
showing it in his work form:

28.03 log 1.44762
0.4637 log (—) 9.66624
60.448 log 1.78138.

Any number can be added to the characteristic as long as that same number is also
subtracted. Conversely, any number can be subtracted from the characteristic as
long as that same number is also added.

To extract a root of a number, divide the logarithm of that number by the root
indicated, and find the antilogarithm of the quotient. Thus, to find y7 by logarithms:

7 log 0.84510 (+2)
2.6458 log 0.42255.

To divide a negative logarithm by the root indicated, first modify the logarithm
so that the quotient will have a —10. Thus, to find V0.7 by logarithms:

0.7 log 29.84510—30 (+3)
0.88792 log 9.94837—10
or, carrying the —30 and —10 mentally,

0.7 log 29.84510 (+3)
0.88792 log 9.94837.

013. Cologarithms.—The cologarithm (‘‘colog’’) of a number is the value obtained
by subtracting the logarithm of that number from zero, usually in the form 10—10.
Thus, the logarithm of 18.615 is 1.26987. The cologarithm is:

10.00000 — 10
(—)1.26987
8.73013 — 10.

Similarly, the logarithm of 0.0018615 is 7.26987 — 10, and its cologarithm is:

10.00000 — 10
(—)7.26987—10
2./3013.

APPENDIX 0: MATHEMATICS 1015

The cologarithm of a number is the logarithm of the reciprocal of that number.
Thus, the cologarithm of 2 is the logarithm of 4. Since division by a number is the
same as multiplication by its reciprocal, the use of cologarithms permits division prob-
lems to be converted to problems of multiplication, eliminating the need for subtraction
of logarithms. This is particularly useful when both multiplication and division are
92.732 X 0.0137 X 724.3

0.516 3941.1
one might add the logarithms of the three numbers in the numerator, and subtract the
logarithms of the two numbers in the denominator. If cologarithms are used for the
numbers in the denominator, all logarithmic values are added. Thus, the solution
might be made as follows:

involved in the same problem. Thus, to find

by logarithms,

92.732 log 1.96723
0.0137 log 8.13672
724.3 log 2.85992

0.516 log 9.71265 colog 0.28735
3941.1 log 3.59562 colog 6.40438
0.45248 log 9.65560.

O14. Various kinds of logarithms.—As indicated above, common logarithms use
10 as the base. These are also called Briggs’ logarithms. For some purposes, it is
convenient to use 2.7182818 approximately (designated e) as the base for logarithms.
These are called natural logarithms or Naperian logarithms (loge). Common loga-
rithms are shown as logi, when the base might otherwise be in doubt.

Addition and subtraction logarithms are logarithms of the sum and difference of
two numbers. They are used when the logarithms of two numbers to be added or
subtracted are known, making it unnecessary to find the numbers themselves.

O15. Slide rule.—A slide rule is a convenient device for making logarithmic solu-
tions mechanically. There are many types and sizes of slide rule, some designed for
specific purposes. The most common form consists of an outer “body” or “frame”
with grooves to permit a ''slide" to be moved back and forth between the two outer
parts, so that any graduation of a scale on the slide can be brought opposite any grad-
uation of a scale on the body. A cursor called an “indicator” or “runner” is provided
to assist in aligning the desired graduations. In a circular slide rule the “slide” is an
inner disk surrounded by a larger one, both pivoted at their common center. The
scales of a slide rule are logarithmic. That is, they increase proportionally to the
logarithms of the numbers indicated, rather than to the numbers themselves. This
permits addition and subtraction of logarithms by simply measuring off part of the
length of the slide from a graduated point on the body, or vice versa. Two or three
complete scales within the length of the rule may be provided for finding squares,
cubes, square roots, and cube roots.

Full instructions for use of a slide rule are provided with each rule, and given in
some mathematical texts. Properly used, a slide rule can provide quick answers to
many of the problems of navigation. However, its precision is usually limited to from
two to four significant digits, and should not be used if greater precision is desired.
It is frequently used to provide a quick, approximate check on answers obtained by
a more laborious method.

Great care should be used in placing the decimal point in an answer obtained by
slide rule, as the correct location often is not immediately apparent. Its position is
usually determined by making a very rough mental solution. Thus, 2.93 8.3 is about
3x8—24. Hence, when the answer by slide rule is determined to be “243,” it is known
that the correct value is 24.3, not 2.43 or 243.

1016 APPENDIX O: MATHEMATICS

016. Mental arithmetic.—Many of the problems of the navigator can be solved
mentally. The following are a few examples. r

If the speed is a number divisible into 60 a whole number of times, distance prob-
lems can be solved by a simple relationship. Thus, at 10 knots a ship steams 1 mile in
256 minutes. At 12 knots it requires 5 minutes, at 15 knots 4 minutes, etc. As an `
example of the use of such a relationship, a vessel steaming at 12 knots travels 5.6

miles in 28 minutes, since 25 =5%=5.6, or 0.1 mile every half minute.

For relatively short distances, one nautical mile can be considered equal to 6,000
feet. Since one hour has 60 minutes, the speed in hundreds of feet per minute is equal
to the speed in knots. Thus, a vessel steaming at 15 knots is moving at the rate of
1,500 feet per minute.

With respect to time, 6 minutes ==0.1 hour, and 3 minutes —0.05 hour. Hence, `
a ship steaming at 13 knots travels 3.9 miles in 18 minutes (130.3), and 5.8 miles
in 27 minutes (13 X 0.45).

In arc units, 6'—0?1 and 6"=0/1. This relationship is useful in rounding off
values given in arc units. Thus, 17?23'/44" —17?23'7 to the nearest 0:1, and 17°4 to
the nearest 0?1. A thorough knowledge of the six multiplication table is valuable.
The 15 multiplication table is also useful, since 15°=1". Hence, 16"=16X15=240".
This is particularly helpful in quick determination of zone description. Pencil and
paper or a table should not be needed, for instance, to decide that a ship at sea in
longitude 157?18'4 W is in the (4-)10 zone.

It is also helpful to remember that 1?—4" and 1'—4*. In converting the LMT
of sunset to ZT, for instance, a quick mental solution can be made without reference
to a table. Since this correction is usually desired only to the nearest whole minute,
it is necessary only to multiply the longitude difference in degrees (to the nearest
quarter degree) by four.

Vectors

O17. Scalars and vector quantities.—A scalar is a quantity which has magnitude
only; a vector quantity has both magnitude and direction. If a vessel is said to have
a tank of 5,000 gallons capacity, the number 5,000 is a scalar. As used in this book,
speed. alone is considered a scalar, while speed and direction are considered to constitute
velocity, & vector quantity. "Thus, if a vessel is said to be steaming at 18 knots, with-
out regard to direction, the number 18 is considered a scalar; but if the vessel is said
to be steaming at 18 knots on course 157?, the combination of 18 knots and 157? con-
stitutes a vector quantity. Distance and direction also constitute a vector quantity.

A scalar can be represented fully by a number. A vector quantity requires, in addi-
tion, an indication of direction. This is conveniently done graphically by means of a
straight line, the length of which indicates the magnitude, and the direction of which
indicates the direction of application of the magnitude.
Since a straight line has two directions, reciprocals
placed along or at one end of a vector to indicate the
is apparent or indicated in some other manner.

O18. Addition and subtraction of vectors.—Two vectors can be added by starting
the second at the termination (rather than the origin) of the first. A common e
tional use of vectors is the dead reckoning plot of a vessel. Refer to figure O18. Ifa
ship starts at A und steams 18 miles on course 090? and then 12 miles on es 060°,
it arrives by dead reckoning at C. The line AB is the vector for the first run, and

Such a line is called a vector.
of each other, an arrowhead is
direction represented, unless this

APPENDIX 0: MATHEMATICS 1017

BC is the vector for the second. C
Point C is the position found
by adding vectors AB and BC.
The vector AC, in this case the
course and distance made good, is X za B

the resultant. Its value, both Ne q

in direction and amount, can be Šā a1

determined by measurement. Supt“

Lines AB, BO, and AC are all o

distance vectors. Velocity vec- FiGurE O18. Addition and subtraction of vectors.

tors are used when determining

the effect of, or allowing for, current (art. 807) or interconverting true and apparent
wind (art. 3709).

The reciprocal of a vector has the same magnitude but opposite direction of the
vector. To subtract a vector, add its reciprocal. This is indicated by the broken lines
in figure O18, in which the vector BC' is drawn in the opposite direction to BC. In
this case the resultant is AC'. Subtraction of vectors is involved in some current
and wind problems.

Algebra

O19. Definitions.—Algebra is that branch of mathematics dealing with compu-
tation by letters and symbols. It permits the mathematical statement of certain
relationships between variables. When numbers are substituted for the letters,
algebra becomes arithmetic. Thus if a=2b, any value may be assigned to b, and a
can be found by multiplying the assigned value by 2. Any statement of equality
(as a=2b) is an equation. Any combination of numbers, letters, and symbols (as 2b)
is à mathematical expression.

020. Symbols.—As in arithmetic, plus (+) and minus (—) signs are used, and
with the same meaning. Multiplication (X) and division (-+) signs are seldom used.
In algebra, «X0 is usually written ab, or sometimes a-b. For division a=b is usually
written jo a/b. The symbol > means “greater than" and < means “less than.”
Thus, a>} means “a is greater than b," and a 2 bora > b means “a is equal to or greater
than b.”

The order of performing the operations indicated in an equation should be observed
carefully. Consider the equation a=b+cd—e/f. If the equation is to be solved
for a, the value cd should be determined by multiplication and e/f by division before
the addition and subtraction, as each of these is to be considered a single quantity in
making the addition and subtraction. Thus, if cd=g and e/f=h, the formula can be
written a=b+ g—h.

If an equation including both multiplication and division between plus or minus
signs is not carefully written, some doubt may arise as to which process to perform
first. Thus, a=bXc or a/bXc may be interpreted to mean either that a/b is to be
multiplied by c or that a is to be divided by bXc. Such an equation is better written
ac/b if the first meaning is intended, or a/dc if the second meaning is intended. Paren-
theses, ( ), may be used for the same purpose or to indicate any group of quantities
that is to be considered a single quantity. Thus, a(b+c) is an indication that the
sum of b and c is to be multiplied by a. Similarly, a+ (b— c)? indicates that c is first to
be subtracted from b, and then the result is to be squared and the value thus obtained
added to a. When an expression within parentheses is part of a larger expression

1018 APPENDIX O: MATHEMATICS

which should also be in parentheses, brackets, [ ], are used in place of the outer
parentheses. If yet another set is needed, braces, { }, are used.

A quantity written /3 ab is better written ab y3 to remove any suggestion that
the square root of 3ab is to be found.

O21. Addition and subtraction.—A plus sign before an expression in parentheses .
means that each term retains its sign as given. Thus, a+(b+ce—d) is the same as
a+b+c—d. A minus sign preceding the parentheses means that each sign within
the parentheses is to be reversed. For example, a—(b+e—d)=a—b—c-+d.

In any equation involving addition and subtraction, similar terms can be com-
bined. Thus, a+b+c+b—2c—d=a+2b—c—d. Also, a+3ab+a*—b—ab=a +2ab +
a?—b. That is, to be combined, the terms must be truly alike, for a cannot be com-
bined with ab, or with a’.

Equal quantities can be added to or subtracted from both members of an equation
without disturbing the equality. Thus, if a=b, a+2=b+-2, or a--z—b-4-z. If x=y,
then a+x=b+y.

O22. Multiplication and division.—When an expression in parentheses is to be
multiplied by a quantity outside the parentheses, each: quantity separated by a plus
or minus sign within the parentheses should be multiplied separately. Thus, a(b+ed—
e/f) may be written ab+acd—ae/f. Any quantity appearing in every term of one member
of an equation can be separated out by factoring, or dividing each term by the common

quantity. Thus, if abe P ga, the equation may be written a=b (c+5—0+ 1)

2
Note that j= and v=o. This is the inverse of multiplication: aX1=a, but

axa=a 0 Also, a*Xa*=a". and Ga, Thus, in multiplying a power of a number by
a power of the same number, the powers are added, or, stated mathematically, a” Xa"
=a"*". [n division, Ta or the exponents are subtracted. If xn is greater than m,
a negative exponent results. A value with a negative exponent is equal to the reciprocal

of the same value with a positive exponent. Thus, at and

In raising to à power a number with an exponent, the two exponents are multi-
plied. Thus, (a?)?—a?*?—a5, or (a*)"—a"". The inverse is true in extracting a root.

2 ni

Thus, Va? — a! =a", or “/ar=a”.
Both members of an equation can be multiplied or divided by equal quantities
without disturbing the equality, excluding division by zero or some expression equal

to zero. Thus, if a=b+c, 2a—2(b4-c), or if x=y, ar=y(b+c) and Fr Sometimes

there is more than one answer to an equation. Division by one of the unknowns may
eliminate one of the answers.

Both members of an equation can beraised to the same power, and like roots of both
members can be taken, without disturbing the equality. Thus, if a=b+c, a?=(b+0)?
or if x=y, a=(b+c). This is not the same as a=b + cv, Similarly, if a=b+e Jom
Vb+c, or if r=y, Va=Ybc. Again, Vb--c is not equal to */b--"/c, as a nume
example will indicate: /100—4/64 4-36, but 4/100 does not equal 464 4-4/36.

If two quantities to be multiplied or divided are both positive or both negative, the

result is positive. Thus, (4-a) x (+b)

—ab and == de But if the signs are opposite,

APPENDIX 0: MATHEMATICS 1019

the answer is negative. Thus, (--a) X (—5)— —ab, and HTTP also, (—a)x(+b)=

In expressions containing both parentheses and brackets, or both of these and

braces, the innermost symbols are removed first. Thus,— dee

023. m .—To add or FE two or more fractions, convert each to an

expression having the same denominator, and then add the numerators. Thus, P RE

) cbf , ebd. adf 4- cbf -- ebd
T wart 5 DH d a J E ZS : That is, both numerator and denominator of each

fraction are multiplied by the denominator of the other remaining fractions.
To multiply two or more fractions, multiply the numerators by each other, and

also multiply the denominators by each other. Thus, 7X “xs Jā dā
To divide two fractions, invert the divisor and multiply. Thus, - + ce,
C

If the same factor appears in all terms of a fraction, it can be factored out without
ab+actad_b+c+d
ae—af | e—f

'This is the same as

factoring a from the numerator and denominator separately. That is, "TS.

TOR = 1, this part can be removed, and the fraction appears as above.
O24. Transposition.—It is sometimes desirable to move terms of an expression
from one side of the equals sign (=) to the other. This is called transposition, and to
move one term is to transpose it. If the term to be moved is preceded by a plus or a
minus sign, this sign is reversed when the term is transposed. Thus, if a=b+c, then
a—b=c, a—c=b, —b=c—a, —b—c- —a, etc. Note that the signs of all terms can be
reversed without destroying the equality, for if a=b, b=a. Thus, if all terms to the
left of the equals sign are exchanged for all those to the right, no change in sign need
take place, yet if each is moved individually, the signs reverse. For instance, if a=
b+c, —b—c=—a. If each term is multiplied by — 1, this becomes 54-c—a.

A term which is to be multiplied or divided by all other terms on its side of the
equation can be transposed if it is also moved from the numerator to the denominator,
or vice versa. Thus, if ded then ac=b, c 4 el , En etc. (Note that at.) The
C váða 1

same result could be obtained by multiplying both sides of an equation by the same

changing the value of the fraction. Thus,

quantity. For instance, if both sides of a=, are multiplied by c, the equation becomes

oe and since any number (except zero) divided by itself is unity, =l, and the

equation becomes ac=b, as given above. Note, also, that both sides of an equation can
d i i : : À O Te eri
be inverted without destroying the relationship, for if a=b, EÈ and OU Ap

This is accomplished by transposing all terms of an equation.
Note that in the case of transposition by changing the plus or minus sign, an entire
expression must be changed, and not a part of it. Thus, if a=be+d, a—be=d, but it

1020 APPENDIX O: MATHEMATICS

is not true that a--b—c--d. Similarly, a term to be transposed by reversing its multi-
plication-division relationship must bear that relationship to all other terms on its side `

a
of the equation. That is, if a=bc+d, it is not true that ¿=0+d, or that puc but

a Wé as
ida If a=b(cd+e), then b cd 4- e.

O25. Ratio and proportion.—If the relationship of a to b is the same as that of
1 X A JEN M RT
c to d, this fact can be written a : b :: c : d, or =I Either side of this equation, BF

is called a ratio and the whole equation is called a proportion. When a ratio is given a
: MTS
numerical value, it is often expressed as a decimal or as a percentage. Thus, if DA
(that is, a=1, b=4), the ratio might be expressed as 0.25 or as 25 percent.
Since a ratio is a fraction, it can be handled as any other fraction.

Geometry

026. Definitions.—Geometry is that branch of mathematics dealing with the
properties, relations, and measurement of lines, surfaces, solids, and angles. Plane
geometry deals with plane figures, and solid geometry deals with three-dimensional
figures.

A point, considered mathematically, is a place having position but no extent. It
has no length, breadth, or thickness. A point in motion produces a line, which has
length, but neither breadth nor thickness. A straight or right line is the shortest
distance between two points in space. A line in motion in any direction except along
itself produces a surface, which has length and breadth, but not thickness. A plane
surface or plane is a surface without curvature. A straight line connecting any two
of its points lies wholly within the plane. A plane surface in motion in any direction
except within its plane produces a solid, which has length, breadth, and thickness. Par-
allel lines or surfaces are those which are everywhere equidistant. Perpendicular lines

or surfaces are those which meet at right

angles. A perpendicular may be called a

normal, particularly when it is perpendicular

to the tangent to a curved line or surface
at the point of tangency. All points equi-
distant from the ends of a straight line are
on the perpendicular bisector of that line.
The distance from a point to a line is the
length of the perpendicular between them,
unless some other distance is indicated.

C 027. Angles.—An angle is the inclina-

FIGURE O27a. An angle. tion to each other of two straight lines which

meet at a point. It is measured by the

arc of a circle intercepted between the two lines forming the angle, the center of

the circle being at the point of intersection. Referring to figure O27a, the angle

formed by lines AB and BC, measured by the arc shown, may be designated “angle

B,” “angle ABC,” or “angle CBA”; or by Greek letter (app. B), as “angle a.” The

first method should not be used if there is more than one angle at the point, as at G

in figure O27b. When three letters are used, the middle one should always be that at
the vertex of the angle, as G in figure 027b.

An acute angle is one less than a right angle (909). In figure 027b, angles AGB,
BGC, CGD, DGE, and EGF are all acute angles.

APPENDIX 0: MATHEMATICS 1021

A right angle is one whose sides are perpendicular (909). In figure O27b, angles
AGO, BGD, CGE, and DGF are right angles.

An obtuse angle is one greater than a right angle (90%) but less than a straight
angle (180°). In figure O27b, angles AGD, BGE, and OGF are obtuse angles. Angle
AGF is also obtuse if measured counterclockwise from AG to FG.

A straight angle is one whose sides form a continuous straight line (180°). In
figure O27b, angles AGE and BGF are straight angles.

A reflex angle is one greater than a straight angle (180°) but less than a circle
(360°). In figure O27b, angle AGF is reflex if measured clockwise from AG to FG.
Actually, any two lines meeting at a point form two angles, one less than a straight
angle of 180? (unless exactly a straight angle) and the other greater than a straight
angle (1809).

An oblique angle is any angle not a multiple of 90°.

T'wo angles whose sum is a right angle (90?) are complementary angles, and either
is the complement of the other. In figure O27b, angles AGB and BGO, BGC and
CGD, CGD and DGE, and DGE and EGF are complementary. The angles need not
be adjacent. Angles AGB and DGE, and angles BGC and EGF are complementary.

Two angles whose sum is
a straight angle (1809) are sup- C
plementary angles, and either is D
the supplement of the other.

In figure O27b, angles AGB

and BGE, AGC and CGE, B

AGD and DGE, BGC and CGF,

BGD and DGF, BGE and EGF,

and AGC and DGF are supple-

mentary. A E

Two angles whose sum is a G
circle (360%) are explementary
angles, and either is the exple-
ment of the other. The two
angles formed when any two F
lines terminate at a common Ficure 027b. Acute, right, and obtuse angles.
point are explementary.

Since angles AGB and CGD (fig. O27b) are each complementary to angle BGC,
angles AGB and OGD are equal. Similarly, it can be shown that angle EGF is also
equal to angle CGD (and therefore also equal to angle AGB) and also that angles BGC
and DGE are equal to each other. Since AGO and CGE are both right angles with a
common side, CG is perpendicular to AE. Similarly, DG is perpendicular to BF : If
the sides of one angle are perpendicular to those of another, the two angles are either
equal or supplementary. Also, if the sides of one angle are parallel to those of another,
the two angles are either equal or supplementary. i

When two straight lines intersect, forming four angles, the two opposite angles,
called vertical angles, are equal. Thus, in figure O27b, lines AF and BF intersect at
G. Angles AGB and EGF form a pair of equal acute vertical angles, and B GE and
AGF form a pair of equal obtuse vertical angles. Angles which have the same vertex
and lie on opposite sides of a common side are adjacent angles. Adjacent angles
formed by intersecting lines are supplementary, since each pair of adjacent angles
forms a straight angle (fig. O27b).

A transversal is a line that intersects two or more other lines. If two or more
parallel lines are cut by a transversal, groups of adjacent and vertical angles are formed,

1022 APPENDIX 0: MATHEMATICS

as shown in figure 027c. In this situation, all acute
angles (4) are equal, all obtuse angles (B) are equal,
and each acute angle is supplementary to each
obtuse angle.
AN B A dihedral angle is the angle between two inter-
B\A secting planes.
028. Triangles.—A plane triangle is a closed
Ficure 0270. Angles formed by a figure formed by three straight lines, called sides,
transversal. which meet at three points called vertices (singular
vertex). The vertices are usually labeled with capital letters, and the sides with lower-
case letters, as shown in figure O28a.

An equilateral triangle is one with its three sides equal. An equiangular triangle
is one with its three angles equal. When either of these conditions is present, the
other always is, so that a triangle which is equilateral is also equiangular, and vice
versa.

An isosceles triangle is one with two equal sides, called legs. The angles opposite
the legs are equal. A line which bisects (divides into two equal parts) the unequal
angle of an isosceles triangle is the perpendicular bisector of the opposite side, and
divides the triangle into two equal right triangles.

A scalene triangle is one with no two sides equal. In such a triangle, no two
angles are equal.

An acute triangle is one with three acute angles.

A right triangle is one with a right angle. The side opposite the right angle is
called the hypotenuse. The other two sides may be called legs. A plane triangle can
have only one right angle. B

An obtuse triangle is one with an obtuse angle.

A plane triangle can have only one obtuse angle.

An oblique triangle is one which does not contain
a right angle. C a

The altitude of a triangle is a perpendicular line
from any vertex to the opposite side, extended if
necessary, or the length of this perpendicular line.

A median of a triangle is a line from any vertex A C
to the center of the opposite side. The three medians b
of a triangle meet at a point called the centroid of the Ficure O28a. A triangle.

triangle. This point divides each median into two parts,
that part between the centroid and the vertex being twice as long as the other part.

Lines bisecting the three angles of a triangle meet at a point which is equidistant
from the three sides, and is the center of the inscribed circle, as shown in figure O28b.
This point is of particular interest to navigators because it is the point taken as the fix
when three lines of position of equal weight and having only random errors do not meet
at a common point.

The perpendicular bisectors of the three sides of a triangle meet at a point which is
equidistant from the three vertices, and is the center of the circumscribed circle, the
circle through the three vertices and therefore the smallest circle which can be drawn
enclosing the triangle. The center of a circumscribed circle is within an acute
triangle, on the hypotenuse of a right triangle, and outside an obtuse triangle.

A line connecting the mid points of two sides of a triangle is parallel to the third
side and half as long. Also, a line parallel to one side of a triangle and intersecting the
other two sides divides these sides proportionally. This principle can be used to divide
a line into any number of equal or proportional parts. Refer to figure 028c. Suppose

APPENDIX 0: MATHEMATICS 1023

it is desired to divide line AB into four equal parts. From A draw any line AC. Along
C measure four equal parts of any convenient lengths (AD, DE, EF, and FG). Draw
GB, and through F, E, and D draw lines parallel to GB and intersecting AB. Then
AD’, D'E’, E'F', and F'B are equal and AB is divided into four equal parts.

The sum of the angles of a plane triangle is 180°. Therefore, the sum of the acute
angles of a right triangle is 90°, and the angles are complementary. If one side of a
triangle is extended, the exterior angle thus formed is supplementary to the adjacent
interior angle and, therefore, equal to the sum of the two nonadjacent angles. If two
angles of one triangle are equal to two angles of another triangle, the third angles are
also equal, and the triangles are similar. If the area of one triangle is equal to the area
of another, the triangles are equal. Triangles having equal bases and altitudes have
equal areas. Two figures are congruent if one can be placed over the other to make
an exact fit. Congruent figures are both similar and equal. If any side of one triangle
is equal to any side of a similar triangle, the triangles are congruent. For example,
if two right triangles have equal sides, they are congruent; if two right triangles have
two corresponding sides equal, they are congruent. Triangles are congruent only if the
sides and angles are equal.

The sum of two sides of a plane triangle is always greater than the third side;
their difference is always less than the third side.

A

p<

FIGURE O28b. A circle in-
scribed in a triangle. FIGURE O28c. Dividing a line into equal parts.

If A=area, b=0ne of the legs of a right triangle or the base of any plane triangle,
h=altitude, c=the hypotenuse of a right triangle, a=the other leg of a right triangle,
and S—the sum of the interior angles:

Area of plane triangle: A="

Length of hypotenuse of plane right triangle: c=ya?+b?
Sum of interior angles of plane triangle: S=180°.

029. Polygons.—A polygon is a closed plane figure made up of three or more
straight lines called sides. A polygon with three sides is a triangle, one with four sides
is a quadrilateral, one with five sides is a pentagon, one with six sides is a hexagon,
and one with eight sides is an octagon. An equilateral polygon has equal sides. An
equiangular polygon has equal interior angles. A regular polygon is both equilateral
and equiangular. As the number of sides of a regular polygon increases, the figure
approaches a circle.

A trapezoid is a quadrilateral with one pair of opposite sides parallel and the other
pair not parallel. A parallelogram is a quadrilateral with both pairs of opposite sides
parallel. Any side of a parallelogram, or either of the parallel sides of a trapezoid,
is the base of the figure. The perpendicular distance from the base to the opposite

1024 APPENDIX O: MATHEMATICS

side is the altitude. A rectangle is a parallelogram with four right angles. f (If any
one is a right angle, the other three must be, also.) A square is a rectangle with equal
sides. A rhomboid is a parallelogram with oblique angles. A rhombus is a rhomboid
with equal sides. : j

The sum of the exterior angles of a convex polygon (one having no interior reflex
angles), made by extending each side in one direction only (consistently), is 360°.

A diagonal of a polygon is a straight line connecting any two vertices which are
not adjacent. The diagonals of a parallelogram bisect each other.

The perimeter of a polygon is the sum of the lengths of its sides.

If A=area, s— the side of a square, a=that side of a rectangle adjacent to the base
or that side of a trapezoid parallel to the base, b=the base of a quadrilateral, h=the
altitude of a parallelogram or trapezoid, S=the sum of the angles of a polygon, and
n=the number of sides of a polygon:

Area of square: A=s?
Area of rectangle: A=ab
Area of parallelogram: A=bh

Area of trapezoid: AR

Sum of angles in convex polygon: S— (n—2)180?.

030. Circles.—A circle is a plane, closed curve, all points of which are equidistant
from a point within, called the center (C, fig. O30); or the figure formed by such a curve.
The line forming the circle is called the cir-
cumference. The length of this line is the
perimeter, although the term “circumfer-
ence" is often used with this meaning. An
arc is part of a circumference. A major arc
is more than a semicircle (180%), a minor
arc is less than a semicircle (180%). A semi-
circle is half a circle (180%), a quadrant is
a quarter of a circle (90%), a quintant is a
fifth of a circle (72%), a sextant is a sixth of
a circle (60%), an octant is an eighth of a
circle (45%). Some of these names have been
applied to instruments used by navigators
for measuring altitudes of celestial bodies
because of the part of a circle originally used
for the length of the arc of the instrument.

Ficure 030. Elements of a circle. Concentric circles have a common center.

A radius (plural radii) or semidiameter
is a straight line connecting the center of a circle with any point on its circumfer-
ence. In figure 030, CA, OB, CD, and CE are radii.

A diameter of a circle is a straight line passing through its center and terminating
at opposite sides of the circumference, or two radii in opposite directions (BCD, fig.
O30). It divides a circle into two equal parts. The ratio of the length of the circum-
ference of any circle to the length of its diameter is 3.14159+, or 7 (the Greek letter pr),
a relationship that has many useful applications.

A sector is that part of a circle bounded by two radii and an arc. In figure O30,
BCE, ECA, ACD, BCA, and ECD are sectors. The angle formed by two radii is called
a central angle. Any pair of radii divides a circle into sectors, one less than a semicircle
(180°) and the other greater than a semicircle (unless the two radii form a diameter).

APPENDIX 0: MATHEMATICS 1025

A chord is a straight line connecting any two points on the circumference of a
circle (FG, GN in fig. O30). Chords equidistant from the center of a circle are equal
in length.

A segment is that part of a circle bounded by a chord and the intercepted arc
(FGMF, NGMN in fig. O30). A chord divides a circle into two segments, one less
than a semicircle (180?), and the other greater than a semicircle (unless the chord is a
diameter). A diameter perpendicular to a chord bisects it, its arc, and its segments.
Either pair of vertical angles formed by intersecting chords has a combined number
of degrees equal to the sum of the number of degrees in the two arcs intercepted by
the two angles.

An inscribed angle is one whose vertex is on the circumference of a circle and
whose sides are chords (FGN in fig. O30). It has half as many degrees as the arc it
intercepts. Hence, an angle inscribed in a semicircle is a right angle if its sides ter-
minate at the ends of the diameter forming the semicircle.

A secant of a circle is a line intersecting the circle, or a chord extended beyond
the circumference (KL in fig. O30).

A tangent to a circle is a straight line, in the plane of the circle, which has only one
point in common with the circumference (HJ in fig. O30). A tangent is perpendicular
to the radius at the point of tangency (4 in fig. O30). The two tangents from a point
to opposite sides of a circle are equal in length, and a line from the point to the center
of the circle bisects the angle formed by the two tangents. An angle formed outside a
circle by the intersection of two tangents, a tangent and a secant, or two secants has
half as many degrees as the difference between the two intercepted arcs. An angle
formed by a tangent and a chord, with the apex at the point of tangency, has half as
many degrees as the arc it intercepts. A common tangent is one tangent to more than
one circle. Two circles are tangent to each other if they touch at one point only.
If of different sizes, the smaller circle may be either inside or outside the larger one.

Parallel lines intersecting a circle intercept equal arcs.

If A=area; r=radius; d— diameter; (= circumference; s=linear length of an arc;
«= angular length of an arc, or the angle it subtends at the center of a circle, in degrees;
B— angular length of an arc, or the angle it subtends at the center of a circle, in radians;
rad — radians (art. O38), and sin— sine (art. O39):

2
Area of circle: Aaa

Circumference of circle: C=2rr=rd=2" rad

2 2
nner O IAS.
Area of sector: A= — ES

360090122
E
Area of segment: Aute ie

O31. Polyhedrons.—A polyhedron is a solid having plane sides or faces.

A cube is a polyhedron having six square sides.

A prism is a solid having parallel, similar, equal, plane geometric figures as bases,
and parallelograms as sides. By extension, the term is also applied to a similar solid
having nonparallel bases, and trapezoids or a combination of trapezoids and paral-
lelograms as sides. The axis of a prism is the straight line connecting the centers of its
bases. A right prism is one having bases perpendicular to the axis. The sides of a
right prism are rectangles. A regular prism is a right prism having regular polygons
as bases. The altitude of a prism is the perpendicular distance between the planes of
its bases. In the case of a right prism, it is measured along the axis.

1026 APPENDIX O: MATHEMATICS

A pyramid is a polyhedron having a polygon as one end, the base d and a point, the
apex, as the other; the two ends being connected by a number of triangular sides or
faces. The axis of a pyramid is the straight line connecting the apex and the center of
the base. A right pyramid is one having its base perpendicular to its axis. A regular
pyramid is a right pyramid having a regular polygon as its base. The altitude of a
pyramid is the perpendicular distance from its apex to the plane of its base. A trun-
cated pyramid is that portion of a pyramid between its base and a plane intersecting
all of the faces of the pyramid.

If A=area, s=edge of a cube or slant height of a regular pyramid (from the center
of one side of its base to the apex), V=volume, a=side of a polygon, h=altitude, P=
perimeter of base, n=number of sides of polygon, B=area of base, and r=perpendicular
distance from the center of a side of a polygon to the center of the polygon:

Cube:
Area of each face: A=s*

Total area of all faces: 4=6s?
Volume: V=s?

Regular prism:
Area of each face: A=ah
Total area of all faces: A=Ph= nah
Area of each base: pes
Total area of both bases: A=nar

Volume: V=Bh= =

Regular pyramid:

Area of each face: A=

Total area of all faces: A-UE

Area of base: B=
Bh narh
Volume: lex we

O32. Cylinders.—A cylinder is a solid having two parallel plane bases bounded
by closed congruent curves, and a surface formed by an infinite number of parallel
lines, called elements, connecting similar points on the two curves. A cylinder is
similar to a prism, but with a curved lateral surface, instead of a number of flat sides
connecting the bases. The axis of a cylinder is the straight line connecting the centers
of the bases. A right cylinder is one having bases perpendicular to the axis. A circular
cylinder is one having circular bases. The altitude of a cylinder is the perpendicular
distance between the planes of its bases. The perimeter of a base is the length of the
curve bounding it.

If A=area, P— perimeter of base, h=altitude, r=radius of a circular base, B—
area of base, and V— volume, then for a right circular cylinder:

Lateral area: 4A=Ph=2rrh
Area of each base: B=rr?
Total area, both bases: A=2rrr?
Volume: V= Bh= rrr?h.

APPENDIX 0: MATHEMATICS 1027

033. Cones.—A cone is a solid having a plane base bounded by a closed curve,
and a surface formed by lines, called elements, from every point on the curve to a
common point called the apex. A cone is similar to a pyramid, but with a curved
surface connecting the base and apex, instead of a number of flat sides. The axis of a
cone is the straight line connecting the apex and the center of the base. A right cone
is one having its base perpendicular to its axis. A circular cone is one having a circular
base. The altitude of a cone is the perpendicular distance from its apex to the plane of
its base. A frustum of a cone is
that portion of the cone between G
its base and any parallel plane in- |
tersecting all elements of the cone. F I
A truncated cone is that portion of / |
a cone between its base and any a d |
nonparallel plane which intersects A ,
all elements of the cone but does 7 DE o
not intersect the base. ED F

If A=area, r—radius of base, c-
s=slant height or length of element, /
B=area of base, h=altitude, and /
V=volume, then for a right circular /
cone: /

Lateral area: A= rs /
Area of base: B=rr? /
Slant height: s—4/r?-- À? 7

Bh Th. /
Volume: E 3 /

O34. Conic sections.—Tf a right /
circular cone of indefinite extent is E
intersected by a plane perpendicular
to the axis of the cone (AB, fig.
O34a), the line of intersection of the
plane and the surface of the cone is
& circle, discussed in article O30.

If the intersecting plane of fig-
ure O34a is tilted to some position
such as CD, the intersection is an
ellipse or flattened circle, figure
O34b. The longest diameter of an
ellipse is called its major axis, and
half of this is its semimajor axis, a
The shortest diameter of an ellipse FiavRE O34a. Conic sections.

is called its minor axis, and half of pons
this is its semiminor axis, b. Two points, F and F”, called foci (singular focus) or

focal points, on the major axis are so located that the sum of their distances from e
point P on the curve is equal to the length of the major axis. That is, PF+PF'=

C
(fig. O34b). The eccentricity (e) of an ellipse is equal to “a where c is the distance from

the center to one of the foci (c— CF— CF"). It is always greater than 0 but less than 1.
If the intersecting plane of figure O34a is parallel to one element of the cone, as
at EF, the intersection is a parabola, figure O34c. Any point P on a parabola is equi-

1028 APPENDIX O: MATHEMATICS

"sd

P distant from a fixed point F, called the focus or `

focal point, and a fixed straight line, AB, called the
directrix. Thus, for any point P, PF=PE. The
point midway between the focus F and the directrix
AB is called the vertex, V. The straight line

A

FIGURE 034b. An ellipse.

through F and V is called the axis, CD.
This line is perpendicular to the directrix
AB. The eccentricity (e) of a parabola is 1.
If the elements of the cone of figure
O34a are extended to form a second cone
having the same axis and apex but extending
in the opposite direction, and the intersecting
plane is tilted beyond the position forming a
parabola, so that it intersects both curves,
as at GH, the intersections of the plane with
the cones is a hyperbola, figure O34d. There
are two intersections or branches of a hyper-
bola, as shown. At any point P on either
branch, the difference in the distance from
two fixed points called foci or focal points, B
F and F”, is constant and equal to the short- Ficure 034c. A parabola.

FIGURE 034d. A hyperbola.

est distance between the two branches. That is PF—PF’'=2a (fig. O
distar | = . 034d). T
straight line through F and F’ is called the axis. The eccentricity e uf & MANET

APPENDIX 0: MATHEMATICS 1029

is the ratio S (fig. 034d). It is always greater than 1. Each branch of a hyperbola

approaches ever closer to, but never reaches, a pair of intersecting straight lines, AB
and CD, called asymptotes. These intersect at G.

The various conic sections bear an eccentricity relationship to each other. The
eccentricity of a circle is 0, that of an ellipse is greater than 0 but less than 1, that of a
parabola or straight line (a limiting case of a parabola) is 1, and that of a hyperbola
is greater than 1.

If e=eccentricity, A=area, a=semimajor axis of an ellipse or half the shortest
distance between the two branches of a hyperbola, b=the semiminor axis of an ellipse,
and c=the distance between the center of an ellipse and one of its focal points or the
distance between the focal point of a hyperbola and the intersection of its asymptotes:

Circle:
Eccentricity: e=0
Other relationships given in article 030.

Ellipse:
Area: A— ab

D C
Eccentricity: e= greater than 0, but less than 1.

Parabola:
Eccentricity: e=1.

Hyperbola:

se? €
Eccentricity: e=; greater than 1.

When cones are intersected by some surface other than a plane, as the curved
surface of the earth, the resulting sections do not follow the relationships given above,
the amount of divergence therefrom depending upon the individual circumstances.
Thus, a “hyperbolic” line of position (art. 1109) is not a true hyperbola.

035. Spheres.—A sphere is a solid bounded by a surface every point of which is
equidistant from a point within, called the center. It may be formed by rotating a
circle about any diameter.

A radius or semidiameter of a sphere is a straight line connecting its center with
any point on its surface. A diameter of a sphere is a straight line through its center
and terminated at both ends by the surface of the sphere. The poles of a sphere are
the ends of a diameter.

The intersection of a plane and the surface of a sphere is a circle, a great circle
if the plane passes through the center of the sphere, and a small circle if it does not.
The shorter arc of the great circle between two points on the surface of a sphere is the
shortest distance, on the surface of the sphere, between the points. Every great circle
of a sphere bisects every other great circle of that sphere. The poles of a circle on a
sphere are the extremities of the sphere’s diameter which is perpendicular to the plane
of the circle. All points on the circumference of the circle are equidistant from either
of its poles. In the case of a great circle, both poles are 90° from any point on the cir-
cumference of the circle. Any great circle may be considered a primary, particularly
when it serves as the origin of measurement of a coordinate. The great circles through
its poles are called secondaries. Secondaries are perpendicular to their primary. W

A spherical triangle is the figure formed on the surface of a sphere by the intersection
of three great circles. The lengths of the sides of a spherical triangle are measured in
degrees, minutes, and seconds, as the angular lengths of the arcs forming them. The

1030 APPENDIX 0: MATHEMATICS

sum of the three sides is always less than 360°. The sum of the three angles is always
more than 180° and less than 540°.

A lune is that part of the surface of a sphere bounded by halves of two great circles.

A spheroid is a flattened sphere, which may be formed by rotating an ellipse about
one ofits axes. An oblate spheroid, such as the earth, is formed when an ellipse is rotated
about its minor axis. In this case the diameter along the axis of rotation is less than
the major axis. A prolate spheroid is formed when an ellipse is rotated about its major
axis. In this case the diameter along the axis of rotation is greater than the minor axis.

If A=area, r=radius, d=diameter, and V=volume of a sphere:

Area: A=4rr?=rd*
4rr* ` adi
SEL

If A=area, a=semimajor axis, b=semiminor axis, e=eccentricity, and V=volume

of an oblate spheroid: i

2 6
Area: A=47a? (1-5-5-5)
dE
a?

Volume: V=

Eccentricity: e= R
4ma*b
3

036. Coordinates are magnitudes used to define a position. Many different
types of coordinates are used.

If a position is known to be at a stated point, no magnitudes are needed to identify
the position, although they may be required to locate the point. Thus, if a vessel is
at port A, its position is known if the location of port A is known, but latitude and
longitude may be needed to locate port A.

If a position is known to be on a given line, a single magnitude (coordinate) is
needed to identify the position if an origin is stated or understood. Thus, if a vessel
is known to be south of port B,
it is known to be on a line ex-
tending southward from port B.
If its distance from port B is
known, and the position of port
B is known, the position of the
vessel is uniquely defined.

If a position is known to be
on a given surface, two magni-
tudes (coordinates) are needed
to define the position. Thus, if
a vessel is known to be on the
surface of the earth, its position
can be identified by means of
latitude and longitude. Lati-
tude indicates its angular dis-
tance north or south of the
equator, and longitude its an-
gular distance east or west of
the prime meridian.

If nothing is known regard-
ing a position other than that

Volume: V=

M

Figure O36a. Rectangular coordinates.

APPENDIX 0: MATHEMATICS 1031

it exists in space, three magnitudes (coordinates) are needed to define its position.
Thus, the position of a submarine may be defined by means of latitude, longitude,
and depth below the surface.

Each coordinate requires an origin, either stated or implied. If a position is known
to be on a given plane, it might be defined by means of its distance from each of two
intersecting lines, called axes. Thus, in figure O36a the position of point A can be
defined by stating that it is z units to the right of line OY and y units upward from line
OX. These are called rectangular coordinates. The coordinate along OY is called the
ordinate, and the coordinate along OX is called the abscissa. Point O is the origin, and
lines OX and OY the axes (called the X and Y axes, respectively). Point A is at position
x,y. Ifthe axes are not perpendicular but the lines x and y are drawn parallel to the axes,
oblique coordinates result. Either type are Cartesian coordinates. A three-dimensional
system of Cartesian coordinates, with X, Y, and Z axes, is called space coordinates.

Another system of plane coordinates in common usage consists of the direction
and distance from the origin (called the pole), as shown in figure O36b. A line extending
in the direction indicated is called a radius vector. Direction and distance from a
fixed point constitute polar coordinates, sometimes called the rho- (the Greek p, to
indicate distance) theta (the Greek 6, to indicate di-
rection) system. Navigators more commonly call it
the “bearing-distance” system. An example of its
use is with respect to a radar PPI (art. 1208).

Spherical coordinates are used to define a posi-
tion on the surface of & sphere or spheroid by indi-
cating angular distance from a primary great circle
and a reference secondary great circle. Familiar
examples are latitude and longitude, altitude and
azimuth, and declination and hour angle.

Trigonometry

O37. Definitions.— Trigonometry is that branch ` Fong O36b. Polar coordinates.
of mathematics dealing with the relations among the
angles and sides of triangles. Plane trigonometry is that branch dealing with plane
triangles, and spherical trigonometry is that branch dealing with spherical triangles.

O38. Angular measure.—A circle may be divided into 360 degrees (9), which is
the angular length of its circumference. Each degree may be divided into 60 min-
utes (^), and each minute into 60 seconds (^). The angular length of an arc is usually
expressed in these units. By this system a right angle or quadrant has 90? and a straight
angle or semicircle 180?. In marine navigation, altitudes, latitudes, and longitudes are
usually expressed in degrees, minutes, and tenths (27?14:4). Azimuths are usually
expressed in degrees and tenths (164?7). The system of degrees, minutes, and seconds
indicated above is the sexagesimal system. In the centesimal system, used chiefly in
France, the circle is divided into 400 centesimal degrees (sometimes called grades)
each of which is divided into 100 centesimal minutes of 100 centesimal seconds each.

A radian is the angle subtended at the center of a circle by an arc having a linear
length equal to the radius of the circle. A radian is equal to 5772957795131 approxi-
mately, or 57?17/44'80625 approximately. The radian is sometimes used as a unit
of angular measure. A circle (360?) —2 radians, a semicircle (180%) — radians, a right

angle (90°) =5 radians, 1°=0.0174532925 radians approximately, 1’=0.0002908882

radians approximately, and 1” =0.0000048481 radians approximately.

1032 APPENDIX 0: MATHEMATICS

b

FIGURE 039a. A right triangle.

O39. Trigonometric functions are the various proportions or ratios of the sides of `
a plane right triangle, defined in relation to one of the acute angles. In figure O39a,
A, B, and C are the angles of a plane right triangle, the right angle being at C. The
sides are a, b, c, as shown. The six principal trigonometric functions of angle A are:

e 1 it
sine A=sin pies Oe EL od ae TI
hypotenuse c

side adjacent b

cosine Á= cos A= E

m . Side opposite o
od sid adjacent b
side adjacent b
side opposite a

cotangent A=cot A=

hypotenuse _ c

secant A=sec A aidā adjacent b

hypotenuse c

cosecant A=csc A=- — =.
side opposite a

Certain additional relations are also classed as trigonometric functions:

versed sine A— versine A=vers A— ver A—1— cos A

versed cosine A=coversed sine A=coversine A=covers A—cov A= 1— sin A

haversine A—hav A=% ver A=% (1— cos A).

The numerical value of a trigonometric function is sometimes called the natural
function to distinguish it from the logarithm of the function, called the logarithmic
function. Numerical values of the six principal functions are given at 1” intervals in

table 31. Logarithms are given at the same intervals in table 33. Both natural and
logarithmic haversines are given in table 34.

in figure O39b.
angle A.

APPENDIX 0:

MATHEMATICS

1033

FIGURE 039b. Line definitions of trigonometric functions.

Various functions may be represented by lines associated with a circle, as shown

sin A= GE
cos A=CE
tan A=HF
ver A=EF

The radius of the circle is considered 1.

Angle BDC=angle ECG=

cot A=BD
sec A=CH
csc A=CD
cov A=BJ.

Some relationships apply only to plane trigonometry and others to both

plane and spherical trigonometry. Those which apply to both are called fundamental
identities. Examples are given below.

Of the six principal functions, the second three are the reciprocals of the first

three. Thus,
m a= A
EST A= Ál
tan A=

From figure O39a:

sin B—— cos A

(LV
COS B=¿=sin A

tan FA cot A
a

= A= A
cot A=
cot B—5=tan A

C
sec B=_=es0 A

ese B=7=sec A.

1034 APPENDIX 0: MATHEMATICS

Since A and B are complementary, these relations show that the sine of an angle is the
cosine of its complement, the tangent of an angle is the cotangent of its complement,
and the secant of an angle is the cosecant of its complement. Thus, the co function
of an angle is the function of its complement. i
040. The functions in various quadrants.—The sign (+ or —) of the functions
varies with the quadrant of an angle. This is shown in figure O40a. k In the left-hand
diagram a radius is imagined to rotate in a counterclockwise direction through 360°

90? 000?

2308 180°

Ficure O40a. Trigonometric functions in the four quadrants. Left, mathematical convention; right,
navigational convention.

from the horizontal position at 0°. This is the mathematical convention. In the
right-hand figure this concept is shown in the usual navigational convention of a
compass rose, starting with 000° at the top and rotating clockwise. In either diagram
the angle A between the original position of the radius and its position at any time
increases from 0° to 90° in the first quadrant (I), 90? to 180° in the second quadrant
(II), 180° to 270° in the third quadrant (III), and 270° to 360? in the fourth quadrant
(IV). If the values of a and b are considered positive in the directions they extend in
the first quadrant (upward and to the right) and negative in the opposite directions,
and if ¢ is regarded as always positive, the signs of the functions can be determined
by considering the signs of the sides involved, as shown in the following table:

Functions I II III IV
sine and cosecant + — —
cosine and secant + — — +
tangent and cotangent + — + —
versine, coversine, and haversine 4 i | +

Taste 040a. Signs of trigonometric functions by quadrant.

The numerical values vary as shown in the following table and in figure O40b:

PIP

Functions
sine
cosecant

cosine
secant

tangent
cotangent

versine
coversine

haversine

I

0 to +1

me 071

--1to 0

+1 to +o

Oto + e
+o to 0

0 to 4-1
+1 to 0

APPENDIX 0: MATHEMATICS 1035
II III IV
+1 to 0 0 to —1 —1 to 0
+1 to + © — o to —1 —] to — o
0 to —1 —1 to 0 0 to +1
— œ to —1 —1 to — o +o to +1
— æ to 0 0 to +œ — oc to 0
0 to — x +o to 0 0 to — œ
+1 to +2 +2 to +1 +1 to 0
0 to +1 +1 to +2 +2 to +1
1 1 1

0 to +5

"TABLE O40b. Values of trigonometric functions in various quadrants.

These relationships are shown

graphically in figure O40b.

9 4

MES

Á

— — —

0° 90° 180° 270° 360°

0° 90°

|
|
l

180° 270°

360°

2

Figure 040b. Graphic representation of values of trigonometric functions in various quadrants.

1036 APPENDIX 0: MATHEMATICS

The functions of any angle in the second, third, and fourth quadrants are numeri-
cally equal to the same functions of some angle in the first quadrant, as follows:

Quadrant Corresponding angle in first quadrant
II 180? — angle
III angle— 180?
IV 360? — angle.
45°
60°
AY 1
V
1
302 902 45° 90°
V3 1

FIGURE 040c. Numerical relationship of sides of 30-60 and 45? triangles.

Since the relationships of 30°-60° and 45° right triangles are as shown in figure
040c, certain values of the basic functions can be stated exactly as shown in the follow-
ing table:

Function 30? 46? 60?
sine 5 = m ET "au
cosine EA 43 ns A) 5
tangent a J3 = 1 ie 43
cotangent = V3 i= 1 SCC
secant F V3 V2 T= 2
cosecant = 2 m. 42 E: 48

TABLE O40c. Values of various trigonometric functions for angles of 30°, 45°, and 60°.

vadā

APPENDIX O: MATHEMATICS 1037

041. Inverse trigonometric functions.—The angle having a given trigonometric
function may be indicated in any of several ways. Thus, sin Y=, y—arc sin x, and
y=sin7' x have the same meaning. The superior — 1 is not an exponent in this case.
In each case, y is “the angle whose sine is x.” In this case, y is the inverse sine of x.
Similar relationships hold for all trigonometric functions.

042. Solution of triangles.—A triangle is composed of six parts: three angles and
three sides. The angles may be designated A, B, and C; and the sides opposite these
angles as a, b, and c, respectively. In general, when three parts are known, the other
three parts can be found, unless the known parts are the three angles of a plane triangle.

Right plane triangles.—In a right plane triangle it is only necessary to substitute
numerical values in the appropriate formulas representing the basic trigonometric
functions (art. O39) and solve. Thus, if a and b are known:

tan A=;
B=90%—A
c=a cst A:
Similarly, if c and B are given:
A=90%—B
a=c sin A
b=c cos A.

Oblique plane triangles.—In solving an oblique plane triangle, it is often desirable
to draw a rough sketch of the triangle approximately to scale, as shown in figure 042a.
The following laws are helpful in solving such triangles:

Gee Og ee
sn A sinB sin C

Law of sines:

Law of cosines: a?=b?+c’—2 be cos A.

B

A b C

FIGURE 042a. A plane oblique triangle.

1038 APPENDIX O: MATHEMATICS

PV Kada

The unknown parts of obligue plane triangles can be computed by the formulas of -
table 042a, among others. By reassignment of letters to sides and angles, these
formulas can be used to solve for all unknown parts of oblique plane triangles.

ze
Known To find Formula Comments
ME a =
a, b, c A cos GE per Cosine law
$ b sin A § : :
a, b, A B sin Bs 9n Sine law. Two solutions if b>a
C C—180?— (A+B) A+ B+ C-—180?
asin C g
C A Sine law
asma
Q, b, O A tan RCA
B B=180°—(A+C) A+B+C=180°
asin C ;
c A Sine law
a, A, B b (ee B Sine law
sin A
Q C=180°— (A+B) A+B+C=180°
c e xn Sine law l
TABLE 042a. Formulas for solving oblique plane triangles.
B
a a
C
b
A

FIGURE 042b. Parts of a right spher-
ical triangle as used in Napier's
rules.

APPENDIX 0: MATHEMATICS 1039

FIGURE 042c. Diagram for Napier’s rules.

Right spherical triangles can be solved with the aid of Napier's rules, devised by
John Napier. If the right angle is omitted, the triangle has five parts: two angles and
three sides, as shown in figure O42b. The triangle can be solved if any two parts
are known. If the two sides forming the right angle, and the complements of the other
three parts are used, these elements (called “parts” in the rules) can be arranged in
five sectors of a circle in the same order in which they occur in the triangle, as shown
in figure O42c. Considering any part as the middle part, the two parts nearest it
in the diagram are considered the adjacent parts, and the two farthest from it the
opposite parts. "The rules are:

The sine of a middle part equals the product of (1) the tangents of the adjacent parts
or (2) the cosines of the opposite parts.

In the use of these rules, the co function of a complement can be given as the
function of the element. Thus, the cosine of co-A is the same as the sine of A. From
these rules the following formulas can be derived:

sin a=tan b cot B=sin c sin A
sin b=tan a cot A=sin c sin B
cos c— cot A cot B=cos a cos b
cos A=tan b cot c—cos a sin B
cos B=tan a cot c=cos b sin A.

The following rules apply:

1. An oblique angle and the side opposite are in the same quadrant.

2. Side c (the hypotenuse) is less than 90? when a and 5 are in the same quadrant,
and more than 90? when a and 5 are in different quadrants.

If the known parts are an angle and its opposite side, two solutions are possible.

A quadrantal spherical triangle is one having one side of 90?. A biquadrantal
spherical triangle has two sides of 90?. A triquadrantal spherical triangle has three
sides of 90°. A biquadrantal spherical triangle is isosceles and has two right angles
opposite the 90? sides. A triquadrantal spherical triangle is equilateral, has three right
angles, and bounds an octant (one-eighth) of the surface of the sphere. A quadrantal
spherical triangle can be solved by Napier's rules provided any two elements in addition
to the 90? side are known. The 90? side is omitted and the other parts are arranged
in order in a five-sectored circle, using the complements of the three parts farthest from
the 90? side. In the case of a quadrantal triangle, rule 1 above is used, and rule 2
restated: angle C (the angle opposite the side of 90°) is more than 90° when A and B are
in the same quadrant, and less than 90° when A and B are in different quadrants. If the

1040

APPENDIX O: MATHEMATICS

rule requires an angle of more than 90° and the solution produces an angle of less than
90°, subtract the solved angle from 180°.

Oblique spherical triangles. An oblique spherical triangle can be solved by
dropping a perpendicular from one of the apexes to the opposite side, extended if neces-
sary, to form two right spherical triangles. It can also be solved by the following
formulas, reassigning the letters as necessary.

Comments

cot G=cos A tan be

tan H=tan A cos b

S=% (A+B+C)

tan D=tan a cos C

tan H=tan A cos c

tan F=tan B cos c

Two solutions

Two solutions

Two solutions

cot K=tan B cos a
Two solutions

Two solutions

Known To find Formula
. hav a—hav (b—c)
a, b, c A hay A= sin b sin c
__—cos S cos (S—A)
E * WE sin B sin C
a, b, C c hav c=hav (a~b)+sin a sin b hav C
sin D tan C
A tan A um (6—D)
E SI E BED
B sin Doke RE
c, A, B C cos C=sin A sin B cosc—cos A cos B
t _ tan c sin E
f an asin (BEE)
tan c sin F
b tan UA
b, A C sin (c+ eo aa
SE cos b
; sin A sin b
B sin ini e
O sin (C+H)=sin H tan b cot a
a, A, B D A
cos B
: sin a sin B
b sin DA
c sin (c— M) —cot A tan B sin M

tan M —cos B tan a
Two solutions

TABLE O42b. Formulas for solving oblique spherical triangles.

APPENDIX 0: MATHEMATICS 1041

Calculus

O43. Definitions.—Calculus is that branch of mathematics dealing with the rate
of change of one quantity with respect to another.

A constant is a quantity which does not change. If a vessel is making good a
course of 090°, the latitude does not change and is therefore a constant.

A variable, where continuous, is a quantity which can have an infinite number of
values, although there may be limits to the maximum and minimum. Thus, from lati-
tude 30° to latitude 31° there are an infinite number of latitudes, if infinitesimally small
units are taken, but no value is less than 30? nor more than 31°. If two variables are
so related that for every value of one there is a corresponding value of the other, one of
the values is known as a function of the other. Thus, if speed is constant, the distance
a vessel steams depends upon the elapsed time. Since elapsed time does not depend
upon any other quantity, it is called an independent variable. The distance depends
upon the elapsed time, and therefore is called a dependent variable. If it is required
to find the time needed to travel any given distance at constant speed, distance is the
independent variable and time is the dependent variable.

'The principal processes of calculus are differentiation and integration.

O44. Differentiation is the process of finding the rate of change of one variable
with respect to another. If x is an independent variable, y is a dependent variable, and
y is a function of z, this relationship may be written y=f (x). Since for every value of
z there is a corresponding value of y, the relationship can be plotted as a curve, figure
O44. In this figure, A and B are any two points on the curve, a short distance apart.

Y

Figure O44. Differentiation.

The difference between the value of z at A and at B is Az (delta x), and the correspond-
ing difference in the value of y is Ay (delta y). The straight line through points A and
B is a secant of the curve (art. O30). It represents the rate of change between A and
B, for anywhere along this line the change of y is proportional to the change of z.

1042 APPENDIX O: MATHEMATICS

As B moves closer to A, as shown at B’, both Az and Ay become smaller, but at a
different rate, and z changes. This is indicated by the difference in the slope of the
T

secant. Also, that part of the secant between A and B moves closer to the curve and
becomes a better approximation of it. The limiting case occurs when B reaches A or
is at an infinitesimal distance from it. As the distance becomes infinitesimal, both Ay
and Az become infinitely small, and are designated dy and dz, respectively. The straight
line becomes tangent to the curve, and represents the rate of change, or slope, of the
k "a d O;
curve at that point. This is indicated by the expression r called the derivative of y
with respect to z. ] | Es.

The process of finding the value of the derivative is called differentiation. It
depends upon the ability to connect x and y by an equation. For instance, if y=x",
Y att. 1h»-2,.2-325 and Vr, This is derived as follows: If point A on the

x
curve is z, y; point B can be considered z+ Az, y+Ay. Since the relation y=2? is true
anywhere on the curve, at B:

y+Ay= (z4- Az)*—- z?--2zAz-4- (Ax)?.

Since y=x?, and equal quantities can be subtracted from both sides of an equation
without destroying the equality:

Ay=2xA1x+ (Azx)?.

Dividing by Az: AU —22-- Ax.

As B approaches A, Ar becomes infinitesimally small, approaching 0 as a limit. There-
fore ay approaches 2z as a limit.
This can be demonstrated by means of a numerical example. Let y=z?. Suppose

at A, r=2 and y=4, and at B, x=2.1 and y=4.41. In this case Ar=0.1 and Ay=
0.41, and

From the other side of the equation:

21+Ar=2X2+0.1=4:1:

If Az is 0.01 and Ay is 0.0401, Y 401. If Az is 0.001, AU — 4.001; and if Az is 0.0001,
Ay — NAT a A
AQ, 40001. As Az approaches 0 as a limit, N: approaches 4, which is therefore the

d :
value Bn Therefore, at point A the rate of change of y with respect to z is 4, or y is

increasing in value 4 times as fast as z.

An example of the use of differentiation in navigation is the Ad value in H.O.
Pub. No. 214. This is the change of altitude for a change of 1’ of declination. In this
case, declination is the independent variable, altitude is the dependent variable, and
both meridian angle (H.A.) and latitude are constants. The rate of change at the
tabulated value is desired, so that the table can be entered with the nearest tabulated

APPENDIX 0: MATHEMATICS 1043

value of declination, and interpolation performed in either direction (either larger or
smaller values of declination).

045. Integration is the inverse of differentiation. Unlike the latter, however, it
is not a direct process, but involves the recognition of a mathematical expression as
the differential of a known function. The function sought is the integral of the given
expression. Most functions can be differentiated, but many cannot be integrated.

Integration can be considered the summation of an infinite number of infinitesimally
small quantities, between specified limits. Consider, for instance, the problem of finding
an area below a specified part of a curve for which a mathematical expression can be

Y

AX |AX|AX AX|AX|AX

A D
FIGURE 045. Integration.

written. Suppose it is desired to find the area ABCD of figure 045. If vertical lines
are drawn dividing the area into a number of vertical strips, each Az wide, and if y
is the height of each strip at the midpoint of Az, the area of each strip is approximately
yAz; and the approximate total area of all strips is the sum of the areas of the indi-

r2
vidual strips. This may be written >) yAz, meaning the sum of all yAz values between

x, and z,. The symbol >) is the Greek letter sigma, the equivalent of the English S.
If Az is made progressively smaller, the sum of the small areas becomes ever closer to
the true total area. If Ax becomes infinitely small, the summation expression is written
J. i ydz, the symbol dz denoting an infinitely small Ax. The symbol |, called the

Zi
“integral sign,” is a distorted S.

An expression such as IE ydx is called a definite integral because limits are
T1

specified (x; and z;). If limits are not specified, as in [ves the expression is called

an indefinite integral.

A navigational application of integration is the finding of meridional parts, table 5.
'The rate of change of meridional parts with respect to latitude changes progressively.
The formula given in the explanation of the table is the equivalent of an integral repre-
senting the sum of the meridional parts from the equator to any given latitude.

1044 APPENDIX O: MATHEMATICS

046. Differential equations.—An expression such as dy or dz is called a differential.
An equation involving a differential or a derivative is called a differential equation.

As shown in article 044, if y=2’, - —=2x. Neither dy nor dz is a finite quantity,
but both are limits to which Ay and Az approach as they are made progressively smaller.

Therefore E is merely a ratio, the limiting value of z and not one finite number

divided by another. However, since the ratio is the same as would be obtained by
using finite quantities, it is possible to use the two differentials dy and dxindependently
in certain relationships. Differential equations involve such relationships.

APPENDIX P
INTERPOLATION

P1. Introduction.—If one quantity varies with changing values of a second
quantity, and the mathematical relationship of the two is known, a curve can be
drawn to represent the values of one corresponding to various values of the other.
To find the value of either quantity corresponding to a given value of the other, one
finds that point on the curve defined by the given value, and reads the answer on the
scale relating to the other quantity. 'This assumes, of course, that for each value of
one quantity, there is only one value of the other quantity.

Information of this kind can also be tabulated. Each entry represents one point
on the curve. The finding of a value between tabulated entries is called interpolation.
The extending of tabulated values to find values beyond the limits of the table is called
extrapolation.

Thus, the Nautical Almanac tabulates values of declination of the sun for each
hour of Greenwich mean time. The finding of declination for a time between two
whole hours requires interpolation. Since there is only one entering argument (in this
case GMT), single interpolation is involved.

Table 19 gives the distance traveled in various times at certain speeds. In this
table there are two entering arguments. If both given values are between tabulated
values, double interpolation is needed.

In H.O. Pub. No. 214, azimuth angle varies with a change in any of the three
variables latitude, declination, and meridian angle. With intermediate values of all
three, triple interpolation is needed.

Interpolation can sometimes be avoided. A table having a single entering argu-
ment can be arranged as a critical table. An example is the dip (height of eye) correc-
tion on the inside front cover of the Nautical Almanac. In such a table limiting values
of the entering argument are given. Another way of avoiding interpolation would be
to include every possible entering argument. If this were done for H.O. Pub. No. 214,
interpolation being eliminated for declination only, and assuming declination values
to 0/1, the number of volumes would be increased from nine to more than 5,000. If
interpolation for meridian angle and latitude, to 0/1, were also to be avoided, a total
of more than 1,800,000,000 volumes would be needed. A more practical method is
to select an assumed position to avoid the need for interpolation for two of the vari-
ables. For stars, which change declination slowly, interpolation for the third argu-
ment can be avoided by using values for the declination of each body in the prepara-
tion of the table, as in H.O. Pub. No. 249, volume I. Another way of avoiding inter-
polation is to portray the information graphically. Still another way is to solve the
appropriate equation each time a value is needed.

Notwithstanding all these available devices, the need for interpolation is frequently
encountered in navigation. The person who thoroughly understands it is least likely
to make mistakes in its use.

P2. Single interpolation.— The accurate determination of intermediate values
requires knowledge of the nature of the change between tabulated values. The simplest
relationship is linear, the change in the tabulated value being directly proportional to

1045

1046 APPENDIX P: INTERPOLATION

the change in the entering argument. Thus, if a vessel is proceeding at 15 knots, the
distance traveled is directly proportional to the time, as shown in figure P2a. The
same information might be given in tabular form, as shown in table P2a. Mathemat-
ically, this relationship is written Dote where D is distance in nautical miles, and
t is time in minutes.

In such a table, interpolation can be accomplished by simple proportion. Suppose,
for example, that the distance is desired for a time of 15 minutes. It will be some

Minutes | Miles

= 0 0.0
ið 4 1.0
F 8 2.0
E 12 3.0
= 16 4.0
D | 20 5.0
2 24 6. 0

28 720

32 8.0

TABLE P2a. Table of
TIME IN MINUTES D=

plo

t
FiGURE P2a. Plot of Daa

value between 3.0 and 4.0 miles, because these are the distances for 12 and 16 min-
utes, respectively, the tabulated times on each side of the desired time. The propor-
tion might be formed as follows:

12 3.0
3 D
15|4 dis VE
16 4.0
Aa U
SKD)

r= = =().75 (0.8 to nearest 0.1-mi.)

4
y=3.0+1=3.0+0.8=3.8 mi.

A simple interpolation such as this should be performed mentally. During the
four-minute interval between 12 and 16 minutes, the distance increases 1.0 mile from
3.0 to 4.0 miles. At 15 minutes, % of the interval has elapsed, and so the distance

increases % of 1.0 mile, or 0.75 mile, and is therefore 3.04-0.8—3.8, to the nearest
0.1 mile.

APPENDIX P: INTERPOLATION 1047

This might also have been performed by starting with 16 minutes, as follows:

12 3.0

1514 S
y |1.0
1 Fa
16 4.0
del dë
4.4 41.0

x=(—)0.25 (—0.2 to the nearest 0.1 mi.)
y=4.0—0.2=3.8

Mentally, 15 is one quarter of the way from 16 to 12, and therefore the distance is %
the way between 4.0 and 3.0, or 3.8.
This interpolation might have been performed by noting that if distance changes

1.0 mile in four minutes, it must change 120.1 mile in =04 minute, or 24 seconds.

This relationship can be used for mental interpolation in situations which might seem
to require pencil and paper. Thus, if distance to the nearest 0.1 mile is desired for
132155, the answer is 3.3 miles, determined as follows: The time 13"15* is 115° (172
approx.) more than 12". If 1.2 is divided by 0.4, the quotient is 3, to the nearest whole
number. Therefore, 3X0.1=0.3 is added to 3, the tabulated value for 12 minutes.
Alternatively, 13"15* is 2"45* (278 approx.) less than 16", and 2.8+0.4=7, and
therefore the interpolated value is 7X0.1=0.7 less than 4, the tabulated value for
16™. In either case, the interpolated value is 3.3 miles.

A common mistake in single interpolation is to apply the correction (x) with the
wrong sign, particularly when it should be negative (—). This mistake can be avoided
by always checking to be certain that the interpolated value lies between the two
values used in the interpolation.

When the curve representing the values of a table is a straight line, as in figure
P2a, the process of finding intermediate values in the manner described above is called
linear interpolation. If tabulated values of such a line are exact (not approximations),
as in table P2a, the interpolation can be carried to any degree of precision without

Å : a à 1.5 :
sacrificing accuracy. "Thus, in 21.5 minutes the distance is 5.0 + 7-X 1.0— 5.375 miles.

Similarly, for 29.9364 minutes the distance 1s 7.0 + 9995, 97 4841 miles, a value
which has little or no significance in practical navigation. If one had occasion to find
such a value, it could most easily be done by dividing the time, in minutes, by 4, since
the distance increases at the rate of one mile each four minutes. 'This would be a case
of avoiding interpolation by solving the equation connecting the two quantities. For
a simple relationship such as that involved here, such a solution might be easier than
interpolation.

Many of the tables of navigation are not linear. Consider figure P2b. From
table 29 it is found that for latitude 25? and declination 8?, same name, the variation
of altitude in one minute of time from meridian transit (the altitude factor) is 670
(0/1). For a limited angular distance on each side of the celestial meridian, the change
in altitude is approximately equal to at’, where a is the altitude factor (from table 29)

1048 APPENDIX P: INTERPOLATION

and t is the time in minutes from meridian transit. Figure P2b is the plot of change in
altitude against time. The same information is shown in tabular form in table P2b.

To be strictly accurate in interpolating in such a table, one should consider the
curvature of the line. However, in most navigational tables the points on the curve
selected for tabulation are sufficiently close that the portion of the curve between
entries can be considered a straight line without introducing a significant error.
This is similar to considering the line of position from a celestial observation as a
part of the circle of equal altitude. Thus, to the nearest 0/1, the change of altitude
for 3.4 minutes is 0:94-(0.45«0:7) 20:94-0:3— 1:2. The correct value by solution
of the formula is 1/156. The value for 6.8 minutes is 4/6 by interpolation and 4/624
by computation.

If the direction of curvature of the curve changes between entering arguments,
an erroneous result might be obtained. Thus, in H.O. Pub. No. 214, the tabulated
altitude for latitude 53? and meridian angle 0? is 89%30/0 for declination 52°30’ -
same name, and 89?00:0 for declination 54°00’ same name, the next entry. By

N

Min- | Altitude

utes change

o

a

^

uw

N

CHANGE IN ALTITUDE IN MINUTES

O ADRIANO
PIR WIN ==)
PORMMBORHO

(0) 1 2 3 4 5 6 7 8
TIME IN MINUTES

TABLE P2b. Table of
altitude change — at?,

== ,
FIGURE P2b. Plot of altitude change=at?. where a—0*1

linear interpolation for declination 53? same name the altitude is 89920/0. The correct
value is 90?00:0. Between declination 52°30’ and 53°00’ the altitude increases to
90%00'0 and then decreases as declination increases. Such instances are infrequent in
navigation, and generally occur at a part of the table that is not commonly used, or for
which special provisions are made.

P3. Double interpolation.—In a double-entry table it may be necessary to inter-
polate for each entering argument. "Table P3a is an
Dem extract from table 27 (amplitudes). If one entering
argument is an exact tabulated value, the amplitude

Lat. can be found by single interpolation. For instance, if
215 22?0 latitude is 45? and declination is 2178, amplitude is
à : :
3122+(5X028)=311240%5=3107. However, if nei-
o o o

ther entering argument is a tabulated value, double
E. pe R interpolation is needed. This may be accomplished
H i in any of several ways:

TABLE P3a. Excerpts from
amplitude table.

APPENDIX P: INTERPOLATION 1049

1 "Horizontal method. Use single interpolation for declination for each tabulated
value of latitude, followed by single interpolation for latitude. Suppose latitude is
45°7 and declination is 21°8. First, find the amplitude for latitude 45°, declination

2178, as above, 31°7. Next, repeat the process for latitude 46°: 31°8+($X0°8 )=

32°3. Finally, interpolate between 31°7 and 32?3 for latitude 45?7: 31°7+(0.7X
0°6)=32°1. This is the equivalent of first inserting a new column for declination
21°8, followed by single interpolation in this column, as shown in table P3b.

Declination Declination
Lat. Lat.
21°5 21°8 2220, 2125 MES 22°0
o o o o [0] [0] O o
45 ` 3132 3179 32.0 45 3189 32. 0
45.7 3271 46.7 Sil, O SOL, dl 89.4
46 31. 8 SANS 32.6 46 3178 32. 6

TABLE P3b. “Horizontal” method of double TABLE P3c. “Vertical” method of double
interpolation. interpolation.

2. “Vertical” method. Use single interpolation for latitude for each tabulated
value of declination, followed by single interpolation for declination. Consider the
same example as above. First, find the amplitude for declination 21°5, latitude
45°7:31°2-+ (0°7 X0°6)=31°6. Next, repeat the process for declination 22°0:
32°0-+ (0°7 X 0°6) =32°4. Finally, interpolate between 31°6 and 32°4 for declina-

tion 21%8:3126+(5x028)=3221. This is the equivalent of first inserting a new line

for latitude 4527, followed by single interpolation in this line, as shown in table P3c.

3. Combined method. Select a tabulated “base” value, preferably that nearest the
given tabulated entering arguments. Next, find the correction to be applied, with its
sign, for single interpolation of this base value both horizontally and vertically. Finally,
add these two corrections algebraically and apply the result, in accordance with its
sign, to the base value. In the example given above, the base value is 32°6, for declina-
tion 22°0 (21°8 is nearer 22°0 than 21°5) and latitude 46° (45°7 is nearer 46° than 45°).
The correction for declination is =x (—) 0°8=(—)0°3. The correction for latitude is
023x(=)0%6=(—)0%2. The algebraic sum is (—)0°3-+(—)0°2=(—)0°5. The in-
terpolated value is then 32°6—0°5=32°1. This is the method customarily used by
navigators.

P4. Triple interpolation.—With three entering arguments, the process is similar
to that for double interpolation. It would be possible to perform double interpolation
for the tabulated value on each side of the given value of one argument, and then
interpolate for that argument, but the method would be tedious. The only method
commonly used by navigators is that of selecting a base value and applying corrections.
Suppose, for instance, that the azimuth angle is desired for latitude 41°3, declination
21°9 contrary name, meridian angle 16°6 using H.O. Pub. No. 214. The base value
(lat. 41°, dec. 22°, t 17°) is 162°6. The corrections are

lata 4123: 0.3: (FE) 0315 020
dec. 21%9: 0.2 X (—) 0%1= 070
6911016285 rte oE (04

Total (—) 0°4.

1050 APPENDIX P: INTERPOLATION

The triple interpolated value is 162°6—0°4=162°2. A convenient navigational
form for solving this problem is shown in article 2007 and appendix Q.

P5. Interpolation tables.—A number of frequently used navigation tables are pro-
vided with auxiliary tables to assist in interpolation. Table 32 (Logarithms of Num-
bers) provides columns of “d” (difference between consecutive entries) and auxiliary

:
5

D
VM

‘proportional parts" tables. The auxiliary table for the applicable difference “d” is -

selected and entered with the digit of the additional place in the entering argument.
The value taken from the auxiliary table is added to the base value for the next smaller
number from the main table. Suppose the logarithm (mantissa) for 32747 is desired.
The base value for 3274 is 51508, and “d” is 13. The auxiliary table for 13 is entered
with 7, and the correction is found to be 9. If this is added to 51508, the interpolated
value is found to be 51517. This is the same result that would be obtained by sub-

tracting 51508 from 51521 (the logarithm for 3275) to obtain 13, multiplying this by

0.7, and adding the result (9) to 51508.

Tables 31 and 33 provide the difference between consecutive entries, but no pro-
portional parts tables.

In H.O. Pub. No. 214, Ad and At values are given, with “multiplication tables”
to make the correction. The use of these tables is explained in chapter XX. The Ad
of H.O. Pub. No. 249 (vols. II, III) is similar, except that a sign is given and interpola-
tion is always made from the tabulated value of declination next smaller than the given
value. This table is explained in chapter XXI.

The Nautical Almanac “Increments and Corrections” are interpolation tables for
the hourly entries of GHA and declination. The use of these tables and the interpola-
tion tables of the Air Almanac is explained in chapter XVIII.

The method of table 3 of using additional decimal places is still another form of
interpolation.

P6. Extrapolation.—The extending of a table is usually performed by assuming
that the difference between the last few tabulated entries will continue at the same
rate. This assumption is strictly correct only if the change is truly linear, but in most
tables the assumption provides satisfactory results for a slight extension beyond tabu-
lated values. The extent to which the assumption can be used reliably can often be
determined by noting the last few differences. If the “second differences” (differences
between consecutive differences) are nearly zero, the curve is nearly a straight line,
for a short distance. But if consecutive second differences are appreciable, extrapola-
tion is not reliable. For examples of linear and nonlinear relationships, refer to the
first page of table 33 and compare the tabulated differences of the logarithms of secant
(approximately linear on this page) and sine (nonlinear on this page).

As an example of extrapolation, consider table 27. Suppose the amplitude for lati-
tude 45°, declination 2473 is desired. The last declination entry is 2490. The amplitude
for declination 23°5 is 34°3, and for declination 24°0 it is 3591. The difference is (+)
0°8. Assuming this same difference between declinations 2420 and 24°5, one finds

the value for 24°3 is 35° 1+(5>0%8)=35%6. Below latitude 50° this table is so nearly

linear that extrapolation can be carried to declination 30% without serious error.

For double or triple extrapolation, differences are found as in single interpolation.

P7. General comments As a general rule, the final answer should not be given
to greater precision thari tabulated values. A notable exception to this rule is the
case where tabulated values are known to be exact, as in table P2a. A slight increase
in accuracy can sometimes be attained by retaining one additional place in the solution
until the final answer. Suppose, for instance, that the corrections for triple interpola-
tion are (+)0.2, (+)0.8, and (—)0.3. The total correction is (+)0.2. If the total

APPENDIX P: INTERPOLATION 1051

correction, rounded to tenths, had been obtained from the sum of (+)0.17, (+)0.26,
and (—) 0.34, the correct total would have been (+)0.09=(+)0.1. The retaining of
one additional place may be critical if the correction factors end in 0.5. Thus, in
double interpolation, one correction value might be (-+) 0.15, and the other (—)0.25.
The correct total is (—)0.1. But if the individual differences are rounded to (+)0.2
and (—)0.2, the total is 0.0.

The difference used for establishing the proportion is also a matter subject to
some judgment. Thus, if the latitude is 17%14/6, it might be rounded to 17°2 for
many purposes. Slightly more accurate results can sometimes be obtained by retain-

: S um 14.63; ?
ing the minutes, using "en instead of 0.2. If the difference to be multiplied by this

proportion is small, the increase in accuracy gained by using the more exact value is
small, but if the difference is large, the gain might be considerable. Thus, if the

difference is 0°2, the correction by using either CR or 0.2 is less than 0°05, or 0°0 to

the nearest 0°1. But if the difference is 322, the value by i is 0?8, and the value

by 0.2 is 0?6.

If the tabulated entries involved in an interpolation are all positive or all negative,
the interpolation can be carried out on either a numerical or an algebraic basis. Most
navigators prefer the former, carrying out the interpolation as if all entries were posi-
tive, and giving to the interpolated value the common sign of all entries. When both
positive and negative entries are involved, all differences and corrections should be
on an algebraic basis, and careful attention should be given to signs. Thus, if single
interpolation is to be performed between values of (4-)0.9 and (—)0.4, the difference
is 0.9— (—0.4)—0.94-0.4— 1.3. If the correction is 0.2 of this difference, it is (—) 0.3
if applied to (+)0.9, and (+)0.3 if applied to (—)0.4. In the first case, the inter-
polated value is (+)0.9—0.3=(+)0.6. In the second case, it is (—)0.44-0.3—
(—)0.1. If the correction had been 0.4 of the difference, it would have been (—)0.5
in the first case, and (4-)0.5 in the second. "The interpolated value would have been
(+) 0.9—0.5— (4-)0.4, or (—)0.44-0.5— (4-) 0.1, respectively.

With practice, much of the interpolation used in navigation can be performed
mentally, and is not customarily shown in the work forms. Notable exceptions are
the interpolation for GHA and declination in the almanacs, and interpolation for dec-
lination (and meridian angle and latitude, if used) in H.O. Pub. No. 214.

Because of the variety in methods of interpolation used, solutions by different
persons may differ slightly.

APPENDIX Q
WORK FORMS

The use of standard work forms reduces the probability of mistakes, by relieving
the mind of details taken care of in the forms. It also provides a permanent record
that can be checked, and that improves the appearance of the navigator’s work book.
The best forms to use are those which seem easiest, and provide a solution with the
least probability of mistakes. The forms used throughout this book have been found
effective in teaching navigation. The more commonly used ones are repeated on the
following pages.

The individual navigator may wish to develop his own forms to reflect his own
personal preferences. If the addition of a line or label, or the shifting of position of
some part of a form assists in the avoidance of mistakes, or makes the solution seem
easier, it serves a useful purpose. The mere changing for the sake of change, on the
other hand, may encourage mistakes. The forms of this book are the result of consider-
able thought and the application of logic. The new navigator would do well to start
with them, making changes only as the need arises.

The principal change sometimes made is the placing of a sight reduction form in a
single column so that several observations can be solved in parallel columns. Methods
such as H.O. Pub. No. 214 (Ad only) and H.O. Pub. No. 249 lend themselves readily
to this type solution. A solution by cosine-haversine formula and some of the “short”
methods of chapter XXI do not.

In these forms, and throughout the book, the standard abbreviations and
symbols of appendix A are used.

The best use of a form is to first copy the entire form, then fill in all given or known
information, and then proceed with the solution.

In the forms, entries such as “NS” or “TA” are given to indicate that a label is
needed. Only the applicable label should be used. Where “Local date” or “Gr.
date” appears, the actual date should be used. Zeros are used to indicate the units
to use and, in general, the number of places that should be used. The numbers given
in parentheses are article numbers where an example is given of the solution of a
problem by the use of the form or forms.

1052

APPENDIX Q: WORK FORMS 1053

Mercator Sailing (art. 817)

Course and distance by computation:

L, 00%00/0 NS M, 0000.0 M 000%00/0 EW
L, 00%00'0 NS M; 0000.0 N 00°00/0 EW
| 090010 NS m 000.0 DLo 00%00/0 EW
i | 00010 NS DLo 0000/0 EW
DLo 0000/0 EW log 0.00000
m 000.0 log (—)0.00000
C NS 0090070 EW (tan 0.00000 l sec 0.00000
l 000/0 NS log 0.00000
D 0000.0 mi. log 0.00000
Cn 000°0
Course and distance by traverse table:
L, 00%00/0 NS M, 0000.0 A, 000%00/0 EW
L, 00?00:0 NS M, 0000.0 A, 00%00/0 EW
| 0%00:0 NS m 000.0 DLo 00%00:0 EW
l 00010 NS DLo 0000/0 EW
DLo 0000/0 EW log 0.00000 l D (000°) D (000°)
m 000.0 log (—)0.00000 000.0 000.0 000.0
DLo=m 0. 000 log 0.00000 00.0 000.0 000.0
C NS00°0 EW 0.0 00.0 00.0
Cn 000°0 0.0 0.0 0.0
D 0000.0 mi. 000.0 000.0 000.0

Great-circle Sailing (art. 822)

Course and distance:

^, 00070010 EW D 000%00/0
A, 000°00/0 EW col; 0070010
DLo 000%00/0 EW ¿hav 0.00000 D=coL, 00900:0
L, 00%00/0 NS J cos 0.00000 l sec 0. 00000
L, 00%00/0 NS J cos 0.00000
Pan 3E l hav 0.00000 n hav 0.00000
i 00°00/0 NS n hav 0.00000
D 000%00/0 n hav 0.00000 lese 0.00000
coL, 0070010 n hav 0.00000
D=coL, 009?00:0 n hav (—) 0.00000
n hav 0.00000 l hav 0.00000
Cn 00070 C NS 00%00/0 EW l hav 0.00000
D 0000.0 mi.
Vertex:
L, 00°00/0 NS I cos 0.00000 l cos 0.00000
C NS 00%00/0 EW l sin 0.00000 l cos 0.00000
L, 00%00/0 NS l cos 0.00000 l esc 0.00000
My 000%00'0 EW DLo, 00%00/0 EW l sin 0.00000 l sin 0.00000
D, 00°00/0 l sin 0.00000
D; 0000.0 mi.

1054 APPENDIX Q: WORK FORMS
Points along the great circle:
DLo, 0020070 00°00/0 00°00/0 0090070 00?00:0
l cos DLo,, 0. 00000 0. 00000 0. 00000 0. 00000 0. 00000
l tan L, 0.00000 0. 00000 0. 00000 0. 00000 0. 00000
l tan L, 0. 00000 0. 00000 0. 00000 0. 00000 0. 00000
L, 0090070NS 00%00/0NS 00%00/0NS 00%00/0NS 00°00‘0NS
A, 000%00/0EW 000%00/0EW 000°00/0EW 000%00/0EW 000%00'0EW

=

Correction of Sextant Altitude (arts. 1628-1632)

Solution by Nautical Almanac:

r 000°00/0EW 000%00:0EW 000%00/0EW 000?00:0EW 0009?00:0EW

Jupiter, Saturn,

Sun LL Moon UL Venus, Mars Star
IC 010 IC 010 IC 0/0 IC 0/0
D 0:0 D 0/0 D 0:0 D 0/0
© 00/0 € 00:0 x-P 0:0 x-P 0/0
sum 00/0 0/0 Ur 020 add’l 0/0 sum 0/0 0/0
corr. (+)0:0 add'l 30/0 sum 0/0 0.07 -corr? (+)0:0
hs 00%00'0 sum 00:0 00:0 corr. (+) 0/0 hs 00?00:0
Ho 00%00/0 corr. (+)00'0 hs 00°00/0 Ho 00°00/0
hs 0070010 Ho 000010
Ho 00700'0
Solution by Air Almanac:
Sun UL Moon LL Planet, Star
nid ge p oe TEDL a
KO IC D 1650
D 0’ D 0’ D 0’
R 0’ R 0’ R 0’
SD 00’ SD 00’ sum 0’ 0%
sum 0’ 00’ P2007 corr. (+) 0’
COIT. (+) 00" sum 00’ 0’ hs 00°00’
hs 00°00’ corr, (+) 00’ Ho 00°00’
Ho 00°00’ hs 00°00’
Ho 00°00’
Low altitude observation, sun:
Nautical Almanac Tables 23, 24 Air Almanac
Tangī qe mo dē HO a
IC 0/0 ee 0:009 IO 9 g*pon Y
D 0/0 D 0/0 D 0’
sum 0/0 0/0 sum 0/0 0/0 sum. 0’ 0’
corr. (+)0/0 corr. U0) 0/0 corr. (+) 0’
hs 000 hs 090010 hs 0°00’
hr 090010 hr 0900/0 hr 0°00’
© 00/0 © 00:0 R d
TB 0:0 T 0/0 BAYO! i
sum 0/0 0/0 B 0:0 SD 00'
corr. (+) 0/0 sum 00/0 00/0 sum 00’ 00’
hr ` 0%00/0 corr. E0090! corr. (88:004
Ho 0°00/0 hr 0°00/0 hr 0°00’
Ho ` 0900/0 Ho WM U. 98007

Note: Some corrections may be either (+) or (—). See text if in doubt.

APPENDIX Q: WORK FORMS 1055

Sight Reduction by H.O. Pub. No. 214 (art. 2008)

Solution by Ad only and Nautical Almanac, sun observation:

Local date Sun Aad Oe ER
GMT 00*00*00* Gr. date 00^ 00%00/0NS d IC 0/0
00* 0070070 corr. (+)0/0 (+)0 D 0/0
00™008 090010 d 00°00/0NS © 00:0
GHA 00°00/0 sum 00/0 0/0
ad 00900:0 EW corr. (+)00/0
LHA 00%00/0 hs 00°00/0
t 00°00/0EW Ho 00°00/0
d 00°00/0NS d diff. 0/0
aL 00900/0NS Z NS 00070 EW
ht 00%00/0 Ad (+) 0.00
corr. (+)0/0
He 00°00/0
Ho 00°00/0
a 0.0TA aL 00%00/0NS
Zn 000°0 ax 00%00/0 EW

Sight Reduction by H.O. Pub. No. 249 (art. 2113)

Solution by volume I and Air Almanac:

Local date Name of star + + —
GMT 00°00™00° Gr. date IC 0’

00^00" 000°00’ D 0’

09005 0°00’ R 0’
GHAT 000°00’ sum 0’ 0’
a^ 000°00’ EW corr. (+) 0’
LA 0002004 hs 00°00’
aL 00°00’ NS Ho 00°00’
He 00°00’
Ho 00°00’
a 00 TA aL 00°00’ NS
Zn 000° ar 00°00’ EW
Solution by volume II or III and Air Almanac:
Local date Name of body + P —

GMT 00*00*00* Gr. date IC 0’

00500" 000°00’ D 0’
090085 0°00’ R 0’
GHA 0009?00' sum 0’ 0’

ad 000°00’ EW corr. (+) 0’
LHA 000°00’ hs 00°00’
d 00°00’ NS d diff. 00’ Ho 00°00’
aL 00°00’ NS
ht 00°00’ “qd” (+) 00 Z NS000° EW
corr. | (+)00’
He 00°00’
Ho 00°00’
a OTA aL 00°00’NS

Zn 000° ad 000°00’ EW

1056

APPENDIX Q: WORK FORMS

Sight Reduction by Cosine-Haversine Formula (art. 2109)

Local date Name of body + + —

GMT 00°00700* Gr. date IC 0/0
00^ 000°00/0 D 0/0
007008 090010 x-P 0:0
SHA 00070010 sum 0:0 0:0
GHA 00070070 COIT (+)0:0
ad 00%00:0 EW hs 0070010
LHA 00°00/0 Ho 002000
t 00900:0EW l hav 0. 00000 l sin 0. 00000

aL 00%00/0NS l cos 0. 00000

d 00?00:0NS
0 a

l cos 0. 00000
l hav 0. 00000

l cos 0. 00000
n hav 0. 00000

l sec 0. 00000
l sin 0. 00000

L=d 00°00/0 n hav 0. 00000
z 00%00:0 n hav 0. 00000
Hc 00°00/0
Ho 00%00/0 Z NS 00%00/0 EW
a 0.0TA aL 00%00/0NS
Zn 000°0 ar 00°00'0 EW

Sight Reduction of Polaris Observation (art. 2105)

Solution by Nautical Almanac

Local date Polaris ipo Fee
GMT 00°00700° Gr. date — — IC 0/0
00^ 000°00/0 do 00/0 D 0/0
007008 0°00/0 a, 0:0 Y-P 0:0
GHAT 0007000 @ 0/0 sum — 0/0
A 00°00/0 EW add'l 60/0 corr. (+) 0/0
LHA Y 000°00/0 sum 00/0 00/0 hs 00°00/0
Ho 00°00/0 corr. (+) 00/0 Ho 00°00/0
corr. (+) 00/0
L 00900/0N
Azimuth
Solution by H.O. Pub. No. 214 (art. 2007):
Local date
GMT 00^007»00* Gr. date
00^ 000°00/0
00™00° 090010
GHA 000%00'0
an 00°00‘'0 EW
LHA 00090070 di E
t 0090 EW t diff. 090 Z diff. (+) 0°0 commo o 1
d 00°0 NS d diff. 0°0 Z diff. (+) 0%0 d corr. 0?0
L 00°0 NS L diff. 0?0 Z diff. (+) 0°0 L corr. 0°0
tab. 000°0 sum 090 5 090
corr. (+ ) 0°0 COIT. (+) 090

Z NS000-0 EW
Zn 00070

APPENDIX Q: WORK FORMS

Solution by H.O. Pub. No. 260 or H.O. Pub. No. 261 (art. 2126):
Local date

GMT 005002005 Gr. date
00^ 000%00:0
0000» 0700'0
GHA 000900/0
an 000%00/0EW
LHA 000700/0

t 00%00/0EW diff. for diff. corr. for +
t 0°0070 EW 10™ (+) 00’ 070
d 0°0NS 12 (+)00' 0°0 00’
L 00°0 NS 12 (+)00' 0?0 00'
tab. 000900" sum 00’
corr. (+)0°00’ COIT.
Z NS 000°00’ EW
Zn 000°0

Sunrise, Sunset, Twilight

Solution by Nautical Almanac (arts. 1810, 1811):

L 00°00/0 NS Local date
A 000900/0 EW

Sunrise Sunset
00°NS 0000 00%NS 0000
TI (+)00 TI (+)00
LMT 0000 LMT 0000
dA (+)00 dà (+)00
ZT 0000 ZT 0000
Twilight Twilight

00° NS 0000 00° NS 0000
TI (+)00 DIE (25.00
LMT 0000 LMT 0000
dA (+)00 dA (+)00

ZT 0000 ZT 0000

Solution by Air Almanac (art. 1811):
L 00%00/0 NS Local date

A 00?00:0 EW

Sunrise Sunset

00°NS 0000 002NS 0000

corr. (+) 00 corr. (+) 00

LMT 0000 LMT 0000

dà (+) 00 dA (+) 00
ZT 0000 (sunrise) ZT 0000 (sunset)

dur. (—)00 dur. (4-)00

ZT 0000 (twilight) ZT 0000 (twilight)

1057

(+) 00’

1058

APPENDIX Q: WORK FORMS

Moonrise, Moonset (art. 1812)

Solution by Nautical Almanac:

Moonrise
00°NS 0000 Date
TI (+)00
LMT (G) 0000 Date
009 NS 0000 Date
TI (4)00
LMT (G) 0000 Date
LMT (G) 0000 Date
diff. 00
T II (+)00
LMT (G) 0000 Date
LMT 0000 Date
dà (+)00
ZT 0000 Date

Solution by Air Almanac:

Moonrise

diff. (+)00
00°NS 0000
coris (E )00
LMT (G) 0000
corr. (+)00
LMT 0000

dà (+)00

ZT 0000

L 00900/0 NS Local date
^ 00%00/0 EW

Moonset
00°NS 0000 Date
TI (+)00
LMT (G) 0000 Date
00°NS 0000 Date
TI (+)00
LMT (G) 0000 Date
LMT (G) 0000 Date
diff. 00
T II (+)00
LMT (G) 0000 Date
LMT 0000 Date
d^ (+)00
ZT 0000 Date

L 00?00/0 NS Local date
A 000°00/0 EW

Moonset

diff. (+)00
00°NS 0000
corr. (+)00
LMT (G) 0000
corr. (900
LMT 0000

d^ (+)00

ZT 0000

"joquinu J10N89 uodn Ugy} 19UI81 ‘S[BAIOJUI JOUA-3AY 98 'sjoux ut poods pum uodn paseq ueeq savy SIOQUÁS deur 19YI89M “9061 ‘T 41BNUBL VdUIS :930N

033-203 | 6 I9-I 94 | 961-921 | STI-60I LI
"peonpou A} 8015 TOZ-P8T | 099-0 IS | SZI-SIT | SOI-001 9I
6 gp 1940 6 pesnguo() "93eurep Aniara ‘Avids SUIATIP YIM TUM 9UB9[ JN | SUBOLILME | E8T-L91 | 6 08-2 9v | PII-POT | 66-06 ST
*"eusuro—9! 9jo[duroo BIS ‘UIBO, IM poy JI OI-0SI | 1'9P-S "TP | S0t- 8-18 I
i šā peaidseprm Aq poruedurooos Eege 2 ps p SS SAS EAR SH M
Tre UO a Appius ENN ELT-STT | 698-2238 | ze-e2 | 1/49 | i
“poonpel o10ul [1195 E T d E y
Betz 104314 put OF AYIIQISIA ‘soyoqed UIBOJ ƏM YPM UII04S
8 "0210 4194 8 “SDOUIBJUNO JA : P3219409 VƏS (SIABM u3rq A[[euorjdoox ce JUSTOTA UI104$ | LIT-€0T | 9 3€-S 86 | 3L-P9 £9-99 UI
"peonpoz ANTA
-ISIA pue AAB9UY SI JUN[OL “SHBOIIS
0-07 *S1N990 93RBUIBP 1810990195 9Su9p ÁJ9A UL UMOIQ SI UIBO] Se
Z 0£-0c USIH A "0210 4194 epqe1episuoo “pajooidn JO uo9xXol1q sousivodde oi S948] BOS :S]S919 9183
seem] “pue uo pəvuəədxə urop[og | SUIBUBUIDAO UJIM S9AEM yzy LIDA TUIJOJS NOYM | ZOI-68 | b'Sc-G "FZ | s9-eg | S9-8h KT
x " AYIIQISIA
r SJOOJ WIO1J UMO]Q aa; iii
9 03-21 ‘USI ‘ gonper Agur Avids "got JO sxv94]s 9183 oped
99815 :S1N990 opp [8INJONAIS JUSS | osuap "001 0} SUIBOq BOS {SOAR USTH 3U011S 3uoijg | 88-92 | $ 36-8 0c | v9-2v | 2b-1p 6
"Sq991]Ss poxeur
Ia -[[9M ut UMOTQ ST 1803 :3Jt1purds o3ut
9 *y3n01 AIA y» "pepedurr A[[819ua3 sseis0id :59919 R8231Q 0% ui29q S}S919 Jo Sedpe :t13uo[
H “y3no =k = A yo U9401g S9y9UBIĢ BWS pue s31M L | 1938913 JO SIABM U3IY ÁTOJBISPOJA ey | 9183 (said | $4-c9 | 203-321 Oto | OR 8
"S4891JS
“PUIA JSUICSB ŠUTJIEM ut UI uAO[q 9q 0j Suldoq S9A8M ZUL 9183
319] 99UEJSIS91 {UOTJOUI UL $9904) 9[OU 44 | -4891G UOJ UIBOJ NYA ‘dn sdeoy vag | 9183 WEN | 9IBIMPOJA 19-09 T'ZT-6 EL | 88-08 EEE ELE
"S9 IĻM UI PIB9U Sur[]STu A "ĀBIdS 9IOUI 1919]M KI9A9 97991 929914
g €1-8 ‘ysnoy {UOI}OUI UI S991] jo soqouelq 19318] | sdeoayiyM ‘Juruloy SIABM JIOBIBT 310119 3u01}S | 6+-6€ | 8'$I-8 OI 18-93 16-06: | 9
‘ygno *Áds euros ‘sdvooq1yM Auteur 979910 929914 $
+ 8-4 “9IRISPOJA Y od “ABMS 0) UIZO JB UL S991) [[EUIS | ‘wog 193UO] ZULY “SIABM 9]€J9p0]JAT US9IA US91 T 86-67 10108 vo 61 12-21 G
“234001 S9Y9UB1Ģ peus ‘dn 'sdv909jIqA sno 929910 929910
g ES posie1 soded esoo[ pue 'seAgo] ‘ISNA | -1eurnu :193U0[ Zurur009q "S9ABA [[BUIS | AJBISPON | 99YI9POW 82-07 62-88 SKOÐI t
841-84 ‘SIA "pepuojxo savy 3431] tuor *"SABIIJ1UYA P9199789S 929910 929941q
[^ -9A9A “YIO0QUIS g g-¢ '9]€19po]A -OW quejsuOo UL SIM} [[BUIS ‘SIAVIT | :4891G 0} uo giga “SJO[IABM 931BT ` kulia) epuer | 6131 ES DES? OI-L £
84-0 ‘pad "ƏAOUI 09 uidoq “SuLyvaIq jou 'oous1eod 92991q 9Z991g
I -d11 “UNED ^ £-1 113118 S9UBA 'o[jsni soAv9[ ‘IVJ UO J PULIM | -de Ásst[d JO sjs0l0 :S19[9A8M [[BUIS réie? qusrT | 11-9 o J LÆ 97 med
1 uey} *9A0UI JOU OP S9UBA *S]S91) UIBOJ
0 0 ‘Asses “meo I Seat 'YJ00UIS “101J991P pula S9JBIIPUI UUD IAOUIS | ou ‘savas Jo vouvsvodde ujr^ se[ddr | ure 143rT 1e3g2rT | GTI | 9T60 PT s I
0 0 ‘Weoo "Á[[€91319A SOSTI 940UIS “UE O *JOJITUI OXI[ BIS meso wo | 119pun | 20-00 | TJopun | 1 1əpun 0
399] UI ‘SOAR 99] UI ‘SAAB ($96) moq puooes
9p09 J0 443194 9pon Jo 443194 pue[ uo P9A195g40 8399] A U9S JB p9A19590 5799Y H Uuor]jez 19d wy 19d ydu s}ouy 1oquinu
pue WIL pu? u119 J, -[ue31() w13} Si949U1 110)
Teor3oT S ueureog ma
- -01094191N - -— Au
UOTjezrue210 soo MUYARIZOIPA oods pura Zus DUOA əəds put
[89[30[010999X Doan WO I4 PAH P pur BUSH P PUIM

Sado) ALVIS VAS DNIGNOdSAT4O0
TIVOS LHOAIVAA

U XIGNadddV

HLIM

1059

APPENDIX S
MARITIME POSITIONS

With the 1958 edition, this appendix has been completely revised to reflect changes
in United States Government approved names and to provide ready reference to sources
of additional information about the individual entries. With very few exceptions, the
newly approved names are native names. This revision presented an opportunity to
provide a world-wide listing of such names. Well-known secondary names from older
charts and publications are listed in parentheses, following the approved name. Abbre-
viations have been avoided wherever possible, except for the frequently used Island
(1. or 1), Islands (is. or 1s), and Light (rt), which are usually abbreviated, except when
used as headings.

The appendix contains 25 major headings (ARCTIC REGIONS). Lesser headings,
given in boldface type (Greentand), have been chosen from both political and geographical
subdivisions. Where desirable, a further subdivision is provided by the use of headings
given in capitals and small capitals (srrevmoy (Srnowo max»). Entries preceded by dashes
follow each such capitalized heading, the dashes indicating that such entries are integral
parts of that heading.

All entries appearing in italics (Tue) are listed in H.O. Pub. No. 150, World Port
Index. All entries followed by the abbreviation Lt (Kajartalik: Lt) are listed in the appro-
priate H.O. light list for that area. Coordinates for these two types of entries were
obtained from the above-mentioned publications. The remaining entries and their
coordinates were selected from charts and sailing directions.

Where the larger political subdivision (State or nation) of a port (italic entry) is
not otherwise apparent, this information is included as part of the entry. Because of
changing political boundaries, geographic names or their spellings do not necessarily
reflect recognition by the United States Government of the political status of an entry.

Because some of the newly approved names may not be familiar to all users, both
the approved names and the secondary names are listed in the alphabetical index. For
this reason, the alphabetical index should be used only as an aid to locating entries in
the main listing. Jn all cases the main listing should be referred to for positive identi-
fication of the desired position and the approved name.

The index has been extensively cross-indexed, particularly in the case_of trans-
literated and hyphenated names. In some instances strict alphabetization has been
sacrificed in the interest of logic. For example, spain, east coast and Spain, north coast are followed
by Spain, south coast, rather than by Spain, Port-of-.

Each entry in the alphabetical index is identified by a four- or five-digit number
corresponding to the numerical sequence in the main listing. Where two or more
alphabetical entries possess identical or similar names, the general location is provided
in parentheses, following the entry. Thus the user may easily distinguish between
Aberdeen (Scotland) and Aberdeen (Washington).

Entries are listed in the following geographical arrangement.

; Page Page
ATCH CA REGIONS sa de lo eed 1061 [Red Sea T L.T ME He 1088
East Coast of North America___________ 1063 | Islands of the Indian Ocean____________ 1088
West Coast of North America _________. 1067 mouths Coast of Asia - 1089
SE GE TAR E EIN Y SURE 1069.-|-Indonesiacee— — ME. RC EIN 1090
ERIC eee a, 1070 i
East Coast of South America- 1071 Pid ce Bl 4. MI CUm wie
West Coast of South America... 1078 New 7 la id Ki 7 ei ira Ge
Islands of the Atlantic Oeean. 1073 o El ja m 7r 1094
British Tales. als o MM 1074 East Coast OMASI SF Z] 1094
West Coast of Europe_.__._.____.____. 1076 |. Japane:- Eta cd - Ne e 1096
Mediterranean and Black Sea. 1081. | Philippines |o EN 1098
West Coast of Afra. sāga eee 1086 | Lesser Islands of the Pacific... 1099
East Ooastiof Africa. EL 4)... 90 M 1087. FAntarctica e CEA d MN 1100

1060

Greenland

Kap; Morris: Jesup Putre t Zog
Dragon Points c x. tt
KAPSTANO <= <<.
EE
Thank God Harbor _ : |
Kap Dryanss focos wa e
Kapi TROÉSODEA M E

Kap Parry ME E
Th

Kap York
Kapi Melville. eege a
LEE crt c
render. ees

Godlhann, Disko m 339€ 222 Le ae
EE

ee 8
Holsteinsborg te. settes M_L
Camp Lloyd, Sondre Strom-
fjord
ESOO i o e
O some
Godthaab I 22-6 c pte
ieringehapon IL Alea 4. (LE
EE ee
Ravns Storo Havns.............
rrederikshaab P 2397 TS BS 1,

Sydprģven (South Próven). - -----
Nanortalik
edema EC ecco a
Kap Farvel (Cape Farewell)....
Igalalik I., Prince Christian

IKaptiBill6 tās LE mm
Kap dels Peak Seeerei E
Kap D VONOED == hs ass Si
Dannebrogs Ø (Kivdlak I:

Angmagssalik .
Kap Irminger
Rignys Bjerg (Mount Rigney) --
Kap-Brewstert56.—: EE,
ISconesbysumd--- eec
Kap Wardlaw i-s -SLA
Bontekoe Z i ss css E IRE
RIMON GS S. ole IE A tn
pille Pendulum 13 Æ x
Nanok, Fangst Station-----------
KapibhilipiBroke-----------.-—
Kap EE Ies.
Nordostrundingen (Northeast
Foreland) 5-04... eee avons

Jan Mayen Isiand

Sørkapp (South Cape)..........
Nordaustkapp (Northeast Cape).

Iceland

Dyrhólaey (Portland): Lt......-
Vestmannaeyjar, Stórhofdhi: Lt-
Eyrarbakki

Reykjanes: Lt S
Gardhskagi (Skagi): Lt.-----..-
Keflavik ME ie ao A
Reykjavik____-
Malarrif: Lt
Eeer eege,
Bjaretangar lio EE
Bvalvorar io este
Straumnes RE

100
anos

ALAS GE
HO D GOD O

838388

SERBÉBEBEPESS

naD
oooo

mew

APPENDIX S

MARITIME POSITIONS

ARCTIC REGIONS

R3 OG 99) mo dO "2
ZZZZZZZZZZZZZZZZZ ZZZZZZZZZZZZZZZZZZZZZZZ

DO V NO D

00 00 O5 00 00 W OD O0» 6r t5 GO

e
Ó
Z ZZZZZZZZZZZZZ ZZZZZ

HORDOKR AO

ETRE HARTA AAA

En En CN OO OA EN OND DDD A ER ER CR CD N Gm Gu
&3 E E: E168 EQ CA £n 3 DR DONA OD Sd S o

i OV P Hu WO ur A D1 +

KEES

wor

Iceland— Continued

Hornbjarg Lt —— 8 ae
Gjögur tiee se-
Skagatá: Lt....-
Saudhanes: Lt...

Matoys Z Des
Raudhinüpur: Lt..
Raufarhófn: Lt.....

Papey: WEE

Faeroe Islands

Sudhuroy (Sydero), Sunnbóur

(Sumbo): Lt
Nolsoy, Kabelen: Lt...
STREYMOY (STROMO ISL:
--Trshatn E € pats

Kongshavn, Eysturoy (Ostero I.).
Kallsoy, Sydhradalur: Lt.......
Mykines (Myggenaes),

kinesbygd JL tie 22... 27222

Svalbard

VESTSPITSBERGEN (WEST SPITS-
BERGEN)
== Spedgruia A ers
—Kapp Martin, Bellsund: Lt. -
—Isfjord, Kapp Linné: Lt......
BUCEO ete eee ee
—Longyearbyen___-
—Ny-Alesund
Prins Karls Forland, Fugle-
hüken E se ee
Austervāg, Bjørnøya (Bear I.

USSR

Pechenga (Petsamonvuono) - -----
Mys Nemetskiy (Majakkanie-

mi): Lt
Mys Tsyp-Navolok: Lt...
Mys Set'-Navolok: Lt.....
Murmansk

Mys Svyatoy Nos: Lt.
Mys Malyy Gorodetskiy: Lt...
Mys Orlovs Listom ester. T
Ostrov Sosnovets: Lt...

Foret Ee e N
Arkhangel’sk (Archangel) - -------
Mys Zimnegorskiy (Zimnie):

Mys Voronova Lt........-
Ostrov Morzhovets: Lt.........
Mys Tolstik (Konushin):
Mys KaniniNos: Iin eee
Ostrov Kolguyev (Kolguey I.),
N. extremity: Lt
Zemlya Frantsa-Iosifa (Franz
Josef Land), Ostrov Vil’cheka_
NOVAYA ZEMLYA
—Mys Chernyy Nos: Lt-------
—Mys Severnyy Gusinyy Nos:

65

ep op een ch e

SEREOOSSSSS
GROSS NSESg2Ssh-

ZZZZZZZZZZZZZZZZ

1061

Inde
No Place Lat. Long. ES Place Lat. Long.

un
a
SY A c Cu 020r WaAWanmadenh |

4444444444442444

NI ODIO QQ
E Cc m4 WP
O oben QO
= ¿333 42

58 30 E
53 20 E

51 51 E
53 56 E

1062

APPENDIX S
MARITIME POSITIONS

ARCTIC REGIONS— Continued

Des Place Lat. Long. Index Place Lat.
USSR— Continued d > Northwest Territories—Cont. Lai
o o
2940 | —Mys Zhelaniya: Lt........... 76 59 N 68 30 E 3820 | Somerset I., Port Leopold. ..... 73 50 N
950 | —Ostrova Pakhtusova: Lt...... 74 AN 59 08 E 3900 | DEVON ISLAND
960 | —Mys Vykhodnoy (Cape Vuik- 910 | —Graham Harbor............... 74 30 N
hodnoi)s Lt cose. ose K 7314 N 56 42 E 920 | —Dundas Harbor...............| 7432 N
970 | —Mys Men'shikova: Lt........ 70 42 N 57 36 E 4000 | Axel Heiberg I., Hyperite Point.| 78 08 N
3000 | Khodovarikha Sopka, Mys 4100 | ELLESMERE ISLAND
Russki Zavarot: Lt- ase- 68 55 N 53 39 E 110, | —Slidre Bag. e TEC 79 59 N
010 | Mys Greben”, Proliv Yugorskiy 120 | —Eureka: Weather Station..... 80 00 N
Shar (Yugorski Strait): Lt....| 69 40 N 59 59 E 13007 — Ward Hunt TV — E 83 05 N
020 | Ostrov Vaygach, Ostrov Kolyu- 140 | — Alert: Weather Station....... 82 30 N
balances crac 70 15N 58 20 E 150 | —Cape Sheridan____---_-------- 82 28 N
0307|- Bolvanskiy Nos: LE ees EE 70 27N 59 04 E 160 | —Fort Conger, Discovery Har-
040 | Ostrov Belyy (Byeli I.): Lt___-- 73 22 N 70 03 E DORA eee r= gain. 3 RE INE
050 | Ostrov Shokal'skogo, Obskaya 1705 = Gape Bara S TN 81 31N
Guba (Gulf of Ob): Lt........ 72 59 N 74 22 E 1805! Cape) Sabines: ¿22:20 X 78 44 N
060 | Ostrov Dikson (Dickson) ........- 73 30 N 80 25 E 19044 —Craig Harbor: 5... ca S 76 12N
070 | Ostrov Sverdrup: Lt--.......... 7431N 79 32 E 4200 | Coburg I., Cape Spencer........ 75 54 N
080 | Ostrova Izvestiy Tsik: Lt....... 75 53 N 83 17 E 210% Bylot T ¡Cape Hay... ==. 73 51 N
0009 Ostrov EE Die eem 77 10 N 96 26 E 4300 | BAFFIN ISLAND
3100 Mes Chelyuskin: Lt........... 7742 N | 104 38 E 310 | —Arctic Bay: Weather Station.| 73 00 N
MON OStioy+Kotelnyy... coca ae 0 N | 139 00 E 82014 — Pond) Inid.—— — ee 72 45N
120 | Mys Shelagskiy: Lt 170 24 E 3302] = Riven Giyde--—--— ——- — 70 22N
190 Mys Billingsa theses Oe 176 08 E 340 | —Padloping I.: Weather Sta-
140 | Ostrov Vrangelya (Wrangel I.)_| 71 15 N | 179 00 W tion: ¿ARAS m 67 06 N
1505 Mys Uelen stase a eee ree 66 09N | 169 41 W 860. RR E EE 66 40 N
160 | Mys Dezhneva, Bering Strait: 360 | —Cape Mercy.................- 65 02N
116221 S a 001.00 et ---| 66 01 N | 169 43 W 370 | —Pangnirtung..--.------------- 66 06 N
170 | Ostrov Ratmanova (Big Dio- 380 | —Cape Murchison.............. 63 18 N 64 0
mede E). AM CR 65 50 N | 169 06 W 390 | —Frobisher Bay, Koojesse In-
Asu, eee idea rate EE 63 44 N
3200 Alaska UDSON STRAIT
20 410/| —Resolution 17: Ltzi_- re < 61 18 N
3210 | Cape Prince of Wales: Lt... 65 36 N | 168 05 W 4201 — Lake arb of 2 === SE 62 48 N
220 | Cape Espenberg: Lt-------.---- 66 35 N | 163 40 W 430 | —Big L, Rabbit L: Lt ==) 62.32/N
9201 Decning ec Eech 162 44 W AAO) — Dorset eee e 64 15 N
240 | Kotzebwe___________ 162 35 W 450 | —King Charles Cape........... 64 14 N

166 46 W 4500 | BAFFIN ISLAND

160 00 W 510 | —Cape Dorchester..... ANE EE.
156 47 W 520 | —Cape Hallowell......

530 | —Cape Kater...

3300 Yukon Territory Ze GE PER

- 620 | Pelly Bay: Mission
8310.) Herschel Tae == ee eee 69 35 N | 139 05 W 630 | Cape Englefield-

640 | Igloolik: Mission

250 | Point Hope: Lt...
260 | Wainwright...
2705 dE Neue NI NR ee

3400 Northwest Territories 650 | Cape Penya ec MAN
34101] Kitligazuit! REPEAT T e 69 21 N | 133 43 W 4700
420 | Port Brabant (Tuktoyatuk)....| 69 26 N | 133 02 W reper e
4301 Cape Bathurst... IEM 70 36 N | 128 00 W 4800 | SOUTHAMPTON ISLAND
440 Cape Parry- e cxi Cd 7012N | 124 33 W 8101 —Seahorse Point? "C0 2s 63 46 N
ADO Pearce Ront rar SAn ERES 69 55 N | 122 45 W 820 | —Coral Harbor, N. W. T__.._.. 64 06 N
4601 Cape) Bexley ces. RT Xu 69 03 N | 116 00 W 4900 | Chesterfield Inlet: Lt. 63 20 N
ATOM COPDENTUINC case INĀ 67 48 N | 115 03 W 910 | Churchill, Manitoba____________- 58 47 N
480 | Cape Alexander... aad 68 56 N | 106 11 W $20 | Port Nelson, Manitoba 57 08 N
3500 | BANKS ISLAND 930 | Moosonee, Ontario ð TRA 51.17 N
510 | —Cape Kellett 72 02 N | 125 40 W 940 | Charlton Depot, N. W. T... 52 02 N
520 | —Sachs Harbor... 71 56N | 124 40 W 950 | Port Harrison, N. W. T.........| 58 28 N
530 | —Nelson Head 71 03 N | 122 30 W || 960 | Smith T., N. W. T ----| 60.44 N
3600 | Victoria I., Cambridge Bay: 970 | Coats I.: Lt... 62 10 N
Weather Station. ............. 69 07 N |10501 W | 980| ManselL: Lt 62 27 N
EN King Wilian alos Haven...| 68 38 N 95455. W ||. 4035 96 7 VERI
rince of Wales Lol. wd 72 30 N 99 00 W i
630 MR WEE Harbor..... 74 47 N | 110 48 W M Web rr
640 rince Patrick I., Mould Bay: 5010 | Digges Is.: Lt...
Weather Station.............. 76 17 119 28 W 020 Nottingham TE 63 06 N
3700 | RINGNES ISLANDS 030 | Charles I., Cape Moses Oates:
R SR tici m di [sis 78 30 N 101 00 W lib E 62 36 N
—Isachsen: Weather Station....| 78 47 N | 103 32 W 040 | Wakeham Bay, Quebec.
3800 | Bathurst I., Cape Cockburn....| 75 04 N | 100 22 W 050 | Cape ee RT TP m m N
810 | Cornwallis I., Resolute Bay: 060 | Fort Chimo, Quebec ES 0s N

Weather Station S 74 43 N 94 59 W 0701 ‘Cape Chidley, can 60 26 N

ex
ao

at $556 SHEERS SSSS

3588

44454444425

APPENDIX S
MARITIME POSITIONS

EAST COAST OF NORTH AMERICA

1063

EIS leca Let. | Longin] dex Place Lat. | Long.
6000 Labrador ; W Newfoundland—Continued ais rq
eos Urm c c Roe e 12N 62 38 W 6800 | Ferryland Head: Lt............ 47 01 N 52 52 W

MET I OEA SS eren 29 N 61 47 W 810 | Cape Race: Lt 46 39 N 53 05 W
ON A 33 N 61 41 W 820 || Trepasseyo== 2222 46 44 N | 53 24 W
AURA E io sees eee rene 28 N 61 11 W 830 | Cape Pine: Lt 46 37 N 53 33 W
050 | Cape Harrigan: Lt, 51 N 60 19 W 840 | Point la Haye: Lt... 46 54 N 53 37 W
060 | Napakataktalik (Manuel 850 | Cape St. Marys: Lt... 46 49 N 54 12 W
Jat Oe e aS new nine ine 32 N 60 14 W 860 | Point Verde: Lt 4714N | 5401 W
OrOsVETopedales «€. o 27N 60 12 W 3101 Placentia: Tunn 47 15 N 53 58 W
080 | “‘Rikkerasuk T.: itz oes oe. 20 N 59 43 W 880 | Latine Point: Lt... 47 19N 54 01 W
0905! Cut Throat T.:- Dt. =--===222 29 N 57 06 W 890% Argenti me! 47 18N 58 59 W
6100 | Goose Bay Narrows: Lt........ 27N 59 57 W 69007 BOT: Lipa see 47 21 N 54 00 W
TIO Terrington SP Jar ansin, "< 21 N 60 24 W 910 | Marticot I.: Lt.- 47 19N 54 35 W
120 | Packs Harbor: Lt......... 62N 56 59 W 9203 ron IS IUe eto EE 47 03 N 55 08 W
KOA WOON OT IGN Sess nonton 42N 57 02 W 930 | Dodding Head, Burin I.: Lt....| 47 00 N | 55 09 W
140"| ‘Cape North: Lt:--../..: 46 N 56 26 W S40 Buri ss dere deso cias 47 03 N 55 10 W
"aga WihitesPoint: lifosedzseezseoceede 35 N 56 01 W 950 | St. Lawrence Harbors, Middle
Tao" VÐomino Roinnt E EE 28 N 55 44W Head; LA Sr E 46 54 N 55 21 W
170 | Double I., Battle Harbor: Lt...| 52 15 N 55 33 W 960 | Lamaline Bay, Allan I.: Lt..... 46 51 N 55 48 W
1804 VA mour Points ebe 5127 N 56 51 W 90107 Green b DU ductos aaa 46 52 N 56 05 W
6200 Newfoundland 7000 | St. Pierre and Miquelon Islands
6210 | Belle Isle, South Point: Lt..... 51 53 N 55122 WV MOI I Ee -46 47 N 56 11 W
ZV 3Eloywens Mei EEN 51 18 N 56 45 W 0201 Gallantry, Head: Lt ca 46 46 N 56 10 W
230 | Cape Norman: Lt s2msssn 51 38 N 55 54 W EE 46 49 N 56 25 W
240” Capa Bauld Et: oSI. E 51 38 N 55 25 W 040.) Cape Blanci D "122222 47 06 N 56 25 W
250 | Saint Anthony - --------- E5129 N 55 35 W
2607] Fox Point:JLt-2..----.-.- OU 20N 55 33 W 7100 Newfoundland
270% Cape Box tee oia SDOT 52 NI 55 54
280 Bell Creve LA sa. To 50 42 N 55 37 W 7108 Orand Bank eee eicere 47 06 N 55 45 W
290 | Canada Bay, White Point: Lt__| 50 43 N 56 06 W 1205 Garnish Lib. 00-10 EI B 47 14N 55 22 W
6300 | Orange Bay (Great Harbor 130 | Long Harbor Point: Lt......... 47 34 N 55 08 W
IS PE 50 23 N 56 23 W 1407 St. Jacques [10922 m See 47 28N 55 25 W
310 | Western Arm (Western Cove) ....| 49 47 N 56 37 W 150 | Brunette I., Mercer Head: Lt..| 47 15N 55 53 W
320 | Partridge Point: Lt_-.----------| 50 10 N 56 09 W ICON Pass ELA tee => o ore e ERE 47 29 N 56 12 W
380") Bale (Bay) Verte 22212202202 49 57 N 56 10 W 1700 Cape La Hune: Lt--— 47 32 N 56 52 W
340 | Saint Barbe (Horse) Is.: Lt..... 50 12 N 55 44 W 1807 “Penguin ls: Dt- 2.22 2-9 47 23 N 56 59 W
DO ascii ass sc S SS. | 49 58 N 55 36 W 1005 SEH EE AE 47 31 N 57 25 W
Egor Gull Tete. dunt 50 00 N 55 22 W 7200 | Burgeo Is., Boar I.: Lt......... 47 36 N 57 36 W
870 Nippers Ts.: Lre 49 47 N 55 50 W 210 Ireland FLN. 47 38 N 58 22 W
380 | Little Bay I.: Lt 49 38 N 55 46 W 220 | Rose Blanche Head: Lt......... 47 36 N 58 42 W
SOU GIRO CA LSS een 49 41 N 55 42 W 2300 Edi Anz Basques n ee A 34 N 59 08 W
6400 | Long I., Southern Head: Lt....| 49 36 N 55 35 W 2404 (Cape EE 37 N 59 18 W
410 | Leading ‘Tickles: Lt.-.--------2- 49 30 N 55 24 W 250 | Cape Anguille: Lt 54 N 59 25
420 | Fortune Harbor: Lt............| 49 32 N 55 14 W 260 | St. Georges---------- 26 N 58 30 W
4307) Botond SE 2. 303-5 ---| 49 09 N 55 20 W 270 | Indian Head: Lt 30 N 58 31 W
440 | Surgeon Cove Point: Lt --.| 49 31 ` 2» K Ww R Ee Pond at N ES i w
ABOS beuisDortece- cen ---1 49 15 5 ca Wit cce
460 Twillingate (Toulinguet) --......| 49 40 N 54 47 W 78008 Ong Point lbs. ee 47 N R A V
470 | Bacalhao (Bacchalhao) I.: Lt...| 49 41 N 54 34W 310 | Port Au Port (Aguathuna) 34 se
4807 Togo: ae’ Ss 1.5 L6 a Z 49 44 N 54 16 W 320 | Little Port Head: Lt.. 49 07 N 58 25
490 | Brooks Point, Joe Batts Point: 330 | Frenchman Head: Lt_ 49 03 N 58 09 Y
quisque dane SB Te eS eee A B 49 45 N 54 09 W 3401 /CormerzBrook — -------...- 48 57 N 57 57 >
6500 | Little Fogo I.: Lt__.....-- ---1449N 54 05 W 350 | Lobster Cove Head: Lt... 49 36 N n e d
EE -..| 49 35 N 54 11 W 360 | Cow Head Harbor: Lt.....--.-- 49 55 N a SE
SE EE -|4927N 54 23 W 370 Keppel E qi 0 50 38 e eens
580 | Offer Wadham I.: Lt_---- -.| 49 36 N 53 46 W 380 | Riche Point: Lt----- 50 42 HELL
40m) Peektordu. Dt --| 49 32 N 58 51 W 3009 Eerola Roinnt: It w ` === 51 01 N
S60 Pengwin T SL rrr -| 49 27N 53 49 W
560 | Cabot (Stinking) I.: Lt... E 2 V N 3 1 x 7400 Quebec
TON VEINS teuer = 5 5 12N 57 11 W
adi Tit Denier 15 Bn N Wl Eech Se i
i dE
590 | King's Cove: D — --| 48 35 N a a M 430 | St. Mary Is.: 50 18 N 59 39 W
KO EE Li- ------- Ss E ES N 5 03 W 440 Canon y D la, Cormorant be
-------------------- == DIE Jee
EE -| 48 30 N | 53 03 W 450 | Natashquan Point: Lt. 50 05 N | 61 44 W
ESO E Ty 101 ee -| 48 22N | 53 22 W 4 k 50 12N | 63 34 W
SV ERES Ti AE NUM 48 14 N | 53 27 W 460 | Walrus I. (Ile au Marteau): Lt. SOL NUM GS 195
650 | Random I., Motion I.: Lt...... 48 06 N | 53 33 W 470 | Havre-St.-Pierre_---------------- $0 13N | 6412 W
660 | Hopeall Head: Lt N | 53 34 W 480 | Perroquet L.: Lt--.-------------
670 | Jeans Head: Lt N | 5322 W || 7500 | Anticosti ISLAND N | 6409 W
6809]! Perliean IS db sense == c. N |) 63 01 W 510 | —Cap de Rabast: Lt Á N | 6257 W
690 | Baccalieu I., North Point: Lt.. N 52 48 W 520 | —Carleton Point: Lt IN SE
6700 | Carbonear I.: Lt--------------- N | 5310W 530 | —Table Head: Lt 5N | 61 42 W
710.1 Harbor Grace. ..-.:-.--:::l.--.1. 47 41 N 53 13 W 540 | —Heath Point: Lt....... AN 62 16 W
7207 Bay oberts eerte ei 47 36 N | 53 15 W 550 | —Bagot Bluff: Lt-------------- 49 23 N | 63 36 W |
730 | Brigus Bay, North Head: Lt...| 47 33 N 59012: Wi 560 SE Pointa dee ON 64 21 W
740' Salmon Cove Point: Lt...--.-.- 47 28 N 53 10 W 570 R ort UR TE E Ak, 64 32 W
TD APA ED Rp ANT I eee 47 87 N 52 56 W 080 West Point: eege
EN Lloret Erancis guess sess. ae 47 48N | 52 48 W ti Em E Nen B) | 50. 12 N | 66 23 W
EN GO dl ari Ape dalās šai nd P A N 5 En ud 60 Ly Is., Carrousel L: Lt....| 50 05 N | 66 23 W
AAA Mi 7 4 5
700 Bull Head, Bay BIS 47 19 N 52 45 W 630 | —Pointe des Monts: Lt 49 20 N 67 22

— LS

1064

APPENDIX S
MARITIME POSITIONS

EAST COAST OF NORTH AMERICA-—Continued

indes Place Lat. Long. ee Place Lat. Long.
Quebec—Continued Cape Breton Island—Cont.
o + o + o Li o ,
7640 | —Baie-Comeau...--.------------ 49 14N 68 08 W GELIES 46 54 N 60 28 W
650-| —Quebec-.--------- 46 49 N 71 13 W 6104 ¡White Pointe: Dit 46 53 N 60 21 W
660 | — Trois Riviéres.... 46 Dia 72 33 W 62011 Neil Harbor: Dp: RE 46 48 N 60 19 W
670 | —Montreal-------- mw ADS IÓN 73 33 W 6307 Zaemer ss Se EE ETS 46 38 N 60 23 W
080'| —Rimouski--.-.-:::---- 15-1. 48 27N 68 31 W 640 | St. Anns Harbor, Beach
690 | —Father Point: Lt.... ene 4S DINI 68 28 W Polit MA 2 eee eee 46 17 N 60 33 W
77004 Cap Chat Lt ----| 49 05 N 66 45 W 650 Cibona AA 46 23 N 60 23 W
710 | — Sainte Anne-des- Monts........| 49 08 N 66 29 W 660 | Great Bras d'Or, Blackrock
720 | —Cap de la Magdalen: Lt N 65 20 W Point gle. ooo eee 46 18 N 60 24 W
SOT ame trono ne N 64 36 W 670 dne EE SO E. ERE 46 09 N 60 12 W
7800 | Cap des Rosiers: Lt N 64 12 W 680 | Low (Flat) Point: Lt..........- 46 16 N 60 08 W
SION E EE N 64 29 W 6907 ¡Glace LEE Ee 46 12 N 59 57 W
820 | Cap d’Espoir: Lt---- N 64 19 W 7004 SPIInt eg Lo ES SSS 46 11 N 59 46 W
BION Chad lene we fe eM 64 40 W 710 | Scatari I., Mainadieu: Lt....... 46 00 N 59 48 W
840 | Pointe au Marquereau: Lt..... 48 12 N 64 46 W IZZI ELO USO UIT S a 45 55 N 59 58 W
EE E 48 02 N 65 15 W 730 | Guyon (Guion) L: Lt.......... 45 46 N 60 07 W
860 | Carleton Centre, Tracadigash 7405) St. Esprit Lis Lt 50 0 45 37 N 60 29 W
Pon Lia AE 48 05N 66 07 W zb GreendzeLb 5 sa - 3 45 29 N 60 54 W
7900 | MAGDALEN ISLANDS 8800 | MADAME ISLAND
910 | —Havre Aubert (Amherst Har- 810 | —Cap Rond: Lt 35 N 60 53 W
Or) SEE SEE 47 14N 61 50 W SOT EM Reese ee cf 31 N 61 01 W
920 | —Grand Entry Harbor ---------- 47 34 N 61 34 W 80000 Bear Tee tae sE 33 N 61 18 W
910 | Port Hawkesbury 37 N 61 22 W
8000 New Brunswick 920 | Balache Point... 39N | 61 25 W

80108 "Campbellton o 1N | 66 40 W || 9000 Nova Scotia
020 | Dalhousie. - 4N 66 22 W
030 | Bathurst . . . TN 65 39 W 90107 ¡Cape “Porcupine: 38 N 61 25 W
040 | Miscou I., 1N 64 29 W 020 | Eddy (Sand) Point: Lt......... 31N 61 15 W
O50R UNewcastles S. Senor I ON 65 34 W 03051 Guysborough- "Tx aa 24 N 61 30 W
060 | Chatham. ------ 2 N 65 28 W 040 | Queensport, Rook I.: Lt 21. N 61 16 W
070 | Portage I.: Lt 0N 65 02 W 050 DI E aC Pee a E 20N 61 00 W
080 | Point Escuminac: Lt........... 47 05 N 64 48 W 0608) "Cranberry 15.: Lotsa eee 19N 60 56 W
090 | Richibucto.........- E Ee ME 46 41 N 64 52 W 070 | Sable I., West Point: Lt.. 56 N 60 02 W
8100 | Caissie (Cassie) Point: Lt....._ 46 19 N 64 31 W 0801 Whitez:Hesd 1: Tí oo 12N 61 08 W
110 | Cape Jourimain: Lt_....------- 46 10 N 63 48 W 090 | Whitehead (Whitehaven) ---------- 14 N 61 11 W
120 | Cape Tormentine Harbor: Lt..| 46 08 N 63 47 W 9100 | Tor Bay, Berry Head: Lt....... 4511 N 61 19 W
110 | Country I.: Lt
8200 Prince Edward Island 120 | Wedge Me Í 1 35 Aa riadas o N el 5 Y
130 | Liscomb I.: Lt 59 N 61 58 W
82108 *Port Border Li 46 15 N 63 42 W 140 | Beaver I.: Lt........ 50 N 62 20 Wi
220 | Seacow Head: Lt............... 46 19N 63 49 W 1501 lee tre 54 N 62 30 W
230 WSumnierside= 5 < etc e 46 24 N 63 47 W 160 | Tomlee Head, Spry Bay: Lt....| 44 49 N 62 36 W
2400 Cape Egmontas Lt ee 46 24 N 64 08 W 170 | Ship Harbor 44 47 N 62 49 W
250 West Point: i SE si a 46 38 N 64 23 W 18071 DL E aE 44 40 N 62 52 W
200) eMiiniinegash, Tits 46 53 N 64 14 W 190 | Jeddore Rock: Lt__-- 44 40 N 63 01 W
270 North Points Dt L 47 04 N 63 59 W 9200 | Devils I.: Lt 44 35 N 63 28 W
Ee 46 32 N 63 30 W O Hafan toca 44 39 N 63 35 W
290 | Shipwreck Point: Lt......_..... 46 28 N 62 25 W 220 | Chebucto Head: L 44 80 N 63 31 W
GE 46 27 N 61 58 W 230 | Sambro I.: Lt 44 26 N 63 34 W
S108 EE EE 46 21 N 62 14 W 2407 Betty Ly Brie POT JEE 44 26 N 63 46 W
2201 650018 T RE 46 21 N 62 15 W 250. Begg yaoi P TER 44 80 N 63 55 W
330 | Georgetown Å 46 II N 62 32 W NET A dee, 2 44 41 N 63 58 W
340 | Panmure I., Cardigan Bay: Lt_| 46 09 N 62 28 W 27011 East Ironbound' 12 Dt---------- 44 26 N 64 05 W
3000 Cape Bear to se C 46 01 N 62 27 W 2807] earl TARA E Ee EE 44 23 N 64 03 W
360 Wood Is.: [Ueber eie E ee 45 57 N 62 44 W 200/| Chester sacs PARA 44 32 N 64 15 W
S708 Prim Point SN 46 03 N 63 02 W 9300: | Mahone Harbor EL 44 27 N 64 23 W
3807 | Charlottetown we em 46 14 N 63 08 W SLO Cross o dte SEE 44 19 N 64 10 W
S908 dE 46 07 N 63 11 W GE 44 23 N 64 19 W
: 330 | West Ironbound I.: Lt_---_____- 44 14N | 64 16 W
8400 Nova Scotia 2m pue voc EN 44 23 N | 64 31 W
ü edwa fro gl bj ete o. aa
8410 | Coldspring Head: Lt........... 45 58 N | 63 52 W 360 | Coffin i Le DERE "xp ú 02 N ER 38 M
420 Pugwash... SE Wepre oes 45 51N | 63 40 W 370. || Liverpools enea sā 1 44 02N | 64 43 W
ER eme m Quac PEPPER SS 45 50 N 68 11 W 380 | Port Mouton, Spectacle I.: Lt__| 43 55N 64 48 W
a Cori ou Point, Gull L: Lt...... 45 46 N | 62 41 W SHEET 43 48 N 64 47 W
ron - Seal Point (East 9400 | Lockeport Harbor, Gull Rock:
den Pisce ISS EE 45 49N | 62 31 W Lge eter ae 43 39N | 65 06 W
do o Gg Da 45 40 N 62 43 W 410 | Shelburne 43 45N | 65 19 W
R Ser UE Dt oS FEMME CINE 45 53N | 6154W 420 | Cape Roseway: Lt.........--..- 4337N | 6516W
f or auso MAA 4542N | 6129 W joti Cas Negro l:a Lt" na 43 30N | 65 21 W
accaro Olt Di ees 43 2
8500 Cape Breton Island "a Cape Sables eege 43 23 N EE 37 Ww
k 0 ELSE LGS NES ti
os DOS d Ee ES 45 59N | 6136 W 470 | Seal I.: Li orth ca 43 24 N 68 o W
a «aka! x (es EE Ee ið ds N a z W 480 | Pubnico Harbor, Beach Point:
SCH Sea Wolfe (Margaree) I.: Lt.... 46 21 N | 61 16 W 490 Pu L a reit HRS R ol W
550 drei ia S ee 40123 NO 61 04 Ee ee ON | 6607 W
Soe) Ga Ü em nn DIM 8N | 61 00 W DLO Cape Bourchu ND OS 43 48 N | 66 09 W
WEM OE ZN | Saw || 50 | Cape St. Mary: Li- E 0200077 4405N | 6613 W
590 | St. Paul T., Atlantic Cove: Lt: | 47 12N | 6009 w || 340 | Boars Henge LO U RN OSW

Index
N

10200

Place

Nova Scotia—Continued

Prim Point: Lt
Te AS
Port Lorne: Lt
Cape Split, Minas Channel.....
J AT fe JR EE
Cape OIL ITA REEL |

fle Haute: Lt

ape Spencer: Lt
Sd (NS eee

Gannet Rock: Lt
Machias Seal “E Dt —— <<:
Campobello I., Mulholland

Point De ee ee NM

Maine

West Quoddy Head: Lt........
WAH CUR Vel lite. see as
PADD Yn Ss Lit...

Petit Manan I.: Lt

IMonheranyle Db. - am
Boothbay Harbor
Segun bi 7...
Bath

Portland Ica ce=sos
Cape Elizabeth: Lt
Mood Ds dotes. loo.
dek DEE om AS
Whaleback Reef: Lt-----------

New Hampshire

POLLS MOUENZ- desām sa 2 2 isto
Isles of Shoals, White I.: Lt....

Massachusetts

Net buru noris eee E
Annisquam:) Ltr ce. =
Cape Ann, Thacher T.: Lt......
Eastern Point: Lt
Gloucester eo a «T
Bakers It ptt

Lat.

wea

plo pl pi pi pi pi pi pl PP Pp
He Or Or O Or Or Or Or Or Or Zn O
me Oe DDO Owe

AA
KE)
BR kä OD th o o0 +

A a
$5 65
mo

>
to
FN
oo

42 3

ES
SEN
ZZZZZZZZZZZ

va
t2
t2
tú

42 23

APPENDIX $
MARITIME POSITIONS

EAST COAST OF NORTH AMERICA—Continued

Long.

AADDDDA

O) Or Or On ma R

O DIH a I
>= C2 09 Or NN Y D

83888

Se PIRES

dd4 dggggggggags

66 5
66 47 W

EE EE EE

nc cho CH Genen enen CD
© O Dos D oo O0 O0 O0 O0 N
M GI Or O De -

Index
No.

Place

Massachusetts—Continued

Quinc
Minots Ledge Tt EM U
Gurnet Point; Li-- sr
Plymouth OUR E
Cape Cod Canal Eastern En-

trance: Breakwater Lt.......
du NEE
Race Point: L
Cape Cod: Lt.....
Nauset Beach: Lt. oiT

Monomoy Point: Tower.......
Hyannis TES «at
Bankat Head Dtm
Nantucket 22-2222 Ee
«Vineyard Haven sens sean
WestiChop Tt mE a ae
Cuttyhunk dy Li
Woods t Holes = rep
Buzzards Bay. vs n E
Cleveland Ledge: Lt...........
New: Bedford Te TY va
KOW River E

Rhode Island

INNATA ee ee ee
Davisville Depot -<-s airi
Quonsel Politi m
UN DOTS as allume
BeavertailPoint:"Dt::=<<e--
Pont Judio bic
Watch Hill Point: Lt..........
Block I., Southeast Point: Lt.-

Connecticut and New York

LONG ISLAND, NEW YORK
—Montauk Point: Lt..........
—Shinnecock Inlet: Lt.........
IA E vv 2
Re Inlet: Breakwater
EE SCR
— Port«Jefferson---------- c-r
< FWatons Point: LX
—Kings Point: U.S. Merchant
Marine Academy ----------
Race Rock TETAS se
A EMS A e
New London, Connecticut:
U.S. Coast Guard Academy..
Ee
New Haven, Conneciieut
Stratford Point: Lt ð E
Bridgeport, Connecticut_--------
Execution Rocks: Lt...........
City Is Spiron. 2r ms <<
New York, New York.----------

New Jersey

Sandy Hook:910----72: 5
Ses Intus aes sa
Barnegat Inlet: Breakwater Lt.
Atlantic CHE saa
Hereford Inlet: Lt............-

Delaware Bay

Cape May Point: Lt..........-
Camden, New Jersey------------
Philadelphia, Pennsylvanta------
Chester, Pennsylvania.----------
Wilmington, Delaware.......-.-
Reedy Point, C. & D. Canal

Bast'Entrance: Lt--------.--
Cape Henlopen: Harbor of

Refuge = iem

Dela ware and Virginia

Fenwick lI
Assateague I.: Lt---.-.--------
Hog I.: Little Machipongo Lt. -

>
Kä
e
uo oo

$
sx
ZZZZZZZZZZZZZZZZZZ ZZZZ

Lat.

~

ex
Lii S DO

m.

Lea SE SE X]
O RG NN NRO

o
to 00

be
Z

37 N

—— pa ago e ce
NORD NON SSR

ZZZZZZZZ ZZZ ZZZ ZZZ

SRS SR
DOG OO +0

1065

ul
o
a
Ooo 0

Zazzzzzzzazzzzzz HEEE

Y O Y 0 0) O00 -1

73 46 W
72 03 W
72 06 W

72 06 W
72 39 W

75 34 W
75 06 W

75 03 W
75 21 W
75 40 W

1066

APPENDIX S

MARITIME POSITIONS
EAST COAST OF NORTH AMERICA— Continued

NNNM DM... Ve d

XE Plate Lat. Long. Todes Place Lat Long.
11700 Chesapeake Bay be: m3 12700 Mississippi 2 ay Kg
EU EIN Gape Charles: Tee ees 37 07 N 7554YW||12710u Homes ute = ee 30 13 N 88 29 W
720 | Chesapeake City, Maryland; 120 | Pascagowla._-_------------------ 30 21 N 88 34 W
C. & D. Canal: Spire 39 32 N 75 49 W DEU LEE 80 28 N 88 53 W
780 | Baltimore, Maryland_-_---------- 76 85 W 7400 Ship Lo Lt3- —— sees rms 30 18 N 88 58 W
740 | Annapolis, Maryland: U. S. 500 QuifDortsss a EE EE 30 21 N 89 05 W
Naval Academy.....--...... 38 59 N 76 29 W
7601 PointeLookout: Li-----------—- 38 02 N 76 19 W Tonis
760 Vee a a Columbia. = " N 77 02 Wi 12800 ninang
770 Point Comfort: Lt........- 76 18 a E
780 | Newport News, Virginia........ 36 58 N 76 26 W || 12810 Chandeleur ee Lt...-.......-- 30 03 N 88 52 W
790 | Portsmouth, Virginia A 70:18 MER Tad
11800 | Norfolk, Virginia.....-- TOUS Wille) CI ee ES ae ae:
810 Cape Henry: tee ee 76 00 W 920 | —Southwest Pass: Lt..... ---128 54 N 89 26 W
13000 nee Beer os —— a i 57 e P^ 0> D
z 010 arataria Bay: 38 =-| 2916 5
11900 North Carolina 020 | Ship Shoal: Lii = 2 55N + 04 w
" int-au-Fer Reef: Lt.
E Ee EE 30 2 ` n d wW 040 ius onde r E 30 13 N 93 15 W
930 | Cape Hatteras: Lt... 35 15 N 75 31 W
940 | Ocracoke I.: Lt...... 35 06 N 75 59 W || 13100 Texas
950 | Cape Lookout: Lt-----+4- =. 34 37 N 76 32 W
0608 Beaufort te --- | 34 438N 76 40 W || 13110 | Sabine Pass: Coast Guard Sta-
970 | Cape Fear: L EEN ES 77 58 W aja Ee -=|-29 42 N 93 51 W
980: Wilmington? o ao M 34 14 N 77 57 W 1204) Porb Arthur: -— — L -| 29 50 N 93 58 W
130 ae oo eee E ee 30 05 N 94 05 W
i 140 e E TE na 29 19N 94 47 W
IND STD Corea 150 Teras CUERO idan T zo 29 23N | 94 55 W
12010 | North I.: Georgetown Lt........ 3313N | 7911 W 160 | Houston a 29 45N | 95 17 W
EE 170 | Matagorda I.: Lt ee 2820N | 96 25 W
ki o Due "S PES Aransas Pass: Dt 27 50 N | 97 04 W
190 orpus Christi am Lt 8 27 49 N 97 24 W
12100 Georgia 13200 | Brazos Santiago: Lt 26 04 N | 97 10 W
12110 Savanah 3205 N | 81 05 W 2101" Brownsville. e e Lo A 25 57N | 97 24 W
120 | Tybee I.: Lt 32 01 N 80 51 W
1301 Stø Simons I. DU eee = 31 08 N 81 24 W 13300 Mexico
Ek 31 09 N 81 30 W
cos Funta Jerez. pie a 22 54N 97 46 W
i 2 (UV DICOR EE. SES RSS Ø 22 13 N 97 51 W
SN klorida 330 | Isla de Lobos: Lt 21 28 N | 9713 W.
129104 Amelia Ie. LH C < Ad pesos sa 20 59 N | 97 20 W
220 | Jacksonville. EE Se ^ N RE a W 350 | Tecolutla: Lt = = 20 30N | 97 01 W
EE 3023N | 81 24 W 360 | Rio Nautla: Lt.-...-..........- 2017 N | 96 47 W
240 | St. Augustine......-----------.- 29 54 N | 81 19 W 370 | Punta del Morro: Lt 19 51 N | 96 28 W
250 | Ponce De Leon Inlet: Lt... 29 05 N | 80 56 W 380 | Arrecife Blanquilla: Ltr 1914N | 96 06 W
260 | Cape Canaveral: Lt. 28 28N | 80 33 W 390 | Anegada de Adentro: Lt___-____ 19 14N | 96 04 W
270 | Jupiter Inlet: Lt... 26 57 N | 80 05 W || 13400 | Veracruz. cnn naan 19 12N | 96 08 W
280 | Palm Beach...................- 26 46N | 8003 W 410i Isla Verde apte 1912N | 96 04 W
2008 Hillsboro Inlet D Ee 26 16N | 80 05 W 420 | Isla Sacrificios: Lt 19 10N | 96 05 W
123008 Fort Everglades MARTES. CRM 26 06 N 80 07 W 430 | Isla Blanquia (Blanca Reef): Lt.| 19 05 N 96 00 W
510] Miami EA- emi ak? 25 47N | 8011 W 440 | Arrecife de Enmedio: Lt........| 19 06N | 95 56 W
320 | Fowey Rocks: Lt..-.---.....22 25 35 N 80 06 W 450 | Arrecife Santiaguillo: Lori 19 09 N 95 49 W
330 || Garystort Reef: Lt... 25 13 N 80 13 W 460 | Punta Roca Partida: Kiev 18 4 N 95 11 W
340 | Alligator Reef: Lt.............. 24 51 N | 8037 W 470 | Punta Zapotitlán: Lt..... eer 18 33 N | 94 48 W
350 | Sombrero Key: Lt............. 24 38N | 81 07 W 480 | Coatzacoalcos (Puerto Mezico)...| 18 09 N | 94 25 W
360 | American Shoal: Lt. 24 32N | 81 31 W 49001 Tonala: II 18 12N | 94 08 W
OMC SE 24 33 N | 81 49 w || 13900 | Alvaro Obregon (Frontera)... 18 35N | 92 39 W
3801 Sand Rey: Lt US 24 27N | 81 53 W 510 | Punta Xicalango: Lt.-.-------- 1838N | 91 53 W
390 | Rebecca Shoal: Lt... q m 24 35N | 82 35 W 520 | Isla del Carmen: Lt............ 18 39N | 91 50 W
12400 | Dry Tortugas, Loggerhead Key 090 Aguada Ut. eec Y 18:47 N | 91 29 W
[eee c P ONT e Cu 24 38N | 82 55 W 540 | Champotón: Lt.................| 19 21 N | 9043 W
ALO Sanibel IE I tas. eM 26 27N | 82 01 W 550 | Punta Morro: Lt_-------------- 1941N | 90 42 W
420 (Gasparilia Routes na 26 43N | 8216 W 5001 Campeche! ecd 1951N | 90 33 W
d300 EHE monnik eyi ds ana 27 38N | 8246 W 970 | Cayos Areas: Lt. "== 20 13 N | 91 58 W
440% TAPA ee oa et inā ail 27 55N | 8227 W 580 | Triangulo Oeste Arrecife: Lt__| 20 58N | 92 19 W
GENEE Të 27 46 N | 8237 W GU) | (COGS At = esac eno 20 51N | 90 24 W
4608 Anelote Keys) TAR 28 10 N | 82 51 w || 13600 | Punta Palmas: Lt.............. 2102N | 9017 W
470 | Seahorse Reef: Ltr- SME Tae 28 58 N | 83 09 W 610 | Sisal: Lt... eege 21 10N | 90 03 W
480 | Cedar Keys: North Bank Lt. 1_| 2908N | 83 06 W 6205 Cayo Arenas lt NEIN 2207N | 91 24 W
ASA os a 30 09 N 84 13 W 630 | Arrecife Alacrán: Lt 22 24 N 89 42 W
12500 | Crooked River: Lt. 29 50N | 84 42 W EU AO EN 21 17N | 89 40 W
5103 Apalachtcolas ECCO OS 29 43N | 84 59 W 650 | Yalkubul: Lt 2132N | 88 37 W
520 | Cape St. George: Lt 29 35N | 8503 W 660 | El Cuyo (Monte de Cuyo): Lt.| 2131N | 87 43 W
5301 Cape San Blas Ee 29 40N | 85 21 W 670 | Cabo Catoche: Lt.............. 21 37N | 87 04 W
640 Porta Jocs a ane SER MS 29 49 N 85 19 W 680 | Isla Mujeres: Lt 2 Lo 21 12N 86 44W
5509 Panama City) qs NEE 30 08 N | 85 39 w || 13700 | ISLA DE COZUMEL
BOOM" Pensacola- ss 3 D ERR T 30 24 N | 8713 W Meel 2036N | 86 44 W
2 mu Pel de Sn KE ør 20 30 N 86 58 W
= punta Celeraln: Lt rr 2016N | 86 59 W
12600 Alabama eh Tunta pu Ibl. eee do 19 18 N 87 27 W
12610 | Sand I.: Lt..... y L anco Chinchorro, Cayo Norte:
620.) Mobile. Ze EE N E E essere eae 18 46N | 87 19 W
h 7 8204), Xonlak Done rem 18 16 N 87 50 W
————————————M ———— á— — — O |

APPENDIX S
MARITIME POSITIONS

EAST COAST OF NORTH AMERICA—Continued

1067

Index
Na. Place Lat. Long. Index Place Lat Long
13900 British Honduras tu Honduras— Continued
o + o + o ,
E3010. | Rocky. Point: Lt- -------.———.- 18 21 N 88 05 W || 14450 | Isla Roatan: Lt 16 18 N 86 38 W
14000 | TURNEFFE Cays 460 | Cabo Falso (False Cape): Lt... :
pe De Cay: TUE 17 36 N | 87 46 W ( AO r EE
=Ø E) es! 17 10N 87 54 W || 14500 Ni
14100 | LIGHTHOUSE REEF ERE.
110 | —Northern Two Cays, Sanbore 14510 | Cabo Gracias á Dios: Lt........ 15 00N 83 09 W
Uer (Én 17 28 N 87 29 W 8205) Æ untai Gorda Li 1N 83 12 W
120 | —Half Moon Cay: Lt..........| 17 12N 87 32 W 530 | Puerto Cabezas.------- 1N 83 23 W
eR deg S o A 17 30 N 88 11 W 540 | Little Corn I.: Lt 8N | 82 59.W
«100 Bugle Days: DO es 16 22 N 88 19 W UN ed ĻUC TIE (LS EEN 1N 83 45 W
220 | East Snake Cay: Lt. 16 13 N 88 31 W 560 | San Juan del Norte (Greytown)..| 10 56 N 83 43 W
14600 Costa Rica
14300 Guatemala
140101 Citta nes SSS Rei 10 N 3 01 W
143100 "Puerto Barrios-7--— - —--—--- 15 44 N 88 36 W E Sr
320 | Cabo Tres Puntas (Cape Three 14700 Panama
POINTS) poe 15 57 N 88 36 W
Echt PAU Tr S a 918N 82 24 W
720 | Punta Toro (Cape Toro): Lt...| 9 22N 82 12 W
14400 Honduras 7305 LOTO Pont AN 922N | 79 57 W
740 | Cristobal, Canal Zone 9 21N 79 55 W
H 441013] Puerto Cortés = IT —- 15 50 N 87 57 W 750 ¡CIO á 9 22N 79 54 W
420 Punta Caballos; eset. E 15 52N 87 58W 76071 Farallon sucio: bi: 9 39 N 79 38 W
MCRL CLO pi e ši atl cR dos 15 46N 87 27 W 140351 TslaiGrande TT lobo 222902 9 38 N 79 34 W
TATU e 16 08 N 86 53 W SON EE 935N 79 28 W
WEST COAST OF NORTH AMERICA
15000 Panama 15700 Mexico
o , o , o , o 12
[50107 Isla Pantinito Lt. 22-220 816N 18 28 W 112157107 eeng Bendos mees es 14 43 N 92 27 W
0207) Isla:San José: TAS s= ur 8 13.N 79 08 W 720 | Salina Cruz, Golfo de Tehuan-
03079 sla Pacnieca; Dicen 8 40 N 79 04 W Lë 16 10 N 95 12 W
0400) slarChepillo: Ti: IIA 857 N 79 08 W 730 Puerto Angel (Port Angeles) ----- 15 39 N 96 31 W
H uic A ere ee 8 57N 79 32 W 7401 pelntaGalerasmt sess scene 15 58 N 97 41 W
060 Iamencoji pp see ee 8 55N 79 31 W 750 | Punta Maldonado: Lt.... -.| 16 20 N 98 35 W
070 | Balboa, Canal Zone. "Ð 8 57N 79 34 W TOO Vei (es ss IE 16 51 N 99 56 W
080 cislarPaboguillas its == 8 48 N 79 31 W 770 | La Roqueta (Grifo 1.): Lt...... 16 49 N 99 56 W
Uo Bis eng y oce 834N 79 35 W 780 | Punta San Telmo: Lt 18 19 N | 103 30 W
15100 | Punta Mala (Cape Mala): Lt__| 7 28N 80 00 W 790 | Punta Campos: Lt....... 19 01 N | 104 21 W
POG) cBralesdelsur bt: 720N 80 08 W || 15800 | Manzanillo__-_------------ 19 03 N | 104 20 W
120 | Morro de Puercos: Lt. ......... 714N 80 25 W 810 | Cabo Corrientes: Lt.........-.- 20 24 N | 105 43 W
tað NīslajJicaritas Ice <a as 712N 81 48 W 8208 pan Blas: (SS es eee 21 82 N | 105 19 W
140. | Puerto Av mulles- === TT" 816N 82 52 W 830 | Isla Maria Madre: Lt 21 36 N | 106 33 W
1504 wisiatBurica ii Lits t 80N 82 53 W S409 Mazal lai See eee A 28 12N | 106 26 W
8309 Ygtdrosi o cu === aaa 26 42N | 109 31 W
860 ISa Lobos: TP nee ee 27 20N | 110 38 W
15200 Costa Rica STO Guaymas ee = eee 55 N | 110 55 W
3307 Cabo Haro iv one 50 N | 110 54 W
Mett, argent ek ere eer 839N 83 10 W 890") ¡Santa Rosalia r sso 20 N | 112 17 W
2200 adel Caño tocara 8 43 N 8374W |11590002 c NTuleté: 1567222 54N | 111 58 W
GENEE 924 N 84 10 W OID] ALTOS NE eS ee 01 N | 111 21 W
240 | Isla Herradura (Isla Caño): Lt.| 9 87N 84 40 W 9204 PEC Paa sae mr 10 N | 110 19 W
ADALAT EE EE 9 59N 84 50 W 9300 Punts Eriota; EE 13N | 110 18 W
260 | Isla Cabo Blanco: Lt 932N 8507 W 940 | Bahía San Jose del Cabo: Lt...| 23 04 N | 109 40 W
950% Cabo San Lucas coco eos 22 52N | 109 53 W
9609 Cabo BalsoX DAP--2----—— Æ 22 52 N | 109 58 W
HEES ELTER 24 19 N | 111 43 W
15300 Nicaragua 980 | Punta Redonda: Lt............ 24 31 N | 11201 W
990 | Cabo San Lazaro: Lt......----- 24 48N | 112 19 W
15310 | San Juan del Sur. .............- 11 15 N | 85 53 W | 16000 | Isla Natividad: Lt.............- 27 52 N | 115 10 W
3208 Corinto? es et antonia 12 28 N | 87 11 W 010 | Islas San Benito, Benito del Á
nees ie s si er 28 18 N | 115 36 W
15400 Honduras 020 | Isla Cedros (Cerros I.): Lt...... 98 22N | 115 12 W
030 || Isla Todos Santos: Lt---------- 31 49 N | 116 49 W
ISO Ama pala ISBN A R 13 18 N | 87 39 W 0407 Ensenada A oh. o 40990 31 52 N | 116 38 W
050 | Islas Los Coronados: Lt.......- 32 24 N | 117 14 W
KE El Salvador, 16100 California
P5510ul La- Unión rs ae Eee REM er 13 20N 87 50W ģ À V
520 | La Libertad 13 29 N | 89 19 W || 16110 | National City-_--..-------------- = 2 N ny a P
530 | Acajutl 1335N | 89 50 W 10d ofr, DEO) = e eee eee : N i
ACAIULIG. ae k 5 1508 Pont Loma bi Arn ren 32 40 N 117 14 W
1307 | Newport Beachz---———-—-—-— 3337 N | 117 54 Ww
15600 Guatemala 150 | Long Beach... .-- pe cH
160 | Los Angeles------ 33 45 N | 118 15 E
156101 PUET de San OSCE = == aan 13 55 N 90 50 W 170 | San Pedro. .....- 3 Šā N i T Y
620 | Champerico 14 18 N 91 56 W 180 | Wilmington 3 46 M 24 ) w
630^ OOS SUD DAN met Ee "deu dde eene 14 30N | 9211 W 1908 Bont Bermin: Li -nna 33 42 N | 118 18

1068

Index
No.

WEST CO

Place

California—Continued

Point Vicente: Lt F TT a
SANTA BARBARA ISLANDS
(CHANNEL ISLANDS)
—San Clemente I., Pyramid
Head: ii m
Sa Catalina I., West End:

L

—San Nicolas I., East End: Lt.
To Rosa I., South Point:
—Santa Cruz I., Gull I.: Lt....
—Anacapa I.: Lt
Port Huenemes= ete £
Santa Baroni EE
Point Conception: Lt..........
Point Arguello; Les eee
San Luis Obispo: Lt...........-
Point Piedras Blancas: Lt......
Point Sur: Lt
Pointi Pinos), EE
Monterey E Eë
Santa) Ee
EE uti Eta esat
Point Montara) tse
Mile Rocks: zeg
San FRANCISCO BAY

—Alcatrazilos Ib. 22. ee 208
~ San EE
Redwood City em
=Alameda ene SE

Point Bonita: 140-99----2----
Southeast Farallon I.: Lt_-
Point Reyes: m
Polnt Arena” Lte essee
Point Cabrillo: Lt.........
Cape Mendocino: Lt......
Table Blut po

Trinidad Head: Lt........
St. George Reef: Lt.............

Oregon

CaperBlanco mL same EE EE ETE
Cape Arago Lt -- 2

Coos Bay (Marshfield)
HecetāfHead: d S
Yaquina Head: Lt........
Cape Meares: Lt..........
Tillamook Rock: Lt

Columbia River

Astoria, Oregon EE
Longview, Washington...
Portland, Oregon
Vancouver, Washington

Washington

Cape Disappointment: Lt
North Head: Lt

Cape Flattery, Tatoosh I.: Lt...
Slip Point: Lt

RortrAngeles tao. EE
New Dungeness: Lt
Port Townsend

APPENDIX S

MARITIME POSITIONS

AST OF NORTH AMERICA—Continued

Lat.

35 40 N

E
&

<
GO
ZZZZZZZZZZZZZZZZZZZZ ZZZZZZZ

Qo N —

S

4
3
37 4
4
5

9
2
7
9
5
38 03
7
6
6
9
2

37 4

Index

Long. No Place
Washington—Continued
o ,
118 25 W || 17300 | PUGET SOUND
310] == SeaHle EE
3204 —— Bremerton- E aos
380'| TACO Mac cnn a
118 21 W 349, —Olympla- rt
144008 BU en ee Med EE
118 36 W ALOR Smiths) Lies seo sea
E le EE EE
119 02 W 4800 BAVARIA ee
119 26 W 440% Point Roberts EE
450: Patos E. ULA 13 c IO
120 07 W 4603]. Skipjack Lo Lose h loans ra
119 50 W 470 | Turn Point, Stuart I.: Lt_..----
119 22 W 480) Kellett Bluf: Lts. RPP
119 12 W 490 | San Juan I.: Lime Kiln Lt.....
119 41 W
120 28 W || 17500 British Columbia
120 39 W
120 46 W || 17600 | VANCOUVER ISLAND
121 17 W ou —Vicloria---- Em as
121 54 W 620 | —Esguimalt______...
121 56 W 630 | -—Race Rocks: Lt
121 53 W 640 | —Sheringham Point: Lt........
122 01 W 650 | —Carmanah? Lt---..--.-------7
122 24 W 660 | —Pachena Point: Lt...
122 31 W 670 | —Cape Beale: Lt
122 31 W 680... Alberni sī em
690 | —Amphitrite Point: Lt.........
122.25 W'|| 17700 | —Lennard L::DLb-3...-...-.----
122 25 W 710 | —Estevan Point: Lt............
122 12 W 7201 wgl KA Ell Ee EISE
122 16 W 730 | —Cape Cook, Solander I.: Lt...
122 20 W 740! Port AA oct c
122 22 W 50.4 Kansai 1 c
122 01 W 760 | —Cape Scott: Lt
121 18 W UR EE MOS = ee
122 15 W || 17800 | New Westminster
122 16 W SION a Vancounņer eee ere eee a
122 32 W 8202 Hog T: OU SAS cee ee y
123 00 W || 17900 | QUEEN CHARLOTTE ISLANDS
123 01 W 910 | —Cape St. James: Lt n
123 44 W 920411 —Langara DL: btt
123 50 W 930 | —Lawn Point: Lt
124.24 W 1| 18000) ||) ‘Ocean Faus aT rem
124 16 W UN url Rupert =o eee ce
124 11 W
124 09 W || 18100 Alaska
124 22 W
181107 Tree Pont
120 | Barren I.: Lt.....
180) |. Ketchikan ene eege S
124 34 W 140 | Cape Chacon: Lt
124 22 W 150 | Cape Muzon: Lt
124 13 W 160 | Cape Bartolome: Lt_____._____-
124 08 W ON VU GIG Cline = ES
124 05 W 1SQ Petersburg me ee
123 59 W 1901 ‘Cape: Decisions Tits ee
124 01 W || 18200 | Cape Ommaney: Lt............
2102) SURA ERA
220 | Cape Edgecumbe: Lt...........
23011 KlokaehetL El UE SM
123 50 W 240 | Lisianski Strait Entrance: Lt...
122 56 W 250 UNE. o CE
122 40 W 2604 Skagway fi ty S ees
122 41 W 270 | Cape Spencer: Lt..
23011, Ocean Cape: TTP
2900 Y arta
18300 | Cape St. Elias: Lt
124 03 W 810 | Cape Hinchinbrook: Lt.
124 05 W 320 | Cordova
sedlu Valdez ET
124 04 W 340 | Whittier
850 | Point Elrington: Lt. 2200
124 07 W 360 | Cape Resurrection, Barwell I.:
123 49 W Tb... VBA EE
123 54 W STOMP Seward Cot ae e EU ENORMES
124 29 W 380 | Pilot Rock: Lt.
124 44 W 3908 EScalsRockss Ae
124 15 W || 18400 | East Chugach L: Lt
123 24 W 4104). Berl Le bota 2. eee ee eee
123 26 W EE
123 07 W 490. Elat I LGS T 2 An
122 45 W 440 | Seldovia

Lat.

`

ES]

S82%8

"000 foo kauko

ZZZZZZZZZZZZZZ

TEE
Par

Seele
C CO O OQ «o «o HO O GO do 00 GO O0 00 00

SENOS Hiro NISNISA IN bS
ZZZZZ ZZZZZZZZZZZZZZZZZZZZ

SPR DO ja R

a

00
IISPASE SSISRSESSONSARSLSSSRESESESE
ZZZZZZZZZ ZZZZZZZZZZZZZZZZZZZZZZZZZ

E Sa or
a

m
La
N
Bv wW h
SAZSRRSS

444444444 E

123 0.

123 1
123 1

CL
SINT Or 00 020» O1 Or b O» Ha

33333 HERTZ

Di
Eë
Ei
Yengo
SNane

132 5
134 0
134 4

134 2

149 17 W
149 26 W
149 28 W
149 38 W
151 26 W
151 38 W
151 57 W
152 00 W
151 44 W

1069

APPENDIX S
MARITIME POSITIONS

WEST COAST OF NORTH AMERICA—Continued

In
od Place Lat. Long. oe Place Lat. Long.
Alaska—Continued R F Aleutian Islands—Continued
o , o ,

18450 | Anchor Point: Lt 22.2 40 IN. 161.62 W || 1903011 Dutch Harbor =... 4N | 166 32W
460 Kenai LE Eeer op Ai 33 N | 151 16 W 040 | Makushin........ 6N | 166 59 W
470 Chisik ee ee ee ee eee 06 N | 152 34 W 050 | Seguam I.: Lt 8 N | 172 26 W
480 | Kalgin L: Lt_____ 29 N | 151 50 W 060 | Atka I., North Cape: Lt........ 52 26 N | 174 11 W
490 | East Foreland: Lt 43N | 151 24 W 070 | Great Sitkin I., Swallow Head:

18500 | Anchorage........ cocer eA 13N | 149 54 W EI GAR 52 07 N | 176 09 W
510 | Afognak I., Tonki Cape: Lt....| 58 21 N | 151 59 W 080 | Adak T., Sweeper Cove........... 51 52 N | 176 38 W
520 | Spruce Cape: Loran Station....| 57 49 N | 152 20 W Amchitka I., Constantine Harbor_| 51 24 N | 179 18 E
E] rs, A AAN 57 AUN | 152 24 Will, 18100) || isha Harborne a 51 58 N | 177 33 E
540 | Womens Pan. sec 57 43 N | 15231W 110 | Shemya T., Alcan Harbor... 52 44 N | 174 04 E
550 | Cape Chiniak: Lt.......... 57 38N | 152 09 W 120 | Attu T., Massacre Bay.-.-----.--- 52 50 N | 173 14 E
560 | Dangerous Cape: Lt 57 16 N | 152 43 W || 19200 | PRIBILOF ISLANDS
570 | Sitkinak I., Whirlpool Point: 210 | —St. Paul I., Village Cove____-- 57 08 N | 170 16 W

AE e ee, ns o 56 37 N | 154 06 W
580 | Cape Alitak: Lt 56 51 N | 154 18 W
5904 Cape Uyak! Lt. ot es 57 38 N | 154 21 W || 19300 Alaska

18600 | Raspberry Strait, Cape Nuni-

MARI c c Tad 58 10 N | 153 13 W || 19310 | Sealion Rocks: Lt-.........-.-- 55 28 N | 163 11 W
610 | Alligator I.: Lt 58 28N | 152 48 W Song EE MOTERA rr een 55 59N | 160 34 W
6204 Capel EN == = € E - 57 26 N | 156 02 W 330 | Cape Seniavin: Lt.............. 56 23 N | 160 08 W
630 | Foggy Cape: Lt............ -.| 96 32N | 156 59 W SOMO leen eue ver 56 53 N | 158 42 W
SAC IICA. c Pea 56 18 N | 158 24 W SOON DA R RAS 57 33 N | 157 36 W
650 | Mitrofania T se Lies" . 55 50N | 158 42 W ANA a A E tes E 57 82 N | 157 25 W

18700 | SHUMAGIN ISLANDS EYÐ EGEE s o ES 58 12 N | 157 22W
710 | —Cape Wedge: Lt.............. 55 18 N | 159 53 W SOI OREA. cores eo tee tee 58 48 N | 157 01 W
(204 Sand Point s.n E ES 55 20 N | 160 32 W B00 ml Clark TPoint To eae ene 58 51 N | 158 33 W
430 |s—Unga Spit: Lt...-...........- 55 25 N | 160 44 W || 19400 N Dillngham S Tórð S n 59 02N | 158 29 W

ESOO AA TEA Points Lt — — eee 55 12 N | 161 54 W || 19500 | NUNIVAK ISLAND
o CA E Bt es ee 55 02 N | 161 56 W 510 | —Cape Mohican: Lt............ 60 13 N | 167 27 W
ENTORNOS 55 03 N | 162 19 W 6204/43) Harbor TES SES EE 60 12 N | 166 59 W
830 Hague Rock: Lt.--...----i=<22 54 33 N | 162 24 W || 19600 | St. Lawrence I., Savoonga----.-- 63 41 N | 170 24 W
SAORI Saks rere pr T re 54 29 N | 162 49 W CLOW PointyRomanol Di nnna 63 12N | 162 50 W

18900 | UNIMAK ISLAND GP De nete Michael as eaten eens Sees 63 29.N | 162 02 W
910 | —Cape Pankof: Lt............. 54 40 N | 163 04 W (6610660514 NL cel AREAS ae eee eae 63 52 N | 160 46 W
920%) — Seoten Cap: Ee 54 24 N | 164 45 W Moa CapesDanby NCS Ss m 64 20 N | 162 47 W
930 | —Cape Sarichef: Lt 54 36 N | 164 56 W Go0E Solomon E casco EM 64 38 N | 164 24 W

DOMINA SE ene senate ZS 64 80 N | 165 25 W

19000 Aleutian Islands 6704 Slede I ele ae IS 64 30 N | 166 11 W

6805) Cape Rodney) Lycos 64 40 N | 166 24 W

19010 | Akutan Harbor: Lt. 54 09 N | 165 44 W 6900 Point Spencers tess = oo se == 65 17 N | 166 50 W

OSO nin CITGO Shee ee SES rr REST, 53 52 N | 166 32 W || 19700 | Grantley Harbor_----------===--- 65 16 N | 166 20 W

ee

HAWAIIAN ISLANDS

o , o ið o , o Li

20000 | HAWAII MorokaAr—Continued

010 | —Kauhola Point: Lt 15N | 155 46 W || 20530 | —Makanalua Peninsula: Mo-

020 | —Kukuihaele Landing 08 N | 155 34 W NOK abl (S a eee 21 13 N | 156 58 W

030 | —Laupahoehoe Point: Lt... 00 N | 155 15 W || 20600 | Oanu

0409 > Eeneekeo Foluts Lt 51 N | 155 05 W || ` 610 | —Makapuu Point: Lt..--------- 21 19 N | 157 39 W

NEE e lr 1620 —Diamond Head: Lt..-------.. 21 16 N | 157 49 W

0 p o nm : 630 | —Honolulu_.....------- LER

070 | —Cape Kumukahi: Lt.... 81 N | 154 49 W 640 | —Pearl Harbor.............--.-- 21 22N | 157 58 W

080 | —Ka Lae: Lt--------------- 55 N | 155 41 W || 650 | —Barbers Point: Lt....--------- 21 18 N | 158 06 W

090 | —Kauna Point: Lt. ....-------- 02N | 155 53 W | 560 | —Kauna Point: Lt......-------- 21 35 N | 158 17 W
eg gen EE Ee, Eelere

ELA E Ae aa sis d$ Zen, ERT WE Ur A Tits ee use LC AS

120 | —Keshole Point: Lt----------=- 44N | 156 04 u 20700 | KAUAI

D A E m 710") — Kilauea Point: e et 22 14N | 159 24 W
aie RI 720 | —Kahala Point: Lt... 22 09 N | 150 18 W

čauiki : 730^ | —Nawiliwili Bay------.--------- ü 2

ENEE 165900 W || 740 | —Makahuena Point: It 21 52 N | 150 27 W

e Li_.....05 ENEE JV ||. EE EL

NE Karali A BL 20 54 N | 156 28 W 760 e SEH Bay: Puolo erte

E E EE 21 59 N | 159 46 W

Sol E | 20 52N | 156 40 W || 20800 | Lehua T.: Lt EE

280 | —Cape Hanamanioa: Lt-------- 20 35 N | 156 25 W Cl Ni H pa; Sa Vj
203008 MolokinlT.: eegen sN 156530 W lv oe) Neer 23 35 N | 164 42 W

310 | Kahoolawe I.: Southwest Point |. | 156 40 w || 840 | French Frigate Shoals, East 1---| 23 47 N | 166 13 W
20400 | L cot; ap eat YT F b 850 | Gardner Pinnacles 25 00 N D vi w

410 | —Cape Kaea: Lt. 20144 N | 156 58 W || 860 DT MS. ien 158 W

420 | —Kaumalapau Harbor ..........- 20 47 N | 157 00 W UR IA EGER
20500 | MOLOKAI 20900 | Mipway ISLANDS N ier od ve

Sith | DEI Tbe eret eee 2106N | 157 18 W 910 | —Sand I.: Aero Lt inr — 28 13 N 177 23 W

KIELEN 21 05N | 157 02 W 920 | — Welles Harbor, Midway I------

1070

APPENDIX S

MARITIME POSITIONS
WEST INDIES
—_—_ŘŘŘ—

Long. Index Place

i

Jamaica

Morant Point: Lt

Port Antonio

Galina Point: Lt

Montego Bay

South Negril Point: Lt 2
Little Pedro Point (Port Kaiser).
Portland Point: Lt

Port Royal

Kingston

Caribbean Sea

ES
ANO
C t2 Or

ZZZZ ZZZZ ZZZZZZ 22422

Gun Cay: Lt

Great Stirrup Cay: Lt..-

Great Abaco I. (Hole in the
Wall): Lt

Elbow Cay (Little Guana): Lt.-

Andros I., N. end: L

BEER
44444 4445
SRERERR ER `
GER
AESPNSANE >
344444344

Cat I., Devils Point: Lt

San Salvador (Watling I.),
Dixon Hill: Lt

Long I., South Point: Lt

Bird Rock, Crooked I.: Lt

Castle I.: Lt

Navassa I.: Lt

CAYMAN ISLANDS

—Cayman Brac: Lt 79 44 W
—Gorling Bluff, Grand Cay-
man: Lt 81 06 W
Swan Is.: Aviation Lt 83 56 W
Quita Suefio Bank: Lt 81 07 W
Isla de Providencia (Old Provi-
Cuba dence I.): Lt
Cayos del Ese (Courtown

o oooua
gas SEES IIVE

Punta Maisí (Cape Maysi): Lt.

Cayo Grande de Moa: Lt
Puerto Tanamo -
Haiti

Cap-Haitien

Pointe Picolet: Lt

Pointe Ouest, Tortuga: Lt

Cap du Mole (Cape St. Nicolas

8s
OAA
00D

Mole): Lt

A pi ki i
00 00 00 O O

898888

ZZ ZZZ ZZZZZ ZZZ

Cayo Verde: Lt

Cayo Paredon Grande: Lt Île de la Gonâve, Pointe Fan-
Cayo Caiman Grande: Lt tasque: Lt
Cayo Frances: Lt Banc de Rochelois: Lt

Caibarién Cap Dame-Marie: Lt
Cayo Fragoso: Lt Vis

Ile A Vache: Lt

La Isabela (Sagua la Grande)...
ae oe rr TL Jacmel

ayo Bahia de Cadiz: Lt ini :
Cao Cruz del Padre: Lt Dominican Republic
Cayo Diana: L Isla Alto Velo: Lt
Cardenas Punta Palenque: Lt
Cayo Piedras del Norte: Lt Jaina (Puerto Rio Haina)
Punta de Maya: L Santo Domingo (Ciudad Trujillo).

Motanzas ao) T 3 San Pedro de Macorís
Punta Seboruco: Lt

Castillo del Morro (Morro

Castle): Lt x Cabo Engaño: Lt
Habana ( Havana )- Cabo Samaná: Lt
Puerto Vita Cabo Viejo Francés: Lt
Puerto Plata

orcs GO

Ici IEEE Yy
ZZZZZZZZZZZZ
444444444444

m w n h a O c Di

OO HH 00 ONAN

Punta Gobermadora: Lt

Cayo Jutias: Lt

Cayo de Buenavista: Lt Puerto Rico

Cabo San Antonio: Lt

Cabo Corrientes: Lt Isla Mona: Lt

Cabo Francés: Lt Punta Jiguero: Lt

Isla de Pinos, Caleta Cara- Punta Borinquen: Lt
pachibey: Lt. San Juan

Surgidero de Batabanó

Cayo Guane del Este: Lt

Cienfuegos

Punta Colorados: Lt

Cayo Blanco de Casilda: Lt...

Cayo Blanco de Tunas: Lt

Cayo Breton: L

Cayo Cachiboca: Lt

Cayo La Perla: Lt......

Manzanillo

Cabo Cruz: Lt.

Santiago de Cuba...

OND

DDD
SASS
cona

D
a
o
00 AAA O DA

dd
ZWA Massage
HA
ww

Onn

dadddd ddzd4dd-

Ore ornare oo

Lesser Antilles
eg wands Poet, Bahia Ee de Vieques, Punta Este: Lt.
Punta Caleta: Lt "dd iid

1071

APPENDIX S
MARITIME POSITIONS

WEST INDIES—Continued

Index
No. Place Lat. Long. miey Place Lat. Long.
Lesser Antilles—Continued AU sbi Lesser Antilles—Continued
o , o +
22900 | VIRGIN ISLANDS 23500 | ST. LUCIA
910 | —Buck I.: uses Este aesti eoi ger à 18 17 N 64 54 W BLO = Cas tried set nau A 1401 N 61 00 W
920 | —Charlotte Amalie, St. Thomas I_| 18 21 N 64 56 W 520 | —Brandon Point (Cape Moule
IET CONT Dare a oe ea 18 20 N 64 45 W a Chique): Lt 60 57 W
940 | —Frederiksted, St. Croiz I______- TRES A EA o dd [ue Pid Ls F
950 | — Road Town, Tortola I......... 18 25 N | 64 37 W 610 Hārrkai Le
A eA nerada EE 18 45 N 64 20 W —Harrison Point: Lt 59 39 W
pada a 620 | —Ragged Point: Lt... 59 26 W
23000 | Sombrero: Lt 18 36N 63 26 W 630 Bridget
EE 18 12N | 6806 W | al ae; de e ke I 59 37 W
23100 | tLe Sarnt-M : ingstown, St. Vincent.......... 61 14 W
110 | —Marigot ( Franca r r 18 04 N | 63 06 W 710 | The Grenadines, Carriacou I____| 12 28 N | 61 27 W
120 | —Filipsburg (Netherlands) ......... 18 01N | 63 03 W IE time)
urā SE E Ste CONES Ð ae J A 61 45 W
nem kori Ile Saint-Barthelčmy--.. a = E ps t w $20] salino POL el a2 Ww
220 | Oranjestad, Sint Eustatius______- 17 29 N | 62 59 W || 23900 | Scarborough, Tobago 60 44 W
230 | Basseterre, St. Christopher (St. 910 | Isla Testigo Grande 63 07 W
Hide Nu 0 ate 17 26 N | 6248 W 9200] Los Roques: Lt — — 8 66 41 W
240 | Charlestown, Nevis I..---------- 17 08N 62 37 W || 24000 | BONAIRE
2908 Barbuda e Loses xL. 17 38N 62 48 W 010 | —Boca Spelonk: Lt 68 12 W
260 | Saint Johns, Antigua. ----------- 17 07 N 61 50 W 020 | —Lacre Punt: Lt....... 68 14 W
20 punni onise a PORNE E 16 42 N 62 14 W 030 | —Kralendijk____---------- 6817 W
asse- Terre, Guadeloupe. ....... 16 00 N 61 44 W “loi i ip
290 | Pointé-a-Pitre, Grand Terre TEEN 6f s2ny |2 dal Een Curnego: Lt 68 39 W
2330011 Ka Desfrade: Lt... sb]. 16 20 N | 6101 W || 24200 | CURAĢAO 1
310 | Grande Bourg, Marie Galante___| 15 53 N | 6119 W 210 | — Caracas Baai.........-........ 68 52 W
32090 Isla) Aves (Bird E) 12 ene 1542 N | 63 38 W 220: — Willemstad- ...-...-..-.-.-...- 68 56 W
330 | Roseau, Dominica..............- 1517 N 6124 W 230 | —Bullen Baai 69 01 W
23400 | MARTINIQUE 24300 | ARUBA
EL UE Os 1.14 rum 14 45 N 60 58 W 310 | —Sint Nicolaas 69 54 W
4204 = Cara vele: Lt. L 2:00 2-2 532220 14 46 N 60 53 W 320 | —Oranjestad. 70 02 W
430 | —Fort-de-France________--.--.-- 14 36 N 61 05 W 330 | —Druif 70 04 W
EAST COAST OF SOUTH AMERICA
25000 Colombia 25600 Surinam
o F; o , ov o ,
250108 TSla Fuerte: Lt. IZSIT ALI 5956108 Paramaribo 1 = <= -- 4. 549N | 55 09 W
020 Isla Tesoro: EL t--=== 202555222 10 14N | 75 44 W 620 | Galibi, Maroni River: Lt... 545N | 53 59 W
030 | Isla Tierra Bomba: Lt.......... 10 21 N 75 35 W
GE), ‘Cartagena E ll A docs cri ide 10 19 N 75 35 W || 25700 French Guiana
050^ | Punta Canoas: Lt- 2 sets 2322 10 35 N 75 30 W ^ p
060 | Punta Hermosa: Lt 10 58 N 75 01 W || 25710 | Ile Royale, Iles du Salut: Lt....| 517 N 52:36 W
070% Barranquilla 222 Sešas === ss 11 00 N 74 48 W 7208) HV Entant ee EE ss: 5 03 N 52 22 W
080 (Santa Marta $22. ut... 1115N 74 13 W ISO E 4 56 N 52 20 W
090 | Cabo de la Vela: Lt 1213N 72 10 W
25800 Brazil
25100 Venezuela
25810 | Ilha de Maracá: Lt............. 212N 50 17 W
251109 IMaracaibor A oc eege 10 38 N 71 37 W 820 | Ilha Bailique, Amazon River
19001 E 11 42N 70 13 W (Rio Amazonas); -Lt---------—- 100N 49 55 W
130 | Punta Macolla: Lt 12 06 N 70 13 W 830 | Ilha Machadinho: Lt........... 0 098 48 44 W
140 | Cabo San Román: Lt.......... 12 12N 70 00 W 840 | Cabo Maguari, Simao Grande:
150") (Cayo Borracho: Lib 22222292202 10 59 N 68 15 W AT A 0178 48 25 W
160 | Puerto Cabello 10 22 N 68 01 W 850 | Belém (Pará) -i-...--.-. AS 48 30 W
LOM ea Guairi 35...—--.----- 10 37 N 66 56 W 860 | Ilhas das Gaivotas: Lt..........| 0358 48 03 W
180 | La Tortuga, Punta Oriental: Lt. | 10 55 N 65 13 W 870 | Ponta Atalaia (Salinópolis): Lt.| 0 36 S 47 22 W
IOQDT Guanta! IICA TEE 10 14 N 64 36 W 880 | Ilha Boiucucanga (Camara-
252009 Puerto Ouere ic 10 28 N 64 11 W ASENTADA E UA E 0508 46 38 Ww
210 | Isla de Margarita, Cabo de la 890 | Ilha Maiau (Sao Joao I): Lt...| 1178 44 55 W
Isla (Cabo Negro): Lt........ 11 10N 63 53 W || 25900 | Ponta Itacolomí: Lt...........- 2108 44 25 W
2201 Cartipano_ Ee 10 40 N 63 15 W 910 | São Luís (Maranháo) . .......... 2328 44 17 Ww
BJ Una Ee game aue 10 34 N 62 18 W 920 | Ilha de Santana: Lt............ 2168 43 36 Ww
2A08 Ourio- zs SB Tees te tests comme 10 10 N 63 03 W 930r MACHT mm REED BET 2468 42 16 W
25300 | Río ORINOCO 940 | Ponta Pedro do Sal: Lt........- 2508 41 44 W
310 | —Punta Barima: Lt............ 8 36 N 60 25 W OG Oil 2177 ana AEEA TA A 3 00 S 41 46 wW
3207 ——Puerto-Ordaz-----------—..T 822N 62 42 W 960 | Ponta de Itapagé: Lt..........- 2508 40 00 W
970% Hortalezas(@eara) mes es. «< <= 3 435 38 32 W
25400 Trinidad 980 | Ponta de Mucuripe: Lt--------- 3428 38 28 W
990 | Rochedos de Sáo Pedro e Sáo d
25410 | Ieacos Point: Lt 1004N | 6156W Paulo (St. Paul Rocks)-----. =| 056N | 29 22 W
4200 POr EE tk De 10 39 N 61 31 W || 26000 | ARQUIPÉLAGO DE FERNANDO
430 | Chacachacare, Dragons Mouth DE NORONHA stir
(Boca de Dragon): Lt.......- 10 42N 61 45 W 010 = Atol das Rocas: ees 3518 33 49 W
4403 Galera Font II EE 10 50 N 60 55 W 0207 — hba Rata: sb. 123 neo. eee 3 49 S 32 23 W
26100 | Cabo Calcanhar: Lt...-.----.-- 5.10 3 35 20 W
25500 British Guiana 110 | Cabo de São Roque: Lt........- 5298 35 15 W
1909) Natal MP AÁ or uc 5478 35:12 W
25610 Georgetown as a eee ae = 6 50 N 58 10 W (80 WontasP mito MU esee 5 488 35 11 W

p O T ——— ———————

1072

APPENDIX S

MARITIME POSITIONS
EAST COAST OF SOUTH AMERICA—Continued

| ITS

Index 1
SAC Place Lat Long. No. Place Lat. Long
Brazil—Continued Sei E 27000 Río de la Plata aj 5
7 en LA 34 58 S 54 57 W
a eee g ee 2388 | 34 49 W || 020 Maldonado, Uruguay ees. 54558 | MEN
i x a er eras Lb-. e ee 55
RE E E EE ee 34 578 | 55 56 W
170 | Recife ( M UN S 8208 34 56 W 0504 Punta Bravar DIS oe 34 568 56 10 W
190 E a egene GE 060 | Montevideo, Uruguay ----------- 34548 | 56 13 W
262007! Maceió= 2220 22222 9408 35 44 W 070.) La Panela; Lt_-....--========== E 2 5 z E Wi
210 | Aracaju: Lt 10 58S | 37 03 W 080 | Colonia, Uruguay--------------- E 60 387 W.
220 | Ponta Itapuã (Itapoan): Lt....| 12 578 | 38 21 W 090 | Rosario, Argentina-------------- S E 5 15 W
230 | Ponta de Santo António: Lt....| 13 01 S 38 32 W || 27100 | Isla Martin García: Lt........- E eee ai
240 | Salvador (Baia) (Bahia). 12 58S 38 31 W 110 | Buenos Aires, Argentina--------| 3 3
250 | Morro de Sáo Paulo: Lt 13 28 8 38 55 W 120 | Puerto de La Plata, Argentina..| 34 52 S 57 54 Ww
HON Gamamr E 13 548 39 02 W Punta Piedras: Lt.------------- 35 27S 57 09 W
270 | Ilhéus (São Jorge dos Ilheos)____| 14 48 S 39 02 W 130 | Cabo San Antonio, Punta Se
280 | Morro Pernambuco: Lt......... 14 488 39 01 W 140 daaa E Ee 36 18 S 56 47
300 | Porto Beguro: Di: 162088 | 39 04 W
26300 | Porto Seguro: Lt___---- ^
310 Ponta otām Lt V n e 2 or 2 27200 Argentina
330 17 58 S 88 42 W || 27210 | Punta Mēdanos: prep. ee 36 53 S 56 41 W
340 19 37 $ 39 49 W 220 | Faro Querandí: Lt.............- 37 288 57 07 W
350 20198 40 20W 230 | Punta Mogotes: Li. 2 >see 38 06 S 57 33 W
860 20 198 40 16 W 240 | Queguén------------ il seo am 38 358 58 42 W
370 20 448 40 26 W 250 | Baineario Claromecó: Lt....... 38 51 S 60 03 W
380 20 548 40 46 W 260; Earo.Reécalada: bt. ...- See 39 00 S 6116 W
390 27300 | BAHÍA BLANCA
22 03 S 41 03 W 310 —Punta Alla. ... Ne £ : 38 58 S 62 06 W
26400 22 26 S 41 42 W 320 | — Ingeniero White____..--.-.---- 38 48 S 62 16 W
410 23 018 42 00 WM 27400 CEL Rincon: Ls os 39 23 8 61 01 W
420 22 58 S 42 40 W 410 | Faro Segunda Barranca: Lt..... 40 478 62 16 W
430 23 01 8 42 55 W 420 | Río Negro: Lt. Lar 41 04 8 62 50 W
440 23 04 S 43 09 W 430 | Faro San Matias: Lt----------- 40 498 64 43 W
450 22 548 43 10 W 440 | San Antonio Oeste............... 40 44 8 64 55 W
460 23 028 43 12 W 4250 € "POTIS RL El T 42 058 63 46 W
470 23 058 43 34 W 460 | Punta Delgada: Lt............. 42 46 S 63 38 W
480 | Laje da Marambaia: Lt........ 23 07 S 43 50 W 470. | Morro Nuevo: Lt__-......-_..-- 42 53S 64 09 W
490 | Ilha Grande, Ponta da Cas- 480 | Puerto Madryn. --............... 42 46 8 65 02W
telhanos IU c cc 23 10 $ 44 06 W 490) Punta Ninfas: Lt... 2 = 42 58S 64 19 W
26500 | Ilha Pau a Pino: Lt............ 23 06 S 4407 W 7500 | Cabo San José: Lt 44 318 65 18 W
510 | Angra dos Reis... El 0178 44 19 W 510 | Isla Rasa: Lt... 45 06 S 65 24 W
520 | Laje do Coronel: Lt SE 2320078 44 24 W 520 | Isla Leones: Lt................. 45 03 S 65 37 W
530 | Ponta Joatinga: Lt............. 23 18 S 44 30 W 530] Gabo Aristazábal: Lt: mAn 45 13 S 66 32 W
Tee 23 458 45 01 W 540 | Cabo San Jorge: Lt............. 45478 67 22W
550 | Ilha de São Sebastião, Ponta 550 | Comodoro Rivadavia------------- 45 528 67 28 W
do Bols Lt: E E 23 58 S 45 15 W 560s) (Cabo Blanco? DU 47 128 65 45 W
560 | Ilha de Alcatrazes: Lt... 24 06 S 45 42 W 910] Deseado i-am 47 458 65 54 W
670) || Laje de Santos: Lt-3--2ulce- gë 24 19 8 46 10 W 580 | Isla Pingüino (Isla Penguino):
580 | Ilha Moela: Lt 24 03 8 46 16 W Bs 47 558 65 43 W
UE eet EE 23 56S 46 19 W 590 | Cabo Curioso: Lt............... 49 118 6737 W
26600 | Laje da Conceição: Lt. 24 145 46 40 W || 27600 | Cabo San Francisco de Paula:
610 | Ilha Queimada Grande: Lt..... 24 20 8 46 41 W LI c rab rir jis 49 44 S 67 48 W
620 | Ilha de Bom Abrigo: Lt........ 25 07 S 47 52 W 610: | Santa Crus i Se. or. bg 50018 6831W
630 | Ponta das Conchas, Ilha do 620 | Cabo Buen Tiempo: Lt........ 51 338 68 57 W
Mel Etre- as ee 25-83 S 48 17 W 630r (e 51 378 69 13 W
6408) Paranaguá Sie E 25 80 S 48 30 W 640 | Cabo Virgenes: Lt.......... "| 0229009 68 21 W
650 | Ilha Caiobá (Caiova I.): Lt... 25 52 8 48 33 W 650 | Punta de Arenas: Lt -.| 53 098 68 13 W
660 | Sdo Francisco do Su! v 26 158 48 38 W 6604 Cabo Peñas: Ut... Eme WE 67 35 W
on" let prp eee 26 118 48 29 W 670 | Cabo San Diego: Lt............ 54 40 S 65 07 W
680 | Ponta das Cabecudas: Lt....... 26 56 S 48 87 W 680 | Islas Año Nuevo, Isla Observa- Y
690 Liha da Gales Li ce nome 27118 48 25 W torio bbs ee 54 39 S 64 08 W
26700 | Ilha do Arvoredo: Lt. 27 188 48 22 W 690 | Estrecho de Le Maire, Isla de
LON Florianopolis SE 27 865 48 34 W los Estados: Lt 64 44 W
720 | Ponta dos Naufragados: Lt..... 7 508 48 35 W || 27700 | Cabo Buen Suceso: Lt... 65 13 W
730 | Ponta de Imbituba (Ponta 710 | Cabo San Pio: Lt 66 32 W
Grande) Reis me see eee 28 178 48 40 W
740 | Tlhas das Araras: Lt. 28 218 48 40 W || 27800 Chile
DON Laguna: dee s cc woe es 28 29 S 48 47 W
760 | Cabo de Santa Marta Grande 21781041 Capo Hornos. S E 55 69S 67 16 W
DEE, 28 378 48 50 W || 27900 | MAGELLAN STRAIT
770 | Capáo da Canoa (Tramandaí) 910 | —Punta Dungeness: Lt......... 52 24 S 68 26 W
li. ote 29 47 S 50 03 W 920 ||| — CaborPosesion; Lt-—---—---* 52 18 8 68 58 W
EH Cidreira 3 Lio EM 30 118 50 12 W 930.1 = Cerro Direccion: EE 52 228 69 30 W
790 | Ponta da Mostardas: Lt........ 3L 15.8 50 54 W 940" — Pinta Delgada: aes eee 52 28S 69 33 W
26800 Rio Grandes Ee E ee 32 03 S 52 06 W 950 | — Punta Mendez: Dte o2 aaa 52 328 69 35 W
SIM 8/8 07 (0. Alegres ao EBENEN 30 00 S ól 13 W 960 | = Punta Satelite: Lt_--.--.----. 52 39:8 69 40 W
820 Albardáo: Lūsis eget ee 33128 52 45 W 970 | —Cerro Cono (Cone Hill): Lt___| 52 40 S 70 28 W
S908 CHUN. Lt. AN 33 44 8 53 22W 980 | —Cabo San Vincente: Lt....... 52 47 S 70 26 W
990 | —Isla Santa Magdalena: Lt____| 52 558 70 34 W
26900 Uruguay 28000 | —Isla Contramaestre (Quarter-
À master Ið ALDER 52 57 S 70 22 W
269101 (Cabo Polonio: Lto 2) eee 34 248 53 48 W 010 | —Punta Arenas (Magallanes) ...| 53 10 S 70 54 W
920 | Cabo Santa Maria: Lt. 34 408 54 09 W 020 | —Cabo San Isidro: Lt.......... 53 47 S 70 58 W
9301 Hislaide Lobos 35 028 54 53 W 030 | —Cabo Froward: Lt.---------.- 53 548 71 18 W

1073

APPENDIX S
MARITIME POSITIONS

WEST COAST OF SOUTH AMERICA

Place Index
lace Lat. Long. No.
Chile
o , o ,
MAGELLAN STRAIT 29870
—Isla Rupert, English Reach: 880
Di... mere | 53 40 S 72 13 W 890
= Isla Cohorn: Ltd ee 53 33 S 72 20 W || 29900
—Paso Tortuoso (Crooked 910
Reach), El Morrión: Lt...| 53 348 72 31 W 920
—Monte Radford (Radford 930
(HI) Li MĒRENS ede 53 26 S 72 57 W 940
—Cabo Cooper Key, Paso Largo 950
(Long Reach): Lt...-...... 53 158 73 13 W 960
—Isla Centinela (Sentinel I.): 970
Lietas — ee ES 53 058 73 35 W
— Bahía Félix: up --| 52 58 S 74 04 W || 30000
—Isla Fairway: Lt -.| 62 448 73 47 W
SOON) 1 2 ei ad 52 43 S 74 41 W || 30010
Groupo Evangelistas: Lt_______ 52 248 75 06 W 020
IsleuSan Pedro: Lk. -- eg 47 438 74 55 W 030
Cabo Raper: Li-.-......... 46 50S 75 37 W 040
Isla Falsa: Li...........:--- 43 538 73 44 W 050
Molinos RL 2 A ee 43 558 73 44 W 060
Isla Guafo (Huafo): Lt 43 34 S 74 50 W 070
Cabo Corcovado.. ---------- 43 08 S 72 55 W
DuentotMonM a 41 298 72 57 W 080
ISLA CHILOE 090
zIsladaltee: Lt... == DK 4 43 17 S 73 85 W || 30100
Punta Corona: Li........ 41 478 78 53 W 110
~ Punta Abut iit vel. 41 508 73 52 W 120
S ANO ET 1 eee 41 528 73 50 W 180
Cabo Quedal: Lt........... 40 58 S 73 56 W 140
Punta Galera Lib: 22. es: 40 00S 73 45 W
Morro Gonzalo: Lt......... 39 508 73 28 W 150
Conta lo 3 c ER ur aa 39 528 73 26 W 160
Katon + A rS 39 48 S 73 15 W 170
Punta Boeura: ts C 39 47 S 73 24 W 180
IsLa MOCHA 190
—Morro de las Torrecillas: Lt..| 38 22 S 73 58 W || 30200
—Punta Anegadiza: Lt......... 38 23 S 73 54 W 210
Punta Morguilla: Lt........... 37 478 73 42 W 220
VENTA AAA 87 37 38S 73 40 W 230
Punta Lavapié: LES. 37 09S 73 35 W 240
Isla Santa Maria: Lt........... 36 59S 73 32 W 250
WI TE T. IA EE 37 068 73 09 W 260
COLON EE e oia e 37 028 73 10 W 270
Bunta Gaulpén: Lt Sse 36 45S 73 11 W
Bunta. Tumpes: Lt-----—--.* 36 37 S 73 07 W || 30300
Zulcahuamol------— ET 4r 36 428 73 06 W
Isla Quiriquina: Lt_--24 - 222s: 36 36 S 73 03 W || 30310
Gabo Carranza bi---—---- ās 35 348 72 38 W 320
Punta Topocalma: Lt__-------- 34 08 S 72 01 W 330
Isla Juan Fernandez, San Juan 340
Batistas būs 5-5 4 sā 33 38 8 78 50 W 35
dE EE | amoo Æ 33 358 71 38 W 360
Punta) Panuali Lib. 053030 33 34 $ 71 38 W 370
Punta Curaumilla: Lt.......... 33 04 S 71 45 W 380
Punta, Angeles: Lm rm A 33 01 S 71 39 W 390
Valpanaiso F ee specs 33 02 $ 71 37 W || 30400
Cabowlablass E =: <. 31 518 71 34 W 410
Punta Lengua de Vaca: Lt..... 30 158 71 38 W
Puntavrortuga: Lt. pe 29 56 S 71 22 W || 30500
CoquitboB 1- ` 22 Xn stus 29 57 8 7121W
Islas Pajaros Lí: 9 3 eT x cr 29 358 71 33 W || 30510
Crun Grande gees enee b T Se 29 27 S 71 20 W 520
Isla Chañaral TEE 29 02 S 71 36 W 530
TT UL SCORE AA ee ce 28 28 S 71 14W 540
(RE Un 27 088 70 51 W 550

ISLANDS OF THE

Bermuda

North Roc lites === =======e2
Sta Georgela- =+ Balls te
St. David's L: Lt
Gibbs

Hamilton... Y RENE See Tio

Azores

Ilha do Corvo, Ponta Negra: Lt.

o

Q2 O2 W UW 9
"SO EO EO FO FO
ANS ^
ZZZZZ

39 40 N

o ,

64 46 W
64 41 W
64 39 W
64 50 W
64 47 W

31 07 W

Place Lat. Long.
Chile—Continued
o , o ,
Punta Ballenita: Lt... 25 458 70 47 W
Raualt ms a tm 25 248 70 29 W
Antofagasta___----- 28 38 S 70 25 W
Punta Tetas: Lt 23 31S 70 38 W
Punta Angamos: Lt... 23 02S 70 32 W
Mejillones.............- 23 07 8 70 28 W
Tiocopillase- E C =: 22 05 8 70 14 W
Punta Gruesa: Lt 20 228 70 12 W
IQUAGUE: 22-2 Ace ab 20128 70 10 W
Isla Alacran: Lt..... 18 29 S 7021W
Apate A E 18 29 8 70 20 W
Peru
Punta Coles Lia doo tE 17 428 71 22 W
OMoUendow E 17018 72 02 W
Buntallslay: Lt ⁄ LAOS 72 07 W
Matarani OF teet sz bäi A 72 07 W
ATICO TAS E o s == Eat 73.37 Wi
Punta San Juan 201 75 10 W
Punta Doña Maria, Islotes
Infiernillo: Lt__... ----| 14 408 75 56 W
T1900 AA eee pe 134318 76 15 W
Islas de Chincha: Lt............ 13 39 S 76 25 W
Grupo de Palominos: Lt........| 12 08S 77 15 W
Isla San Lorenzo: Lt............ 12 05 $ TANS W
Callao m ER ort T 230375 77 10 W
ISlauMIazoreagqb Use ae ae 11 248 77 44 W
Punta Cabeza Lagarto, Puerto
Huarmey E rs SR 10 07 $ 78 11 W
9058 78 36 W
8358 78 57 W
8148 78 58 W
7 498 79 29 W
6 568 79 52W
6578 80 43 W
6 26 S 80 50 W
5 558 81 09 W
5 188 81 13 W
5 05S 81 07 W
4408 8120W
4348 81 17 W
Cabo Blancos === one em shit 4168 81 15 W
Ecuador
Isla Santa Clara: Lt.:..-...-.. 3108 80 25 W
Punta Jambeli: Lt....... SIE 80 02 W
Punta Arena: Lt...... stab 3500 S 80 07 W
Bund m. ss ones L 2.445 79 55 W
Guaydaquile od ==). 2) 1218 79 53 W
Punta Santa Elena: Lt.- AS 81 00 W
Isla La! Plata: Lít..--— S A S] 81 06 W
Cabo San Lorenzo: Lt_ 210510358 80 55 W
Cabo Pasado: Lt ---1- a Pants) 80 30 W
Punta Galera: Lt -| 0 50N 80 06 W
HEH 0 58 N 79 42 W
Colombia
Tumaco as a ee = wg Ee HAN ca 150N 78 45 W
Isla Gorgona (Gorgonilla I.): Lt.| 2 56 N 78 14 W
Buenatentürd..--.--.-..-.-----n. 3 54N 77 05 W
Punta Charambirá: Lt....-...- 415N 77 32 W.
Punta San Francisco Solano: Lt.| 6 18 N 77 29 W

ATLANTIC OCEAN
mg

Azores—Continued

ILHA DAS FLORES
— Ponta do Albernas: Lt.......
SAN MOTE so. erroe
— Ponta Lagens (Lages) (Lajes):
I is XS wn X ME en
ILHA DO FAIAL (FAYAL ISLAND)
—Ponta Comprida (Capellin-
NOS) PMU oo eco eee faa £
=Horta ET =. 5. A

— Ponta da Ribeirinha: Lt......

OX

39 31 N
39 27 N

39:22 N
38 36 N

38 32 N
38 36 N

QUE

31 15 W
31 08 W

31 11 W
28 50 W

28 38 W
28 86 W

1074

35000

35100
110
120

130
35200
210

APPENDIX S

MARITIME POSITIONS

ISLANDS OF THE ATLANTIC OCEAN—Continued
EEE VE E

Place

Azores—Continued

ILHA DO PICO
— Ponta da Areia Larga: Lt....
—Ponta da Ilha: Lt. -..........
São Jorge, Ponta do Topo: Lt...
Graciosa, Ponta da Barca: Lt...
TERCEIRA
—Ponta da Serreta: Lt.........
—Angra do Heroísmo............
— Praia da Vitoria (Bahia Praia).
SAN MIGUEL
—Ponta da Ferraria: Lt........
= Poma Delgadaz--3-—..----———-.
—Ponta do Arnel: Lt...........
ILHA DE SANTA MARIA
—Ponta do Castelo (Goncalo
Velho): Lt
==Vila do Eiter se `
Ilhéus Formigas (Rocas Formi-
Cor LIC eos

Madeira Islands

ILHA DA MADEIRA
—Ponta do Pargo: Lt..........
—Funchal-::..-.-..324. 24 001.

Ilha de Porto Santa, Ilhéu de
Cimas Lt: SLU dun 40

Canary Islands

LA PALMA

—Punta Cumplida: Lt.... ....
—Punta de Fuencaliente: Lt...
— Santa Cruz de La Palma. .....

bal? qe. E ccce eno
'TENERIFE
— Punta de Teno; Ltz--—— m
—Punta Rasa Lti sosesc
— Santa Cruz de Tenerife. ...=..-
—Punta de Anaga, Roque Ber-
mejo:-Df:....3-.. em
GRAN CANARIA
—Punta Sardina: Li- n
—Punta Mas Palomas, Morro
Colchas: Lt

= Toleta te ee eee eee
ISLA FUERTEVENTURA
—Punta de Jandía: Lt,
= Puerto de Cabras- mnn
—Punta de Tostón: Lt
Isla de Lobos: Lt
Isla Lanzarote,
guers Li o tet ees
oe Alegranza, Punta Delgada:

Punta Pechi-

Cape Verde Islands

ILHA DE SANTO ANTAO (ST.
ANTONIO ISLAND)
—Ponta do Cháo de a Mansrade
(Ponta Oeste):
—Ponta do Sol: hl

England

SCILLY ISLES

Lands End bakām Lt
Wolf Rock:

28 35N
28 10 N
27 44 N
28 09 N
28 11 N
28 03 N
28 29 N
28 42 N
28 45N
28 51 N

29 24 N

17 04N
17 12N

Long.

28 3

27 1

25 A

didi ¿33 339343

35 W
25 W
25 W

31W
51W
01 W
49 W
52 W

29 W

25
25

22 W
07 W

Index
No.

33130
33200
210

Place

Cape Verde Islands—Continued

—Ponta de Tumba (Fontes
Pereira de Melo): Lt.......
ILHA DE SAO VICENTE (ST.
VINCENT ISLAND)
No dos Passaros (D. Luiz):
— porto Grande (Mindelo)_-_-_--
A Machado (D. Amelia):

ILHA DE SĀO NICOLAU (ST.
NICHOLAS ISLAND)

E E. Barrikenn ee

—Pre

—Ponta Gaiheta (Ponta Leste):

—Ponta do Sol: Lt d AUS, d
—lIlhču do Sal-Rei: Lt----------
Ilha de Maio, Forte de S. Jose:

ILHA DE SAO TIAGO
—Ponta do Lobo: Lt...........
EE S ET 1...

Ilha do Fogo, Ponta do Alca-
Led 2 << cs šas O
Ilha Brava, Ponta Nho Mar-
tinho: Lt

Islands of the South Atlantic

Ascension I., Georgetown...
St. Helena, Jamestown. -
Ilhas Martim Vaz..........
Ilha de Trinidade (Trinidad I.).
Tristan I. (Tristan da Cunha),
Tristan Settlement ._.._----__-
e Ieee ES
Bouvetøya (Bouvet I.)---------
FALKLAND ISLANDS
—Cape Meredith: Lt.
— Cape Pembroke: Lt
—ÁPOrtiStanley == EE
=BHagRocks IN € E mel
SOUTH GEORGIA ISLAND
—Cape Saunders: Lt.
El ee
= Grytviken Harbonzs---— SES
—Right Whale Rocks: Lt......
SOUTH SANDWICH ISLANDS
—Zavodoski I.

SOUTH ORKNEY ISLANDS

= aune] SO EROR
~ Signy IS Borge Bay---——--—
SOUTH SHETLAND ISLANDS

— King George I., Admiralty Bay.
TRAE 15 Harmony Point:

— Cape Moris: Lt
—Deception I.,
Lt

Collins Point:

BRITISH ISLES

England—Continued

St. Anthony Heads Lise
St. Catherines Point: Lt
Fowey

eg Nur
wo DON
e wwn
5555 S55 888 S585
AR NNNNA MNVNN ANNA NANDN

S
Ny
As

Long.

24 59 W

25 01 W
25 00 W

25 05 W
24 25 W
24 17 W
24 00 W

22 55 W
22 54 W

22 56 W
22 57 W

23 13 W

36 38 W
36 30 W
36 31 W
36 24 W

27 35 W
27 18 W

44 41 W
45 36 W

58 30 W
59 12 W
59 30 W
59 48 W

60 33 W

1075

APPENDIX S

MARITIME POSITIONS
BRITISH ISLES— Continued

Place 5 N Place

England— Continued Scotland— Continued

Eddystone Rocks: Lt
Plymouth

Start Point: Lt..
Dartmouth

Berry Head: Lt

Bill of Portland: Lt
Portland Harbor

Anvil Point: Lt

Hurst Point: Range Lts
ISLE OF WIGHT

PENTLAND FIRTH

—Pentland Skerries, Muckle
Skerry: Lt

—Swilkie Point, Stroma: Lt....

—Swona: Lt

ORKNEY ISLANDS

—Scapa Bay

—Copinsay: Lt

—Auskerry: Lt

—Start Point: Lt

—North Ronaldsay, Dennis
Ness: Lt

—Noup Head: Lt

—Brough of Birsay: Lt

—Tor Ness: Lt

Sib aas 444444444

3383383333 o
SwBZEZSSSYZZS BOBNBEBDZ ~

I D O Cr ma po vs pl On Aa IO Fa
EN ES EE
hV Od AND

Noma COM

—Egypt Point: Lt
Southampton
Portsmouth

2282222
ZE Bom
LAURA. ALI PEZ LZ LA AAA
CQ ^J C1 C Ha O 00 Cr ONON
SIEN

RADA JDD AE zl ANG

—Sumburgh Head: Lt

—Out Skerries: Lt

-Norin Unst, Muckle Flugga:
t

—Esha Ness:

Sule Skerry: Lt

Cape Wrath: Lt

Point of Stoer: Lt

Rudh’ Ré: Lt

HEBRIDES

—Tiumpan Head: Lt

—Butt of Lewis: Lt

—Loch Carloway: Lt

—Flannan Isles: Lt

—Barra Head: Lt

—Usinish: Lt

—Scalpay: Lt

Eilean Trodday:

Neist (Ness) (Eist) Point: Lt...

Oigh Sgeir: L

Point of Ardnamurchan: Lt....

Skerryvore: Lt

Dubh Artach: Lt

Rhinns of Islay, Orsay I.: Lt...

Mull of Kintyre: Lt

Campbeltown

Pladda: Lt

FIRTH OF CLYDE

—Little Cumbrae I.: Lt..

— Glasgow

— Greenock__-

o mow cw HC bt HO

aaa g
Hee ba CD
Qo N Or
NNO
Fäi

RIVER THAMES
— Woolwich

HHOOO DHHHODOO O HH kd ed ki i ka

aa oo
DD

DON
ZZZ

nonon on
& 60 00 Go
RHR 2

He O2 02 ONN

Spurn Head: Lt
RIVER HUMBER

— Grimsby

— Hull

Flamborough Head: Lt
Ling Hill: Lt

Whitby

Hartlepool

The Heugh: Lt...
Sunderland

ROUTINES

ong
ZZZZZZZZZ
HH HHDODDODOODOO Omm
OS gb for

Wat RU ON a)
pl pl H B A

SENSES BESSSBLAS 885 BISBE
3333333333333 di ¿333 3333 sees aaa

Da Or D Q2 4 O2 Du D A Hx a 02m GI CO

Coquet I.: Lt
Farne Is., Longstone: Lt...
Berwick upon Tweed

En Cn Cn Cn Or Gr ox
QA Or C Or A Or

ZZZZZZZ
DO ji ka kat
Caro BONDS Co SUERO OS

tank D

| Ailsa Craig: Lt
Scotland Corsewall Point: Lt
Black Head, Killantringan Bay:

Eyemouth
St. Abbs Head: Lt
Barns Ness: Lt

ZZA ZZZZZZZ ZAZAZAAZLZAALZLALZAAAA ZZZZZZ ALAA ZZZZ was Z2
PP COUR RRR HR CUNO OAIAARPROINIBAAD GOOD CHEE WWWN NNNUNN O0 N

ass 4444434

Noo
NOC
OOO
D 0N
coco cocco

England

ISLE OF MAN
— Point of Ayre: Lt

— Chicken Rock: Lt
—langness: I-------------
— Douglas

—Maughold Head: Lt

St. Bees Head: Lt

Barrow in Furness

SASS zzz

—Isle of May: Lt
Bell Rock: Lt

NOWNWWHE PEP PP
RO Ha A OED Wort

HP» O NA 000000 NO NN

E
Buchan Ness: Lt

Rattray Head: Lt

Kinnairds Head: Lt

Covesea Skerries: Lt

Inverness

Cromarty

Clyth Ness: Lt...
Noss Head: Lt
Duncansby Head: Lt
Dunnet Head: Lt

Great Ormes Head: Lt
Point Lynas: Lt

The Skerries: Lt
Holyhead

South Stack: Lt
Caernarvon

Bardsey I.: Lt

Saint Tudwals I. West: Lt

Pe PPR A e Ei
Läb to 0202 OT
00 00 NN 00 C» -1 DO

Dä D TI O2 M» f. GO BO I I BO DO DO BO O DO DO DO DO GO 02 GO DO DO Nu

1076

APPENDIX S
MARITIME POSITIONS

BRITISH ISLES—Continued

Place i Long. index Place
Wales—Continued Gef SA 38500 Northern Ireland qe” p
=== 54 15 N 5 50 W
i E kt = us A 52 01 N 4 59 W || 38510 Dundrum.------ mb ciel
37800 eech Head ee 52 02 N 5 04 W 520 | St. Johns Point: Lt..----- E g N 4 2 w
810 | South Bishop: Lt-------.------- 51 51 N 5 25 W 530 SE LM FOR 531 W
Ce | Dho Smals ND Eee e OPNS 5143N 540W 540 | Mew I.: Lt....----------- DÉEN kt
EES 51 42 N 517 W 550 Bangon LM GE 550W
S402 (St) Amis: Head: Die 5141 N 510W 560 elfast .... Rd M 48 Ni 541 W
350,11 Milford Haven a vienne BS Nile. TT g I esmu A 54 56 N | 544 W
i 590 | Rathlin I., Rue Point: Lt 5515N | 611W
37900 Gu io nnne 38600)| “Bondondefry "5220 Se 55 00 N 7 20 W
Colly o iy Bae see EE 5138N | 441 W ;
den Mur pl tree ee 51 34 N 3 58 W 38700 Ireland (Éire)
Males ie M ere 51 37 S
940 Bens Daka PE E 51 24 N 3 E W 38710 inshore 1 Head, Dunagree S uM
Cardiff, Wales RE 51 27 N 3 10 POTN pip
060 Nene. Wales.---- 51 35 N E W ie Veika. LA E d N 4 ^ w
Bristol, England. - 51 28 aln Heads
080 Flat THO 5122N 307W R Fanad Head: ts Bi T N T ag w
i een eee fanes
sity KD LA. 5115N 3 47 d Us ees bi arkas Fola: pu 2 R x 3 4: W
int boo 55-0 e 61 12N 4 12 athlin irne d
E ee 780 | Killybegs-------------- 38N | 827W
790 oneg Mo eer e
aen Katarā MES Slip. MOI ERES MIN | 828W
108 Lund y- NO Dit 51 12N 4 41 agletībs Bb 2 de ER m
SECH Hartland Point Lists = e 51 01 N 4 32 W 8201 "Blackrock: Li:.-—— ——— os 54 € y le i w
(908 Trevose Head: Ct eiT 50 33 N 5 02 W 830 Clare a Das LSL O di PS Ha
1407 Giodrevy EE 5014 N 524W 840 Westport.z e Lee c eee 8 Hep
ANE ccc em THERE Eoo FN
; ock Isle er IIA
a ikea aes as BES | a ME 870 Galway... eE E ARA 53 16 N 9 03 W
Bi 880% fInishesr S Inte sete. e
kā IE ook Hot EIA Sree a a 52 34 N 9 56 W
Rock: Lt Å 51 23 N 9 36 W || 38900 IVER SHANNON
on puse M 51 29 N 9 22 W 910 | —Kileredaun Point: Lt---------- 52 35 N 9 43 W
23011 Galley Heads Lt = etn 51 32 N 8 57 W 920 | —Limerick 52 40 N 8 38 W
240 | Kinsale, Old Head: Lt.......... 51 36 N 8 32 W 93011: ——Hoynesz- 2 vere 52 37 N 9 07 W
200w Cork- ss sā C EE a E 51 54 N 8 274W 115390007] i Traleett = —— ss 52 16N 9 42 W
260 | Cobh (Queenstown) --------=----- 51 51 N 8 18 W 010 | Tearaght I. (Inishtearaght): Lt_| 52 04 N 10 40 W
HON ee Dee ere 51 47 N 8 15 W 020 | Valencia I., Fort Point: Lt._.... 51 56 N 10 19 W
2800); Ballyeottonz bocas 51 49 N 7 59 W 0303) /Skellig$ Rocks LRA oe eee eee 51 46 N 10 32 W
2000 Y OUGKGL = see E 51 57 N 7 50 W 04041" Ther Bulls bts eee 51 35 N 10 18 W
38300), Mine Head: Dio. 51 59 N 7 35 W
SLOG Waterjor een SE 52 15 N i M w 39100 Channel Islands
3201 Hook Head I E ee Ee 52 07
3300 Mhuskar Rock: LA. eee eee 52 12 N 6 12 W || 39110 | Casquets: Lt.......... pee 49 43 N 223 W
340 | Wicklow Head: Lt 52 58 N 6 00 W 120 | Alderney, Quenard Point: Lt...| 49 44 N 2 10 W
3901 | Muglins SLE ra 224 Ee 53 16 N 6 05 W || 39200 | JERSEY ‘
640) | GU AAA 58 18 N 6 08 W 210 | —Sorel Point: Lt---—-— — 4916 N 210 W
370 | Dublin (Baile Atha Cliath) -_----- 53 21 N 6 18 W 220111 SA? Helier EI S ESM 49 11N 2 06 W
3804) ‘he Bailey; tis. = 3-54 102422 iN, 6 03 W 230) =a Gonbirej D1 < 49 11N 2 15.W
sDoupRockabillz? Too nee TTE 53 36 N 6 00 W || 39300 | Sark, Point Robert: Lt_________ 49 26 N 2 21 W
38400 | Drogheda 53 43 N 6 21 W || 39400 | GUERNSEY d
ALO EE 54 00 N 6 24 W 410 | —Platte Fougēre: Lt. 49 31 N 2 29 W
420 | Haulbowline Rock: Lt.......... 54 01 N 6 05 W 420), SS: Peten Ports Mac fone 49 27 N 2 32 W
430 miCarlingfond talco EEE 54 03 N 6 11 W 430 | —Les Hanois Rocks: Lt 49 26 N 2 42 W

WEST COAST OF EUROPE

nes
40000 Norway Norway—Continued
o , o + o , o +
40010 IF BAKOLA ALt Ze 30 11 E 40200 | VESTERÁLEN
020 | Bugøynes, Oterneset: Lt 29 40 E 2100 ——Amdenes: all, (SS e 9N 1607 E |
EU ads E Ee 29 44 E 270 ANA A A 4 N 15 11 E
(040 Vardo Tem e 81 06 E 230 | —Frugga: Lt r ON 14 34 E
050 | Hornģy: Lt.. 31 10 E 240 | —Litlóy: Lt__.... 6N 14 19 E
060 | Kjølnes: Lt.. 29 15 E 250 | —Kleivheia: Lt 7N 13 35 E
070 | Sletnes: Lt... 28 13 E 40300 | LOFOTEN
0807 Eelnes LAR 26 14 E SIONES OMV E in enero eee 67 25 N 11 53 E
090 | Knivskjelloden: Lt.............. 71 11 N 25 41 E s201 S VEST OV Me Due ee 67 39 N 12 44 E
401009 Früuholmen: Lt Lm 71 06 N 23 59 E S80 AE Gla pena DURO ERN 67 53 N 13 03 E
NAL TEMERE 70 40 N 23 40 E 3401 — Mioholmens Et?" vr 68 09 N 14 25 E
1204" Tarhalseny Lime SE 70 52 N 23 19 E 350 | —Skrova (Skraven), Saltveer-
180g Hasviky Ee 70 28 N 22 10 E holmen Le cien 68 09 N 14 39 E
140 | Fuglgykalven: Lt............... 70 19 N 20 10 E 40400 0 Narviko ee Ee 68 20 N 17 25 E
1504 Ors veers pes: see R 70 15N 19 30 E 4104 Crangy mt mt 15 ol ES 68 11 N 15 36 E
1607 Hille Lyngdys lb eee 69 55 N 18 28 E 420 | Mālģy-Skarholmen: Lt_________ 67 46 N 14 25 E
17046 TE 69 39 N 18 58 E 430 | Landegode, Eggeldysa: Lt..____| 67 27 N 14 23 E
180 “Hekkingens biie 69 36 N 17 50 E 4406 Giro ye To RA A 67 23N; 13 51 E

1077

APPENDIX S

MARITIME POSITIONS
WEST COAST OF EUROPE—Continued

Place S ND! Place

Norway—Continued Norway—Continued

Tennholman: Lt
Kalsholmen: Lt

oo m
ow

Bremsteinen, Heimģy: Lt
Sklinna: Lt

Q0 h9 -1— 2»

ZZZZZZZZZ
AS
S588525

ZZZZZZZZZZZZZZ

Kya: L
Buholmrāsa: Lt S
Kaura, Kaurleden: Lt... Vinga: L
Góteborg
Yttre Tistlarna: Lt
Nidingen: Lt
Varberg
Morups Tánge: Lt___--_._____-
Falkenberg
leren Ge
Halmstad

ES

Exi Ed Ed Ed [xd Ed Ed d Ed Ed [xd Ed Ed xd Ed daad El Ed

Or Or Or OF OV o OF
QONNNNNN
O m ua a
C --1 00 DO O 4

m m

NVON

A DN nn

Sletringen: Lt
Trondheim
Haugjegla: Lt
Skalmen: Lt
Grip:
Kristiansund

m
Hn
N
a

O «5 (O «D 00 00 00 OO —1—1 —1 0» O3 OQ» O» OQ». D Dt On O1 Ot d O1 Ot Ot OY. ATE PP PPP POONA OA A O 00 00 «o cO O cO co
he
t2
w

$3139 RS RIAD DURADO BROS >
HEHEHE HEHEHE

MH. O2 V OTNHIVONNROOIYHBROWONABR H Or

Hälsingborg
Ven, Haken: Lt
Landskrona

na: Lt
Storholmen: Lt
Alesund
Alnes, Godøy: Lt
Gressøyene: Lt

Klagshamn
Falsterbo: Lt.

Pd p pl ki pi ji ka ba i
DO DO C2 DO DO DO hV DO DO BO
A gr O Cn OT > He GO DO OS

e
OO PRO RO O ON NT GO ODO OF

t2

Yttergyane: Lt
Geita: Lt...

Holmengrá: Lt
Hellesģy: Lt
Skarvøy: Lt
Bergen

Marsteinen: Lt
Slátterdy: Lt
Ryvarden, Mylstrevág: Lt
Haugesund
Rģversholmen: Lt
Utsira: Lt
Geitungen: Lt
Stavanger

Feistein: Lt
Obrestad: Lt
Egerģy: Lt

Lille Prestskjeer: Lt
Egdeholm: Lt
Varnes: Lt

ON U a or
00 42 O Gb O Ha

x

Utklipporna: Lt

Kalmar

OLAND

—Olands Sédra Udde: Lt
—Kapelludden: Lt
—Olands Norra Udde: Lt
GOTLAND

—Stora Karlsó: Lt
—Hoborg: Lt

— Ostergarn: Lt

Cc rnmttoo5

O OO NC
NAO A O) a A Sos

(TV VO K ENEE on
Paad HES

— Fårösund

— Fårö (Holmudde): Lt
— Visby

Oskarshamn

Västervik

Häradskär: Lt
Arkösund

Norrköping

Oxelósund
Grankubben: Lt.
Landsort: Lt
Huvudskár: Lt...
Sandhamn

Stockholm

Grónskár: Lt

Svenska Högarna: Lt--
Sóderarm: Lt
Tjárven: Lt
Svartklubben: Lt
Understen: Lt

Oregrund

Orskür: Lt
Bjórn: Lt

W

Homborsund: Lt....... bani.’
Torungen: Lt

Ytre M¢kkalasset: Lt

Lyngør: Lt

Jomfruland: Lt

Dä Cu CC Ru DOR

ee a A
Guldholmen: Lt

Torgauten (Strómtangen): Lt...
Fredrikstad
Struten: Lt 59 07 N

OOo BON S U DO DAN SROS
Did bidd id

ANTAWA NW

1078

APPENDIX S
MARITIME POSITIONS

WEST COAST OF EUROPE—Continued

LEE

Index RRE dex Place Lat.
No? Place Lat g NO
Sweden— Continued rier K % 43100 USSR Arr:
17 34 E 43110 | Ostrov Sur-Sari (Hogland),
17 10E Mys Launat-Revi: Lt........ 60 01 N
17 21E 120 | Ostrov Narvi as (EA 60 15N
17 05 E 430 | Ostrov Hall: Lts:---3 9 60 24 N
17 25E 140 | Vyborg Geet Ee 60 43 N
17 28 E 150 | Serkoluoto (Sárkkáluoto): Lt...| 60 18 N
17 07 E 160 | Mys Styursudd (Seivástó): Lt..| 60 11 N
17 34 E 17011 Leningrad i... — —--...—— 59 56 N
17 38 E 180, | Krokahmadi_---1 — bað 59 59 N
17 45 E 190 | Ostrov Kotlin, Ostrov Kron-
17 19 E Shlots EE 59 59 N
17 44 E 439009 "T'olbukhmios ZO ===> 50 03 N 29 33 E
18 03 E 210 | Ostrov Karavalday, Shepelev-
1757 E ski: dis 4 20202. acc e DS S
18 06 E 220 | Ostrov Bol'shoy Tyutyarsari
18 28 E (Iso Tytarsaari): Lt...-....-- 59 51 N 2711 E
is n S 43300 Estonia
19 03 E || 43310 | Narva-J6esuu_.----------------- 59 28 N | 28 02 E
19 36 E 320. | Póhja-Ubtju: Li-. 2205 59 41 N. | 26 31 E
20 03 E 330 | Vaindlo (Stenskar): Lt. 59 49N | 26 22E
20 17 E 340 | Mohnisaar (Ekholm): Lt... 59 41 N. | 25 49 E
420 | Gadden (Holmogadd): Lt...... 63 36 N 20 45 E S50: || Kerik(Kokskarji Lt t ete 59 42N 25 01 E
43001 Jüparorens Diss ce c so 6341 N | 2056 E 360 | Aegna (Wulf EV: Lt............ 59 36 N 24 44 E
440 | Stora Fjüderügg: Lie oe ee 63 48 N 21 00 E 370. | Tallinn(dzenal)- 5 59 27 N 24 46 E
EE 64 00 N 20 54 E 380 | Naissar (Nargen): Lt... -| 59 36 N 2431E
460 | Yttre Vánnskár: Lt 64 10 N 21 08 E 390 | Suurup (Sourop): Lt... 59 28 N 24 23 E
470 | Blackkallen: Lt....... 64 20 N | 2131 E | 43400 | Pakrineem (Paker Ort): Lt.....| 59 23N | 2402 E
48011 Bjuroklubb: Lie ea 64 29 N 21 35 E 410 | Osmussaar (Oldensholm): Lt...| 59 18 N 23 23 E
490 | Rönnskär: Lt.. 65 02 N 21 34 E 490 | Takhuna Nina: Lt--__ ` -= 59 05 N 22 36 E
42500 | Ródkallen: Lt. - 65 19N | 22 22 E 430 | Kópu Poolsaar (Dagerort): Lt__| 58 55 N | 2212E
GUNDAM SS E E 65 35 N 22 10 E 440^| Ristnas pia ae oe 58 56 N 22 03 E
520.1 EE E EE e 65 32 N 23 34 E 450 | Vilsandi (Filsand): Lt.......... 58 23 N 21 49 E
460 | Sērve Nina (Svalferort): Lt.....| 57 54 N 22 04 E
470, | Alliranussi:js see te traer 58 10 N 2247 E
42600 Finland 480 | Kūbassadres Utes xe S 58 26 N 23 I8 E
490 | Kihnu (Kind): Lt 58 06 N 23 58 E
426105] SONAR Mee es A 65 51 N 24 OVE 48500 | Parnas E. esa eee eee E ` 58 23 N 24 30 E
AO Ce ae Saal EE 65 44 N 24 34 E
630 | Ajossaari (Ajosholm): Lt....... 65 41 N 24 31 E 43600 Latvia
6407) OU eee oe TE TEE ee 65 01 N 25 BE
650 Hailuoto (Karlö), Marjaniemi: 43610" | Ainaži! 9 T ee eee Es ed 57 52 N 24 23 E
B S sa i as 5 02 N 24 34 E 620 | Kurmrags: Lt e 57 33 N 24 22 E
660 Uikpicatia: Ait te eee to ed 64 20 N 23 27 E 630: | Arga ERGO EE 56 57 N 24 06 E
ee 63 57 N 22 51 E 640 | Daugavgrīva: Lt. 57 04 N 24 01 E
680 | Hállerund (Khelerund): i LE 63 39 N 22 25 E 650! || Miērsravs Ee 57 22N 28 07 E
690 | Valsórarne (Valassaari): 63 25 N 21 04 E 660 | Kolkasrags: Lt 57 48 N 22 38 E
a 1; a da a uu EECH A 7 ` 20 36 E 670 | Mikelbëka: Lt 57 36 N 21'59 E
710 aasa (US) see EE 3 07 21 34 E T
b 4 680 Oviši “(Lyser Orð) Lt- 57 34 N 21 43 E
£29 dan: E Eee ee e s 20 45 E 690 | Ventspils (Vindau) (Windau)...| 57 24N | 21 32E
ti Ņina Gy E 21 11 E || 43700 | Užava (Backofen): Lt... 5713N | 21 25 E
SE DARE li | S08: 710 | Akmenrags (Stein Ort): Lt... 56 50 N | 2104E
750 Yttergrund: below EE 61 59 N 21 I8 E 720. | Liepaja Liban) ai 56 32N 20 59 E
760 | Sāppi (Sebbskár): Lt______..... 6129 N 2121 E i :
770 | Nurmisaari (Nurmes L): Īt---| 61 12 N | 21 208 rel ALES
CUM RA sets sti MR, s Et 61 08 N 21 30 E iné
790 | Kylmapiblaja: LE... 2.22... 61 09N | 2118 E || 43810 | Klaipēda (Memel)....-..-.------ 55 42 N | 21 09 E
4280 NSKA TS cue. Vds ce PE IS 60 43 N 21 01 E
810 | Salskar, Södra Salskar: LL 60 25 N | 1936 E || 43900 USSR
AAA Cc ..| 60 18 N 19 09 E
830 | Heligman (Hellman): Lt. 60113 N^" 19193 Ee ee ECS:
8409 EE EE eses 60 10 N 1018 H9 EE 12
850 | Korsó: Lt 60 02 N | 1954 E 920 | Baltiysk (Pillau) -—.......-..... 5438N | 1954 E
860 Nyhamn: i CU 59 58 N 19 57 E 930 | Kaliningrad (Konigsberg)--------| 54 42 N 20 32 E
POR UT ØL bs sos EEN 59 51 N 19 55 E
= as den eer asis res 5930N | 2021 E | 44000 Poland
‘okarsorens) Lūse ---| 59 46 N 21 01 E i e "
KEE s Eet cig ere
910 | Turku (Abo)... 60 27N | 2 ENEE? Q
OL EE Ch 22 16 E 030 | Nowy Port (Neufahrwasser) ----- 54 24 N 18 40 E
920 | Bengtskār: Lt -1 -..| 5943 N 22 31 E 040/| Caynia BRA < Sc e] 54 32 N 18 34 E
930 Russaró: Lt. S Pe 59 46 N 22.57 E 0500! Hebhtbt-393 5-2 md 54 36 N 18 49 E
940 | Hangó (Hanko) 59 49 N 22.57 E 060 | Rozewie (Rixhóft): Lt... .. 54 50 N 18 20 E
SCH Ge tea E Hi N 23133 E 070 pup (Stilo d [t INS 54 47N 17 44 E
orkala Kalibada; aa 52 M 24 20 080 eba: Radiobeacon............. f J E
970 | Kytö (Kytö Karingen): Lt.....| 60 04N | 24 45 E spe oen
eism rc 60 10 N | 24 58 E | 44100 German
ja Ger bate): ies 60 06 N 25 00 E E
€ oderskünwLisec cce e (60007 25 26 E 130 | Ozolpino (Scholpin): Lt 54 43 N 17 15 E
010 Orrengrund: DIE CEN 60 16 N 26 27 E 140 | Ustka (Stoipmtlndes NER ARES 54 35 N 16 52 E
020 | Ródskür (Ruuskeri): Lt 59 58 N 26 42 E 150 | Jarostawiec (Jershóft): Lt... 54 32 N 16 33 E
030 | Someri (Sommars): Lt--------- | 60 12N 27 40 E 160 | Dartowko (Rügenwaldermünde)..| 54 27 N 16 23 E
A A en ter ese, |

1079

APPENDIX S
MARITIME POSITIONS

WEST COAST OF EUROPE—Continued

Place ; Index Place

Germany—Continued Denmark—Continued

Gaski (Funkenhagen): Lt — Nykgbi

Kotobrzeg (Kolberg) 490 citando Rev: Lt

—Sejerģ (Sejró): Lt

eye (Revsnees) Puller:

Swinoujšcie (Swinemúnde)

Szczecin (Stettin)

Greifswalder Oie (Greifswald
I): Lt

ESER

RÜGEN 50 | — Vordingborg

— Sassnitz Vejrģ (Veiro): Lt

Omg, Langelands Øre: Lt
Agersģ, Helleholm: Lt
Sprogģ: Lt

FYN

—Nyborg

—Knudshoved: Lt

aga a a Cn O Or
Ga da OY cr Ot O Gr Or

©

on

Ki
Hw
OD

EELER
ZZZZZZZZZZZZZ

g
Cr rn or or

A TO Ct 2000 HH OI NU CI Rm

—Æbelø: Lt
—Strib
—Middelfart _-
—Tvingsbjerg: Lt
—Assens_---
—Helnes: Lt.

GBGRR RER RER

Travemūnde

Pelzerhaken: Lt__

Dahmeshóved: Lt

FEHMARN

—Staberhuk: Lt

—Marienleuchte, Ohlenburgs
Huk: Lt

—Westermarkelsdorf: Lt

LI Blügsespic338 070 K

Neuland: Lt

Kiel, Nord-Ostsee- Kanal

Wik (Vik)

Friedrichsort: Lt..

Bülk: Lt

en
ooo ooo oo

En Cn CnCn Cn on
Ga O OY OY O
GEZ

— Svendborg
—Elsehoved: Lt
LANGELAND

— Rudkøbing
—Frankeklint: Lt

—Traneker: Lt

—Keldsnor (Kjelsnor): Lt
ZERĢ d

—Vejsnes (Veisnes) Nakke:

a
a

=
©

Aona Aa O22 CY CA OY a a i

BOOOOW IIRDRDADO

o SB43E8B588B88B8S
Sibbi) BEK

Ex Ex Ex End End End Ex Ex En Sees

ZZZZZ ZZZZZZZZZZZZZZ ZZZZZZZZZ ZZZ

oowvooH
EE
Loo

= hv
wn

Haddad i!

t
—Skjoldnes: Lt
ALS
— Sønderborg
—Kegnæs (Kekenis): Lt
— Pøls Huk: Lt
—Traner Odde (Tranerort): Lt.
—Nordborg: Lt

SSRRS
ZZZZZZZZZ

m

«OD C «5 «o «D do «D «Deo codd O O OG SOS oo

H CO CO r2 e Q2 dH» 01 Q5 Dä Q2 Gi C — Ot bäi G2 A C Cn Or a a O2 = bäi G2 = O1 O GO OT HR POPE e EV IR OT O OT vs

QQ Cn Cn Qu en
ad DAA O 00 0 OQ» t9 OQ» O KO «O QD O0 O tO P Go N Y A a IN DO C tà 00 Co O» O2 A RO

> P CO Ka
NOHO

Denmark

Christiansø: Lt
BORNHOLM
—Hammer Odde: Lt
—Sandkaas Odde: Lt

ooo
23528

SAA ES 0B GS 3 cO CO Sd ri CA ED Y CR OO FO O3 DU EO CD RO GO A FO 09 OD 00 C» CD OR

S995» v
ZZZZ Z

a GO OO CD

Mon

—Hellehavns Nakke: Lt
—Mgģn (Mčen): Lt

FALSTER

— Stubbekøbing

—Hestehoved: Lt

—Gedser (Gjedser) Odde: Lt...
— Nykøbing

LOLLAND (LAALAND)

"S 388
ZZ

Sletterhage: Lt
ZEbeltoft (Ebeltoft)

Aone 22298
ZZZ ZZZZ ZZ

zz

Fornes: Lt

Gerrild, Knudshoved: Lt
Udbyhģj (Elkjerbakke): Lt....
Anholt: Lt

Hals Barre: Lt-

Aalborg

Læsø, Syrodde: Lt

—Drogden: L Nordre Rģnner: Lt

—Nordre Rģse: Lt Frederikshavn

= Hirsholm: Lt
Se Ge Skagen, Jutland (Jylland)

—Mi : Gamle Skagen (Hojen): Lt
Zīlaktort. Lt. Se Hirtshals: Lt

— Helsingør Rubjerg Knude: Lt

— Kronborg: Lt Hanstholm: L
—Nakkehoved: Lt
— Gilleleje

E Dī K Lyngvig, Holmsland Klit: Lt--

—Spodsbjerg: Lt Ringkøbing, Jutland ( Jylland )..-| 56 05 N

37338 wm OOo

00 tà Nu G2 00
ZA ZA
NWP b9 B2 2 HO O1 | O2 UN b C OO OY GO

1080

APPENDIX S
MARITIME POSITIONS

WEST COAST OF EUROPE—Continued

| m,

Ka Place Lat. Long. index Place Lat
Denmark—Continued jas T France— Continued me
46590 | Blaavands Huk: Lt...........- 55 33N 805 E || 47790 | Somme, Le Hourdel: Lt-------- 50 13 N
46600 | Graadyb, Skallingen: Lt....... 55 28 N 8; 10:00 1147800811 Treporti? meee ae = E 50 04 N
610 | Esbjerg, Jutland (Jylland) ------- 55 28 N 827 E 810) t Dieppe ¿== arra 49 56N
620-| Fang, Fang Lo: Li-.........-.- 55 28 N 8 25E $20: || Pointe:d^A1Uuys Lí----—---.—— 49 55N
830 | Saint- Valery- En-Cauz. --| 49 52 N
46700 Germany 840. greomp COT S EA E t _-| 49 46 N
850 apid'Antifer:Lbt--—— 22223%= < 49 41 N
46800 | SYLT 860 der dela Heéeve: Lb F æ 49 31 N
Hee 55 03 N 824E 47900 | SEINE
E SO ot a ee 54 57 N 8 21 E O1041 = és avy eee... Hate Ke 49 29 N
830 | —Hórnum Odde: Lt............ 54 45 N 8 17 E 0209]. — Rowen Ik 23.1... ee 49 27 N
46900 | Amrum, Norddorf: Lt__-------- 54 40 N 8 19 E 48000 Trouver EA. Ee 49 22 N
EE 54 29 N 9 03 E 010s) Onistroehami Lt... cese - 49 17 N
920 | Westerhever Sand: Lt.......... 54 22N 839 E 0204) Caen: Seu 2-1- «En 49 17 N
930 Tenning r E AAA å R ` d a 3 0301 Pointe.de Ver: lut "= — 49 20 N
sams E e C ees 2 T ; 1
9509” Helgoland; Lt------3-—--—-- 54 11N 7 53 E Kë c ier e Hesen 49 30 N
Šo iC Lt..........--.------ 53 55 N 8 30 E 050 | Pointe de Barfleur: Lt..........| 49 42 N
010 | —Brunsbúttelkoog, Nord-Ostsee- Go SE K Ak p a `
Kanal (Kiel Canal) --.------ 53 53 N | 909E (SOM Geet Gin
020 (en 5333N | 956E Ae CSR 2. AN
STan ege 33.933 Nal F 9 58.8. bt Clap da Carta LU Es
040 | —Harburg- Wilhelmsburg - ------- 53 28 N 9 59 E Ga ett EE LEN
Vð Ð 0712027 a e ce BN n a PECI
47100 | WESER 110 | Grande Ile Chausey: Lt........ 48 52 N
1101 Roter sand: Ee 53 51 N 805E 120 | Pointe du Roe (Cap Lihou):
1200 = Hoher Wer n 53 43N | 815E Lt---------------------------- 48 50 N
130 | —Bremerhaven._.--.-.---------- 53 33 N 8 34 E 130 | Granvtlle--------------=------ 48 50 N
O Wesermande oS 53 32 N 834 E 140 | Pierre de Herpin: Lt 48 44 N
150 | —Nordenham------------------- 53 30 N 8 30 E 150 | Rochebonne: Lt...............-
1608 Bremena s TN 53 07N | 843E 160 | Saint-Malo. .....
47200 | Wilhelmshaven...-.------------- 53 31N | 809E 170 | Cap Fréhel: Lt.-..............-
210 | Wangerooge: Lt 53 47 N | 75E 180 | Grand Léjon: Lt
Gales Aë ees 53 43 N 714 E 190 | Roches Douvres: Lt
230. || Borktum® TP 499. ee 53 35 N 6 40 E 48200 | Les Heaux de Brehat Lt....... 48 55 N
2409 Fondene AV Ee 53 22N 713E 20 ae Sept et U ee £ 48 53 N
MEX Netherlands 230 [UP den ied Secus Ë R
i Delfzijl ri OIEA TEL 53 X N 656E 240 | Īle Vierge: TE AIRIS 48 38N
: Schiermonnikoog: Lt........... 53 29 N 609E 4 1 d d d
330 | Ameland, Amelander Gat: Lt__| 53 27 N 5 38 E SR EE STAND 48 28 N
340 | Terschelling, Brandaris: Lt.....| 53 22 N 5 13 E 320: | = Orea h LAF C aa te meee 48 27 N
350 | Vlieland, Vuurboetsduin: Lt...| 53 18N | 504E 880) | Ba Jument: Lí B 48 25 N
360 | Texel, Eierland: Lt..-.----....-| 83 11 N | 4 51 E | 48400 | Binte de Corsen: Lt.-----------| 48 25 N
` a van Texel, Kijkduin: 410 | Presqu’ile de Kermorvan: Lt...| 48 22 N
380 | Zanddijk (Grootekaap): LU... 52 53 N | 443E || 430 | Chaussee des Pierres Noires: LE| 48 19 N
P Egmond aan Zee: Lt...........| 5237N | 437E 440 [ye E ee Hm 48 2 N
MITT RENE 5228N | 434E 450 | Pointe du Toulinguet: Lt. .....| 48 17 N
ZION Amsterdam EE 52 22N 4 54 E 460 | Douarnenez 48 06 N
420 | Noordwijk aan Zee: Lt 5215N | 426E 470 | Chaussée de Sein, Ar Men: Lt.
430 | Scheveningen ta anaa 52 06 N 4 15 E N d gn, Ar Mens dtc dg
440 | Hoek Van Holland. 5159N | 407E 480 | Ile de Sein: Lt.................. 48 03 N
45001. Feotterdami EV eaa 51 55N 4 30 E 490 | La Vieille: Lt----------------- 48 02N
460 | Dordrecht 5148 N 4 39 E || 49900 | Audierne—__...------.-------__- 48 01 N
470 | Goeree, Westhoofd: Lt 51 49 N | 352E O A
480 | Schouwen: West Schouwen Lt.| 51 43 N 341 E r mühD: Lt_------------------- 47 48 N
490 Westkapelle: i tc eee 51 32 N 3 27 E 520 Concarneau ee RES 47 52 N
E HEU FIA) 51 27 N 336 E 530, || [le de Penfret: Et: coma 47 43 N
erneuzen (Neuzen)--------- 51 20 N : y 1 i :
520 | Nieuwesluis: Lt................ 51 24 N 3 30 E in Tee Pep Mth lara 47 25 N
47600 ST 48000 | BeLLE-ÍLE m
610 | —Pointe des Poulains (Poulains
47610 | Antwerpen (Antwerp)........ 51 7 Islet): Lt-------------------
620 | Gent (Ghent)... Cee SN) 34k || 62 | —Ooulphar: T4 aanub sut
DEI Lëns 51 20 N 3 12 E || 48700 | Le Palais. .........-....-......-
640 | Brugge (Bruges) ........... 51 13 N 3 13 E 710 | Les Grands Cardinaux: Lt
650 | Oostende (Ostend) 51 14 N 2 55 E 720 | Port Noaio.
660 | Nieuwpoort (Nieuport) .......... 51 08 N 2 44 E En Au SE
47700 France 810 | —Saint-Nazaire. .... complica
820) ||| = Donges ERE I
277403 JB ap a e tees 2 21 E 830 | Paimboeuf a
720)|| Gravelines: = nx A 18 207E 840 | Nantes- aaa celeres
OC. 3 0 ko 1 51m || 28900 | Pointe de Saint-Gildas: Lt
dem pss cd MI. ESA 135E 910; Tle dute
CUE, S n > , $ A
TOU ap dC. Ee i 2 E 920 | Ile d’Yeu, Petite-Foule: Lt
110: Lo Touquet: Lt. 08.0 das 136 E 930 | St. Gilles sur Hie een
780 | Pointe du Haut Bane: Lt 1 34 E 940 | Les Sables-d' Olonne. ............

Long.

ococoro O O DOD DOD O HERO
PRORRDI HO

mi pi jā kj ja ji i
s55czs5EH 555% LEE
3344:3 24334437 ds dienā

EE
p

3 39 W

STD cre
Rocheforte Ee
Īle d'Oleron, Pointe de Chassi-

ron: Lt
` GIRONDE

Tere Nepre? Dt? of ct.
id (As $id kt T
az DOT UA Eee ee E c EM

Cant Barret ites e ea Manas
LA EE

Ee uet TES as T
Pointo St. Martin: Dt---— —-—
Biarritz: c tn Aie 1 ES

Spain

CaborEBguerc Li- cameo ===
Pasajes de San Juan
Cabo ha blata t Et- -i

Sapniodng A 1. u.c rrullc eae eei.
Cabo de Ajo: Lt
Santander... -------
Cabo Mayor: Lt
Suances (San Martin de la

¡ARE Mi besos buscad
San Vicente de la Barquera_-----
Ribūdestll di 2.22 i
Monte Somos: Lt.
Guon T Aisa: ts

Isla. Tapias Lt 7 s
Punta de la Estaca de Bares:

Lat.

43 31 N

A

KI
UNPAA PEPSSILEBNEN UN
DATA AAA AAA V

APPENDIX S
MARITIME POSITIONS

WEST COAST OF EUROPE—Continued

Long.

Or hn
e
Ka
=

[un
t2
a
3

ka ren A pl be pol jomi pol Feat pl Feat CO pl po Feat jr
=
o
z

CD WN CO BO GO DO DO DO 6 5
o
N
P
=

Index
No.

50000
010
020
030
040
050
060
070
080
090)

50100
110
120
130

140
150

50200
50210

220
230
240
250
260
270
280
290
50300
310
320

Spain—Continued

Lig Gomi R toe E EE
Torre (Tower) de Hercules: Lt_
Isla Sisarga Grande: Lt
Cabo Mitano Lis
Cabo Toriñana: Lt...
Cabo Finisterre: Lt...

Islas Cies, Isla del Faro: Lt.....
ER de San Martin, Cabo Vicos:

Portugal

Cabo Montedor: Lt............
Ee lte o
Porto de Leizūes_--------
Porto (Oporto) "==
PAU CIN ORE RENEW ane no ae eee
Cabo Mondego: Lt.............
Penedo da Satidade: Lt
Farilhāo Grande: Lt....
Ilhas Berlengas: Lt...
Cabo Carvoeiro: Lt.....

Cabo de Sáo Vicente: Lt.
Ponta de Sagres: Lt......
Ponta da Piedade: Lt..... »

Ponta de Alfanzina (Cabo Car-

voeiro do Algarve): Lt........
Cabo de Santa Maria: Lt
Vila Real de Santo António......

Spain

Punta del Rompido (Rompido
defCantaya): Li--- em
Re 4 TA uer
Punta del Picacho: Lt
SevillanSeville) == ERES
Chipionaiblit= 5-4 t
IU De 1 Eit S
Cadiz e ees y 26
Castillo de San Sebastian: Lt...
Cabo Trafalgar: Lit... ma:
IEEE US deduci o a DE

S
to
Essen `
ZZ ZZZZZZZZZZZZZZ

39 46 N

e
EBS SSSSEIUNSERANNE
LATA VE AAAA ARZ

8 2
DEER AE
ZZZZZZZZZZZZ

1081

Long.

2000 0000000000000 «O «O «o «D 00 00 o
XS SBSESSESSSSEREZNR.
44 44444444444444

wow 4 PO
EXACT
il ll
233233

54 W

~N NO 00 90 00 Ø 00 00 00 O O “O O cO “O “O «O SO O 00 00 00 00 00
D
o
<
<

aa au O) O O ODO O DOD N
t2
to
=
^

E —————————— Áo
MEDITERRANEAN AND BLACK SEAS
€——€———————————————— —— SSS S SS SSS SSS S I EET TTT IE TE —

Gibraltar

Malaga qm RARA Pe

tO Q2 CO 92 i. ARE
AONO
Nor 06 -1 0n 00 O2 cO

LAAÐAALA LA
HERE EZ

Spain—Continued

ALIMENTA Šā qq. sime eee a
Caboide Gata Lt eee e
Mesa de Roldan: Lt............
Cabo Minoso: lb... eER
Cartagena e
Isleta de Escombrera: Lt.......
Cabo de Palos: Lt
ISl Hormiga- Li- cecesicasos
Isla de Tabarca (Plana): Lt.....
Cabo de Santa Pola: Lt ``

38 21 N
38 34 N

1082

APPENDIX S
MARITIME POSITIONS

MEDITERRANEAN AND BLACK SEAS—Continued
— ——S TT

Place ; Long. | Index Place

Spain—Continued France—Continued

Cap Cēpet: Lt

Īle Grand Ribaud: Lt
Cap d'Armes: Lt

Cap Bénat: Lt

Ile du Levant (Titan): Lt
Cap Camarat: Lt

St. Tropez

SSNESSBE -

Islas Columbretes: Lt
Cabo de Oropesa: Lt
Peñíscola: Lt

Vinaroz

Puerto de las Alfaques
Punta de la Baña: Lt...
Cabo Tortosa: Lt

Cabo Salou: Lt
Tarragona

Villanueva y Geltrú: Lt.-

or 00
HOD Ln ARSS

sch 100 NSS NW
tz Ed Ed Ex Ed xd Ed nd HE

Villefranche
Cap Ferrat: Lt

JAY YANINA OO
Liras < NA

ISS
EE
Cu W Wh DO

Monaco

Monte-Carlo

Ee
to
a
E

Corsica

Ceng Senetosa (Aquila Point):
t

Ajaccio

Ile Sanguinaire: Lt

Pointe de Revellata: Lt

Cap Corse: Lt

Bastia

Alistro: Lt

Pointe de Chiappa: Lt....

Ile de Lavezzi: Lt
Balearic Islands Cap Pertusato: Lt

A GO NH
Q3 O» HN «D Q5 C» DY CO ROR

ss
MAD oo oo O = mo RO O
Extr ted Er Er Ed Rello

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
GI GI GI GO GO U0 GI DO t2 DIODI OO ODO DOD ODO DOD ODO DOD ODO DOD O DOD ODO o
Rasas SE tssR EE -

i pi i O Or

«O O an Go >
(OD COOOMOGO 0000
Re RO» EL Pe

RO CORO TIR ROS 000
Be dd HE

FORMENTARA Sardinia

Capo Testa: Lt
Isola Razzoli: Lt
Capo Ferro: Lt
Olbi

nm
nw
on

IBIZA (Iv1ZA)

—Isla Conejera: Lt
—Isla de Tagomago: Lt
—Isla Botafoch: Lt

SENSU

beba ag = dora Na

Capo Comino: Lt

Capo Bellavista: Lt..

Isola dei Cavoli: Lt...

Capo San Elia: Lt......

Cagliari

Capo di Pula: Lt

Capo Spartivento: Lt..

Capo Sandalo: Lt

Capo San Marco: Lt...

Capo Caccia: Lt

Punta dello Scorno (Punta
Caprara): Lt

MALLORCA (MAJORCA)
— Cabo de Salinas: Lt

—Cabo Cala Figuera: Lt
—Sóller

NNW N Nee
wwe JS
oo

EE e
SEES

ORU DN WO
Exi Ed Exi Ex] End Ed End Ed cd xd rd d d

o 000000 %0 D O O «O tO «O OO OO OOO

Italy

Capo dell’ Arma: Lt
Porto Maurizio

Capo Mele: Lt
Capo di Vado: Lt..

Capo del Faro: Lt
Genova (Genoa)

Punta Vagno: Lt
Punta di Portofino: Lt

— Puerto de Mahón
Isla del Aire: Lt

deu» Rw wo
PHO NH

Cap Leucate: Lt
La Nouvelle

[un
O «o «o «oO 00 00 00 OO 00 00 NI

Pointe de drei bu Lt

Livorno (Leghorn)

Secche di Vada: Lt

Isola di Gorgona, Punta Cala
Scirocco: Lt

Pointe du Sablon (Pointe de
Beauduo): Lt

Faraman (La Camargue): Lt...

Port-St.- Louis-du- Rhóne

Port-de- Bouc

Cap Couronne: Lt

Marseille

Pointe de Mourepiane: Lt.

Īle d'If: Lt

ELBA

—Punta Polveraia: Lt
—Portoferraio

—Porto Azzurro

Scoglio d'Africa: Lt

ISOLA DEL GIGLIO

—Punta del Fienaio: Lt

— Punta del Capel Rosso: Lt....

NRO Oana Ha a Ka IDO w w w w

aan

Index
N

Place

Italy—Continued

Punta: Lividonia Dt E
UN A sad

Isola di Ponza, Punta della
Guarda quite. cemere
Isola d'Ischia, Punta Impera-
fores pee ne Sere ES
Isola di Procida, Punta Piop-
petas Ie erre
NODO NEE
Castellammare di Stabia...
Punta Campanella: Lt.........
ISOLA DI CAPRI
= Punta Carena: Lt............
0 Capo bites. cao cnn
Capo d'Orsos Lt. :
Salerno c E a:

Capo Palinuro: Lt
Capo Bonifati: Lt.........
Capo Suvero: Lt. .........
Capo Vaticano: Lt
Soa A E. 22

Bunta Pezzo: bt

ISOLE EOLIE (ISOLE LIPARI)
—Isola Vulcano: Lt.............
—Isola Stromboli (Isolotto

Strombolicchio): Lt........
—Isola Salina, Capo Faro: Lt...
ISOLA D’USTICA
—Punta Uomo Morto: Lt......
—Punta ‘Gavazzi: Lt...........

ISOLE EGADI (AEGADEAN Is-
LANDS)

—Isola di Levanzo, Capo

Grosson Lifi-- ose e Leer.

—Isola Marettimo, Punta Li-
pooni alut Eaa Sa oss
—Isola Favignana, Punta Sot-
tile: Lt
ISOLA DI PANTELLERIA
—Punta Spadillo: Lt
—Punta Limarsi: Lt
ISOLE PELAGIE
—Isola di Lampione: Lt........
—Lampedusa, Capo Grecale:
L

HN OI Lt RK LS genti
Sicily

Capo Peloron it-2- 2822222. en
Capo di Milazzo Sit 22222 -
Capo d'Orlando: Lt. --.-----=--
Capo Zafferano: Lt-.....--.----
Palermo JET? ci ERES

Capo Granitola: Lt----------=--
CapotRossellos Tits" 4
"Porto Empedocle--------.------—-
ECOL ð vw tue es e ek
Gels c. os ed]. DA
Capo Scaramia (Capo Sealam-

bri poe dde noces
Isola delle Correnti: Lt.........
Capo Passeto:ALit-e----c-.
Capo Murro di Porco: Lt.......
Siracusa (Syracuse) - ---------2--

Capo Molini L6s:2------.---..
Mesana se ee em Ee eege 22
Punta San Raineri: Lt 22-22:

APPENDIX S
MARITIME POSITIONS

MEDITERRANEAN AND BLACK SEAS-— Continued

Index

Lat. Long. NO! Place Lat.
E cL 55000 Italy D
42 27 N 11 06 E 550105 Capo del Armi toes: TE 37 57 N
42 23 N 11 13 E 020 | Capo Spartivento: Lt..........| 37 55 N
42 23 N 11 13 E 0001 Capo Stilo: Eteen SS Pe IN)
42 14 N 1107 E 040 | Capo Rizzuto: Lt...... ---| 38 54 N
42 05 N 11 47 E 050 | Capo Colonne: Lt...... -| 3901 N
41 46 N 12 13 E DST Prol ome SES OS -2139.08 N
41 27 N 12 38 E 070 | Punta dell” Alice: Lt.... ---| 99 24N
41 13 N 18 04 E 080 | Capo Trionto: Lt....... exe BYLINE
40 58 N 13 03 E Wa Taranto ee -| 40 26 N
55100 | Capo San Vito: Lt..... -| 40 25 N
40 53 N 12 57 E MON v Gallipolise EE nasa -| 40 04 N
120% Gem tree 40 03 N
40 43 N 13 51 E 130 | Capo Santa Maria di Leuca:
SM REM ARA 39 48 N
40 46 N 14 01 E 140 | Capo d'Otranto: Lt...... 40 06 N
40 50N 14 16 E 150 | Punta San Cataldo: Lt... 40 23 N
40 42 N 14 29 E 160 -Brindisi eik K m acc 40 39 N
40 34N 14 20E 170 | Capo Gallo: Lt... 40 41 N
180 Ari Stee. 2 41 08 N
40 32N 14 12E 190 | Molfetta- 4113N
40 34N 14 16 E 55200 “Barletta "=" 41 19 N
40 38 N 14 41 E 2104 Manfredonia Neres namu ee 41 37 N
40 40 N 14 46 E 220 | Vieste, Scoglio Santa Croce: Lt.| 41 53 N
40 15 N 14 54 E 2809 Isola Pianosa blico. <. 42 13 N
40 01 N 15 17 E 240%) "Isola Gaprara: Lt r L-E 42 08 N
39 33 N 15 53 E 250 | Isola San Domino, Punta del
38 57 N 16 10 E Diavolos EE 83 42 06 N
38 37 N 15 50 E 260 | Punta della Penna: Lt......... 42 10 N
38 15N 15 43 E Kette EE 43 37 N
38 14 N 15 38 E 2800 E -| 44 04 N
BOOM VKavenna "e Pues RA 44 29 N
38 22 N 15 00 E 55300 | Punta della Maestra: Lt........ 44 58 N
S100 (ChtūggiassvastT a 45 14N
38 49 N 1515E 320 | Porto di Lido: NE Breakwater
38 35 N 14 52 E TE AA ti eene 45 25N
330.1) Venezia (Venice)----.---—----.-- 45 25N
38 43 N 13 12E 340 | Porto di Piave Vecchia: Lt..... 45 29 N
38 42 N 13 10 E 350 | Punta del Tagliamento: Lt..... 45 38 N
360: Monfalcone mr y ca 45 48 N
370 Eriesios-va aa EST 45 39 N
380 | Muggia 45 36 N
38 01 N 12 20 E
55400 Yugoslavia
37 57 N 12 04 E
55410 | Rt Savudrija (Capo Salvore):
37 56 N 12 16 E AA a 45 29 N
4201 EZ UD ES 45 18 N
36 49 N 12 01 E 430 | Poreč (Porenz0)------- 45 14 N
36 44 N 1202E 440 | Rovinj (Rovigno) 45 05 N
450 | Hrid Sveti Ivan na Pučini: Lt..| 45 03 N
35 33 N 12 19 E 4604) ula. 9098 86 sads 44 52 N
470 | Hrid Porer: Lt... 44 45 N
35 31 N 12 38 E 480 | Hrid Galiola: Lt........ ----| 44 44 N
490 | Rt Mrlera (Pta. Merlera): Lt..| 44 48 N
35 52N 12 58 E 55500 | Rt Crna (Nera PO) Lt -S 44 57 N
SION! Prieta T en oes eee 45 20 N
520 | Sušak 45 19 N
530 | Bakar 45 18 N
38 16 N 15 39 E 540 | Ostrvo SuSak (Isola Sansego):
38 16 N Se HEES RETI Ee eg 44 81 N
88 10 N 14 45 E 550 | Ostrvo Grujica: Lt 44 25N
38 07 N 13 32 E BOOM Veli Rat P Lib ise SE 44 09 N
38 08 N 13 22E DIO ETA ed e dol T er cm 44 08 N
38 13 N 13 19 E 580 | Ostrvo Sestrice (Port Tajer): Lt.| 43 51 N
38 11 N 12 44 E 590 | Ostrvo Blitvenica: Lt 43 88 N
38 00 N 12 29 E 65600 Erid are 48 31 N
37 47N 12 26 E GLOW SES NES SEC 43 30 N
37 34 N 12 40 E 620 | Rt Ražanj: Lt.---.-.-.------..- 43 19N
37 18N 18 27 E 630 | Ostrvo Hvar, Rt Pelegrin: Lt--| 43 12N
87 17 N 18 32E 640 | Ostrvo Vis, Rt Stončica: Lt....| 43 04 N
37 06 N 13 57 E 650ml Ostrvo REES 42 45 N
37 04 N 14 15 E 660 | Ostrvo Lastovo, Rt Struga: Lt. | 42 43 N
670 | Lastovski Otočiči (Lagostini
36 47 N 14 30 E LEE ME A EE acis 42 46 N
36 38 N 15 06 E 680 | Ostrvo Lirica: toros se 42 52 N
36 41 N 15 09 E 690 | Ostrvo Sveti Andrija: Lt
37 00 N 15 20 E 557008 Era AM ta a see: =< <
37 03 N 15 18 E 2304] dubrodtikt Lee do IE
37 13 N 15 15 E 7201 HOST RE DU S S EET SEES
37 80 N 15 07 E EN es
37 85 N 15 11 E 740 | Ostrvo Sveti Nikola: Lt....
38 12 N 15 34 E 750 | Rt Volovica: L
38 12 N 15 35 E 760 | Mendre Rt: Lt

1083

Long.

17 0
16 4

16 1
15 5
16 1
15 4

hu
-1
ar

OLA Ol ON O OO DO Y 0D NN OO OO t2 Oo Ot i EB

RUDA x
eS
BERR SE Se nana

m
to
t2

a NON 0: — O2

12 2
12 3
13 0
13 3
13 4

DD ONO ao

=
kær]

AA eon

KI C b Hx C» O1 Or bà tV D K 00

ALARM e oli ii!

=
oo

Souakwoonne

CPN ONNANDO

1084

APPENDIX S

MARITIME POSITIONS

MEDITERRANEAN AND BLACK SEAS—Continued

Place

Albania
Kep i Rodonit (Cape Rodoni):
Lt

Greece

vs (Fano I.), Akra Kastri:
t

Andipaxoi, Kira Ovoroú (No-
vara Pt.): Lt

Ákra Doukáton (Cape Dukato):
t

Akra Yerogómbos (Cape Ghero-
ghambo): Lt

Vardhiánoi: Lt.

Argostólion

Zakinthos, Akra Skinári: Lt...

Mesolóngion - ES
Ayios Sóstis: Lt
Akra Andírrion: Lt

Ákra Melangávi: Lt
Ki órinthos

Ákra Pápas (Áraxos): Lt
Akra Killíni (Cape Glaréntza):
Lt

Strofádhes (Staniphatil Put
Pilos (Navarino)
Sapiéntza (Sapiénza): Lt

Akra Tainaron (Cape Mata-
pan): Lt
Yithion

Kithira, Akra Spathi: Lt
Se Ákra Apolitáres:
Lt

Parapóla (Belo Pulo): Lt
Navplion

Akra Zourva: Lt

vina (Aegina I.), Vrakhos
Tourlos (Cape Turlo): Lt....
Psittália E TH Et

Kéa (Zea), Ákra Tamélos: Dt
"EY: (Serpho I.), Ákra Spāthi:

Folégandros,
pounda: Lt

Thíra (Santorin), [uH
(Cape Akroterion):

Páros (Pharos I.), d (Ko-
rakis): L

Mikonos, Akra Armenistí: Lt.

E (Syros), Ákra Trímeson:

Akra Fássa (Cape
Phassa): Lt

37 09 N
37 29 N

37 31 N

37 57 N

Place

Greece—Continued

Ákra Kafirévs (Cape Doro): Lt.
Vrakhonisís Kaloyéri: Lt
Prasoüdha (Prassudo Islet): Lt.

Skíros (Skyros), Ákra Lithári:
TA

Skópelos: Lt
Psathoúra: Lt

Ákra Posidhion (Kassándra
Point): Lt
Thessaloniki

Turkey

DARDANELLES

—Ilyasbala Burnu (Cape
Helles): Lt

| —Kumkale (Mendires Cape):
L

— Canakkale

—Gelibolu (Gallipoli):
Tekirdag

Mana adi

eM Burnu (Stefano Pt.):

Ičneada Burnu (Cape Kuri): Lt-

Bulgaria

E Ivan (Megalo-Nisi

g
Nos Emine (Cape Emineh): Lt.
Nos Galata: Lt
Varna (Stalin)
Nos Kaliakra: Lt

Capul Tuzla: Lt
Constanta
Insula Serpilor (Fidonisi I.): Lt.

USSR

Mys Bol ui Fontan (Cape
ontana)

Tendrovskiy (Tendra Pt.):Lt..

Mys Dzharylgach: Lt

Mys Tarkbankut (Cape Tark-
han):

Mys Voi
toria Pt.): Lt

Sevastopol’

Mys Khersonesskiy
Khersonese): Lt

Mys Sarych (Sarich Pt.): Lt..

Mys Aytodor (Cape Aitodor):

Mys Meganom: L
pre Il'i (Cape St Ili) (Elias):

40 08 N

40 01 N
40 09 N
40 24 N
40 58 N
40 58 N

40 57 N

ER

NESS
ZZZZZZ

APPENDIX S

MARITIME POSITIONS

MEDITERRANEAN AND BLACK SEAS—Continued

Place Lat. Long.
USSR—Continued
o , o ,
AZOVSKOYE MORE (SEA OF
AZOV)
—Mys Yenikale (Fonar): Lt....| 45 23 N 36 39 E
—Osipenko (Osipyenko) ---------- 46 45 N 36 47 E
—Belosarayskaya Kosa (Bye-

losaraD: E ee e ee? 46 53 N 37 20 E
A ATA ic c eee 47 04N 3735 E
Rostov Na Don... oe 47 12N 39 42 E
—Primorsko- S mp
j (Akhtar): LI 22 costae 46 06 N 38 11 E
—Mys Zen EE 45 26N 36 47 E
VE Anapskiy (Anapa): Lt....| 44 53 N 37 18 E
Novorossivek? oe e ene K 44 43 N 37 47 E
MysKodosh: Lb" S 44 06 N 39 02 E
Mys Pitsunda: EE 43 09 N 40 21 E
Mys Sukhumiyskiy (Sukhum

Mel O | 42 59 N 40 59 E
OEA O A A 42 09 N 4135 E
Batumi (Batumskaya) ----------- 41 39 N 41 39 E

Turkey

"UIrahzons ptem 2 Lov. 41 01 N 39 46 E
Sinop Burnu (Cape Sinub): Lt.| 42 01 N 35 I8 E
Ince (Injeh) Burun: TÆ 418 42 06 N 34 58 E
Kerempe Burnu: Lt............ 42 01 N 33 17 E
Olüce Burun (Kisi Agsi): Lt....| 41 19 N 31 26 E
Sile (Kilia) Burnu; Lt----=----- 4110N | 2937 E
LORO DOTA i SE ea sa 40 59 N 29 01 E
Fener (Fanar) Burun: Lt...... 40 58 N 29 02 E
Yelken Kaya Burnu: Lt........| 40 45 N 29 21 E
Ëer 40 46 N 29 55 E
¡BOZABurun LL FL et 40 32 N 28 47 E
HenernsAdasl: d ----..---- 40 38N 27 46 E
Hayirsiz Adasi (Khairsiz Ada)

LOU P ST uec 4 40 39 N 27 29 E

Aegean Sea

Bozca Ada (Tenedos I.), Bati

Burnu (Ponente Pt.): Lt. 25 58 E
Baba Bunu bt 26 05 E
Sígri (Megalonisi): Lt 25 50 E
Kara Burun. tee OMi 26 23 E
Orak Adasi (Oghlak I.): Lt.....| 38 41 N 26 43 E
Izmir (Smyrna), Turkey.--------- 38 26 N 27 08 E
AS pie GE 38 32 N 25 37 E
PASA aa 38 30 N 26 19 E
Menpeko Mite. ey oo 38 08 N 26 02 E
Samos, Akra Pankosi: Lt....... 37 48 N 26 40 E
Ikaria, Akra Papas: Lt.......... 37 31N 26 00 E
DODECANESE
—Levitha, Akra Spano: Lt......| 37 00N | 26 31 E
—Andileoúsa (Kandeliusa I.):

AAA Ee 36 30 N 26 59 E
—Akra Prasonisi, Ródhos: Lt...| 35 52 N 27 47 E
<= Rodhosj(Ibhodes)----------=-+ 36 26 N 28 14 E
—Strongili (Hypsili I.): Lt 36 06 N 29 41 E

Crete (Kriti)
Agria Gramvoūsa (Grabusa): Lt.| 35 38 N 23 34 E
Elatonisosees tose AP 35 15 N 2331 E
Gávdhos, Akra Tripití: Lt...... 34 48 N 24 07 E
Akra Líthinon (Cape Littinos):

RT MES A 34 55 N 24 45 E
Iontontsi- e 34 56 N 26 08 E
An Sídheros (Cape Sidero):

JE E EAS. RA SR 35 19 N 26 20 E
Dia (Sandia te. ese 35 28 N 25 14 E
TEO IID Tiss on) eur a d 35 20 N 25 09 E
Akra E (Cape Dre-

Pano) io e eras 35 28 N 24 15E
Soúdha sulā) Pt ai AA 35 29 N 24 04 E
Akra Melékhas: Lt_------------ 35 35 N 24 10 E
i tavu t eo eee sree mE 35 31 N 24 01 E

Index
No.

1085

Place Lat. Long
Turkey
o , o ,
Antalya Adana) -ee es... t 36 52 N 30 46 E
Kaleardi Burnu (Cape Kil-

Garda) Alanya: ee 36 31 N 32 02 E
Anamur Burnu: Lt. -| 36 01 N 32 51 E
dE EE AI Ltda at Je 36 48 N 34 38 E
Fener Burnu (Karatas Burnu)
Mie 36 33 N 35 20 E
Iskenderun (Alexandretta) ............ 36 36 N 36 10 E
Hinzir Burun (Domuz Burnu):

Lil s etalon Er. 36 19 N 35 46 E

Cyprus
Edidhes' Islet: Lto EN 35 41 N 34 37 E
Cape/Kormakiti; bt 220 e 35 24 N 32 56 E
Paphos Point: lU mE 34 45 N 32 24 E
Cape Gata: Lt....... ---| 94.84 N 33 01 E
Limassol 2 = -| 84 40 N 33 03 E
| Cape Greco: Lt...... ---| 34 56 N 34 06 E
Famagusta T e 35 08 N 33 56 E
Syria and Lebanon
Rays ton Hani Diem 35 43 E
Al Ladhigiyah a, Sy 35 45 E
Jazirat/Ramkins Tt F Var 35 45 E
Tarabulus ( Tripoli Lebanon....| 34 26 N | 35 50 E
:Bayrüt (Beirut), Lebanon-------- 33 54 N 35 30 E
Saydā (Sidon), Lebanon.......... 33 35 N 35 22 E
Sar (Tyre), Lebanon............. 33 17 N | 3512E
Israel

5N 35 05 E
ifa 9N 35 00 E

Har Hakarmel (Mount Car-

mel): Lt ON 34 58 E
TROL ATID een nee ees 4N 34 46 E
QUE MIC bU eee een CE E raceme se 3 N 34 45 E

United Arab Republic (Egypt)

Port Said (Bor Sa IA) EEE ene = 31 16 N 32 18 E
Damietta,Mouth:"L( geess 31 32 N 31 51 E
Cape Burullus (Brulos): Lt..... 31 35 N 31 05 E
Roseta ðb ecc Ee 30 19 E
Ras et Tin: Lt 29 52 E
ALCOR iento 29 54 E
AA A PEA 27 14 E
Libya
RESTA vz Zo em 31 58 N 24 59 E
Tous ee ee ee eee en ee 32 05 N 23 59 E
ELIO eei a eee ee 32 45 N 22 39 E
Ras fol A T to eR RE 32 55 N 22 10 E
EE 32 07 N 20 03 E
Bj there pe tent SIMII Ni 16 35 E
Ras Zarrugh (Raz Zorug): Lt...| 32 22 N 15 13 E
iBasel Hallabq sr rr 32 48 N 13 48 E
TD A is 32 54 N 13 11 E
GU T BR EN RUE PRU PCENA 32 56 N 1207 E
Gozo and Malta

Gozo? Lise mb: eru 36 04 N 14 13 E
MALTA

—Ponta ta Delimara: Lt........| 35 49 N 14 34E
THAO. A C T ut 35 54 N 14 31 E

Tunisia

Ile de Djerba (Jerba I.), Rass d

Mourguenesss "Dt: Mm TR 33 49 N 11 03 E
S 33 51 N 10 07 E
(ij ss E ce eti 4 10 46 E
Mahdia (Mahedia) 1104 E
Tekin Mime 8 11 02E
(SOS CIM e eeh EAS, A 0 10 38 E
Hammamet: Lt 6 24 10 37 E
ADE AS ee eae 36 50 N 11 08 E
Capi BOn JI 37 05 N 11 03 E

1086

APPENDIX S
MARITIME POSITIONS

MEDITERRANEAN AND BLACK SEAS—Continued

Place . Place

Tunisia—Continued Algeria— Continued

Cap Matifou: Lt
CapiGerthage; tusi eee GTS
i d ap Caxine:

lle Plane (El Kamela): Lt Tiptsa CTipaza)
Iles Cani (Cani Rocks): Lt Cherchel

Bizerte Cap Ténés (Ténéz): Lt
Rass Engela (Ras Enghela): Lt. Cap Ivi: A

Cap Serrat: Lt Mostaganem
Ga iton Galitons de l'Ouest: Arzew

t Pointe de 1'Aiguille: Lt
0

Mers el Kébir

Cap Falcon: Lt

Iles Habibas: Lt

Île Rachgoun (Rashgun): Lt....
Nemours

NAONS >
aoe

ZZZZZZZZZZZZ

HON

A Or O1 On O 92 03 Q2 IP a a
RÈS pd

HH HH DODOOOOOOHNNNWN o
Pi O + `
Ho O B5 09 Q9 00 RE NA ES P

did dīgst IS IS e s fes

MN O PP

Cap de Garde: Lt
Cap de Fer: Lt
Philippeville
Ile Srigina: Lt
Cap Bougaroun (Cap Bouga-
roni): Lt
Rass Atia: Lt.
Djidjelli___-
Bougie..... 3
Cap Carbon: Lt.
Cap Sigli: Lt
Cap Corbelin: Lt

Morocco

Ook K bo
W MO UO ASN

b HES bb

Islas Chafarinas (Zafarin Is.),
Isla Isabel Segunda: Lt

Cabo de Tres Forcas: Lt.

Isla de Alborán: Lt

Cabo Quilates: Lt... Tres.

Pefión de Velez dela Gomera: Lt.

Río Martin, Ensenada de Ta-
merabel (Tetuan Bay): Lt....

Ceuta

Punta Almina: Lf -2 is z

Punta Malabata: Lt

KI A a o O Or O) O) a> O»-1-1-10000
Aan K WW hV DO BO
SASS 555925
2332 444444

Lë c cum
E DD OU Y O 00

AFRICA

Morocco Gambia

Senegal

Casamance (Kasamanze River),
Pointe de Diogué (Jogue
Point): Lt 16 48 W

Carabane 16 42 W

Portuguese Guinea

Ilhéu de Caio (Cayo I.): Lt
Ilha Orangosinho, Cabo Came-
laeo (Cameleon): Lt

Ilha Poilāo: Lt
El Hank (Pointe el Hank):

Mazagan

zzzzzzzz

=
=

De Matakong: Lt

OO oma Rh oo au ŠO

dis

Sierra Leone

C100 ek O OO DG O) NOD
ZZZZZZZZZZZZZ
OO OO OO OO OO NN de e O
Fi le DET

Spanish Sahara (Rio de Oro)

00 00 00
S88
ZZZ

Cabo Juby: Aviation Lt
Punta Durnford: Lt

Mauritania

Gan Blanc. D Cape Mesurado: Lt

Pe ti, t Grand Bassa Point: Lt
enne Sinoe (Sinu) Bay: Lt

Cape Palmas: Lt

He Or QD O

SS Boss
ZZZZZZ

Ivory Coast
16 80 W
17 31 W Pointe Tafou: Lt
17 27 W Sassandra: Lt

17 26 W Grand-Lahou

CUR
Quan
oa
ZZZ
aan
con
OAN
zzz

1087

APPENDIX S
MARITIME POSITIONS

WEST COAST OF AFRICA—Continued

3
P'ace Lat. Long. mper Place Lat. Long.
Ivory Coast—Continued ali 4; 63300 Gabon and Congo
[- 7 OE
AA AAA 519N 4 00 W || 63310 | Librevilie, Gabon
- 4 h Gabon 22: 22 35 023 N
Grand-Bassam* E ansa 512N 3 43 W 320 | Pointe Gombé: Lt....... 0 18N 3 18 E
Ghana 330 | Port-Gentil, Gabon 0 438 8 48E
3407] (Gap Lope Bee 0388 8 42E
dtum reme de ar nan 452N 215 W 350 Loango Congo a eneo et 4 38 S 11 49 E
Bobawaskhe b. 4 52 N 215W 360 | Baie de Pointe Noire (Black
Dane Three Points: Lt......... 445N 2 06 W Point Bay), Congo. ---------- 4468 11 50 E
AE tee As
Br a CEA Cabinda
456N | 142W || 63410 | Landana: Lt 5148 | 1209E
506N 114W 420 | Cabinda (Kabinda) 5328 12 14 E
d = A 7 R W || 63500 Republic of the Congo
5 50 N 0 58 E || 63510 | Moanda: Lt 557S | 12
Togo and Dahomey A Om ee es a tere ae 5 518 13 03 E
MOMO T6000. SE 6 07 N 11437 63600 Angola
Cotonou (Kotonu), Dahomey....- 6 21 N 225E
it. 63610 | Ponta do Padrao (Padron Pt.),
Nigeria Congo River? io ee 6058 12 20 E
s 620 | Ponta de Moita Seca (Mouta
Beecroft Point: Lt 6 24N 323 E Bees): b bass o 1216 E
Banot m X IIO 6 24 N 3 24 E 630 | Ambrizete (Foreland Bluff):
Forcados. TE EE 5 22N 526 E pills e.t e t UE 12 52 E
Palm Point, Cape Formosa: Lt.| 4 16N 6 05 E 6407 AMD ———— 13 06 E
Cameroon 650] "Dagostas:: Lit-:------- 13 18 E
660 | Luanda (Loanda)...-....-.--..- 49S 13 14 E
Debundscha (Debundga) 670 | Ponta das Palmeirinhas, Cabo
Pot DDR ee 406N 900E USNR Wipe conse 04 S 13 00 E
Cape Nachtigal: Lt. 3 57 913E 680 | Pôrto Amboim......-..-.-.----- 448 | 13 45 E
Douala (Duala), French COURSE me S 1334 E
Cameroons Let 403N 941E 63700 Benquela... .....- SARA 58 13 24 E
Spanish Guinea (Rio Muni 710 | Ponta das Salinas: Lt.. 0S 12 56E
pa F do P6 720 | Giraül (Ponta do Giraül): Lt...| 15 08S 1207 E
and Fernando Póo) 730 lija (Mossámedes) ------- 15 128 12 09 E
740 onta Albina (Albino Pt.): Lt..| 15 53 S 11 43 E
Ó TRI Sr i ti N 3 S 750 | Baia dos Tigres (Great Fish
FERNANDO P60 E l Bay) wire ec E 16 31S 11 44 E
—Punta Europa (Los Frailes): -W i
á D Ee Tk 3 n N 847E 63800 South- West Africa
—Santa Isabel------------------- 3 45 8 46 E || 63810 | Swakopmund: Lt. 22 418 14 31 E
—Islote Horacio: Lt.---------.- 3 46 N 8 55 E 820 | Walvisbaai (Walvis Bay)-------- 22578 | 14 30 E
Sáo Tomé e Príncipe 8308 Pelican) Point Lt NT 22 54 S 14 25 E
2400 Ludebiz-. tee 9S 15 09 E
ILHA DO PRÍNCIPE (PRINCE'S 850 | Diaz Point: Lt 8 S 15 06 E
ISLAND)
—Ponta da Garça: Lt___-------- 138N 727E 63900 | Republic of South Africa
— Santo Antgnig. 1 38 N 7 26 E
—īlhdu'Bombom:*Ltt:=.- 142N 7 24 E 639107) "Porta Nooh S P 5 r 29 15 $ 16 52 E
ILHA DE Sao Tomé (SAO 920 | Cape Columbine: Lt........... 32 50S 17 51 E
THOMĒ) (ST. THOMAS Is- 930 | Dasseneiland (Dassen I.): Lt...| 33 26 S 18 05 E
LAND) 940 | Robbeneiland (Robben I.): Lt.| 33 49 S 18 23 E
—Ilhéu das Cabras: Lt_-------- 0 24 N 6 43 E 950 | Cape Town (Capetown)--------- 33 548 18 26 E
Er odo TOMÓ Le ALBAL tt Ku 021N 6 44 E 960 | Table Bay, Green Point: Lt....| 33 54 S 18 24 E
—Ilhéu Gago Coutinho (Ilhéu 970 | Slangkoppunt (Slang Kop
dassRólgs): Lites sso a 0 00 631E ROM e 34 09 8 18 19 E
980 | Cape of Good Hope: Lt........- 34 218 18 29 E
EAST COAST OF AFRICA
Republic of South Africa Republic of South Africa— Cont. m
o , o , o , ,
Simonstow ās es sans 34 115 18 26 E 64160 | Cape Hermes: Lt............... 31 28 S 29 33 E
Roman Rock: Jit... ux. 34118 18 27 E 170 Port: Sh. JOMSL--=-=======2e=83= 31 385 29 33 E
DaneerPolmb Lt S eto = 34 378 19 18 E 180 | Port Shepstone: Lt............- 30 45S 30 28 E
CapejAgulhass Li---— —- — — 34 508 20 01 E 1005) Green Points Lt Fæ r = 30 158 30 47 E
Cape Sto Blaize? ios 34 115 22 09 E 64200 | Cape Natal (Natal Bluff): Lt...| 29 52S 31 04 E
Mosselbaai (Mossel Bay) -------- 34118 22 09 E 210 | Durban (Port Natal) ------------ 29 528 31 04 E
(CapeStaBrancis:1Lb-------—— — 34 128 24 50 E 220 | Durnford Point; Li------------- 28 55S 31 55 E
Cape Recife: Lt 34 028 25 42 E 230 | Cape St. Lucia: Lt..--------==- 28 318 32 24 E
Port Elizabeth --- =e eee Em 33 58 S 25 37 E
Bird Is CHE TE cem ne 33 50 S 26 17 E 64300 Mozambique
Great Kish Point: Lt-—-—--2— 33 318 27 06 E
Hood Points: Lt eee EES 27 54 E || 64310 | Ponta do Ouro: Lt..............| 26 508 32 54 E
GastlelPoint Lie 33 02S 27 55 E 320 | Cabo da Inhaca: Lt--------.-- 25 58 S 33 00 E
Fast London V EE 33 028 27 55 E 330 | Lourenço Marques. ------------- 25 58 S 32 35 E
Bashee Entrance: Lt........... 33 14 8 28 55 E 3400 Monter Belo libcr 25 118 33 30 E
— Ll

1088

APPENDIX S
MARITIME POSITIONS

EAST COAST OF AFRICA—Continued
pos Place Lat. Long. Indes Place Lat. Long
Mozambique— Continued hs Eat Zanzibar—Continued ae SI
64350 | Ponta Závora: Lt S 35 12 E MEAR Æ Ð Aar 6 108 39 11 E
360 | Cabo das Currentes: Lt.... S 35 30 E 740 | Mwana Mwana: Lt............ 5458 39 I3 E
370 | Ponta da Barra: Lt S 35 32 E 750: | Ras Nungwe: Lt.......... 08 5438 39 18 E
380 | Ilha do Bazaruto: Lt S 35 29 E 760 | Ras Kegomacha, Pemba: Lt....| 4 53S 39 41 E
3907 Beira SEA Seo SE S 34 50 E
64400 | Ponta Macúti: Lt S 34 54 E
410 | Zambezi River, Ilha Timbué: 64800 Kenya
AA eec ca e 9S8 36 28 E
4204 CIRQUE Lo ERE SL rra ege 28 36 30 E 048108] IMombasme E 4048 39 41 E
430 | Vilhena: Lt. 6 S 36 55 E 820 | Kilifi Entrance: Lt. -=m =| 3:98: 39 52 E
440 | Ponta Matirr 68 38 11 E 8300) Mandt- zzz- = ae v en 3138 40 08 E
450 | Ponta Caldeira: Lt 8S 39 30 E SAVN) Ge A A 2.198 40 54 E
460 | Ilha de Mafamede: Lt 18 40 02 E
470 | Rio Sangage e EI EA oder E v Us E
480 | Ponta Namalungo: Lt_________- 15 38 64900 Somali Republic
490 | Ilha de Géa (St. George 1.): Lt__ 15 03 S 40 47 E P
64500 | Mocambique- ooo 64910 | Chisimaio (Kisimayu) ........... 0228 4233 E
510 | Baía de Memba, Ponta Cogune 920 lato: ü pow 4 2 BO, EE 0158 42 38 E
(Cape Loguno): Lt_---------- 14 128 40 43 E 6300 len e me S AO 106N 44 03 E
520 | Ponta Maunhane: Lt...........| 12 58S 40 36 E 940 | Mogadiscio-- LL. LLL. 202N 45 21 E
9304 LF orto Amelia ees. 2 ENB 12 58 S 40 30 E SEO AT EE ELE. 245N 46 19 E
5407 HL TDO: Tres Se RN 12 208 40 30 E 960) | Obbia (Obist): Lt = mn 521N | 4831E
550 | Cabo Delgado: Lt.............. 10 41 S 40 39 E 970» Hil Marmas LE = ke, 7 58 N 49 51 E
2 2807 ¿Ras Hattun lb < UI 10 26 N 51.253
64600 Tanganyika 990 Cano ra: de biedē ci 11 50N | 5117E
3 65000 | Ras Illaue (Alula): Lt: 11 58 N 50 46 E
EE 9 595 39 44 E 010 | Bender Cassim (Bandar Kas-
62011. addoye Lc 14- 22-22 532 ds 8348 39 34 E sim) 1117N 49 11 E
6307 Ras Mkumbi" (Moresby PE) dē cat ue RE IN A za EM CE alas
Mafia Dh cpl raae tee eee m 7388 39 55 E
EH RE Konziu ltem CE 2 7018 39 33 E
650 | Dar es Salaam TT 6498 | 3918 E || 65100 Gulf of Aden
De anas Sa ecc E 5 05S 39 07 E F
CO Uldis LC Ð: s 018 [135 942" ei | Bugutrās(Socotra). S E 1230N | 54 00 E
120 | Berbera, Somali Republic... 1027 N 45 02 E
64700 Zanzibar 130 Djibouti, French Somaliland____- 11 36 N 43 09 E
140 srles3Moucha: Dcos seaee 11 44 N 43 13 E
04/10 Pungume I3 LIZ ae 6268 39 20 E 150 | Obock, French Somaliland... . | 11 59 N 43 19 E
20 Chumpe E ETE T 6178 39 11 E 1604 AE —— oU PE 11 59 N 43 22E
emm
RED SEA
— MÓ—Ó
o , o , o 7 o ,
66000 | Barim (Perim I.), Balfe Point: 66140: | Sanganeb: Lt eeh, 19 43 N 37 26 E
me m deene 12 39 N 43 93 E 150 | Juddah (Jidda), Saudi Arabia___| 21 29 N 39 11 E
010143340, Ethiopia EEE V 13 00 N 42 45 E 160 | Daydalàs (Daedalus Reef): Lt__| 24 55 N 35 52 E
020 | Al Mukha (Mocha), Yemen... 13 19N | 43 15 E 170 | Al Ikhwån (El-Akhawein) (The
030 | Abu Ail Ts., Quoin L: Lt_______ 14 05 N 42 49 E Brother) tess ec es 26 19 N 34 51 E
040 | Punta Shab Shakhs: Lt_______- 14 39 N 41 07 E 180 | Jazirat Shakir (Shadwan L):
050 Jeza in es (Zubair: ls) be Ale ce TS 27 27 N | 3402 E
entre Pea 15 0L N | 42 10 E 190 | Jazirat Jūbāl as Saghirah: Lt...| 27 41 N | 33 48 E
060 | Jabal at Tā'ir: Lt... 15 32N | 41 49 E || 66200 | Juzur Ashrāfī (Ashrafi Is.): Lt_| 27 47 N | 3342 E
070 | Isola Sciumma: Lt.. 1532N | 40 00 E 210 | At Tür (Tor), U.A.R. (Egypt) .| 28 13 N | 33 37 E
080 | Massaua, Ethiopia 15 37 N | 3928 E 220 | Ra's Gharib, U.A.R. (Egypt) ...| 28 21 N 33 06 E
090 | Isola Serie el Abu (Sheikh al 230 | Ra's Za‘faranah: Lt 29 06 N | 3239 E
D DUNS LEER NT ---| 16 02N | 3926 E 210 | Ra's Abü Daraj: Lt 29 23N | 32 34E
66100 | Isola Difnein: Lt... . 16 37N | 3919 E 250 | Newport Rock (Zenobia): Lt_--| 29 53 N | 3233 E
TIO! Masamirit Te ES 1850N | 3845E 260 | Suez (As Suways),
120 | Sawakin, Sudan. 19 08 N | 37 21 E CH Dt) mm" 29 58N | 3233E
130 | Port Sudan, Buden. _ J 19 36 N 37 14 E 270 | Ismailia (Al
U.A.R. (Egypt) 30 35 N | 3217E
—— ee
ISLANDS OF THE INDIAN OCEAN
A o , o , ou o +
67000 ILE DE LA RÉUNION : 67400 | Amirante Isles, Eagle I________. 5078 53 19 E
Co eo a M SpE e i M a are 55 29 E 67500 | CHAGOS ARCHIPELAGO
saint Pauls Its + ee 55 8 55 17 E f
030 | —Pointe des Galets: Lt.________| 20 558 55 18 E SION USE eM oes ae eee 6 40 S 7124 E
040 | —Saint- Dennis-........ 20528 | 5528 E 520 He, Hoddam egene ug 5218 | 7213E
67100 | MAURITIUS 630 O Garda sc c M 7218 72 28 E
R i E a 2 67600 | Maldive Is., Male T 410N 73 30 E
110 Caves Pointa Li ease 20 118 Of 258 `
120 | — Port. Louis 20 108 57 30 E || 9/700 | Cocos (KEELING) ISLANDS
130 | Plat I: Lt. | 19 588 |" 5v 399 1 n DNE m i 12078 | 96 54 E
140) E Le 20 258 57 42 E _720 — Direction E: Lt. ~=+-~-------- 12 05 S 96 53 E
67200 | Rodriguez I., Port Mathurin____| 19 418 63 25 K || 07800 | Christmas I., Flying Fish Cove...| 10 258 | 105 43 E
67300 | SEYCHELLES GROUP 810 | Ile Amsterdam ___________._.___ 37 50S | 77 32:E
2 adi ¡Male 4 378 55 27 E 3207 «Me Saint Pauls. E 38 43 S 77 31 E
‘ EE ts ita NE 4 298 55 32 E 830 | Īles de IKO OM ES 49 358 9 30
3307 DESTA 3488 | 5540 E R40" Eeselen AE 73 34 E
||

aid

1089

APPENDIX S
MARITIME POSITIONS

ISLANDS OF THE INDIAN OCEAN—Continued

Lat. Long. Tease Place

R Mad — i
des get adagascar—Continued

ĪLE SAINTE MARIE

ARCHIPEL DES COMORES
—Moroni, Grande Comore
—Fumboni, Mohéli
—Mutsamudu, Anjouan

—Mayotte, Ílot Dzaoudzi: Lt__

Mananjary
Pointe d'Itaperina: Lt
Fort Dauphin

tv

Ka

&
S
Go
t2

ua ga un un Un Un Un Un un ua Un ua Ua

Madagascar

Nu
Con

Massif Katsepe: Lt
Majunga
Pointe Anorombato: Lt

PROPRE
[er DD 0 -J-JI
ee a O O

Cap d'Ambre (Cape Andre):

BAIE DE DIÉGO-SUAREZ

—]lot des Aigrettes (Nosy Lan-
goro): L M Nosi Iranja: Lt

— Dičgo-Suarez (Antsirana) Tany Kely: Lt

Miné (Cap Andran Omody): Lt.

Nosy Akao: Lt Nosi Faly: Lt

Cap Est: Lt Nosi Anambo (Woody 1.): Lt..

DDWONOHAIO

Oe

H H hV V W GO O? a Ke BV O
Suas

Go R to GTG CO Ca t5 GA tóc

KI
©

SOUTH COAST OF ASIA

India—Continued
Aden, Colony of Aden
Elephants Back: Lt
Ras Marshaq: Lt
Al Mukallā, Aden
Kuria Muria Is

GEES EE
Er] Exi Ed rd Ed Er d
RSR:
wom

Gopnath Point: Lt
Piram I.: Lt
Persian Gulf Damáo

Little Quoin: Lt
Së Shārigah (Sharjah), Trucial

t
Ad Dawhah, Qatar
AL BAHRAYN (BAHREIN Is-
LAND)
—Jazirat Sitrah
—Bahrein Harbor Rājāpur: Lt
Ad Dammam, Al Mintaqah ash Vijayadurg
Sharqiyah (Hasa)
Ra's at Tannürah, Al Minfagah z
ash Shargīyah.____- BEER === Vengurla Rocks (Burnt Is.): Lt_
Jazireh-ye Farsi (Jezirat Tarsi): Vengurla
Lt Aguada: Lt
Mormugáo, Goa

Oyster Rocks: Lt

Al Fuhayhil (Fahayhil), Kuwait.
Al Kubr: Lt Bhatkal: Lt
Al Kuwayt (Kuwait), Kuwait... Kap (Kahp): Lt
Al Basrah, Iraq Mangalore
Khorramshahr, Iran Cannanore
Abādān, Iran Tellicherry
Bandar-e Shāhpūr, Iran Mahé
Büshehr, Iran Kadalur Point: Lt
Jazireh-ye Qeys (Jezirat Qais) Calicut (Kozhikode)

(Kais I.): L Cochin...
Jazireh-ye Tanb-e Bozorg: Lt... Alleppey :
Bandar * Abbas, Iran Tangasseri Point: Lt
Ra's-e Jásk: Lt Quilon
Trivandrum

SEX

O So

_
[en

Eh Feck Fei pu kä
00 O0 00 O O
DINARS R `

A rm pi pi ki pi
a JJ

ka ba je po pol ba Ee +
PO Dä a OT CO Or
= P OT CIT Oe vs Kä

R00 00 00 00 00 O O HH

wo

ur Q = p
S 359833
bora dra

ete
ODIO
Exi Ed Ed xd cd xd Ed cd End o e xd xd Ed 0 e xd d tcd rd Ed xd rd zd xd x zd end xd end Ed rd

Pakistan Cape Comorin

Ras Muari (Cape Monze): E Laccadive Is., Kiltán I.: Lt
Manora Point: Lt
Karachi 59 E Ceylon

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

EE EES

m

Galle
Dondra Head: Lt
Hambantota

KEE KE
TREE
ZZZZZZ

Pirotan I.: Lt
Okka Beyt Harr) asa

1090

APPENDIX S
MARITIME POSITIONS

SOUTH COAST OF ASIA—Continued

Place Place

$

Ceylon— Continued Burma—Continued

o
`~
o

Double I.: L
Mibya Kyun
Tavoy
Mergui

p jr pod pd plo fl pl pu
NAO ao
SESUALVSA `
ZZZZZZZZ
B8BSS5S88S °
EELER
Exi e [xd Ed cd [xd d

DOS RODA
Ed Ex] [xd Ed xd xd Ex] ed Ed Ex] Ed

«d OO OO KEE
HAE Poe CO O bm
OSO 0D HA OPN On Oe
ZZZZZZZZZZZ
BISBSERRRBR o
dā esa said -

70300 Ko Phi (Goh Pee), Pakchan

70310 | Manappádu Point: Lt
320 | Pāndyan Tivu (HareI.): Lt....

Ko Kaeo Noi (Goh Keonoi): Lt.
Ko Taphao Noi: Lt.

ooN NOS
EES EN

Khlong Krabi Yai
Ka Chom Fai Ko Liang (Goh

370 | Negapatam Beng): Lt

380 | Karikal
390 | Tranquebar
70400 | Cuddalore
410 | Pondichéry
420 | Mahābalipur: Lt
430 | Madras

450 | Masulipatam

460 | Sacramento: Lt

470 | Cocanada

480 | Vákalapúdi: Lt

490 | Visakhapatnam (Vizagapat:m)--
70500 | Bimlipatam zA

510 | Santapilli: Lt...

520 | Kalingapatam
530 | Bāruva

Z 2222222

$EgRS55u3539
-0
o
E

ZZ ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Malaya

Sungei Kedah Entrance: Lt....
PENANG ISLAND

—Muka Head: Lt

—Pulau Tikus (Rat I.): Lt
—Penang

o

[CIE E qz ST
8

Tanjong Hantu: Lt

Pangkor

Pulau Katak: Lt

White Rock, Sembilan Is.: Lt___

Bagan Datoh

Sungei Selangor: Lt

Batu Penyu (Glamorganshire
Rock): ti e ae

Pulau Angsa: Lt

Port Swettenham

Klang

Pulau Pintu Gedong: Lt

One Fathom Bank: Lt

ko polo pl pl fl kt
«O «O 00 00 00 N
No
GS Q2 a aa Or O Or Or or
££ GI GO GO GO

88

RWW NRO NI DO GO

on
RARAS o sn SUBAN ESBE

=E aa

Nw
=e DH

ANDAMAN ISLANDS
—Table I.: Lt
— Port Blair

SR ELAIBRARA ADD O O OSOS O os

Fe be
58

SRSENRES

Chalna
Chittagong
Kutubdia I.: Lt
Coz's Bazar

Pulau Undan: Lt...

Pulau Pisang: Lt.

Sultan Shoal: Lt

Raffles, Pulau Satumu (Coney
Islet): Lt

Pulau Sakijang Pelepah (E.
St. John’s I.): Lt 113N | 103 51 E

Keppel Harbor 116N | 103 50 E

Fort Canning: Lt 118N | 103 51 E

Singapore 117N | 103 51 E

123N | 103 58 E

122N | 104 18 E
Petra Branca (Pedra Branca)
(Horsburgh): Lt 120N | 104 24 E

——————MMÁáá— e ee
INDONESIA

KREE SOSORoOUROBO S
ZZZZZZZZZZZZ ZZZZZZZZZZZ Z

Pi BO BO DO DO BO BO DO 02 02 02 02

SENE
NEBE
ZZ
2228
PERE
attie

Akyab

Savage I.: Lt
Kyaukpyu
Beacon I.: Lt

ASES BES
Lark anodcre
NN Y Sd Y 01 00 t2
ZZZZZZZZ
PRRESESS
EE EENS
bad

Oust

PULAU-PULAU Natuna (Na-
TUNA ISLANDS)

Karang Galan
Selat Riouw: L 104 11 E

104 34 E
104 31 E
104 22 E

104 47 E

0 18S | 105 00 E
0528 | 104 24 E
0 32S | 104 02 E

Place

SELAT DURIAN (DURIAN STRAIT)
—South Brother: Lt

Sumatra

Bengkolindse e 3-00
Pulau) Djiemur? Lt...
Pulau Pandang: Lt

Peli eee ae eee E
Teluk Aru (Aru Bay) ...........
nse ERA lic
Diamond Point (Diamant

Punt) (Jambu Ayer): Lt_____-
Pulau Buru: Lt
PULAU WE
—Le Muele: Lt.................
E e E RL al
Pulau Breueh (Bras) (Willem-

lee LL AN RS
Pau Rasa: Lose seja 908
Wfeulabokt ese PIN T A
Tanaktunn eae rie bes =<
Teluk Sinabang, Pulau Simeu-

Que: PLUR E qr ser NC
Singkat TE. Meo AAA
Pendiung Mbana, Pulau Nias:

t

Pulau Pemang Li m
Bula Pangkal pico
PulawSivatas boo 2222222 23+
Pulau Bodjos Lt- sess 2225-22
PulRusKarsik: Dt:
A Bei R ERE E ERE RSS Le NS oe
Udjung Batumandi (Ujung

Sungei Bramei): Lt..........
PulanwNelamuks Cm.
Pulau Katangkatang: Lt.......
IIA PRA RE
Pulau LL kus: Mb ee =

Pulau Pisang: Lt
ý GTS KÓ 1€ 870] TOA ACE SRS
Tjukuh Belimbing (Flat Cape)
(Vlakke HOOK) E = TÐ
TELA EAT m ase
Pulau Sebuku, Tjukuh Ban-
(bis AË EA A
SungaiiGerong: ==. as tae 2
dë Vie Bed ds ea ee
ere a fae teresa
BANGKA
—Tandjung Ular: Lt...........
—Tandjung Kelian: Lt.........
— Muntok

Pelepasan

NAngka) LOSE
— Pulau'Besar: E
—Pulau' Dapur: Lt ==:
—Tandjung Berikat: Lt........
SELAT-SELAT GASPAR (GASPAR

STRAIT)

—Pulau Lepar: Lt............--
Pulau Dijelaka: Di? "eer

—Pulau Langkuas: Lt.........-
—Pulau Kanis: Lt.........
Discovery East Bank: Lt.
Pulau Menjawak (Boompjes I.):

t
Etna. Bank Lie 322
Arnemuiden Bank: Lt.........
Pulau Tuguan (North Watcher):

L

SS

ER DO
Coe kä
Z ZZZZ ZZ ZZ 222222

HO NANG

an oon
ROR, Oo Pe

OO He Orr
O WON We

to
vo

on
O
ID

D DO DO Or

Nu
OD C00 Door

CORN ggg ggga
R

DG? DO DO

APPENDIX S

MARITIME POSITIONS
INDONESIA—Continued

103 46 E
103 46 E
103 37 E

103 21 E

me

e ee

ao ocr AN 000000
TP FERS SS 88 FRERE

o
a
or =

107 37 E
108 12 E
109 10 E

108 23 E
106 54 E
106 44 E

106 28 E

sad PE LES
BulduiPājunes DU SE
Pulau Damar-besar (Edam): Lt-

Java

Djakarta (Batavia)------_------
Tandjungpriok: Lt....... 2
T'jirebon (Cheribon) ---------- E
Hen CONG ONE = mesas a ss 2
Semarang- Æ == < kas £
Pulau Mondoliko: Lt....... =a
Sangkapura, Pulau Bawean: Lt.
Surabaj@ Ð KĀ ee LÐ
MADURA (MADOERA)
—Sembilangan: Lt............-
—Tandjung: Llar
—Pulau Sapudi: Lt........
Zwaantjes Reef: Lt---------
IA d 2 =
PON ATURONE EE
Pulau Karangmas (Pulau Mei-
derts*ReeD:3Lt.— ---—- E
Pulau Tabuan (Duiven Li: Lt-.
'Tandjung Bansering: Lt
Banjuwangi ici tomadas

Tjilatja

Lesser Sunda Islands

BALI

—Tandjung Pasir: Lt..........
—Tandjung Pengambengan: Lt.
Buleleng V 1 s sa asās
Nusa Lembongan, Selat Ba-

—Labuanhadji =. cue
Sakuntji (Maria Reigersbergen
Bank): Lt
Bima, Sumbawa
Bulsutkelapaaelat Ss ss
FLORES
—Pulau Badjo (Bajo)
E-Ende + a Ss x

HalabhiBPulaw Alor= === 120
Waingapu, Sumba (Soemba) ----
Seba, Pulau Sawu..........-

Baa Roadstead, Pulau Rot
Pulau semau: ee

Moluccas

PU deese
Meatij Miarang, Pulau-pulau
Gg AN sete oe es
TP PENU ADH pee e
PULAU-PULAU TANIMBAR
SUME e aE
ALLA K: 3
Dobo, Pulau-pulau Aru (Aroe

Ts:
Elat, Pulau-pulau Ewab (Kai

NID ADAAANH
MODA = OO

Or OO Ha DO NR RGOOA

IIA SU
Lose
RANRANN NNNMNN MNVNNMNNMNNMN

CQ» ~ 00 00 00 00 =
En vs ka CH N P P
CROP BRNO Væ

00 00 N
CAS
one

Bee
Ooo FOC 00000000
ss Sa

=
NNN Mmmm mama AnM

1091

Long.

o ,
105 I3 E
105 53 E
105 56 E
106 17 E
106 33 E
106 50 E
106 48 E
106 53 E
108 34 E
109 42 E
110 25 E
110 55 E
112 39 E
112 44 E
112 40 E
113 54 E
114 16 E
113 07 E
113 13 E
113 56 E
114 26 E
114 28 E
114 26 E

23 E

31 E

00 E

32 E

114
114
115
115

116
116

117

26 E
35 E
06 E

27 E

04 E
34 E

13 E
43 E
14 E

53 E
39 E
59 E
31 E
16 E
51 E
03 E
27 E

35 E

52 E
35 E

44 E

29 E
36 E

18 E
43 E

13 E
59 E
54 E

1092

APPENDIX S

MARITIME POSITIONS
INDONESIA—Continued

Ee Place Lat. Long. Indez Place Lat.
Moluccas—Continued aey SE Celebes—Continued iX;
75100 | CERAM 75690 | Pulau Tuguan (North Watcher
ALO Gesch rer A SE EE 3 538 130 54 E A E 035N
Ee 328 128 55 E 75700 | Tandjung Benar (Stroomen
BO e EMOS AE 3048 128 11 E dEr TES 120N
75200 | Pulau Saparua: Lt.............. 3348 | 128 39 E 7105 Pulau Hulawa: Li c m 058N
210 | Amboina (Ambon I.): Lt. 3478 128 06 E 720 | Manado (Menado)-------------- 130N
220 e Pulat suangei Diet 3188 127 28 E
230 | Leksula, Buru eese dun 3478 126 31E 15800 Borneo
240 | Pulau Sanana, Pulau-pulau `
Su e ro CM 2038 | 125 59 E 75810 | Tandjung Mangkalihat: Lt..... 059N
250 | Labuha, Pulau Batjan_-- 0 38 8 127 28 E 820 | Muaras (Moearas) Reef: Lt..... 146N
260 | Laiwui, Obi 1208 127 38 E 830 | Tarakan (Linkas), Indonesia. ...| 317 N
75300 | HALMAHERA 840 | Tawau, North Borneo. .......... 415N
SIONES eda. i E A 0 20 N | 127 53 E 8500] Batu Tinagat: LCP SAS S 413N
320 | —Buli-serani_-- 052N | 128 18 E 860 | Tanjong Labian: Lt............ 5 09 N
330 | kou 22.5 1 10 N | 127 55 E 8704 Tanjong range: Li TT 525N
340 | —Galela.......... 1 50 N | 127 51 E 880 | Sandakan, North Borneo......... 5 50 N
350 | —Wajabula 216N | 128 12 E 890 | Kudat, North Borneo. ----------- 6 53 N
75400 | Lirung, Pulau-pulau Talaud....| 3 56 N | 126 42 E 75900 | Pulau Kalampunian: Lt... ..... 7 03 N
410 | Tahuna, Pulau-pulau Sangihe...| 8 37 N | 125 29 E 910 | Mantanani Is.) Lt =. 6 43 N
920 | Jesselton, North Borneo =| 559N
93071 ¿Bula Papan: t oe ck 515 N
75500 Celebes 940 | Victoria, Labuan, North Borneo__| 517 N
950 | Pulau Karaman: Lī? 514N
75510 | Tandjung Arus, Pulau Talise: 960) | "Brunet, Brunei ss e e 4 5N
Lot e A e NP P 153N |12505E 9705 Laniong Baran TÆ 4 36 N
520 | Pulau Pondang: L 026N | 124 29 E 980 | Lutang, Sarawak................ 428 N
530 | Gorontalo_______- 030N | 123 03 E 990 | Miri; Sarawak o eae 423N
540 | Tomini Road...... 031N | 12033 E 76000 | Tanjong Lobang: Lt............ 422N
550 | Selat Walea: Lt...... 0258 122 25 E 01071 Tanjong Sirik Lis S060 247 N
5601 Pulau’ Banggal Et sss 1358 123 29 E 020 | Kuching, Sarawak------- 22 134N
570 | Pulau Wangiwangi: Lt, 5158 123 32 E 030% goanjone Poy Lct 143N
580 | Tandjung Djenemedja, Teluk 040% TDanjonsaDavu ee 2 05N
«Bones fetes ease sees 3158 120 26 E 050 | Pulau Murih (Saint Peters I.):
590 | Pulau Pasitanete: Lt 5458 120 30 E U Pk < ee tr RASAS T 154N
75600 | Pulau Sabalana (Postiljon I.): 060 | Pulau Karimata anaa 1368
M Eu CERE TI I 6498 | 119 12E 070 PulauSenutu: 779090 ASES
610 | Taka Rewataje (De Bril): Lt...| 6058 118 54 E 080 | Tandjung Selatan: Lt.......... 4118
620 | Pulau Dewakang-lompo: Lt....| 5 24S 118 26 E 090") Pulat Kun LATE 4058
630 | Pulau Dajangdajangan: Lt..... 528 119 11 E ¿61004|.Dwaalder: EP cra E 4148
640 | Makasar (Makassar) ----------- 5088 119 24 E 110 | The Brothers (Sambargalong
650 | Pulau Kapoposang: Lt, 4 428 118 57 E ds.) Dt e mer Y ap ES 4248
660| Tandjung Rangasa (Huk 120 | Kotabaru, Indonesia............. 3148
Mandar): brc LES SENS 118 56 E 180 | Buton Butona L: Lt 3398
670 | Tandjung Rangas (William 140 | Little Paternoster Is., Pulau
Cape) elite bs ome da: e 2388 118 49 E Balabalangan: Lt 2328
680 | Teluk Palu, Tandjung Karang: 1508 ATU Bank 2158
it: g SPAIN. det R 0 38 S 119 44 E 160 | Balikpapan, Indonesia__________ 1168

119 48 E

120 48 E
122 54 E
124 50 E

118
119
117
117

SES SHS ag iddi

Cape Moreton: Lt

Point Lookout: Lt

Fingal Head: Lt

Capo Byron EE

SES River, North Head:
t

South Solitary I.: Lt
Coffs Harbour

28

528

HUSKHSESISRSans
t Uo Ua tn 0900 (à 02 00 Uo Ya YA Ya

Bean

en
S 8
m n

51 S

AUSTRALIA
o ,
153 I3 E 77250
153 13 E 260
153 08 E 270
153 02 E 280
153 28 E 290
153 33 E 77300
153 35 E 310
153 39 E 320
330
153 37 E 340
153 23 E 350
153 16 E 360
153 08 E 370
153 05 E 380
152 55 E 390
152 57 E 77400
152 45 E 77500
152 33 E 510
152 12 E 520
151 48 E 530
151 46 E 77600
151 35 E 610
151 20 E
151 12 E 620
630
151 18 E 640
650
151 17 E 660

Wollongongs A
Port Kembla
GA ERO PR ERN
Point Perpendicular: Lt
Warden Head: Lt

Cape Everard: Lt
Cliffy I.: Lt

— Geelong

moo WWOOOVUVIRBROHOHNDBRNN
HOND SESASB1B R Ss R a SS ŠB a

DDD hV OT

EELER
NNNMNNN tamatata ANRARRARARRAMRBRARAM

NOAH RE c O o V o oro EN
SS INEA DIANA EA RIA OD ROCA ARS >

^
cs
e
w

ð
Ob Gig ol tii!

=
"S
ba

Wore

COAT EN

Place

APPENDIX S

AUSTRALIA—Continued

Long. Tages

MARITIME POSITIONS

=
-1
Wa NON e Y ERO FO.

KA
o
Qc co Da Q2 Ka a 020503 DOD

HH
oo
& 8

16 55

m
Kai
un un uo Un Un Un Ua Ua Un Un Un Un Un Un Un Ua Una Un Un Un Un Ua Ua Ua Ua On O2 Ua Ua Ua O0 O0. Ua Ua Un O0. 02 O Ua Ua O2 2 Ua Ua Ua Un. O0. Ua Ua Ua O0. 0 Ua Ua Ua UU Ua Ua

tO b2 b2 t9
23353
oxnoo
Ayes

SESS
dem.

N
t2 o

CGI Ka mM ka hä En O
Hp Eau EE bai Ei En OD een"

Vve e
H N Go 63
R

h BV t2 t2
D HH
ka On Eu oO
ka - Odo

ua gaunuauaunua Un Ya Un Y Un Y

o + o Li

77670 | Cape Northumberland: Lt..... 38 04S | 140 40 E $8950 - E Adrlie Nba m. rers
680 | Cape Banks: Lt. 37 548 |14023 E | 360 | North Sandy I.: Lt
690 | Penguin Islet (Rivoli Bay): Lt.| 37 308 140 01 E 370 | Legendre I.: Lt.......

77700 | Cape Jaffa (Bernoulli): Lt_____- 36 58S | 139 36 E 380 | Port Walcott______ E
710 | Victor Harbour. 35 34S | 138 37 E 390 | Port Hedland...... teen
720 | Cape Jervis: Lt...______......- 35 37 S | 138 06 E || 78400 | Bedout L: Lt...................

77800 | KANGAROO ISLAND 410 | Cape Bossut: Lt...

810 | —Cape St. Alban: Lt 35 49S | 138 08 E 42004 Broome: aeons Mau IA 0.0
820 | —Cape Willoughby: Lt.... 35 51S 138 08 E 430 | Gantheaume Point: Lt.
830 | —Cape Couedie: Lt. 04 S 136 42 E 440 | Cape Leveque: Lt
840 | —Cape Borda: Lt......... 46 8 136 35 E 450"& A T GE SD p ous soeee ia. RE D
850 | —Marsden Point: Lt______ 34S |137 37 E 400"! Browse I5; bist 23222. SS

119007 E Glenelg eua ci 01S | 138 30 E 470 | Wyndham____---

910 | Port Adelaide. ............. 518 | 138 30 E 480 | Cape Fourcroy: L M
9201 Wakefield = a = sūc 12S | 138 09 E 490 | Point Charles: L a
930 | Troubridge Shoal: Lt______ 08 S 137 51 E 78500 | Darwin

940i | Althorpe 1: -bt-— u: 23 S 136 51 E

950 |^ Wedge te Lt... 10 S | 136 29 E

960 | Corny Point: Lt....... 548 137 01 E

970 | Wauraltee (Wardang) I.: 30S 137 21 E

8801 Tiparas Roefs Lti enoe 04 S 187 24 E

9907] Winceby/E-Lt5 = C «Ce. 29 S 136 17 E

78000 | Boston Point: Lt_________- 39S | 135 56 E
(DA Porti bincoln. o. cases 43 S 135 51 E
020 | Cape Donington: Lt............ 34 44S | 136 00 E
030 | Dangerous Reef: Lt............ 34 498 | 136 12 E
040 | Neptune Isles, S. Neptune I.:

EI EE M 35 20S | 136 07 E
050 | Four Hummocks, Whidbey Is.:

TUE Mme. ETS E 34 478 135 01 E
060 | Flinders I: Ltr. 33 40S | 134 30 E
070-1! Streaky Bay-----:..222.-: 32 48 S 134 13 E
080.14 Thevenard: ss == somas 82 10 S 183 39 E
090 | St. Francis I.: Lt 32318 133 19 E

78100! |! Esperance: īsas 33 528 121 54 E
110 | Breaksea I.: Lt........ 35 048 118 04 E
dogm t4 Ibüng SE ld 35 028 117 53 E
¡SOME Ch ps bir ta dle ce 35118 117 53 E
140 Cape eeu win; d hc 2 34 22S | 115 08 E EE A
150 | Hamelin I.: Lt 34 138 115 01 E 740 | North Barnard Is.: Lt..........
160 | Cape Naturaliste: Lt... 33328 |11502E OO EBOOKS P eT
ION K Bzusselonses se < 33 39S 115 20 E 760 | White Rock, Palm Isles: Lt....
180 | Casuarina Point: Lt... 33 198 115 39 E TIO WTO WASTE Rr
1907 Bunburgy-e ==: 33 19S | 115 38 E 780 | Cape Cleveland: Lt............

78200 | Woodman Point: Lt... 3208S | 115 47E 790 | Cape Bowling Green: Lt.......
210A E Premanle oa taza 32038 115 45 E 788005 | BOWEN ei orco EE
PDs) | DIES E AAA 31578 115 52 E S810 WHshelbysl[ 4 Lise ee
230 | Bathurst Point, Rottnest I.: Lt_| 31 59S | 115 33 E 8200) Dents Lyset A 2 999
AONE Escape E Lt... 3 115 00 E S30" Mackay E tse Á setup ee
250 | Moore Point: Lt 114 35 E S400 FIat-top. ita em
2609 Geraldion Ee 114 36 E 850 | Pine Islet, Percy Isles: Lt......
270 | Cape Inscription: Lt.... 112 58 E 8604) igh Peak: L$ossss sa
280 | Babbage I.: Lt........ 113 38 E S700) North) Reet: Lt. ass ss
BOOM CUNAT ON ae = es eee € 113 39 E 880| Geh tee

78300 | Quobba Point, Beagle Hill: Lt.| 24 30S | 113 25 E 890 | Cape Capricorn: Lt.-.---------
SLO) Brazer Islets Leesberg 22 38 S 113 38 E 78900 | Gatcombe Head: Lt...........-
320517 Vlaming Heads Di. 21 49 8 114 07 E 9104 I Gladstonesio-————---2 ct
330 | Anchor I.: Lt 114 46 E 9201 Bustard' Head: Tee ss
AONE 07281010 MS V que T T 115 06 E 930 | Lady Elliot Islet: Lt-----------

pn —————— Àr SEGMRSSBD:A)II00000 00) ptf: 000]

TASMANIA

HH EN Em:

o , o D

79000 147 20 E || 79220 | —Currie Harbor: Lt...........-
010 R a È 230 | —Stokes Point: Li--------------
o2 79300 | West Point: Lt-----------------
030 146 49 E 5
O40 Devonport e d See 146 24 E ont d pas HT DET d 3 7e
050 | Mersey Bluff: Lt 146 21 E 320 NGI BOY cct eec
Genk Ee ELS 145 57 E 330/|| Cape Sorrell: Lt----------------
0701 Dablei@apes Et ENS 145 45 E 340 | Maatsuyker Isles: Lt__---------
080 | Hyfield (Highfield) Point: Lt..| 40 448 | 145 17 E 350 Cape Bruny: IE corea
090 | Cape Rochon, Three Hummock 360 || Hobart 25- r =:

Lt See ee E E 40 24S | 14 57 E 370 ||) Iron’ Bot Ls Lt---=--=-=========

791007 Enter [bs 40 29S | 144 43 E 380 || Tasman Ke 14---------------—--

79200 | KING ISLAND 390 | Cape Forestier: Lt..... £
210 | —Cape Wickham: Lt. 39 36 S | 143 57 E || 79400 | Eddystone Point: Lt..........-

1093

PP ba ka ka ji E pol ka ji ji fo pl pu
PPP PP pi pl PP PP ERR
OA A a GO O GO GO GO DO DO ba

Di
EI
Ei
VUNNA AA U m m C 2 02 OS E O O O MO AA O IA _
O RO N NO A C5 GA GO O» Q0 N OO GO CD A 00 tO DA DO HO ED C1 e e (D CH

152 43 E

no do MAS o om m >

RS
au S HHS a Čo
bag pb

pi
e
oo
ORS Es ER EN
Hn

148

1094

Place

South Island

Cape Campbell: Lt
Kaikoura
Point Kean: Lt

Godley (Cachalot) Head: Lt...| 43 3

Lyttelton
Le Bon's Bay: Lt

Cape Saunders: Lt
Nugget Point: Lt
Waipapa Point: Lt
Dog I.: L

STEWART ISLAND
—Akers Point: Lt
—Port Pegasus
Bluff Harbor
Invercargill

Centre I.: Lt
Puysegur Point: Lt
St. Anns Point: Lt
Hokitika

Greymouth_ -

Cape Foulwind: Lt

Kahurangi Point: Lt
Cape Farewell: Lt
Bush End Point: Lt

Stephens I.: Lt
Cape Jackson: Lt
The Brothers: Lt

Malaya

Tanjong Tenggaroh: Lt........
Miersinges bise t ss e ed
Sungel Pahang: Liz ar ane
Kuantan- Err
Pulau Tenggol: Lt
Kuala Trengganu
Tumpat: Lt

Thailand

Khlong Sai Buri (Taluban

River)? A IA eee PAR
Laem Pho (Lem Tachee): Lt
Songkhia: lit — ee E
Laem Talumphuk: Lt:
Ko Prap(Goh Prab) tls
Ko Tawan Tok (Goh Wang

INS Sl; c eM
Pak Nam Lang Suan: Lt
TORR AN Sam eS
Ko Raet (Go Rad): Lt
Krung Thep (Bangkok)
IK) SOON MEE c e NM
Ko Phai (Goh Pai): Lt
Ko Chuang: Lt

Ko Samet: Lt......

Laem Sing; Lt......
Ko Chik Nok: Lt

Cambodia

Sihanoukville (Kompong Som)
Ream

~

A Go

43 3

A 00 DD) Ct

7
7
4
5
9
3

OS Ooo R SŠIBŠU

o

C Cs ma
vcatatatatatatatatatatatatatatatatata NNNMNNN varatatatatatata tata tata tata

Oo om oo mo

o
~

SFS
Bezel

ZZZZZZZZZZZZZ ZZZZZ

Kata E
ooo
CSS
ZZ Z

APPENDIX S
MARITIME POSITIONS

NEW ZEALAND
eg a E

Long.

A A A polo pol pol pl kt Fe jr bh Ft
NT NU
DO O O HH O ND GO GO

F2 06 m rog-1c000dg 050005 r2 -1 `

Arc Hannu a a a a a a a a a a a a

i
oo
ooo

hV OT Tr ia P` W ës Or Cn e e OOPS he

NOA

h i i i i
eoo
CO» -1 00 che
Wand,

Oo bd 200 VDO ODO DO

Ūū

=)

e
PRESS `
SS rd Ed bt d

2

5
toc 02r
Hu IS
¡Solo!

= =

e o

to =
CTS

Cn . NO -100 C 00 CO C R
Ez E Ed Ex] d E d E Ed Ed d 3 d

=
e
Ed
ec
S
Ed

Index

Place

North Island

Ohau Point: Lt

Karori Rock: Lt

Wellington (Port Nicholson)

Pencarrow Head: Lt

Baring Head: Lt

Cape Palliser: Lt

Castle Point (Rangiwha Ra-
oma): Lt

Cape Kidnappers: Lt

Napier Harbor

Portland I. (Te Houra): Lt

Gisborne

Tuahina Point: Lt

Burgess Islet: Lt

Moro Tiri: Lt

Whangarei

Sugarloaf: Lt

Cape Brett: Lt

Whangaroa

North Cape: Lt

Cape Reinga: Lt

Cape Maria van Diemen: Lt...
Kaipara, North Head: Lt
Manukau, South Head: Lt
New Plymouth
Mikotahi I.: Lt

Wanganui
Kapiti I.: Lt

Saigon
Vung Tau (Cap Saint-Jacques)...
Pointe de Ke Ga: Lt

Ile Tre (Mui Rachtrang): Lt
Nha dE EUR
Cap: Varella: Lt,

Poulo Gambir: Lt
LE 9

HsrsHA CH'ÜN-TAO (PARA CEL
ISLANDS) (CHINA)

—Shan-hu Tao (Páttle 1.): Lt__

—Shih Tao (Rocky I.): Lt

Presqu’ile de Tien Sha: Lt

Da Nang (Tourane)

Haiphong At e eee ae

Iles Norway: Lt
Cam Pha

0) Go Go W W Q3 UI W GO Q2 UU P
MON ODN N 00 00 00 O OOO

Q Ora n Co > C24 woo e
SIISE NENA DAN ADA AR
t ua ua un ua Ua ta ua xa Ua Ca (a (o Ua ga ua (a (a Ua a a a ga a EE Ga a Co a En NNNNNNA

+
o

C2 DO CT m hä + kb

NON ANH OOO

121
13 3

to
5 SS EO
ZZZZZZZ ZZZZZZZZZZ

8

AR nc a a a a

GP e C A aA GO OT I WHO

E IS in ES
00 t2 O ON FO IN O0 00 O RO

o F.
104 29 E
104 50 E
106 36 E
106 42 E
106 47 E
106 42 IE
107 04 E
107 59 E
108 07 E
109 01 E
109 03 E
109 13 E
109 20 E
109 11 E
109 27 E
109 22 E
109 14 E
109 11 E
109 08 E

111 36
112 20
108 19
108 13
105 42
105 49
105 50
106 49
106 41
107 09
107 22

Ej Ej Ed Ed eee

———— — M NE NODE LIE E Í

1095

APPENDIX S
MARITIME POSITIONS

EAST COAST OF ASIA—Continued

Place S : No. Beka

China di; China—Continued

Pei-hai (Pakhoi) 109 06 E 1 ii
& Y Wu-ch'iu Hsü (Ockseu Is.): Lt.. 119 27 E
Wei-chou Tao: Lt 109 06 E Niu-shan Tao (Turnabout Is.):
Lt 119 56 E

109 55 E
HAI-NAN Tao (HAINAN) 119 59 E
—Lin-kao Chiao (Lamko): Lt__ 109 42 E Pd (Foochow) 119 id E

—Y ü-lin 109 31E M

= 2 z a-tsu Shan (Matsu I.)-------. 119 55 E
en Tsui: 110 41 E Tung-yin Shan (Tung Yung):
ai-k'ou X 110 20 E Wo 120 30 E
Nao Chou (Ile Nao-chow): Lt.. 110 36 E Ch’ih-chu Tao (Spider I.): Lt... 120 04 E
Aigrettes I., Colline Verte: Lt.. 110 33 E Yin-k'ou-kou Lieh-tao (Incog
110 24 E Is.): Lt 120 28 E
111 18 E Tung-kua Hsu (Shroud L): Lt.. 121 03 E
Macao Pei-yü Shan: Lt 122 16 E
Tung-t'ing Shan: Lt 122 35 E
Ponta de Ká-hó: Lt 113 35 E Lo-chia Shan (Loka I.): Lt 122 27 E
113 33 E Hsiao-pan Tao (Steep I.): Lt... 122 35 E

Hsia-san-hsing Shan (Elgar I.):
Lt 122 31 E

Kuang-chou (Canton) Pd ge
Wan-shan Ch'ún-tao (Ladrone t : e oe
Is.), Chu Chou: Lt Lt 4 122 22 E

Wen-wei Chou (Gap Rock): Lt. Ta-ch'i Shan (Gutzlaff L): Lt 122 10 E
Hong Kong Hua-niao Shan (North Saddle |.
| e 122 40 E
Tsing Chau (Green I.): Lt She Shan (Shaweishan I.): Lt... 122
Shang-hai . 121
(Lamtong I.), 114
Tathong Point: L i 119
Wang Lan: Lt Ch'ing-tao (Tsing- Tao)
China EEN Tao (Ts'ang-chou):

Ta-hsing-tsan Yen (Ped Mu-yeh Tao (Muitao
B z : E (Southeast Promontory): Lt..

Che-lang Chiao: Lt Ch'eng-shan Chiao (Shantung

Lien-hua-feng Chiao (Breaker Promontory): Lt
Pt): dt 116 30 E Wei-hai-wei

Piao Chi H K'ung-t'ung Tao: Lt
y. iao (Cape Good Hope): Tibet Ven Pai (Chefoo)

Lu Hsü (Sugarloaf I.): Lt 116 46 E Hou-chi Tao (Miaotao): Lt
eerie Cien ne akti OF 116 41 E Mu-chi-tao Chiao (Chimatao

Nan-p'eng Ch'ün-tao (High Promontory): Lt
Lamock I.): Lt 117 17 E T'ang-ku (Taku Bar)

Hsia-men Tao (Amoy) 118 04 E Ch’in-huang-tao (Chinwantao) ----

Taiwan (Formosa)

; -tao- i-tzu: L
Pai-sha-t'un (Hakushatou): Lt. 121 04 E Wi ode mer A
Tan-shui Ho-k'ou (Tansui Har- eh oe B Lao-t'ieh Shan (Rotetsu San):

3 : 2 Lt
Fu-kuei Chiao (Fukikaku): Lt. 121 32 E Lao-hu-wei Shan (Rokobi): Lt__
es ow rape Sho) 192 04 E Lú-shun (Port Arthur)

FIBCOUTU 2.7. ss i-k” i Kohahu Shi):
Via -jen-t'ui Pi (Banjintai Bi): i IRE sos i)
121 44 Ta-li "Dui
Chi- F Chiang (Keelung) (Kii- Vai Lt

run Ko) 121 44 E Hai-yang Tao: Lt
San-tao Chao (Sancho-Kaku): Ta-wang-chia Tao: Lt

Lt 122 00 E Ta-lu Tao: Lt
121 51 E An-tung
Hua-lien Shih (Karen Ko) 121 36 E
San-hsien T'ai (Sansendai I.)_--- 121 25 E
T’ai-tung (Taito Ko): Lt 121 09 E r
Huo-shao Tao (Kasho-To): Lt_- 121 28 E Yalu River Entrance, Suun Do
Hung-t'ou Hsü (Koto Sho) Ë 121 32 E (Suiun To): Lt
O-luan-Pi (Garan Bi): Lt 120 51 E Taehwa Do (Daiwa To): Lt
Liu-chiu Hsü (Ryukyu Sho): Lt. 120 22 E Chinnamp'o
Kao-hstung Shih (Takao Ko) 120 16 E Taedong Gang, Chamae Do
An-p'ing: Lt 120 (Shimai TRO) Lat,
P’ENG-HU LIEH-TAO (PESCA- Só Do: L aoe

DORES ISLANDS) Soch'óng Do (Shosei To): Lt....
—Tung-chi Hsü: Lt 119 Sónmi Do: Lt
—Hua Hsú: Lt E 119 Inch'ón (Jinsem) A y po
—P'eng-hu Tao (Boko Ko) 119 An Do (An To):
—Yii-weng Tao (Kissi): Lt 119 Moktok To Cone To): Li-
Te tou Hsii (Mokuto Sho): 'TTonggyóngnyólbi Do: Lt
119 Ong Do (O To): Lt
—Ch’ ac mu Hsü (Sabo Sho): Lt-| 2: 119 4: Och'óng Do (Osei To): Lt
Chi Kunsan Hang

de Mal To (Matsu To): Li. x

Chin-men Tao (Quemoy I.)----- 118 25 E Taerorok To airoruko To
Pei-ting Tao (Dodd L): Lt 118 30 E L 125 59 E

No Orto Oo s 00 00 Ka sl Bäi ka DA ën 06 ke
ZZZZZZZ ZZZ ZZZZZZZ

DO to
OV

H0O On
e an GO
Gba HEHE

1096

APPENDIX S
MARITIME POSITIONS

EAST COAST OF ASIA—Continued

maz Place Lat. Long. De Place Lat. Long.
Korea—Continued eu S49 84200 Sakhalin
SS OM EMOL DI or me EE 34 47 N | 126 23 E 230 | MysSlepikovskogo (Konotoro Mi-
480 | Ch'ilbal To (Shichihatsu To): saki) (Naka-notoro Misaki): Lt.| 47 18 N | 141 59 E
RE ——— 3447N | 125 47 E 240 | Kholmsk (Maoka) __-_------------ 47 03 N | 142 03 E
490. |. Hong Do: Lio ta nee sont 8s 34 43 N | 125 12 E 250 | Ostrov Moneron (Kaiba Tē):
83500 | Sohūksan Do (Kokuzan To): Tica Dodo. 24. JAM 46 15 N | 141 16 E
Tits oe Nas 125 06 E 260 | Mys Kril'on (Nishi-notoro Mi-
BE Er erte 125 51 E saki) (Cape Notoro): Lt------ 45 54 N | 142 05 E
520 | Hajo Do (Kacho Tō): Lt.- 126 05 E 270 | Korsakov (Otomari) ............- 46 38N | 142 46 E
530 | Sangch'uja Do: Lt........ 126 I8 E 280 | Skala Sivuch'ya (Gojo Iwa): Lt.| 46 02 N | 143 24 E
540. |. Mara» Do: Lt-----:-.-—-- 126 16 E 290 | Mys Svobodnyy (Airó Misaki):
550 | Cheju (Saishu)........... 126 32E Det Sen fe ftu Rn 46 51 N | 143 26 E
560 | U Do (Gyu To): Lt D 126 58 E 84300 | Vostochnyy (Motodomari)-------- 48 16 N | 14238 E
570 | Chaji Do (Shashi To): Lt....... 34 06N | 126 36 E 310 | Mys Terpeniya (Kita-shiretoko
580 | Kómun Do (Kyobun To): Lt...| 34 00 N | 127 19 E Misa): b. C a 48 39 N | 144 45 E
590. Hābaek Do: Tjt- eee cece 34 03 N | 127 35 E || 320 | Mys Yelizavety: Lt.----------- 54 25 N | 142 43 E
83600 | Sori Do (Shori To): Lt. -.| 34 25 N | 127 48 E 330 I M ys Mario t. 4 54 18 N | 142 15 E
010 WY sus ee P 2 Ek EE 34 44N | 127 45 E 84400 USSR
620 | Somaemul To: Li- ` aere 3437 N | 128 33 E :
630 | Hong Do (Ko T0): Lt 34 32 N | 128 44 E || 84410 | Nikolayevsk.....................- 53 09 N | 140 44 E
(Muy ado Do RR 34.59 N | 128 50 E 420 | Mys Men'shikova: Lt.......... 58 18 N | 141 25 E
650 | Mok To (Makino Shima): Lt...| 35 03 N | 129 06 E ES 59 22N | 143 12 E
AMO e ar E, 35 06 N | 129 03 E 440 | Ostrov Spafar'yeva: Lt......... 59 10N | 149 06 E
670 | Kanjól Gap (Konzetsu Ko): Lt_| 35 21 N | 129 22 E 4501 [ENagayedo oes tee pet 59 34 N | 150 43 E
680 MAULE (Uru Saki): DEE 35 29 N | 129 27 E 460 | Ostrov Zav’yalova: Lt_--------- 58 58 N | 150 27 E
690 | Changgi Gap (Choki Ko): Lt...| 36 05 N | 129 34 E 470 | Nayakhan_---------------------- 61 54 N | 159 00 E
83700 129 22 E 480 | Ust'-Bol'sheretsk. ------- 22% x 52 50 N | 156 17 E
710 490 | Mys Lopatka: Lt ---------- 50 52 N | 156 40 E
129 26 E 84500 | Mys Povorotnyy: Lt 5219 N | 158 35 E
720 128 22 E 510) Petro paros k- "S= ee 53 01 N | 158 39 E
730 127 26 E 520 | Mys Mayachnyy (Dalni Pt.):
740 127 37 E Lo 2 53N | 158 43 E
750 128 12 E 530 | Mys Shipunskiy: Lt............ 53 06 N | 160 00 E
760 129 12 E 540 | Mys Kronotskiy: Lt...........- 54 45 N | 162 10 E
770 129 43 E 55o E agi «po O 56 13 N | 162 25 E
x d omandorskiye strova,
d Lodi (Gyoro Tan): Lt... 41 23 N | 129 48 E Ostrov Beringa (Bering L)....| 54 54 N | 166 24 E
83800 | Najin..._......_.. 130 18 E 570. | EM ysvA frika: Lb. 7 e e 56 10N |163 I9 E
810 | Unggi > 130 24 E 580 | Mys Navarin Lt__..----.------ 62 15 N | 179 08 E
c pc E ais 590 | Mys Barykova: Lt.............| 63 03 N | 179 28 E
83900 84000 |) Mys Geka” Li--:223. 25 0 64 25N |178 15 E
810 | Arad) e sao 64 44 N [17780
83910 | Mys Gamova: Lt..............- 42 33 N | 131 13 E Ua O VAC EDLY LY
920 | Ostrov Rimskogo-Korsakova: 630 Lesovskogo: Lt..............- 64 20N | 173 30 W
LAM oe UNUM 131 98 E Mys Chaplina: Lt -SNE 64 24 N | 172 14 W
930 | Mys Bryusa: Lt. 131 28 E 6407 | Mys Kygynin: Dt. asna ÆR 64 45 N | 172 04 W
CHE 131 54 E 650 | Mys Nygligan: Lt 65 04 N | 172 06 W
950 | Ostrov Skrypleva: Lt----------- 43 02 N | 131 57 E 660 | Mys Krigugon: Lt 65 29 N | 171 03 W
9602 OStroveASkolids Lice 42 44 N | 132 20 E || 84700 Kuril Islands
970% EIGER ONG ay ee 42 49 N | 132 54 E |!
980 | Mys Povorotnyy: Lt----------- 42 40 N | 133 03 E | 84710 | Mys Kurbatova (Kokutan
990 | Mys Ostrovnoy: Lt............- 42 48 N | 133 44 E LAN A eae 50 52 N | 156 29 E
84000 | Mys Nizmennyy: Lt 43 31 N | 135 09 E 720 | Imai Saki, Vtoroy Kuril'skiy
rie LEE --| 48-44 N | 135 17 E Proliv (Paramushiru Kaikyo):
020 Mys Yegorova: Lit-------------- 44 47 N | 136 26 E Lil ee eS ME 50 46 N | 156 12 E
030 | Mys Belkina (Cape Disap- 730 | Mys Vasil’yeva (Kurabu Saki):
ointment) Is ee. 45 50 N | 137 41 E Tit APA A M RS 50 00 N | 155 24 E
040 | Mys Zolotoy: Lt..........- 47 19 N | 138 59 E 740 | Ostrov Toporkova (Iwaki Jima)
050 | Mys Peschanyy: Lt 48 27 N | 140 11 E (Banjo bo) DU ee 48 05 N | 153 18 E
060 | Mys Krasnyy Partizan: Lt..... 48 58 N | 140 23 E 750 | Ostrov Simushir (Shimushiru
070 | Sovetskaya Gavan cea 48 58 N | 140 17 E T0): Lib mano 46 52 N | 151 49 E
080 | Mys Syurkum: Lt......... ___| 50 06 N | 140 42 E 760 | Ostrov Urup (Uruppu Tō): Lt.| 46 14 N | 150 21 E
090 | Mys Kloster-Kamp: Lt.........| 51 26 N | 140 53 E 770 | Ostrov Hurup, Kasatka (Eto-
POU EEN 51 28 N | 140 47 E rotu To, Toshimoe): Lt-..... 45 00 N | 147 44 E
780 | Mys Lovtsova (Atoiya Misaki):
84200 Sakhalin m E e T SA 44 27 N | 146 34 E
790 uzhno-Kuril’sk (Furukamap-
84210 | Aleksandrovsk_____- LES eee 50 54N | 142 08 E Dit) ae A E. TM oam 44 01 N | 145 51 E
220 | Mys Lamanon (Chirai Misaki): 84800 | Shikotan To: Lt 43 5ON | 146 55 E
Dt. zs S CEN 48 47 N | 141 51 E S10 | v Shakotqm see e A NE 43 52N | 146 50 E

i AD Hokkaido—Continued
o , o ,
GIOIKU | Nutt E T TRE 43 20N | 14535 E 090 | Chikyü isaki:
ammm i ee 4218N | 141 00 E
den B Sakis Kate Cd 43 23 N | 145 49 E 80100) WMi.nor an TE E eee 4220N | 140 59 E
go Hanash e yeer- NAS NIT E 104" OU EE Er A 41 49 N | 141 NE
el SE Sal tt as 1 43 10 N | 145 31 E 120 | Shiokubi Misaki: Lt a 41 43 N | 140 58 E
ta Kaka spots d í 43 08 N | 144 51 E EE 41 47 N | 140 43 E
Ge EE A 2 N E ae E 140 | Kattoshi Misaki: Lt...........- 41 44 N | 140 36 E
080 | Urakawa KO: Lt................| 42 I1 N | 142 47 E Ee EE

Place

Honshü

Fappi sakid Dt- .—- IR
VU Ly sa
Momori-see Ee

Oma Saki: Lt.
Shiriya Saki: Lt...
Odo Sakis bises taa

Sm Ee
Kinkazan Tor lt o læ = 3
Shioya Misaki: Dt...) 2220
Ghoshi Seem E X EA a

Nojima Zaki: Lt
SungSakbeLi- - —— c "TN
dis ANS SN SAO

Daisan Kaiho (Fort No. 3): Lt__
KannonZaki- Lits
Urggd Ew sc lr ee
Ajika Jima (Ashika Shima): Lt.

JTsurugi Sakl--L£.--—-—-— véierel
O SHIMA

—Kazahaya Zaki: Lt.
EE ee e
Mikomoto Jima: Lt...... EPA
nopsakis tie, E
RINA O a

Fukiaino Misaki:
Omae (Omai) Zaki:
EAN E eeh

Trago Zaki: Lt

Udo EEN
Fugu Saki: Lt...

WN GONG. omen eebe rh EE
OREA ene
Kami Jima: Lt

Toba- CE EE
Daio Zaki: Lt

Ko Shima: Lt....

Miki Zaki:

Kandori (Kantori) Zaki: Lt....
Kashino Zaki: Lt........ ee
Shiono Misaki:
Ichie Zaki: Lt.-----
Hino Misaki: Lt....
Wakayama = Æ = 2s =
Tomoga Shima (Okino Shima):
L

Naikai (Inland Sea)

Osaka, Honshii___..-------_-----
Kobe, Honshü.......

Hiroshima, Honshi_-
Tokuyama, Honsht_
Shimonoseki, Honshü
Mojsskyushu ss EE
He Zaki, Shimonoseki Kaikyē:

BEDDU AYUN e a ES TE
Jizo Misaki (Seki Saki): Lt.....
Sada Misaki beeen eee
Imabari, Shikoku......

Takamatsu, Shikoku
HIS s S etta
Sumoto, Awaji Shima. ..........

Shikoku

Ashizuri Zaki: Lt
Mizunoko Shima: Lt

Lat.

35
34

EEN

(O O) OD mn C MHD

0
3
35 N

ZZZZZZZZ

APPENDIX S
MARITIME POSITIONS

JAPAN— Continued

51 E

=
>

SSS

oo d xd Ed d xd d rd xd Ed Ed End Ed ez Ed

ka
el
o
e
e

=
Gi
bo
En cn N 0 O ore to
Qo DOOM NOR O

bd pitt bd bd n Gd Ed E] d

e

[Æ
AROQONMTWA
KEE e

134

wW
e
H

134
134

45 E
18 E
134 11 E
133 34 E
133 01 E
132 11 E

Place

Kyüshü

ee CERE ES CSS
Bóno Misaki:

Kogo Zaki: Lt
Shimo-kareki Shima: Lt........
Ogami Shima: KI =~ 2 a
Danjo Guntó, Me Shima: Lt...
Goto RETTO

—Hirashima;*Lt----——--—— ——

Ko Saki:
II Se es
Kuro Snima Ua = A ee
Mats nime ae V

HE 9e DA pones fM
iutagami.Shima: Dt---------——
Nyaka Shima Lide
Eboshi Jima: Lt...
Genkai Jima: Lt..
Hakata onk EE
OkinojShima: Lt».
WE. AA, ARE MEA
A EE A

Honshú

Mutsure Jima Lt EE
Futaoi Jima: Lt....

MIGS e Pt LL Lu
a MA

EE
Echizen Misaki: Lt.
Saruyama Zaki: Lt....

SADO
—Sawazaki Bana: Lt
—Hajiki Saki: Lt
— Ryūtsu (Ryozu)

Funagawa 2
Nyudo Sake Lt 2-2 Ei.

Hokkaido

Benten JimaswLft-——---—----.-----
ANS Ai lp

Lat.

o

OO RU N OO

ra O25 Co -I

w w

po

to No C ct
ROROAEDO

35 3

W
o
`
AN AW

e
oon
ZZZZZZZZZZZZZZZZZZZZZ

37 4

1097

129 20 E
128 21 E

129 13 E

128 54 E
128 46 E

129 3:
129 4
129 5

130 2
130 0!

SS

©

=
Q5 00 C» ma Aa O Gs GO
llelo lololol]

O A 0200 C 0003 — C tou C 4 O 00 DT SIN

eo
a
CO Omoto One E ba MD N VO ba CH o
Sa ad Ed rd d zd Ed rd End ed xd Ez dad bit

1098

APPENDIX S
MARITIME POSITIONS

JAPAN-— Continued

Index Index
No. Place Lat. Long. No. Place Lat. Long.
Hokkaidó— Continued Nampo Shoto (Nanpo Shoto)—
D. V 5 yv Continued d ej
87330 | Kamome Shima: Lt 140 07 E | o^ o
340 | Inaho Misaki, Okushiro Shima 87550 | Chichi Shima, Ogasawara Gun-
DA. hr ee E e 139 34 E EE sere ae 27 05 N | 142 12 E
350 | Motsutano Saki: Lt. 139 50 E 560. Haba] ima: eee. 26 39 N | 142 09 E
360 | Benkei Misaki: Lt 140 12 = 570 | Iwo Jima: Aviation Lt---..---- 24 47 N | 14119 E
STONE GI eR 140 81 1 å
330. Kerai Misakl: Li 140 21 E 87600 | Nansei Shotó (Ryukyu Islands)
390 | Takashima Misaki: Lt......... 43 14 N | 141 OL E 87700 | TANEGA SHIMA
874001 Otra A E E 4312N | 141 01 E 710 | —Nishinoomote Kō: Lt......... 30 44 N | 130 59 E
4101] Vii | < 43 51 N | 141 32 E 720 | —Otake (Take) Zaki: Lt 30 23 N | 130 58 E
420 | Yakishiri Jima 87800 | Yaku Shima, Nagata Misaki:
SOMA) LE c rm 44 20N | 141 26 E TP Dec NETS 30 24 N | 130 23 E
430 | Oshidomari, Rishiri To: Lt. 45 15 N | 141 14 E 810 | Kusakaki Shima: Lt 3051N | 129 28 E
440, VV akkandises vea ee 45 25 N | 141 41 E 820 imGajashima: 12.2.5: Soe eee 29 54 N | 129 32 E
450 | Sóya Misaki: Lt_--------------- 45 31 N.| 141 56 E d 00000 | AMAMES Bue ^ 7 1
460 | Notoro Misaki: Lt.-............ 4407 N | 144 I5 E 910 age si | bod vu 28 2 N 129 30 E
= 5 5 5 920 | —Sotsuko Zaki: Lt............- 5 9 08
87500 Nampo Shoto (Nanpo Shots) 88000 | Gran ONTO
87510 | Hachijo Jima, Ishizumiga 010" Tsuken Jima: LO 26 15 N | 127 56 E
Hanat Wee La siem P 33 05N | 139 51 E 020 | —Naha, Okinawa Jima.........- 26 13 N | 127 41 E
520) SA ora Snim9 ss ce LES 3227N | 139 46 E 88100 | Miyako Jima: Loran Station...| 24 44 N | 125 26 E
530 | Urania I. (Existence doubtful)..| 31 54 N | 140 00 E 110 | Okino-daitd Jima 8 131 GE
540. "Dori SDIIS I. is 30 29N | 140 19 E Ke RTE 6 131 18 E
PHILIPPINES
o + o , o , o ,
89000. | Batan L: Peak..---.----—. — 122 01 E SOH20MCanimonl ea t a _| 14 08 N | 123 03 E
010 | Babuyan I.: Peak........ 121 57 E 580% Don IL SSS 14 25N | 122 40 E
020 | Didicas Rocks.-....------- 122 12 E 5404 Baliscanu TR SE 14 15 N | 121 54 E
030 | Cape Engaño: Bien 122 08 E 550 | Polite, Polite Ide 14 44N | 121 56 E
040 | Aparri, Luzon...........- 121 38 E 500 eC Chee con ae 15 46 N | 121 34 E
0505 T Eata] Eont: LL A 121 09 E 570 | Cape Calayites Lt" "mmm 13 27 N | 120 18 E
060 | Cape Bojeador: Lt.............. 120 36 E 580 | Escarceo Point: Lt-------=------| 13 31 N | 120 59E
OD) Laoag OTTO Os EE 120 35 E 590 Verde Nes Pontes 13 34 N | 121 05 E
080) | Currimao; Luzon_2--.--- 2-2. 120 29 E 89600 | Calapan, Mindoro sze- TV 13 25 Ni 11-121 1078
090 | Salomague, Luzon eege 120 25 E DIO | Dumali Point lb Io eee 1307 N | 121 33 E
89100) (Pandan, Luzon = ee ee 120 22 E ` 5
110 [dando I4. Le o sanes RE 1201 25 m || Saree RAIL
120 | lagudins Lt: sis 120 26 E 89710 | Tres Reyes Is., Baltasar I.: Lt___| 13 14 N | 121 49 E
180 | San Fernando, Luzon 120 19 E 720 | Casan, Marinduque I........... 18 20 N | 121 51 E
140) | Pore, LUZON- En Æ — GN S 120 18 E 730 | Balanacan, Marinduque I. Slab erreeche 1215248,
150 | Dagupan, Guecet Point: Lt....| 16 04 N | 120 20 E 740 | Santa Cruz Harbor: Lt......... 13 30 N | 122 03 E
160 Bolinao, TUZON Se Eod 16 23 N | 119 54 E 750 | Simara I., Corcuera Point: Lt..| 12 48N | 12201 E
170| Piedra Point, Cape Bolinao: 760 | Tablas I., Gorda Point: Lt..... 12 40N | 122 09 E
(roca pes ees 16 18 N | 11947 E 720) | xApupnansbolnt: Lire eee 1229N | 12217 E
180 | Hermana Mayor I.: Lt......... 15 48N | 119 48 E 780 | Romblon, Romblon I............ 1235N | 122 16 E
190 EalauiciRoimts lote S 15 26N | 119 54 E 790 “Sabang Pointe lbs S 12 36 N | 122 16 E
89200 | Capones I.: Lt........ m US 14 55 N | 120 00 E 80800 ||, Burias Tes SE SS 1300N | 123 05 E
210 | Subic Bay, Sueste Point: Lt...| 14 45 N | 120 11 E 810! "San Miguel RULES 12 43 N | 123 35 E
220 Olongapo, ULA aa. 14 49N | 120 16 E $20) Tiao TL... taas DR 1235N | 123 40 E
230) oa) Monja dis Lt 515 nesesito 14 23 N | 120 31 E 830 |, Bugul EE 1236N | 123 14 E
240) | Mariveles, Eavzon....-_-_-------- 14 25N | 120 30 E 840 | Colorada Point: Lt............. 19:93 NI 1023 Souk
250 Corregidor JE pil o 14 23 N | 120 35 E 850 | Port Barrera, Masbate I.........| 1231 N | 123 23 E
260 St Hee 14 35 N | 120 58 E 860 | Masbate, Masbate I............. 12°22 N al, 12387 E
270) || Cavite, Luzon- F e 14 29N | 120 55 E 870 IDOTOL E 11 50 N | 123 07 H
2 pone Ar Uu Fi M 30 ` 120 55 E 880 I Ploripom Point: Dis <a nm 11 37 N | 122 30 E
g an M Shoals lite ee st 26 120 46 E 90 | Port IZM, z
89300 Caballo dU ee 14 22N | 120 37 E j ce d Kee WEE
310 Fortune D 5 EEN 14 03 N | 120 29 E. || 89900 Visayan Sea
320 ADI «Jt: e d e 13 58N | 120 01 E 89910 | Manigonigo Islet: Lt 11 86 N | 128 11 E
330 | Golo I.: Lt LEO AE © 13 38 N | 120 25E 920 | North Gigante I.: Lt... 9 11 38 N | 123 21 E
340 | Cape Santiago: Lt_.____________ 1346 N | 120 39 E 930) W6Bālietilān HI (CSS 11 12N | 123 2 E
S00 Bala yan pt. <: ze. 18 56 N | 120 44 E 940 Calabazas EI ES 11 05 N | 123 01.E
360 Batangas, Luzon EIA Secs dn TA 18 45 N | 121 03 E 950 | Tanguingui Islet: Lt " 11 29 N | 123 43 E
370 | Malabrigo Point: Lt, 13 36 N | 121 16 E 960 | Malapascua I.: Lt _________ 11 21 N, | 124 07 E
380 | Port Ragay, Luzon-------------- 1347 Nyt 2A 89 li A MM RE Sie Sere ce i
Ne Donsol, Luzon ONCE 1254N | 123 35 E || 90000 Samar Sea
Sorsogon, Luzon................. 12 58 N | 124 00 E || 90010 | Matabao I.: Le, 12 19 N 7
410 | Bagatao I.: Lt... 12 50N | 123 47 E OM 1s Lt onn 11 53 N ui i: x
420 | Bulan, Buzon- -s an a 12 40N | 123 52 E 030 | Catbalogan, Samar. _ __ 11 46N | 124 53 E
430 | Legaspi, Luzon...... 13 09 N | 193 45 E 040 N Calbayog nut RE MN 12 04 N | 124 35 E
4400 C Ungay Boint: Lum cem 13 11 N | 124 13 E 0507 Capul Te T 0. bb
"m" uo Luzoni sac 13 22 N | 123 44 E 060 | Calantas Rock: Lt..............| 12 31 N | 124 05 E
pon A inae: init > ée 13 24 N | 123 43 E 070 | San Bernardino Islet; Lt_______ 1245N | 124 17 E
7 abang: E M aN 1343 N | 123 35 E 080) |) Batasss bus tom nn A 12 40 N | 125 04 E
480 Sialat Point: Lt 18 40 N | 124 02 E 090 | Borongan, Samar_______________ 11 36 N | 125 26 E
490 | Virac, Catanduanes- 13 35 N | 124 I5 E. || 90100 | Divinubo L: Lt 1136 N | 125 30 E
SCH Pandan: Dt... c MN 14 03 N | 124 I0 E 110) Suluan D; ee m lr Ee BIO SESS)
catala Dr AE 8 Tr 13 59N | 123 50 E 120 | Mariquitdaquit Islet: Lt. 11 04 N | 125 09 E

1099

APPENDIX S
MARITIME POSITIONS

PHILIPPINES—Continued

Place

Place : rūdas

Samar Sea—Continued Camotes Sea—Continued

90130 | Tacloban, Leyte M int:
dox Li aotan I., Bantolinao Point:

90200 Mindanao Sea Cebu City, Cebu

Lauis L T

90210 | Liloan, Panaon I. ae at

220 | Malitbog, Leyte

230 | Maasin, Leyte--.-------
Balicasag I.: Lt
Siquijor I., Port Canoan: Lt...
Dumaguete, Negros
Apo I.: Lt
Tagolo Point: Lt....
Polo Point: Lt
Port Misamis, Mindanao__-_---.
Iligan, Mindanao
Cagayan Anchorage, Mindanao. -
Bugo, Mindanao
Mambajao, Camiguin I.
Butuan, Mindanao
Surigao, Mindanao
Rasa I.: Lt

Tañon Strait

Amblan Point: Lt
Pescador I.: Lt
Dumanjug, Cebu
Refugio I.: Lt
San Carlos, Negros
Balamban: Lt

Panay Gulf

Bacolod, Negros
Siete Pecados: Lt

Guimaras I., Lusaran Point:

Sulu Sea

Nogas I.: Lt

Tubigan Point, San Jose
Arasasan, Mindanao Buenavista: Lt
Mati, Mindanao

Cape San Augustin: Lt
Santa Ana: Lt

Davao, Mindanao
Daliao, Mindanao
Malita, Mindanao
Tinaca Point: Lt
Cotabato, Mindanao
Parang, Mindanao
Sibago I.: Lt
Zamboanga, Mindanao
Little Santa Cruz I.: Lt

Camotes Sea
Canigao I.: Lt

Z

Ambulong I.: Lt
Apo Reef: Lt
Culion I.: Lt
Langoy I.: Lt
Manucan Islet: Lt

Sir J. Brooke Point: Lt...
Tubbataha Reef: Beacon
Balabac I., Calandorang Bay....
Cape Melville, Balabac I.: Lt...
Cagayan Sulu I.: Lt

E5553
ZZZZ

Ex] Ed Ed Ed Ed Ed Ed Ed d d cd End End Ed Er] Baa Ed d nd Ed End nd Ed Ed d Ed End rd d d
S
e

BH
oo
Ka +4

IAN, INIA) [ess sess ne
Pearl Bank: Lt

North Ubian I.: Lt

Jolo, Jolo I.

Tatalan I.: Lt

Mataja I.: Lt

Malamaui I.: Lt

EE

LESSER ISLANDS OF THE PACIFIC

Di
o
Di

PUAA ONSON ee

ES
um
o

Palompon, Leyte
Bogo, Cebu
Capitancillo I.: Lt
Bagacay Point: Lt

e
ES
e

=
ZZZZZZZZZZZZZZZZZ

Oo O O O» O» GTG O» O» 00 00 00 «O «o
HR. Q2 OG C» Q2 Co Cn RO R IP IR OD
RA Q3 G3 C5 CO bäi En En CO C H» O» & 00 C

=
e
0 «5 O5 05 CO 00 e o
ZZZZZZZZ
MOO 00H 00 Ct
SEE

m
e
to

o
-

NEW GUINEA 92400 | SOLOMON ISLANDS
— Waigeo 410 | —Kieta, Bougainville
—Tandjoeng Sorong: Lt 0 49 420 | —Choiseul

— Manokwari, Neth. New Guinea 430 | — Vella Lavella

KREE

© OOM 7100 tt ow D O

D
— Hollandia, Neth. New Guinea...
—Madang, North East New

“O O “O «O 00 00 00 N TD

O02 c e Out BWWOOCOQHUKHROHAH
IGN ISORA ATABHASSSSUAS
ANRNNAR UnununuanunU2UnUnUUuaUuU2

Ha

BAR

e doc

rA amr

—Guadalcanal

—San Cristobal

—Ndeni (Santa Cruz I.)--------
NEW HEBRIDES

— Espíritu Santo

—Efate (Sandwich I.)...........
Loyalty Is

Nouméa, New Caledonia
Norfolk I

Lord Howe I

Macquarie 1

Auckland I

Antipodes I...

= Mitre Rock: Di. c
—Cape Vogel: Lt

—Samarai, Papua

—Brumer Is.: L

— Port Moresby, Papua..........
—Bramble Cay: Lt

— Merauke, Neth. New Guinea...
— Fakfak, Neth. New Guinea

Ah ONBWKNWKWOO e ka
pamamama Anh nM

Cr
lor)
Ke
Kaënecnbätäbäe En =

BISMARCK ARCHIPELAGO
—Lorengau, Manus, Admiralty file art `

US ina ee Ee ^
—New Hanover---------------- e Rees cocus y =
—Kavieng, New Ireland Henderson (Elizabeth) I_-
—Rabaul, New Britain 20 | Isla de Pascua (Easter 1,).----
Rossel I Isla Sala y GOmez

1100

92900
910
920

93000
010

020
030

040
050
060
070
080
090
93100
110

93400
410
420

430
93500

96200
210
220

Place

APPENDIX S
MARITIME POSITIONS

LESSER ISLANDS OF THE PACIFIC—Continued

IsLAS JUAN FERNANDEZ

—Mas a Tierra

—Mas Afuera

Isla San Ambrosia_---

Archipiélago de Colón (Gala-
pagos Is.), Isla San Cristóbal:
Lt

Isla de Malpelo
Isla del Coco (Cocos li.

Ile Clipperton

Johnston I.: Aviation Lt
Palmyra I

Washington I

Fanning I

Christmas I

Jarvis I

Malden I

Starbuck I

Tongareva (Penrhyn I.)........
Rakahanga (Reirson I.).........
Manihiki (Humphrey I.).......

M ARQUESAS ISLANDS
—]le Nuku-hiva: Lt
—lle Hiva-oa: Lt
TUAMOTU ARCHIPELAGO
—Mangareva

—Nihiru

—Takapoto: Lt
—Fakarava, Rotoava. -
—Makatea: Lt

SOCIETY ISLANDS

—1le Bora-Bora.-
—Pointe Venus, He Tahiti: Lt..
— Papeete, Ile Tahiti
COOK ISLANDS
—Mangaia

—Rarotonga

—Aitutaki

Kermadec Is., Raoul I
TONGA

—Tongatapu

—Suva, Viti Levu

—Levuka, Ovalau---------
—Koro: Lt

—Vanua Levu, Undu Point: Lt.
—Wailangilala: Lt

PALMER PENINSULA
—Hope Bay

—Cape Legoupil (Joupil)
—Melchior Harbor

—Wilhelmina Bay: Lt
—Port Lockroy
—Useful Islet (Isla Lautaro):

—Horseshoe I.: IGY Station____
—Marguerite Bay (East Base)
Charcot I., Cape Byrd

Peter First I.: IGY Station

Little America: IGY Station

01 W

57 W
51 W
11 W
36 W
15 W

45 W
29 W
34 W

56 W
46 W
46 W
55 W

12 W
08 W
59 W
52 W

58 E
25 E
50 E
22 E

SAMOA
—Apia, Upolu (New Zealand) _-
—Pago Pago, Tutuila I. (U.

S.
TOKEL

Canton (Musick) I
Enderbury I
Baker I

Howland I

GILBERT ISLANDS
—Tabiteuea (Drummond I.)
—Tarawa

—Eniwetok...
Wake I

—Apra Harbor, Guam
CAROLINE ISLANDS
—Kusaie

—Ponape, Senyavin Is
—Dublon I., Truk Is
—Ulithi

PALAU (PELEW) ISLANDS
—Babelthuap
—Peleliu

ANTARCTICA

Ross ISLAND

—Cape Bird

—Cape Armitage

McMurdo Sound: IG Y Station.
Franklin I

Cape Adare: IGY Station
Sturge I

Cape Denison, George V Coast.
Pont Géologie, Adélie Coast...
Budd Coast, Cape Poinsett
Bowman I

Mill I

13 49 8
14178

9 23 $
9128

0 48 N

8318
5 418

LEE

N) 03

13 27 N

5 20 N
6 59 N
722N
10 00 N
930N

730N
700 N
6 54N
5 20 N

Long.

o Li

171 46 W
170 40 W

17115 W
17154W
172 31 W
170 43 W
172 13 W
174 32 W
174 08 W
171 43 W
17105 W
176 29 W
176 38 W

179 13 E
176 09 E
169 35 E
166 56 E

175 00 E
172 58 E
172 46 E

SSR 88

BEERS aa daag HE

4
145
145
144

162 5

00 O Go t» 00 Td 00 O1 co

[2]. E Gi BER
TS

12 00 W
35 00 W

1101

APPENDIX S
INDEX
Index Index
PAlghentag secs c e ea ay 0 Akme 9: No.
Nalboree P nTagS----------------------- 43710 | Alvaro Obregon 13500
A EM Gor radi Point). (See proper dE 75120
arģsund Havn....... -O Shi
KRG Ree ae V eles Cape Annu Shima TR
(AID d Bandar co etm Akrotiri... Amatuli I., East... SC
Aberdeen (Scotland) EE Amazon River 25820
Aberdeen (Washington). 17150 | AEyab- ---------------- Amblan Point 90810
TRA ee ¡ATBAbrayN=====2====== Amb Pô
Ged ALB h oim, Pôrto 63680
i Ze ee E WEE Le asran SE. ae EE 75210
ADEA Is Al Fubayhil.-====---==== AMON IA 75210
Abū Daraj, Ra's.... AT Haddee e dc Ambre, Cap d” 68210
Acajutlai se eta EES Y s ee Ambre e EU 63640
Acapulco -eoa IWS RE PACE TZ EE 63630
Kr ER EE Ambulong TTP eene 91050
PG a a ha >: > EINE m Al Làdhiqiyah....... Amchilikn ss ees, 19090
"ubanmümtt <*>: E AU Mastrah ce VENTUM UE T Ameland === 47330
O E Al Minfaqah ash Sharqiyah..... 69300, | Amelia I_..--------.------ Se E
Vik y | Amélia, Porto 64530
ala ek A America, North_ 6000-14780, 15000-19700
B neu KI America, South. 25000-28030, 29000-30550
aide, Port...........-—- ER Alacrán, Arrecife (M i ) "i nais ae
Ae ie Sais $ e (Mexico)_______ 13630 | Met l--------------------
A délie TL ibat a Alacran, Isla (Chile) Së Amherst Harbor
NOS ARE A. all d Per DEN Jr y | Amour P [sie AA
E Me Alameda | Amoy. BOINIS =e
Admiralty Bayes. = = ee ú Alanya... ---------------------- a e uj er
Admiralty [sok EE Alaska. --------------- EE
EE Amd Ea VAR EL AS: Jas Point
vum. VÐ GO AERIS
A rr Albany Bock LOO | UG QNIN RENE
Nena Ge be ES Albardāo-:----.------ Amsterdam, Īle
Hosea. Sea Cott ER OP UE d Fee Ponta do-------------- Ae Do--------------------
DEE sd n-p'ing--
a "eege h NEE An on ng - IE ES
TNT. AO ne ad 6000 Aipino FOMCA m. NEE add
Mocnak 8 SA a Albir, Punta del------.---------- Anacapa I.
Africa, east coast........... 64000 ARAM e ea wees E
een coast Man arbori seit md "x
rese e C ae me EE EE
Africa, Republic of South... 63900, 64000 tao Ponta do (Cape Verde Anambas, Pulau-pulau.... 72100
Africa, west coast 61000-63980 | Aleatrazes, Tiha de (Drazi E 33800, | A Dambo, Mosi eaters C8770
Afrika, Mya. 5. tes ERAN ar EA pires Ico RE 20560 asti Burnu --- 35 58430
Agadir_._....-------------------- 61330 ie rana lela poer pe ‘aban M 300
E 52600 | Alegre, Pôrto.. oa
B oec al = aa e tic
Amosa coreto BPS E r e Tome 56280 Sing Mr: Anchorage "quac a S RED - 18500
S as E tian an 19780 | Anclote Keys.
Agria Grabusa------------------- 58210 | Alexander, Cape (Canada)....... 3480 | Ancona
Agria Gramvoüsa. ..............- 58210 | Alexander, Kap (Greenland). .... 1090 | Ancud---
Agrihan..... A a 94820 | Alexandretta E a m n 58460 || Anda a a S
Aguada (Indis) e cc a 69880. | Alexandria o S es 58860 | Andaman Is.
Aguada (Mexico)----------------- 13530 | Alexandroüpolis.. ..............- 56710 | Andenes
IE tt 7310 | Alfanzina, Ponta de-------------- 50130 | Andersen Harbor
ARES e teo e 30220 | Alfaques, Puerto delas........... 51450 | ANdikithira
adīt, CAN ss 64040 | Algeciras Andileoūsa
NINE tin (ATS FE 90330) Mier mm es ri PA Andipaxoi
Let = UM eerie 41650 room ad ib O c a 56070
Aigrettes, Dot des (Madagascar ndran Omody, Cap------------- 68400
Algreties ar (Madagascar) Sio | Alguada Bel SE 68210
iguille, Pointe de l’ A A uie dā Andros (Greece) ------------------ 56400
Ailly, Pointe d’ Alico, EU. BP mE fe. 17740 | Andros I. (West Indies)---------- 21060
Allsatraig ` `` EE naa E 55070 | Anegada de Adentro (Mexico) ---- 13390
Mina Mi. o ls E Ismà'iliyah..............--.--- 66270 | Anegada I. (Lesser Antilles)...... 22960
Aure; Isla del: 5-7 R A alt ie 52970 | Anegadiza, Punta---------------- 29520
O LT aa Aīda būri. iešanas sees 18580 | Angamos, Punta___-------------- 29910
ATO Misak] i, Sarah the P = ‘Alleppey MUR ne US RUD id zs an ss Ee «a
todor Oapērlsss = =s < X A EII AA Angel, Puerto. -------.----------- 15730
[UTC A c XE enit EU Florida] eee mn Angeles, Port (Mexico)----------- 15780
tija Skate mesial > ho ——— Bn Angeles, Port (Washington) -...-- 17210
yin A 0 LS Jn EEE DER A 51190 Angeles, DUNA os eee ue 29760
e tee re FE bun g, 39999 | 4nglo-Egyptian Sudan. (See
Ajik Eeer E (I An LAS EE 14710 Sudan.) _
Ajo, abode. eim SÚ SES ae | 40760 Angmagssalik - Sd. P a dan 1470
LEE No r oo E Gita
(jossaariiet (īriem Suet pec Capo] MEE a 47760 Angra do Heroísmo (Azores)----- 31620
Akao, Noe Caro is n eb EGRE CEST 46100 Angra dos Reis (Brazil). --------- 26510
Akaroa S es D TU A ee ___ 27310 Angsa, Pulau _------------------- 71380
Akashi Korea O 22 NCS e Tu e kav cade ez? Anguilla EE E OP RE 2:
Aker Pont eee MN rpe I_----------------------- 77940 | Anguille, Cape-
Akhilleon, Mys Alto Velo, Islas. teense 29410. HAM OLU a =
kko hit s dat rītā de JN SCA gs ee E 47020 | Anjouan --------
INTA Pie Se a ula. Rass ss too Es S = 66000 VAINU Cape S E ee

1102

APPENDIX S

MARITIME POSITIONS

Annapolis AI eee
et UE E

ADOINUECYO EE
Anorombato, Pointe. ....

Anticosti I.
EE
D EE ee ee Ee
Abi 165 TE ee
Antipodes I
Antofagasta £
Antonio Ports See
Antsirana

OM a M T

Apo I. (Mindanao Sea).......
Apo Reef (Sulu Sea). 77 aam 91060

Apolitáres,'Akra---:72 .-——. 7 56240
Apple"Riveree- cc AEN
APTI Harborseesc II 94880
Aupunansbolp F ó F 0 89770
AQUA O mita RI ee 52910
ATM ens e

Aransas Pass

Arras llas idas v OS

Arasasan ALE siem c teak

ATAKOS. ee

Arcachon---.--

Arch Point

Archangel.....

Archer Point

Archipel des Comores___________- 68100
Archipiélago de Col6n__________ -- 93010
Oe 431
LAC (C1 6G JOTIS CNN ai eee ES 1000—5070
Ardela SS EAE det nape a AA 38530
Ardnamurchan, Point of_________ 37130
Areia Larga, Ponta da............ 31410
Arena, Point (California)... 16830
Arena, Punta (Ecuador)......... 30330
Atenas EE 13620

Arenas, Punta (Chile)____._______ 28910

Arenas, Punta de (Argentina). .. 27650
Avent MI MA 6890
Argentina...... 27090, 27110, 27120, 27200
EE CR

Arguello, Point...
Arica

Aroc Is: HP: Is AA TA 75000
Arquipélago de Fernando de Nor-

Ona E 1 AM 26000
Arrecife Alacrán ) a 13630
Arrecife Blanquilla. M 13380
Arrecife de Enmedio_____________ 13440
Arrecife Santiaguillo_.......______ 13450

TIO OE IO ÓN 22690

INDEX
Index
No.

Arsik PEREA TA 1340
Arthur, Port (China) --- 83220
Arthur, Port (Texas) cm 19120
Aru Bank (Borneo)--------- E 79150
Aru Bay: (Sumatra)----—--——--2- 72650
Aru, Pulau-pulau (Moluccas)---- 75000
Aripa E e o da ES 24300
Aras; Tandjung: o <... i22 75510
Arvoredo, Ilha do --- 26700
MIO A E e 59740
Ascension L- = 35 - ma S RE 33910
Wsenyaedyec o AE eee 40600
Ashisharigahe cc 69120
Ashika Shima Ds +1 ee 85440
EE RE KEE e 86160
AShpad ge ee 66200
"A'sim east CONS se ee eee = 81000-84810
Asia, south egast =“ aee 69000-71570
Askol’d, Ostrov cM a AS a E 83960
'Aisprópounda, Akra NEC 56350
ASSI- zelts EE
Assateague: EE ae

eTa a A E O p.
As Suways....-
Astakós ER T
Astholmsudde.
Astoria. se! eoe cM eed
Asuncion-
ASVær SS
AUTE O
Asta ft ON, ca 20 O i ER
Atalaia, Ponta
Atapupuss fe ue ce S
Atholl S Kantes T
Allas Basse: S c IIT ae 59590
Atico.-—- e tres PONO (e UH 30050
Atha DS S S coc EE NM 19060
Atlantic City (New Jersey) ______ 11440

ter GEN 84780
e reet EE 26010
AVI Sea PS EN

Aucklan

Audierne........-

Augusta "E

Auskerry-: 3 eee. E
Austervág

Australias vow c

Al Basques) Boris eee e 7230
Avero E RU EE apa E 49950
Aves, Islas. ep e PEA eee 23320
Avis AP 49630
AAA 86080
Ce Eelere 4000
Axim De T EE e 62410
EE ee e ee 56060
MS E EEN 56280

RT ONCS EE
Azov, Sea of
Azovskoye More
A707, + Ras 2 dde ate CEN
Azzurro, Porto
Baa Roadstead
Baagg ar ok SE
Baba Burmu nn
Babar, Pulau
Babbage I

Bacchalhao I
Backofen
Bacolod

Index
No.

SA 4300, 4500
Bagacay Point ST aa 90680
Baram Datoh e Sra = =a 71350
Bapstaol- 212 m 89410
Bagot Bluff ^": see S 7550
Bahia ties: ors oie eee 26240
Bahía Blanca v" ð E 27300
Bahia de Cadiz, Cayo............ 21420
Bahia de Guantanamo. .......... 21740
Bahia de Nipe- 2:22:22 4d
Bahía Félix ¿2222042322830 y
Bahia Pralac 2002 S$
Bahía San Jose del Cabo
Babrayn, A]-.----:2- E
Bahrein Harbors — 4
Bahrein 1:23 A
at, c c em
Bain de Meinbatta ice
Bala dos Tigres 2528: dr E
Baie-Comeau...........

Balley, The-.-.--.-.. 2-5 MM
Bailique, Ilha
Baineario Claromecó
Baird, Cape
Bajo, Pulau
Bakar: 222/222 E S ROS LM

Bakerl.(Malne)----—:-— SE
Baker I. (North Pacific Ocean)... 94260
Bakers I. (Massachusetts) ........ 10660
Balabac IS ss c šā 91130, 91140
Balabalangan, Pulau Tm 76140
Balache Point-— -— AM 8920
lem ben ege eae 90860
Balanatan:<--22-< 0030) OEA 89730
Balayanissisre 1 89350
Balbis: +=: PAM 15070
Balearic Is: . Ce PO HO PUE 51700
Baleia, Ponta dē- PEA 26320
Baleines, Pointe des. 48950
Baler EE 89560
Bale Poltica ee S 66000
Bállk = sads EE 74100
Balléasag 126. PL ID 90240
Baliguian miosna eee 89930
Bālikpāpāns es S ISS 76160
Baliscan Is A 89540
Ballenita;Punta_. <- SS 29870
Ballycotton T i n E NE 38280

ASOMO E 42270
Baltasar L ¿200 eee 89710
Baltimore (Ireland) ____________1_ 38220
Baltimore (Maryland) 11730
Baltiysk S MT 43920
Baña, Punta de lá" eee 51460
Bane de Rochelois Ts 22300
Banco Ohinchorro ec eR 13810
Banda, Pulau-pulau...... DELLA 75020
BāndārssAbbāss=esēteša 69440
Bandar Kassim- -1 EET n 65010
Bandar, Tandjung -SSP 73010
Bandar-e Shahptr_______________
Bandholm S

PP

APPENDIX S

1103

MARITIME POSITIONS

INDEX
Index e
rð RS m Index
a 701: 5 ģ
ADOrYN eec pu E (0180)! Beecroft Point. -----------.- +. 62610 | Bismarck, Kap (Greenland) _____- 1580
E AAA eT 23250 | Beir i
Barca, Ponta da 31510 Bout TMA ea TT won Dizerto EEN E RNC
"Pontis ie 58650 | Bjargtangar.---.---........
ati Sese iii UT. 51 Séi Belawan 72640! | -Bjamareys se « ll. scope
MUTA e. AES -- 37770 | Belém 258501 Bjorns ee <.
§------=--------------- Belfast 38560 | Biprngya-.-------------
Barfleur, Pointe de i h Bic)
Barhóft' Belgium 476001 WBlūroklūbbēsse = sen e ee
EE e Belitung 73300 | Blaavands Huk-
Parm E Belize 14200 | Black Head (Northern Ireland).. 38570
See ee RAN) IAE" 000 BS My 84030 | Black Head (Scotland)... mi
Barint E R t ----- 25310 | Bell I. (Newfoundland) - ----- 6280, 6750 | Black Point Bay..--.-.------_.-- 633
B Ārta pau = san de 80550 Bell Rock (Scotland) Black Joa. Dara 3. ald
Rene Ponts de << = TË Ge Bellavista, Capo. .-.............- EE
E E cede Belle-Īle (France)...............- Blackrock pese 38820
Burnerat Piet 11430 | Belle Isle (Newfoundland). ...... 6210 | Blair, Port... meme 70620
Barns Ness. .......... 36230 | Bellingham Blanc, Cap (Mauritania) _ 61510
Hora Head (Hebrides) 1:7. = 32050 Belisund ee wee Blane, Cape (St. Pierre and Mi-
Barra, Ponta da (Mozambique).. 64370 UN TEE NR RUP S AD PA eos dE uy P= > so
ae 25070 7 Blanco, Cabo (Argentina) __ vd
Bon Rer e ror 18190 Belo PU TOPA o (Argentina)........ 27560
O OS Belosarayskaya Kosa------------- 57530 Blanco, Cabo (Peru) --============ 30270
PR ner Head c BOIS MO Sto ON 3040 | Blanco, Cape (Oregon)----------- 16910
ipie bonta do =. 33310 Bon Phi Nee oce" EEE 81720 | Blanco de Casilda, Cayo--------- 21650
Barrios, Puerte- — 14519 | Benar, Tandjung + 75700 ape de rd Cayo-- --- 21660
ele Mins cd Ca si ee 52650 | Ee N
IB eave Funes: (England) ae y yonder Cassin o a e 65010 | Blanquilla, Arrecife. ------------- 13380
RO DOCES g ae Bono EE 71080 | Blevec, Pointe-----.-.-----..---- 68520
ERR Bongasi? geg 58050 | Bliss Teen 9810
ion Cape Ee Bengkalis... rr EE = 55390
, engkulucoc e Sr 79980 e a uere IE
A Boca EA dzba EE 14550
Barykova, Ms 1.1 2.22222.. dU (epee a ae Siam, aie Blyth a 7 75 lo
R SR EE “ORE A A e EOD e S eee 7 Ig
ale do m E 48230 Benkei Misaki. bono May cere 299 Boa Vista, Wha da. -------------- 33500
Bashee Entrance__-----.---.----- 64150 | Benngut, Cap... ..............—- 59650 | Boar I. (Newfoundland) - -------- 7200
Barah TA rm 69370 i Benten LEE 87310 | Boars Head (Nova Scotia) - ------ 9540
[e d 36310 | Beppe Tuccio, Punta. ........... adobe i ie 25430
Li EAS DIL E ee $ ¿SUL Eso
Bere fete us a EE 23280 Ber: akit, Tandjung Boca Spelonk- ------------------- 24010
T ristopher)...... EDEL A cee ee d Id n UP iBoddamslesWe to eaaa 67520
Voc in cus mtu t ip === ec 59900. | Bergen" 2222 Bodies 222 5 ee RE 11920
¡Bata See Rain e ae 62810 | Berhala, Pulau... iBodjoybulaue e E eee 72920
Batan AM E 00080! Berikat Tandjung "vT 73170 | BoeroeIs39——--—-------- 0 TEE 75230
Batan etm SOOO ening 4 deeem Tu n 84560 || BOBO n Sees e es 90660
Batanggas = e EE 893601 HBering Stralt v eases eee Se EE --- 42880
Porayia A E Beninga. EE 84560 | Boi, Ponta do_----------- -.. 26550
Pam EE — iBerlenpasjllhasteueee- E 49990 | Boiugucanga, Iha........ --- 25880
mM (oe e. Bermejo, Roque_--_-------------- 32640 | Bojeador, Cape........---------- 89060
parn New runswic Ets S030 Bermuda ss VX 31000 | Bokel, Cay--------------- ---- 14020
Tea) Jape (Northwest Ter- ie ee RA 77700 BORO ee eee --- 40010
E es Zeck EE EE 3430 | Berry Head (England)........... 35320 | Boko Ko.........--.----- --- 82730
SE . (Northwest Terri- Berry Head (Nova Scotia). ------ 9100 | Bolinao--_----------------- --- 89160
es)----------=--------------- 3800 | Berwick upon Tweed------------ 36140 | Bolinao, Cape-------------- --- 89170
Bathurst Point (Australia)....... 78230 | Besar, Pul Bol’shoy Fontan, Mys.---- = ao)
Bál Buna esan Elak ce ES 73150 À a
EE K A EE EE | EE Ostrov- - ------- 2680
Daly Rulau ee ae Berleynðape r 0 rA 3460 ol'shoy Tyutyarsari, Ostrov.... 43220
Ee Ee E B L Boólvanskiyv. Nos e pesao m 3
Battle Harbor R EE 69640 Bom Abrigo, Ilha de
E A Aa Abalos. Tte < - AA JS 69920 ,
Deri Pernan €—— Bd Tu O e res
DIM ECT O aa Biarritz 4» e m wert a E0070) S OLD Dy ceo ea
BS ESA SS cte eege ; ^ Bombomnsllh6ute cem
Ip e n Bien Son, Ile de-- Bon Capss- sec. c ned S
E Ble Diomede Dl Bon Portage ----- 2e a
Batzalleide tien ete eA ERE ee E OS a BonásTsla---—-— --=
b M and (6 Bijol Is............--------------- Bonalro Eeer
, Cape.. a i
Bawean, Pulau -------- PEE O AR E GN ua Cape-------------
JUS o a ndo E ee
Bay manent: A see eee E Bill of Portland BONCH ee A o db e
VOUS re Se dnt Bille, Kap... Bongao----------------------
Bayonne. 3 E BUIN My m Bonham I
TARTS tap: ld a gg BN e E Bonifati, Capo
Bazaruto, ha do ee d Bonin Is------------ -=
Beachy Head. -.-.-----.-- z una Bonita, Point pna E RS
e o AO AH = Bimlipatame ss En Bono Misaki.......-.------------
EE EE Bintan,, Ee sp Bontekoe Ø--
od Oka sd SS Binte de Corson esn ee e < 48400 | Booby I--------------------------
Béar, "Cap (France) Lake Bir, Rass de eee de E TE es 65160 Boompjes I 3
Bear, Cape (Prince Edward L.)... 8350 Bird, Cape (Antarctica).......... 96310 | Boon I. ..--.-----------------
Bear I. (Cape Breton L).......... 8900 | Bird I. (Lesser Antilles)---------- 23320 | Boothbay Harbor..----------
Bear I. (Svalbard)... 2510 | Bird Is. (Republic of South EE
eaudue, Bointe des====>====2=22 52490 A E e 64100 S a A en
Beaulort loss ee ee 11960 | Bird Rock (West Indies)......... 21120 | Bora-Bora, Ile__-.----------------
Beaumont aos NM 13130 | Bishop Rock (England).........- 35110 | Borda, Cape. ...-----------------
Beaver I. (Nova Scotia). 9140 | Bishop, South (Wales) ----------- 37810 | Bordeaux. -----------------------
Beavertail Point (Rhode I.)._---- 11050 | Bismarck Archipelago (South Pa- Borden, Port---------------------
Bedoutnit ae ée SEIN || GRAS Olas ne ee 92200 | Borge Bay- ----------------------

1104

Index

No.
Borinquen Punta 22630
Borkum ---- 47230
Borneo...... GE T5800
Borneo, North 75840, 75880,
75890, 75920, 75940
Bornholm 951-7 10. n 44900
Borongan--.—---- 90090
Borracho, Cayo... 122725150
Bossut, Cape------------- 78410
Boston (Massachusetts). ......-- 10710
Boston Point (Australia)... 78000

iBoLatochpIsla- 222 es.

iB OUCAW ease setae <
Boulogne........

Bowling Green, Cape.....
Bowman.) ee m (NE
Boz Burun----=---
Bozea Ada ===

Bras Pulau cess nes
Brava (Somalia)
Brava, Ilha (Cape Verde Is.)____.
Brava, Punta (Río de la Plata). _
Brazile: e AE
Brazos Santiago
Breaker Point: Dn

APPENDIX S
INDEX
Index Index
No. No.
IBfyuss, Mys: = m» 83930 | Cagayan Sulu I. (Sulu Sea) - ___-- 91150
Bui uot MIDI a EE 439101Gagllari P e AS 53200
Bucas Grande lA 203801 Calbarlén: EE 21380
Buchan Ness Caicos; South: ceso = ee 21150
Buckie Caiman Grande, Cayo. ---------- 21360
Budd Coast tr ES Cao, Ilhóu do == SS 61910
Buen Suceso, Cabo............... Caiobá, Ilha___-- - 26650
Buen Tiempo, Cabo Oalns-- = --- 78720
Buenaventura....... Caisse Point ST SSS SOS 8100
Buenavista, Cayo de Cajas de Muertos, Isla_..-------- 22700
Buenos Aires Cala Figuera, Cabo. Ee 52130
Cala Nans, Punta de............. 51610
UNS - d TUNE Cala Sabina, Punta. ... == ¿01820
LE Ae Cala Scirocco, Punta... ----- 53450
Bugui Point... Calabazas LT eee ðn 89940
Buholmrása...... Calaburras, Punta de. ........... 51130
Galais (France)... E 47730
Calais (Maine) --------- - 10210
Calandorang Bay........ - 91130
Calantas Rock. .........- - 90060
Calapan. E - 89600
Calavite, Cape......... --- 89570
Calbsyors E - 90040
Calcanhar, Cabo......... --- 26100
Calcutta: < A REA 70590
Caldeira, Ponta (Mozambique)... 64450
Caldera (Chil6)s S sat ES 29860
Caldy If 5 TR is - 37910
Calella So. ska - 51540
Caleta Carapachibey--- - 21600
Ere Caleta, Punta (Cuba)............ 21750
las li e cc e o Calheta, Ponta (Cape Verde Is.). 33330
i 15160) | Calicut-225 5550 e ED 6

Urine 69401 California ee

Burma tee A SUS 70800 | Calimere, Point----------

Burnin D NUR ee 79060 allage- m, Sap OO

Burnt Isa RN 69860 | Caloundra Head

Burrlana cet CUN 13904 Can Phase c A
i«Bregksea e ee Buru (Moluccas) A 70280) "Camamu eco E
Bremen oss £ 2 e 47160 | Buru, Pulau (Sumatra)__________ 72680 | Camara-Assu I___________
Bremerhaven (Germany) ________ 47130) | Burullus; ¡Cape NN 58830 | Camarat, Cap------------
Bremerton (Washington)________ 17320 | Bush End Pont 80410 C Cambodia aa
(Bremsteinēnss us S 40510
Brescou Mondone 2 = 52450
(BIOS = c ec e con cm 48440
tee 21670
Brett; Cape: ee 80760
Brouch Ee 72800
Brevoort Kapt O 1040
brewster, Kap: 222 2 1500
Bridgeport (Connecticut)......._ 11360
Bridgetown (Lesser Antilles)...._ 23630
Bridgewater (Nova Scotia) _._____ 9340
Bror le an 3. (9 Uae e 9530
Brig Ponto. 95999: 3:9 C anum 9240
Brigūs: Bay eL. b deu cT sð 6730
Brindisi E SA 55160
Brisbane. teo Ee 77030
Bristolsee-c edere C cM 37970
Bristol Channel “Mr 37900
BritishiColumbia Mn 17500
British’ Gitlanas m UE 25500
British Honduras C 13900
British) [Sl69 a sees 35000-39430
Brook Is) (Australia) L- eee 78750
Brooks Point (Newfoundland)... 6490
Broomegr. AAA (M 78420

Brothers, The (New Zealand)... 80450
Brothers, The (Red Sea)_________ 66170
Brough'of Birsay c c PS EN 36770
Brownsville AN y 13210
Browse Locos arco S 78460
IE EI E 7 47640
yq A ID 47640
Brulos, Cape

Brumer Is... `

Brunei

Brunette: iš NE AVM
Brunsbittelkoog
EEN
Bruny, Cape

Brusterort

Bushehre sess A 69410 | Cambridge Bay------------
ee ter (81701 Camden eee ee
Bustard Head “< eee 78920 | Camelaeo, Cabo
Busto; Obor = EE 49650 | Cameroon. 2 ot e ED
Búsul enee 83770 | Cami, Cape
Büsum rð eee 46940 | CamiguinI______
Buton Butona toes EN 76130 | Camotes Sea
Butt Ee 87020) Camp Lloyds
Button! Rocks 82980 | Campanella, Punta
Butuan— 22.2. 9909208 eee 90350 | Campbell, Cape (New Zealand)...
Buzzards Bayo CNN 10900 | Campbellton (New Brunswick)...
Byelosargi-- -DE c A 57530 | Campbeltown (Scotland)
Bylot ISS IN 2210 Clànipecho" s coo MO MO IANUE
Byrd, Cape (Antarctica). - --- 96200 | Campobello I... ........
Byron; Capes: <: SAM 77070 | Campos, Punta..

- 11560, e Canada: cet e 3300-6970,
Caballo I. (Philippine Is.) ____-___ 89300 | Canada Bay... A

14420 | Canakkale
21530 | Canal, C. & D
--- 26680 | Canal, Cape Cod
== 2 Canal, Chesapeake and Delaware. 11560

22660 | Canal, Panama ........... 14740, 15070

--- 30140 | Canal, Sue. 58810, 66260, 66270

n Canal g» Šīs erger e 14740, 15070

anay iso Ei isiad HMM 32300

Cabinda ee men 63400, 63420 | Canaveral, Cape.. 12260

Cabo (Cape). (See proper name.)
- Cabo Blanco, Isla
Cabot I

Cádiz

Caen... AREA ae 48020 | Canoan, Port... 90250
Cnernarvon............. N Een OD

Cagayan Anchorage (Mindanao). 90320 | Canso, North

APPENDIX S

1105

MARITIME POSITIONS

Cantin, Cap

Canton (China)

Canton I. (South Pacific Ocean). 94240
Cap (Cape). (See proper name.)
- Cap d'Alprech

- Cap d'Ambre

— Cap d'Antifer

- Cap d'Armes...

- Cap d'Espoir.--

— Cap-Haitien

Capáo da Canoa

Cape: (See proper name.)

- Cape Breton I

— Cape Cod Canal

- Cape d'Or

- Cape, East

- Cape North (Cape Breton I.)...
— Cape North (Labrador)

- Cape, North (New Zealand)....
— Cape of Good Hope

— Cape Verde Is

Capel Rosso, Punta del
Capetown

Capitancillo I

Capiz, Port

Capo (Cape). (See proper name.)
- Capo d'Orlando

- Capo d'Orso

— Capo d'Otranto

Capones I

Capraia, Isola

Caprara, Isola (Italy)-------.-----
Caprara, Punta (Sardinia)

Capri, Isola di

Capricorn, Cape

Capstan, Cape

Capul I. (Philippine Is)

Caravelle
Carbon, Cap
Carbonear I

Cardigan Bay
Carena, Punta
Caribbean Sea
Caribou Point

Carleton Centre (Quebec). .

Carleton Point (Anticosti I.) .....

Carlingford

Carmanah si-se o t x. luu

Carmel, Mount

Carmen, Isla del

Carnarvon

Carnero, Punta

Carolina, North

Carolina, South

Caroline I. (South Pacific Ocean).

CarolineIs. (North Pacific Ocean).

Carranza, Cabo

Carrousel I

Cartagena (Colombia). . ---------

Cartagena (Spain)

Carteret, Cap de

Carthage, Cap

Cartwright

Carüpano

Carvoeiro, Cabo (Portugal) - -----

Carvoeiro do Algarve, Cabo (Por-
tugal)

Carysfort Reef

Casablanca

Casamance---

Castellon dela Plana- 2222-2 et
Castelo, Ponta do

Castillo de Montjuich

Chatham Is

INDEX

Index
No.

Castillo del Morro...............- 21500

Castle I. (West Indies)
Castle Point (New Zealand)...
Castle Point (Republic of South

Castro-Urdiales
Casuarina Point
Cat I.

l
Catoche, Cabo
Cauit Point
Caves Point

Cavoli, Isola dei
Caxine, Cap
Cay Bokel

Cayman Brac.

Cayman Is

Cayo, Cayos (Cay, Cays).
proper name.)

- Cayo La Perla

- Cayos Arcas

— Cayos del Ese

"(See

Cebu | City
Cedar Keys
Cedros, Isla__

Celestun
Centinela, Isla

Ch’a-mu Hsú
Chacachacare

Chacon, Cape
Chafarinas, Islas

Chagos Archipelago
Chaji Do

Chalmers, Port...-.--..---

Champerico
Champotón. .

Chañaral, Isla

Chan-chiang

Chandeleur Is

Chandler

Changgi Gap

Channel Is. (British Isles).

Channel Is. (California)

Chão de Mangrade, Ponta do----
Ch'ao-lien Tao

Chaplina, M ys

Chapman Reef-----------

Charambirá, Punta

Charcot I

Charles, Cape (Chesapeake Bay). 11710
Charles I. (Hudson Strait) 5030
Charles, Point (Australia)........ 78490
Charleston (South Carolina) 12020
Charlestown (Massachusetts) -... 10700
Charlestown (West Indies)....... 23240
Charlotte Amalie

Charlottetown

Charlton Depot

Chassiron, Pointe de

Chat, Cap

Chatham (England)

Chatham (Massachusetts)

Chatham (New Brunswick)------
Castillo de San Sebastian.

Chauda, Mys
Chaussée de Sein

roe Point. -

C a Chiao

Chelyuskin, Mys

Chemulpo

Ch'eng-shan Chiao

Chepillo, Isla

Cherbourg

Cherchel

Cheribon.......

Chernyy Nos, Mys (Novaya
Zemlya)

Chesapeake and Delaware Canal. 11560

Chesapeake Bay

Chesapeake City

Chester (Nova Scotia) ---

Chester (Pennsylvania)

Chesterfield Inlet

Cheticamp I

Chi-lung Chiang

Chiappa, Pointe de

Chicago, Port

Chichi Shima

Chicken Rock

Chidley, Cape

Chignik

Ch’ih-chu Tao

Chik Nok, Ko

Chikyú Misaki

Ch'ilbal To

Cie Chiang
Chimatao Promontory

Ch'in-huang-tao
Chin-men Tao
Ch'in-shan Tao
China.... 81600, 81800, 82200, 82400, 82800
Chincha, Islas de 30090
64420
83050
83150
18550
82810
- 83330
- 83040
83150
55310
50250
84220
18470
64910
70720
92420
- 83690
- 83790
10870
85300
1210
44810
67800
93090
82220
- 81230
18400
26830
83510
83710
64720
4910
8650
Cidreira 26780
Clientuegos e- EE 21630
Cies, Islas - 49850
Cima, Ilhéu de 32210
Circeo, Monte

Citadel I

Ch'ing-tao
Ch'in-huang-tao
Chiniak, Cape
Chin-men Tao
Chinnamp'o
Ch'in- shan Tao

Chisimaio
Chittagong V -est
Choiseul

Gi
Christmas I. (Indian Ocean)
Christmas I. (Pacific Ocean)
Cn. Chou.

Chukpyón Man
Churchill

1106

APPENDIX S

MARITIME POSITIONS

INDEX
Index Index Index
0. No. No.
Oliv. A es E Gorenera Pont EM 897501 Dami Kino t a S 85360
Ciudad Trujillo
Civitavecchia. -----------
lared ss AS re
Clarence River" "` M
Clarks) Point e 0 ee
Clerke eebe Cormorant Roeks---------
Cleveland, Cape (Australia) ______ 78780)| Corny Pont m CUE eee x nr
Cleveland Ledge (Massachusetts) 10910 | Corona, Punta___________- ---. 20820) Dalatangi..—— < d
Cliffy o EA A E ae 77350 | Coronados, Islas Los___--- Dalhousie tw. nee
EE 99040] Coronel. — - — — — Daliao---------------------------
Clyde, Firth of (Scotland). 37200 | Corner Brook. nn 7840 | Dalni Point______________________
Clyde, River (Canada)----------- EE
EI EE EE ee EE EE
Coast Castle, Cape 18 624701 Corral eS ee
Coats Ee ati 49701 (Corregidor =a == c |
Coatzacoalcos (es m a 13480] Correnti, Isola.delle-—— — — ——— P
Cóbh mesin mE coa o 38260 | Corrientes, Cabo (Cuba)--------- 21580 | Da Nang n
Cobre Do 4 4200 | Corrientes, Cabo (Mexico) ----.-- 15810 | Danger Point
@ocanadal e e ba "70470 ECorrubedo,Cabo M 49780 | Dangerous Cape (Alaska). .....- 18560
Coehinsw- — fe. ete 70000 Corse npe e eee 52950 | Dangerous Reef (Australia)... 78030
Cochons, fle aux 67920 | Corsen, Binte den 48400 | Danjo Gunto a 86410
Cockburn, Cape. 3800 CORE vell [E or pee ME Cem e GE a eee 1460
COCO, IIE de uN ESEE 93030 SE GE
Cocos I. (Pacific Ocean) 93030 Oe SERES ARES aj Das Pulau --------------------
Cocos Is. (Indian Ocean) ________ 67700 a The do eee 31110 arby, Cape---------------------
Cod Cape Lape A DEE A 10790 ¿Or VO, ina do 5 Dardanelles: = = —
Goda Lina 51810 | Costa Rica. ---------------- 14600, 15200 | Dar es Salaam___.______-_---___._
KEE EE 7 9360 | Cotabato sia 90480 | Darnley, Cape-------
CotsiHarbour a Ga CeO see as = - 62520 | Darsser Ort.
Gozun Pona aa 64510 | Coubre, Pointe de la. .----------- 49110 Dart Capers: fs cp
Conca 29120 | Couedie, Cape- ------------------ (7830: Dartmouth tt Ee
Colbeck, Cape" NN Grup (COMME E ALE EE Ee ss mn
EE 3272) | Couronne, Cap.. 52030 NDaxWin-J--— sc Sees
Coldspring Head sám | Sourtown Cays c 22190! Dassencilandi Son
Coles Punta > c- EE 30010 | Covesea Skerries M 305001 "Datu, Tanjong c- Fa
Colline Verte... (32010007 Head Harbori ec e =m (360! RTE
Collins Point. ..... .......... 34450| G9x's Bazar e Deh bor
Colombia, north coast... _______ 25000 nd, Isla de A aa Oe
Colombia, west coast. .. I 30500 | Craig Harbor. een Davisville Depot- -n mn
Colombo ay | Cranberry Is..... Daydalas
Colón (Panama) Ce SE > DE
Colón, Archipiélago de (Pacific Cron SE 58200 | De-Kastri
Ocean) tevin} Cape a Deal dottin er 2 S
(Oloniasos-e-t o oo MI Hak o7080nereus Cabos c eT Debundga Points os ee
Colonne, Capo Cristobal SEE EE ee Debundscha Point
Colorada Point (Philippine Is.)__ 89840 Cnn Ri RE Deception I- — Tum
Colorados, Punta (Cuba)________ 21640) Cromarty ae = Decision Cape: 2 vÆ
Columbia River Cromer... EES pL Deering ie c OR
Crooked I. (West Indies) DeKashi Co WIPE
Crooked Reach (Chile) EN 29130 del Ese, Cayos ua REN NE 22130
Crooked River (Florida) _________ 12500! Delaware Cie ili MOREM 11600
ross A eee C Ree 9310) Delaware Bay oo sens a. ERE 11500)
eege 50600 Derz 47310
Growidy Head Se: ME 77150 | Delgada, Ponta (Azores)_________ 31720
Crozet, Lest. Ane CE a eee 67900 | Delgada, Punta (Argentina)... 27460
Cruz C IDOL e S K AA 21710 | Delgada, Punta (Canary Is.)_-___ 32920
Cruz del Padre, Cayo____________ 21430 | Delgada, Punta (Chile)__________ 27940
Cruz Grande g Delgado, Cabo (Mozambique)... 64550
(GAĻU PL) Re ee Delimara, Ponta ta
Gubat a Fatto Toto MEN. Denlāteeses? ted wwe
Conni < EE Cuddalore es. 2) Denison, Cape
Conejera, Isla... Culebra, Isla de Denmark e 02 9 S
Coney Isler ce a Culion i. Cs e AE Dennis I. (Indian Ocean)... 67330
Conger Kont e TT Cullera O abos es EMS Dennis Ness (Scotland)
Con bone cse... ATM", Cumplida, Punta Dent Tos eee eins
Congo, Republic of Curacao e Der Dornbusch. T rSn
Congo River M Curaumilla, Punta... Dorna mE RD RTI.
Connecticut oð KS Gurioso Cabo rr Deseado
Constanta mee NER NER 57290 | Currentes, Cabo das Destruction I
Constantine Harbor. EE DE Devgarh 69840
Contises-Bains |... 2-- 49230 Currimao dod Du ue et E ond Devils I. (Nova Scotia). ......... 9900
Contramaestre, Isla... 28000 | Currituck Beach Devils Point (West Indies) _:____ 21090
Cook, Cape (British Columbia) . 17730 | Cut Throat I Devonis- -. + COCA MEM 3900
Cook Is. (Pacific Ocean)... ____ 93500 | Cuttyhunk I Devonport = ooo ae 19040
Cooper Keys Cabos... OE 20150 Cuvier pi ae e Dewakang-lompo, Pulau_________ 75620
Coe: Bay coo ene ee -. 16930 SE A | ebe 3160
SUE Ieren EE 36720 Uyope-c cc E eee á A
GE ENEE oo 3470 iki = se A OL 58500 Da MERE eC a)
¿0queblCAustralla) lo eo TE 78670 A PS 1 ed TEE San
Coquet I. (British Isles)... ______, 36120 | Daedalus Reef Dieu Tuor EE Ga)
COM eo ELM SO OT EE Diamond I (Burma) acci A 70870
Ee 45370) EEN Diamond Point (Sumatra) er 72670
oral Harbor =e CN 45201 BIDS rS ES CS = Diana Carod da 2 21440
gaju Cap EEE 99640 Dahmeshóved-.- ..— Diavolo, Puntade e 55250 §
ZOreovado Capo OS 292501 Dahon VE EE EE Diaz Point 63850

APPENDIX S

1107

MARITIME POSITIONS

Dickson, Port
Didicas Rocks 890
Diego Garcia (Chagos Archipel-
ago) 67
Diégo-Suarez (Madagascar)
Diégo-Suarez, Baie de
Dieppe
Difnein, Isola
gby

Dikson, Ostrov
Dili

Disappointment, Cape (USS R)... 84030
i b Cape (Washing-

on
Discovery East Bank (Indonesia). n
im Harbor (Canada) 4160

Djerba, Ile de
Djibouti
Djidjelli
Dobo

dI
Dd Head
Dodecanese

Domuz Burnu

Don, Cape

Dofia Maria, Punta
Doncella, Punta de la
Dondra Head

Donington, Cape
Donsol
Dorchester, Cape
Dordrecht
Dornbusch, Der
Doro, Cape

Douarnenez

Double I. (Burma)

Double I. (Labrador)
Double I. Point (Australia)
Douglas (British Isles)
Douglas, Port (Australia)

Doukáton, Ákra

Dragon Point (Greenland)
Dragonera, Isla (Balearic Is.)....- 52010
Dragons Mouth (Trinidad) 25430

Dry Tortugas
Drygalski I

INDEX

Dukato, Cape

Duke Ernst Bay
Dumaguete. ------------
Dumali Point
Dumanjug

Dunagree Point
Duneansby Head
Dundalk

Dungeness (England)
Dungeness, Punta (Chile)
Dunkerque

Dunnet Head

Duong Dong

Durian, Selat

Durnford Point
South Africa)

Durnford, Punta (Spanish Sa-

(Republic of

Dyer, Cape
Dyrhólaey-
Dzaoudzi, Îlot
Dzharylgach, Mys--

Eagle Nest Point-_-.-
East Amatuli I

East Cape

East Chugach I

East Foreland 8
East Indies (Indonesia) - --- GE
East Ironbound I 927
East London

East Point

East St. John's I--

East Snake Cay...

East Vernon I

Eastern Grove Flats
Eastern Point

Eatons Point
Ebeltoft

Eboshi Jima
Echizen Misaki

da
Eddy Point (Nova Sootia)
Eddystone Point (Tasmania)---- 79400
Eddystone Rocks (England) 35280

den
lecho! Cape--
Edinburgh
Ediz Hook

Egadi, Isole
Egdeholm..
Egedesminde

Ege

Gn 2 Ý (British Columbia)

Egg I. (Nova Scotia)

Eggegrund

Eggeløysa

Egmond aan Zee

Egmont, Cape (New Zealand)... 80850
Egmont, Cape (Prince Edward I.) 8240
Egmont Key (Florida) 12430
Egypt. 58800, 66210, 66220, 66260, br
Egypt Point 5430

38200, 38700
37110
43340
66170
13660
49710
61250
59420
29130
27400
15500
58220
75010
53500
47000
21050
69010
21080
82960

El-Akhawein.

El Ferrol....
El Hank I
El Kamela
El Morrión...

El Salvador-

Elbow Cay

Elephants Back

Eleuthera Point

Elgar I

Elie Ness

Elizabeth, Cape (Maine)

Elizabeth T (South Pacific Ocean) 92810

Elizabeth, Port (Republic of
South Africa)

Elkjerbakke

Ellef Ringnes I

Ellenbogen

Ellesmere I

Ellingrása
Elrington, Point
Elsehoved

Emine, Nos
Emineh, Cape
Empedocle, Porto

Enderbury I

Engaño, Cabo (Dominican Re-
public)

Engaño, Cape (Philippine Is)

Engels, Rass-22--- SP 2. 00 E

Enghela, Ras

England

Englefield, Cape

English Reach

Eniwetok

Enmedio, Arrecife de

Enragé, C

Ensenada

Ensenada de Tamerabel....

Ensenada Honda

Ercole, Port’

Erimo Saki

Esan Saki

Esbjerg

Escalvada, Ilha
Escape I

Escarceo Point
Escombrera, Isleta de
Escuminac, Point

Eskimones

Esmeraldas

Espenberg, Cape

Esperance

Espichel, Cabo de
Espiguette, Pointe de l’
Espiritu Santo

Espoir, Cap d’

Esquimalt

Est, Cap (Madagascar)

Est, fle de 1 (Tes Crozet)
Estaca de Bares, Punta de la
Este, Punta del (Río de la Plata)...
Estevan Point

Estonia

Estrecho de Le Maire

Eten, Puerto.
Ethiopia

1108

APPENDIX S
INDEX
HH HH ——— M
Index Index
No. 0
Etienne, Port EE lol Eer Cat 59550: lE Blort-Conger------—--..- eed F
IBnajBankgee 2 o s 73490 || Eermin, Eed 16190 |sEont Dauphin--- =>. — —-——
Etorofu TO A eet 84770 | Fernando de Noronha, Arquipél- Fort-de-France
i«pupatoria Polnt--—- E 57380 rr RL 26000 | Fort No. 2 (Tokyo Bay)--------- 85360
Eureka (California) __..-.-------- 16870 | Fernando Póo--------====== 62800, 62900 | Fort No. 3 (Tokyo Bay)--.------ 85410
Eureka (Northwest Territories)... 4120 | Ferolle Point___------------------ H3001|6HOFE-ROSs---5--<S ff es 4600
Europa Point (Gibraltar)--_------ 51020 | Ferraione, Capo...............--- 534601 |kEonlaleza a ene.) e p
Europa, Punta (Fernando Póo).. 62910 | Ferraria, Ponta da--------------- 21710 [orto Buglo- e
Europe, south coast. ......- 51000-56710 | Ferrat, Cap (France, south coast). 52750 Forte la Rocca--—-— — ===
Europe, west coast. .......- 40000-50320 | Ferret, Cap (France, west coast). 49210 | Forth, Firth of
Evangelistas, Groupo. ..........- 29200) EE Capo 65 REM 5 Fortune Harbor (Newfoundland). 6420
Everard, Cape... =. 77840 | Ferryland Head:----------.------ Fortune I. (Philippine Is.)......- 89310
B verett=. ===... --- 17400 | Fidonisi I. Eoul POlni = S 70210
Everglades, Port_---- =.= 12300/16Piðdra ` 222 5d T E Foulwind, Cape.............- -- 80370
iEwabpPulauspulau---—— "= 75010 | Fienaio, Punta del Hour. Humnmocks ss -- 78050
Execution ROCES SS ed 11370 | Figuras, Punta " Hourehu Capo. eee 9510
Eyemonih do. ciešā 302101 EIEE er ds NI Fourcroy, Capos- —— --- 78480
Eyrarbakki -enaena 1730 | Filipsburg Fourth Points. < so -.. 73520
A =m E 2200 Eillsand: «525-8 i quedan Fowey (England) 35270
NEE 45820 | Fingal Head___--_------------ Fowey Rocks (Florida).........- 12320
EE NI 46230 | Finisterre, Cabo_------------- Fox, Cape (Newfoundland) ------ 6270
Perdor- E eee 411701 Finland e eg Fox I. (Newfoundland).........- 90
Færingehavn os sec. 12M EE Ee Fox Point (Newfoundland)
EE es SO000 Rito Lol no S HOY DOS cnn S Ia
Fabaybil--— A ex 60840 "First Point Æ Fragoso, Cayo — =a
Faial Tha dos 2 S 21300. Eirth of Clyde. 0 Cs Frailes del Sur “== SA
Wair ele 36820 | Firth of Forth_____.---------- EE
Fairway, Isla... iBishsustd eee — PM Franco; Fort-de- -n c ce
Fakaofo........ EISE Francés, Cabo (Cubai
Fakarava__-- Fitzroy- o OU Frances, Cayo (Cuba)......
Fakfak ___._.____ Einicio Eo d. Francéz, Ilha do (Brazil)... A
Falcon, Cap.... Blak fortes. E FrankeKlint: es - 45920
Falkenberg. Flamborough Head_------------- Frátikin A - 96410
Falkland Is. . RENE, es Franz Josef Land........... 2870
Falkner I... ES DE esse MM Frazer EE - 78310
Fall River. . Flat Cape (Sumatra)......... Fredericia (Denmark).........-.- 46260
Falmouth. |... 5 Flat Holm (British Isles)..... Frederiksdal (Greenland). ......- 1390
Falsa Isla: (Chilo) ete ee DIEVIEM Je < ss Frederikshaab (Greenland)....... 1310
False Point (India)... Flat I. (Mauritius)--------- Frederikshavn (Denmark).------ 46470
Talshóft- eee reed. _ om Flat (Quebec) m . 7499 | Frederiksted (Virgin Is.)--------- 22940
Falso, Cabo (Honduras).......... 14460 | Flat Point (Cape Breton L.)...... 8680 | Fredrikstad (Norway)...........- 41240
Falso, Cabo (Mexico) - ----------- 15960 | Flat Rock (New Zealand)........ 80710 | Ereotown--3-..--.--- mH 62120
Falster (Denmark)............... 51001 IRE) See Eréhel Cap.:..----....-.. LM 48170
Falsterbo (Sweden). ............. 21580) INTE Rremantlo: 2. MUNI 3 -..- 78210
HalydŅosi itt asi C UT E 68760 | Flattery, Cape French Frigate Shoals.. .......... 20840
Ramagustās =< ee MN 58570) KEE å French Quiahac.--.- eee ER 25700
ee 7780) LGU GS ae EE French Somaliland... _ _-------- 65130,
Wared Head. i. e 38740 PENG ISS SES UEM 65150
Hanan Bunun 2-2. mess es 57780 | Flint I. (Cape Breton I.)......... Frenchman Head.... skiti dē
Kanjovej I 5s <. DR 64620 | Flint I. (South Pacific Ocean)... 93170 | Friedriebeart. --- 44730
manning La E E ee 93080 | Flores (Indonesia)..... 74500 | Erigate Shoals, French........... 20840
Fang (Denmark)..--.------------ 46620 | Flores, Ilha das (Azores)......... 31900 | elo, Gaboz--- S 26410
Hanol. (Greece) r re 55910 | Flores, Isla de (Río de la Plata). . 27040 | Frobisher Bay- ------------------ 4390
Fantasque, Pointes ama 29290 | Florianópolis. iO! Eeer 13500
Farallon I., Southeast (California) 16810 | Florida (Solomon Is.)------------ 92480 | Froward, Cabo-_-.._------------- 28030
Farallón Sucio (Panama)......... 14760 | Florida (USA)_---_--________ eessen JM 40230
Daraman emere pu 2 M 52500 | Floripon Point. Eruholmen--— ..— der 40100
Farewell, Cape (Greenland)... 1400| Flowers I.................... ; LEE 82860
Farewell, Cape (New Zealand)... 80400 | Flüege 2 BuckuclC bido Se 82530
Farilhéo Grande... ct. soe 190801 El NE Lesben Fuencaliente, Punta de.......... 32420
Earne Ig ese 36130 | Flying Fish Cove____________ Á Muerte; Isla- 2 2 i 25010
STO (Sweden). Vr CR e Fuerteventura, Isla. ee 32800
Faro, Capo (Isole Eolie)... ....... 54230 | Foggy Cape............ Fuglehuken- - eae Tov ae 2500
Faro, Capo del (Italy)............ 53360 | Fogo (Newfoundland) Pugloykalvēnieev i as 40140
Faro, Isla del (Spain)............ 49850 | Fogo, Ilha do (Cape Verde Is.)... 33800 Fugu Dakine D eet 85680
BbaroiQüerand í na 27220 | Fológandros. Fukiaino Misskið FT 228 85630
Faro Recalada Fontana: Cape UM MEN Fulkikakusttonco. cC 82530
Faro San Matias 20. | "Poochow nec cene ooa i EE cet NI MEME 86530
Faro Segunda Barranca Fora, Ilhéu de A sm 82530
Inte Forcados. ee pio ALIO Fulehuk 41180
Farvel, Kap.... Ford Harbor. Fumboni -- 68120
Fássa, Ákra 1. Foreland Bluff (Angola) ______ EAU A E 94310
Fastnet Rock... Foreland, East (Alaska)... ¡Na ps EE 87220
Rather Boí ae CP NEN E 7690 | Foreland, North (England) Funchal Sale 32120
Favignana, Isola. ma E 54430 | Foreland, Northeast (Greenland). 1590 unkenhacen e t. 44170
< Foreland Point (Bristol Channel). 37990 Purükamappu Nnnn 84790
--- 45820 Fushik
` 31300 | Eoreland, South (England)....... 35570 | p Ie S 87000
va 11970 | Forestier, Cape__............_____ 79890 | putāšāmi Bhima............-.-.. 86720
3473) EEN 51800 | L00 Jima E 86820
hera 44600 | Formentor, Cabo de.......... 52150 EE AAA 00
292 DE 40970 Formigas, Ilhéus Qabes EE scr 0820)
Fener Adegt 1000 87890 | Formosa. + ek ee eee able Tsleb rs ere PU 80630
ener Burnuec- Ee 58450 | Formosa, Cape (Nigeri Y KEE 7330
Fener Boun F OTO AONE a) Baba, 63300
Renwick, ee MALO Bort Canning AS AMOO eessen 42420
Feodosiya es ne een ei EE Gago Coutinho, Dë... 63230

Gaia Sbima <> os. bee a
Galapagos Is...
Galata, Nos..
Galé, Ilha da...
Galea, Punta...

Galera Point (Trinidad)
Galera, Punta (Chile)

Galera, Punta (Ecuador) ____ - 30400
Galera, Punta (Mexico)... 15740
Galets, Pointe des...........

iunhppe Rd ES

Galina Point...

Galiola, Hrid...

Gallipoli (rale
Gallipoli (Turkey). .......
Gallo, Capo (Italy)........

Gamle Skagen...

Gardhskapi eege 7 1750
Gardner I. (South Pacific Ocean).
Gardner Pinnacles (Hawaiian Is.)
Garnish

Gaspar, Selat-selat
Gasparon IES
Gaspé

Gatcombe Head
GOUDEN, Punti: e
(avez Punta. =
Gavdhos eege

ES

Gentil, Port-
George, Cape (Nova Scotia)------
George V Coast (Antarctica) |...
Georgetown (British Guiana)....
Georgetown (Prince Edward I.)..
Georria (USA) Ee
Georgia I., South (South Atlantic

Océans siaran E 3
Geraldton
Germany, Baltic Sea
Germany, North Sea ---.-------- 46700

Gerong, Sungai
Gerrild 2222222222

(en EA T
Gheroghambo, Cape. ...........-
Ghirapzmm <<
Giannutri, Isola di... Mitos

Giraül, Ponta do

APPENDIX S
MARITIME POSITIONS

INDEX

Index
No.

SAR AA ee And amens
Gibbs Hill CN

31040
51000, 51010

Girdle Ness: -zte — —— c=

Goh (Island). (See proper name.)
(ojo DE We see = =a ert 84280

Gomera mrna
Gonáve, Jle de la
Gonzalo, MOITO = S E
Good Hope, Cape (China)______-
Good Hope, Cape of (Union of
BOUDBRATHICR) S eR eee T.
COMA S M CIS 78550
Goose Bay Narrows (Labrador)...
Goose I. (Tasmania)
COPAS A
Gopnath Point: m. c.
Gorda Point (Philippine Is.)_____ 89760
Gorda, Punta (Nicaragua)....... 14520
Gorgona, Isla (Colombia). ....... 30520
Gorgona, Isola di (Italy)... ....... 53450

Gorgonilla I. (Colombia)......... 30520
Gong Blur 22020
(CHRO THEN le nn 75530
fuoteborgs tee NSS 41400
(ROM ATIC eo ce ET o 41900
COLORE O o a 86500
GOLS ly apte 86270
(ECO (as der ere eee 33960
Ëtt ee An 48620
leen? 59100, 59110

CAE pt em -- 46600
--- 14510

EE A 31510
Graham Harbors 3910
A e dpi tt 42990
(iran O oso --- 42280
Grani(Ganariase ce --- 32700
Grand Babama "===. ===, 21000
Grand: Dantes: > a 7110
Grand Bassa Point (Liberia) _---- 62240

Grand-Bassam (Ivory Coast).... 62350
Ca ee e su sus 22020

Grand Entry Harbor

Granmdelehouseee ce e =
Grand Leon ce ms 3s:
Grand Manan I —— ee 9900
Grand Ribaud, Ile--------- f Ma 52630
Grand Rouveau, Ile du 52600
Grandt Ferro eror oe ee -. 23290
Grande/Dürks---———6--——— 222-2. 21160

1109

No.
Grande Bourg... ee. Mu 23310
Grande de Moa, Cayo. ---------. 21230
Grande Īle Chano ya 48110
Grande, Ilha (Brazil)____________ 26490
Grande, Isla (Panama)........... 14770
Grande, Ponta (Brazil)__________ 26730
Grande «POrtos- eM 33220
Grande) Ro c. HEN 26800
Granitola) Gapo-—-.—---—— dl 54800

Grankubbēns ce e nC T M 42060

Grant- DE Ee 77390
Grantley' Harbors- -eei 19700
Granville asie M
Gravelines___-

Graves, sTh6resesiece sā A
Grays Harbor

Great-Abaco [See ae
Great Basses Reef s
Great Brasd'Or-! ees eig 8660
Great Britain MIMI 35000-37400,
37600-38160
Great Fish Bay (Angola)--------- 63750
Great Fish Point (Republic of
EEN 64110
Great Harbor Deep "= ` s 6300
Great Inagua SEE nn 2 21170
Great Isane c cer TIERE == 21010)
Great Ormes Head........ mc intl)
Great oitkin ES == 900701
Great Stirrup Cay. ....... 521030
Groben Mys -e aea SOLO,
Grecale apos set SE ---- 54620
Greco; Cape aan =--- 58560
Greece AES set Ss 3 PE ---- 55900
Green Cape (Australia).......... 77320
Green 1. (Burma). s ---- 70920
Green I. (Cape Breton L.)........ 8750
Green I. (Hong Kong) m 82310

Green I. (Newfoundland).... 6620, 6970
Green Point (Republic of South
Africa) 63960, 64190
Greenland- oes asss ee
Groenl y 15. - c
Greenock een ave assess
Greenwich... -araic
Greifswalder Oie
Grenaa Sie Ses os
Grenada I S =< = 222 au Ee
Grenadines, The
Gressģyene
rey Mouth... 1e
Greytown

Grimsby_- ¿Y APA að

(drip EE
GrissNezsGspesc-----— ce
Groix tllerde 205-0220 2 es
Cros

Grootekaspessse---—-— n d
Gros dU ENEE
(GrOSSTELOES LS o cocoa m
(Grosso; Capo. 2222522280 ees
Groupo Evangelistas. ------------
Gruesa, Punta... Imoni 3522
Gruica, Ostrvo- eene

Grytviken Harbora sun E
Guadalcanal

Gūtie eee
(ELE EE
Guane del Este, Cayo------------
EE ÆA
Guanta ea == === —
Guantanamo, Bahia de__--------
Guaratiba, Ponta de-------------
Guardafui, Capó- -n-an 64990
Guardia, Punta della----.-------- 53890
Guatemala, east coast - ----------- 14300

21620
22720
25190

p———————— —" | | ĀŠ

1110

APPENDIX S
INDEX
Index Indez
O. 0.
Guatemala, west coast. .......... 15600 | Hanamanioa, Cape Herrero, puntas os INE
Gtāvadu "van ES omm 30350 | Hanapepe Bay------- Hersehel 1 crisol eee
Guavanas = us VK 15870*|«Hanasaki.---.---===> Hesselg. — —.--...-...-5.- ee
Guecet POIDS eee RES 89150 | Haneda Su----------- Hēstēh0vēd-=ss-=s+ see SE
(EAR EE e RA 304001 Hosp eee eee RS Heostskmr.--—--— so MINA
Guiana, British sean) eee E 255001 SE Heugh; De, ee seras
(UCA. o oae a CE RA 262000. |"ELadi=K:OU= == ee Héve, Cap de la
Guimaras TE e P Hey wara Foni = aE RT
Guinean see IDUSOn LIE E
Guinea, Portuguese. : Hicacal, Cayo....--.-----..------
Guinea, Spanish ` see = 62800 | Hanol-.-------------------------- erro» sos EE
Guon 17 216 C DEUM ee 8730.) Hanstholm T sss<asd= High Lamock I
Cia ee ss ne aep OS 25230 | Happisburgh........... High Peak I-< i ti
@Gldholmensses ss <. sm 41210 | Har Hakarmel........- Highfield Pointe. ===: 020123
Guro dense SSS 65100 | Hiiradskár- ...........- Elgner, ¡Cabo sape etae CUN
Guitport = 5 E 12750 | Harbor Grace. --------- Hilal, Ras elas. ce Cem ESM
Gull Cove (New Brunswick) ____- 9920 | Harbor of Refuge................- Hillsboro Inlet....-.-.-----------
Gull I. (Newfoundland).......... 6360 | Harburg-Wilhelmsburg---------- 47040 | Hils tes o RE ERN
Gull I. (Nova Scotia) ----------- EN Haro To oe F Hime Sakis- ie En
Gull Rock (Newfoundland) ----- 6390 | Harmaja Hinako, Pulau-pulau
Gun NE Harmony Point ene 34420 | Hinchinbrook, Cape............-
SE, Point GE Se Hino fusi (Honshü, south
stay EE SPL OSA) Cine eec ec GOBSt) saa A ase 85800
d Xo tnb Haro, Caba AS Hinomisaki (Honshū, north
von Set arrigan, Cape 6050 CONS) === oco e a 86860
Guysborough Harrison Point (Lesser Antilles)... 23610 | Hinzir Burn. 0 2 58470
(Ek EE Harrison, Port (Canada) --------- 4950 | Hirashima (Goto Retto)........- 86510
Gyoro tinis sers Hartland: Pointi sess EM 38120 | Hiroshima (Naikal).........-...- 85970
Gyn oS MON Nr Hartlepool-3-----9*9* — poete 80930.| lee beleen EE 46480
LS IN e EE 69300) TEE 46510
aback Ion Hastie Pointe a 68620 | Hiva-oa, Īle 93220
Hapana Ateo eme SE 40130 Hiürnd ti 2 geen 46290
Habibas, Īles Hatteras, Cape..---.--.-..--..--- 11980 Teln EE ee 46370
EE Haugesund- ee 40920 Hobart + iet A 79360
Hachijó Jima Haugiegla.......-...........-.--- 200701 Oe 41920
Hatun Rase Haulbowline Rock............... 38420 | Hoek Van Holland........-.....- 47440
Hari Kon texas Tc 840 | Haut Banc, Pointe du............ 47780 | Hog I. (Virginia). 11630
Hague, Cap de la (France)_______ ENEE 9610 || ere 41510
Hague Rock (Alaska) 330) Havana M UO ee ine eee ee ie 21510 | Hógbonden.. .............-....-. 42350
Ela ima ra EE Havre Aubert mor 7910 | Hogland (USSR) - 43110
AI Havre-St,-Pierre. JU 7470 | Hoher Wee. Cð 47120
EAN RN Hāga 4 AA 200001 "Elo jeri es ts 46500
A E TRUE Hawalan rs i oEEE EE OR E EEN 82540
Hai-yang Tao- Hawea Point es NIMM 20260, | Hokitika ar v va c2.22-0) A
Haifa. sa PIC Hawkesbury corte. soe) EM 89104 Hokkaido ree nnna 85000, 87300
Hulkoui-s...:--—-——. pM Hay, Cape (Northwest Terri- Hole in the Wall 21040
Hailuoto. -..... I TorieB)s-:— 5248 < Akak 4510 Hollandia ses noia XP PANDA.
IA Tao =r- n nE 000) “Haydanpasa r -sm e 57770 pee UPS At
HabnangDsui c: 2 NN Haye, Point la (Newfoundland).. 6840 | Holmogadd_____________________-
Halphongse- e39 Hayirsiz Adasl. 57830 | Holmsland Klit...............
Haisborough.............. HiZakies equas ol MM 86010 | HoImudde...
BUE erm Head, North (Washington)... -- ENEE EE
Haitien, Cap--.---=======> 22210 | Head, Southwest (New Bruns- Holyhead 499 oi
EE - 83260 | _ wick) Homborsund
ac Sal ceu qi M 87120 | Heard I Home, Cabo del (Spain) 49830
ODIN eie r1 1 EE : Heath Point (Quebec). 540 | Home I. (Cocos Isi 67710
Hakata Ko = 86760 | Heath Reet (Australia) fon Dal Can... ón
Diu doge Ste Hon Dan
Hakushatou. Heceta Head * bietes NA Hon alsa EE
malden eg Hedland, Port onduras, British
Half Moon Cay. A Hedens pir 90 | Honduras, north coast------------ 14400
Haliwāy Rock coco cada o 10390 | Heimdy SS: south coast.----------- 15400
IEM A NE EE Hong Do SE 83490, 83630
Hallab, Ras el... 58980 | Hel foc a 82300, 82320
allands Väderö 1980 ' Helpoðland' = ` O EE
Hállerund (Enlanda -Sm a 0 50 di erat, BuU Ce 85200, 85900, 86800
Hallgrund (Sweden). 49940 MEA rhs Soda ood, Port (Cape Breton I.) ..-- 8520
Halli Ostrovas E. 451301] EEelle Holt kl Hood Point (Republic of South
OEC ecce m ELTE MEE 41350, | Holes Cape, S EE 64120
BENGAROYJS =. 4520 Hellesøy Hooghly Riyer t J 70580
Halmaheras a PÆ. 75300) | Hellman. i Ee 38320
Hita ca de 41470'|Hallvilies. = Cl ace MS Hope Bay (Antarctica)___________ 96010
Hals/Barre "k 46430 | Helnæs (Denmark) Hope, Point (Alaska)... ........ 3250
Hálsing Oe -- 41520 | Helnes (Norway). Hopeall Head (Newfoundland)... 6660
Halen O kājā 40620 Seite ge CL ANDR E Hopedale (Labrador) ------------- 6070
Hanada metis at Helsinki a ay Cape (Hudson
Hambantoln c aes ON MAA MERA nc S Se A eee 5050
SE Eege ` 62930
Hamelin T... REX s pee, A —— 62930
amilton... Ago SAO ESA IS i a 5126
ds iu. iek dk E Horn, Cape (Chile). say Sn 27810
Hammer Odde ______ Horn I, (Mississippi) ee Í 12710
ammerfes Ax JM E 1831
Truk Lr a E HOmpbys ae N 77230
Hāna Bayo. lee Borys r r 40050

ait 7

APPENDIX S

1111

MARITIME POSITIONS

Index
No.

71570

DET stad” Zeie

Or su
A ee
Hotham, Cape
emgeet Tao. Ab EPIO

Howland I
rid Galla r < <a aee

Hrísey
SER ou Chico: tee =
Skaba Ch’ fin-tao ss sae ae
Hsia-men Tao.............

Hsia-san-hsing Shan

ERüsnape A A
Huarmey, Puerto. ........
EE MA cA.
buert Tee

Hudson Bay
Hudson strait — 2.
ENEE,
¡Hironeme, Ports Ø sb
Huertas, Cabo de las
HUKUM andars PA
Ea Wa Pulau recent te
Hull (England)
Hull I. (South Pacific Ocean)---.
Hu-lu-tao

HUTUD Ostrov...... eer

ieūrstsPolnt EES
Húsum "Æ
Huvudskär e- et sus
Hvar, Ostrvo--
Hyannis- Let

EE
Igloolik.... »
Iģneada Burnu...

Igvak, Cape------ 18620
madens uses C3: 5 Ls 47400
EE eg 72500
IA 4. 58010
fle, Īles (Island, Islands). (See
proper name.)

SE AAA 48980
- Ile de l'EsUE e eee 67910
= WG GME Be EE 02000)
- Ile AOS d CUN 49000
-zlled'Oüuessantz---:.-..-....-. 48300
Milo d Y eu. amunt eu roi ter 33 48920
Ilha, Ilhas (Island, Islands). (See

proper name.)

INDEX
Index
No.
ba, Pouta.da..--.. JÆ ecd» 31420

Ilhéu, Ilhéus (Island, Islands).

(See proper name.)

flot (Island, Islet). (See proper

. name.
Tlvasbala Burnu--- < ur 56910
Ree e EE 86050
Imai Saki- 84720
maris sm vene 86710
Imbituba, Ponta de.... 26730
Imperatore, Punta 53900
Inabo:Misaki-----—--- 87340
Ince Burun....-.------ 57730
Inehkelth-s- st — — 36340
Inoh'6ns---41 EEA 83380
Ineog Isic Sas 1 82900
India, east coast 70300
India, west coast 69600
Indian Head iF o es 7270

Indian Ocean, Islands of the 67000-68770
Indies, East (Indonesia).... 72000-76160
Indios Wiests5teen eser tem 21000-24330

Indonesia Ateo e 72000-76160
Infiernillo; islotes: "= 5 5 Sr 30070
Ingenlero;Whlte-—— es 27320
Ingólfshófdhi.......... - 1980
Ingonishesde-- <ooores - 8630
Ingramporis----—--— r 9260
inhacasGOabo da: <: eed Ā ss dus 64320
Tnishoer::-2-222- egle. ne. oue 38880
Inishowen Head--.----- 38710
Inishtearaght.. ---------- --- 39010
lnishirahuls--.--— S --- 3872
EE TEE 57730
Inland Seas? =-===-==2 --- 85900
Inscription, Cape.... 78270
Insula Serpilor........... 57230
LEM
Tubo Saki- ENE
Tavercareill- 22 m-n t
ĪNYernesss A A
so AA A
Iquique a
Irago Zaki. . uae
Trak Nome. AAA 82
Iran. --------------- 69380-69410, 69440
Tranja, Nosi 68730
Taq er 69370
Ireland 38200, 38700
Trelapnd, Northern.-:--..-.....-- 38500
Ireland I. (Newfoundland). . 7210
Irminger, diapente. a 1480
85610
--- 6920
79370
Tronbound L,-East. .-.-....- 9270
Tronbound I., West....... 9330
Isabel Segunda, Isla. ....... 59910
AAA 3720
(O o a ai S et 53900
Isfjord P dr eee o DEM 2430
Ishizumica’ Hana... a a 87510
dee 58460

Isla, Islas (Island, Islands).
proper name.)

= sla Cabo Blanco. es —— ==" 15260

Islay, Eunta `"

Isle of Man----

TSE ONM Ayee E ZE
past AU lee

Isles of Shoals__-

HJAVV ed i A
Isleta de Escombrera............- 51240
IslotešEloracioss dēt < < < 62930
Islotes Infiernillo 30070
Gale A A == J 66270

Index
No.
ISONE y tarsaarlo ==... E 3220
Isola, Isole (Island). (See proper
name.)
ed EM MEI Ee 53900
= sola;dWsticasess IES 64300

ae Æ a 1

MARE M 649
EA AE Late
Tapage Ponta des ss ee "m
Itaperina, Pointe d’-------

Ga OU Arona
Itüzakiehos ss

Izvestiy Tsik, Ostrova
JabolatsPajir sms sesso eno ae
Jacks oint ee e ss 6 eee
Jackson, Cape (New Zealand)----
Jackson, Kap (Greenland)--------

Jacinta a RAS

Jáfaráabád----

Jafía (Israel)

Jaffa, Cape (Australia) ----------- 77700
Jama (Ceylon) Bact A e 70270
Jugaroren sole Ys om 42430
ALE nee: mast" me eco ee 69800
Jaling zene er Eee a ae 22430
Jakobshavnsesse eae eee 1200
Tells c A 94610
Jamaica c t e 21800
Jambeli Punta rc 30320
JamDu-A yer e eee 72670

Jan Mayen [n

Jason Tslet = f e cram 34120
Ja Var Cere e EE eee 73700
Jazā'inaz EE as 66050
Jazirat, Jezirat (Island, Islet).
(See proper name.)

Taziteh-ye EE 69320
Ta7ziteh-ye Qeys teo S 69420
Jazireh-ye Tanb-e Bozorg......... 69430
Jeans Head rs ra nm 6670
deer 9190
Jefterson” Porto certo 11250

(Sd A A AE a 59310
Jerez Puntas- ooo eee 13310
OË VE AA cae 39200
En A pd AE AS 44150
Tenis Cape oat pr 77720
E EE 75920
Jezirat, Jazirat (Island, Islet).

(See proper name.)

dicarita isla sees seen eee 15130
A (6 (6 C A ee 2 66150
Ee UE 22620
A A A 83380
Jintotolod F 07 = / +" 2=T 4S 89870
Jizo Misaki (Naikai) ------------- 86030
Jizó Zaki (Honshü, north coast).. 86870
Joatinga, Ponta 26530

Jogue Point
Jobuston lo

TOLON ES SERE CI SCIES

1112

Joupil, Cape
Jourimain, Cape
Juan Fernández, Isla (Chile)

Juan Fernandez, Islas (South
Pacific Ocean)

Juel, Kap
Julianehaab

Jupiter Inlet
Jutias, Cayo

66200
46490, 46550, 46580, 46610
Ka Chom Fai Ko Liang.......... 7

Ká-hó, Ponta de

Kaea, Cape
Kaeo Noi, Ko
Kafirévs, Akra
Kagoshima
Kahala Point

Kaiser, Port
Kajartalik. 2
Kaketsuka
Kalabahi

IKAlATNAj rosset a es S 56180

Kalampunian, Pulau
Kaleardi Burnu

Kaliakra, Nos
Kalingapatam......
Kaliningrad

APPENDIX S

INDEX

Kao-hsiung Shih

Kap (Cape). (See proper name.)
Kap (India)

Kapelludden

Kapoposang, Pulau
Kara Burun (Aegean Sea)
Kara purun (Black Sea)

Karang Galang.
Karang, Tandjung

Karas-ketjil, Pulau-
Karatas Burnu

Karlshamn
Karlskrona
Karori Rock-_--...
Karrebæksminde ..
Karsik, Pulau

Katákolon, Akra
Katangkatang, Pulau
Kater, Cape
Katsuura Wan
Kattoshi Misaki
(aum ee?

Kaumalapau Harbor
Kauna Point (Hawaii)
Kauna Point (Oahu)
Kaunakakai

Kaurleden
Kavadoni

Kawaihae
Kazahaya Zaki
ss Ga, Pointe de

Kedah Entrance, Sungei
Keeling Is. (Indian Ocean)

MARITIME POSITIONS

Kergulen, Īles de
Keri (Estonia)

Kerí, Ákra (Greece)
Ké ki

Kermadec Is

Kermorvan, Presqu'ile de
Ketchikan

Key West

Khairsiz Ada

Kilauea Point
Kileredaun Point
Kil’din, Ostrov
Kilia Burnu

Kilifi Entrance
Killantringan Bay

Killini, Akra
Kilbarda, Cape
Kiltān I

Kine Cove (Alaska)
Eing George I. (South Shetland '

A AA LEE e A De 34410

King I. (Tasmania)
King William I. (Northwest Ter-

King's Cove (Newfoundland)....
Kings Point (New York)
Kingston (Jamaica)

Kingstown (Ireland)

Kingstown (Lesser Antilles)
Kinkazan TO

( Keelung (Talwan) SES _- 82560
Kami Jima d 1760
Kamome Shima-- Lg e iR rd De 46120
Kamui Misaki sa Ras

1 = S

UND Ux Kitriés, Ákra..
[AREE Kittigazuit
Kelian, Tandjung Kivdlak I
Kélibia
Kellett Bluff (Washington)
Kaneohe Bay Kellett, Cape (Northwest Terri-
Kangámiut sore)
arts Nos Mys iia
Kanis, Pulau čenai eivhela
Kanjól Gap
Kankesanturai

Kannon Zaki (Honskú, Kloster-Kamp, Mys

EG ya. Knight Point
Kannon Zaki (Tokyo Bay)....... 85420
Kannoura Kō

Kantin, Cap. Keppel Harbor (Malaya)

Keppel I. (Newfoundland)
Kerch'

APPENDIX S

1113

MARITIME POSITIONS

søge
Kogo Zaki
Kohahu Shi

Kokutan Zaki (Kuril Is.)--------- 84710
Kokuzan To (Korea)

iKKoleuyov; Ostrovocs cus E
Jah, ER un P
Kolliekerort

Kolyubakin, Ostrov
Komandorskiye Ostrova
Komatsushima

Kompong Som
Kómun Do
Kongshavn.-------- ES qi o S

Konzetsu Ko..
Koojesse Inlet. -
Kópu Poolsaar

Korsakov
Korshavn

Koshikl Jima... S aae
Kotabaru

Kotel’nyy, Ostrov

Kotlin, Ostrov

Kovilan Point
Kozhikode

Kralendijk

Krasnyy Partizan, Mys

Krigugon, Mys ..... —
OA SS a m S 84260
Kristiansand (Norway) - ----
Kristiansund (Norway)
Kristiinankaupunki

Kristinestad

Kronotskiy, Mys
Kronshlot, Ostrov
Kronshtadt

Krung Thep
Kuala Trengganu
Kuang-chou
Kuantan.

Kumkale
Kumukahi, Cape
K'ung-t'ung Tao
Kunjit, Pulau

INDEX

Kunsan Hang
Kupang
Kurabu Saki
Kurbatova,

Kuri, Cape
Kuria Muria Is
Kuriate, Ile

Kurmrags
Kuro Shima..

Kusakaki Shima.
Kushiro-

Kwajalein

Kya (Norway)
Kyaukpyu (Burma)
Kygynin, M
Kylmäpihlaja
Kyobun T

Kits Saki

R Calle...
La Camargue
La Ciotat

La Isabela
La Jument
La Libertad

La Perla, Cayo

La Plata, Cabo (Spain)

La Plata, Isla (Ecuador)

La Plata, Puerto de (Argentina). 27120
La Rochelle 489
La Romana. -

La Roqueta

La Spezia
La Tortuga
La Unión
La Vieille

Labu, Pulau
Labuan (North Borneo)
Labuanhadji (Lombok)

Lacre Punt

Ladrone Is

Lady Biliot Islet- ts. 78930
81120

Læsø

Lagens, Ponta

Lages (Azores)

Lagos (Nigeria)

Lagos (Portugal)
Lagostas (Angola)
Lagostini Is. (Yugoslavia)
Lågskär

Laitec, Isla....-
Laiwui

Lajar, Tandjung
Laje da Conceicáo.----

TjáKka = tots

Pamaline Bay ðn
Lamanon, M ys

Lambda I__

Lampedusa
Lampione, Isola di...

Landegode

Lands End
Landskrona
Landsort

Langanes

Langara I
Langeland
Langelands Qre
Langkuas, Pulau----

Large, Tle du
Las Piedras
Lastovo, Ostrvo...

Lauis R
Launat-Revi, Mys
Laupahoehoe Point

Lautaro, Isla
Lava, Nosi
Lavapié, Punta

Le Hourdel
Le Maire, Estrecho de

Le TOC
Leading Tickles......

avi in, Cape--
Legaspi
Legendre I

Leixóes, Porto de.

Lem Tachee
L'Enfant Perdu
Lengua de Vaca, Punta

1114

APPENDIX S
MARITIME POSITIONS

INDEX
Index Index
o No.
Leningrad ===. mē t Wittle Guana 121.321 æm 210501 Avonern.. Ķan i 1450
Lennard I.... Little Gul T- AA 11310 Ip e SAA
Leones, Isla... Little Hopes 9390 | Low Head 79030
Leopold Port 5 S S Little Paternoster Is. 76140 Ee MM
Lepar, GT 73210 | Little Pedro Point LV 21860 | y DW F ES t
ej Point eee 9800 | Little Port Head. 7820 a iegādi
Iestārtādins m e e adi 22260 | Little Quoin. .__-_-__----_.____-- 69110 alt e Is 92700
Les Grands Cardinaux.---.------ 48710 | Little R1ver. een 10250 Lu Hs& 82450
Les Hanois Rocks..-------------- 39430 | Little Ross----------------------- GEET A 7 ENSE
Les Heaux de Brebat. 48200 | Little Santa Cruz I............... 90520 A ccu Ms EE 83220
Wes SableslOlonne = aima. 480401 Liu chiu Hu 82650 | Luanda: ooo 63660
Yes 48210 | Liverpool (England)------------- 37630 | Lubec (Maine) 10230
es Sept Iles.-..............-.--- Liverpool (Nova Scotia)... 9370 | Lübeck (Germany).............. 44490
Lesovskogo, Mys 84620 pook otia) ES 70 i
SE N eS M E 22800 B: Punta Lucrecia, Cabo
crx O ÍVvorno ee S
i us Is------------------ R EE
Levant, 1le dus ee 52660 o Point
roe = C $8 | Lizard Point (England, south Lungo. E tie 42340
Meri Qu SAS OR PUE SS 58110 coast) ---2-l1---------...2....----- Lusaran Point-:-. =< Sn 90940
Levuka 93930 Tlebeitx, Cabo--=====> Tūsshūn-+$: EOS ee eee 83220
Lévy, Det 48060 | Llobregat, Río. - Lutong. 2.1 93 eks cielo 75080
IOWA OOM ease 6450 Lo Caposs = Luz, Buertode la ss e aa 32730
EC nr EE 90130, | Lo-chia Shan - ooo 82940 | Luzon_________ 89030-89310, 89340-89470,
ve 90220, 90230, 90620, 90640, 90650 Las 2 eee 89510-89540, pices
DATA mln E pty abe ong ei 43 ss ŅAUtOY, E Offr.-<ss« St em ga 6
3 Lobang, Tanjong Lynasvront eee eee 7
Libby... r fis e e Eed LE
Liberia... Sa Lobo, Ponta do......... Lyne vig. EE 46570
Libertador, Puerto_____ Lobos de Afuera, Islas-- Lynmouth Foreland____________ 37990
Fibreville Lobos de Tierra, Isla_ Eeer 45450
Libya Lobos, Isla (Mexico) Lysekil Co A EE 41360
itatsi r eee Lobos, Isla de (Canary Is.) Lyser Orto o e ed
Dicosa, Tsola ee a EE 13330 | Lysica_________
Lido, Porto di__________ ---- 26930 | Lyttelton F
Lien-hua-feng Chiao d ---- 7350 | Ma-tsu Shan (China... 82870
epa a Loch Carlo way a 227310801 VISAS ante SE 90230
Lighthouse F Boca NNNM Uem Mpatsuyker Isles (Tasmania) _____ ion
thou; Caps = 72 0 (48120 H OCKODOTUSELapbore--c => E TN 8530
Lille SE EE 101601 C OCKTOY F Portas ee NUN e Marahi Isla de == 30180
Me Pendulum 12 22: im Lodbiērgi Kirko ooo REN CAO T: See ES 82100, 82120
Lille Prestskjer____________ R aa 203007 Ce, 26200
Ee E LE 12400 | Machadinho, Die ró 25830
Lima Islet, South__________ O 64510 | Machado, Pontare - 33230
TLimarsi Punta e 48800 | Machias SealT_. ... 10010
eee SE ETA Jen SEN ab Ee
O A a eee ackia ye asa ien 4 78830
DLífmnossese ss: ee E MiacollasPunta-- qc St ME 25130
monte cue ac sees peo Cabo See z Macquarie (Australia) 77240
Lin kao Chiao eee ombo Macquarie Harbor (Tasmania). 79320
zila a DV --- tid, I. (South Pacific
mdesnes==== E IAS E SS 92740
Lindi Macquarie, Port (Australia)_____ 77130
Ein HIP esa A Mactan less n < 90690
Lingea, a Mait, Ponty e — 64400
in-kao Chiao.. T gdagascar eee T E C CE ORE 68200
Pinkas Ea e Madame lo. fv EEN 8800
Tinne, Kappa os. Madang- -C ES 92080
inosa, Isola di. ER 32100
ipari A A RN Madeira Ts: -22 LITO SIAM 32000
PIPSO EE Madoera c cc IN 73800

Líthinon, ENEE
Lithuania......... 43800

OS Roquesse C NN
Lola S MON Y Y co MEN

APPENDIX S

1115

MARITIME POSITIONS

Index
0.

IS rer or AM 10200
Malo Tiha des, R 33600
Maski Punti o II ow 21210
Maura pcs 22086920
¡Majakkanlemitia PUES. omi 2620
MORCA sites eee Henda SI! 52100
Majin Gael sien os AU 68690
Niajurgded Lala 10 4 LAN 94620
Makahnena Ront- emt < 20740
Makanalua Peninsula... ........ 20530
Makapuu Point::- or æ= Z 20610
MO E e. A c E 75640
EE A 75640
Makatea E e e EE 93350
ui EI eg A O e 94530
Makino Shhna. 2... 252 83650
DEE „ds
MATOS = Se RT SEI
JME Ae
IMEn Is PUES Se EH
Malabata, Punta
Malabrigo Point
NAC stas sams
NEAL E E E
MINERA oe ee a See
IMulamau ss A
Malapascua I
INES arr iia eee ee a eens TN
Malaya EE cg
Malden: ee SS
Mind esas E
Maldonado (Uruguay) ----------- 27020

Maldonado, Punta (Mexico)_____ 15750
uti Šā el EC ES ae ee ee 67600

Malitbog
Mallorca
Malmo T (Luis deus. OR 41560
BE E corem.
Måløy-Skarholmen--------------
Malpelo, Isla de M

Malta. t.
Malvante tout 69850
Malyy Gorodetskiy, Mys........
Mambsjao <<< store
Mamelle Islet

(Manado- ===

Mananlary-- r - CC
Manappádu Point...............
IManchestero -ene ar
Māndvi
¡Nantredonia ` ` =---=2== eg
Mangaia 2 = 2

¡Mangalore tes ==: a
Mangareva.........

Mangkai, Pulau
Mangkalihat, Tandjung..........
Manigonigo Islet
Maniguin I
Manihik] E lues g

INANOKWATÍ.. - Van ra AÐ
IManora Bolt. DERIT
Mansel I enn
iMantansnijs- «eo ee
WMantangbulaut eet
Manucan'Isletse- e
Manuel, Cap (Senegal)...........
Manuel I. (Labrador)............
Mankan nE

IMamgs dde Ie i IT ee
Manzanillo((Oūba)ss =.=2
Manzanillo (Mexico)

Mara Do

INDEX
Index
No.

Maracaibo... E 25110
Müranhüo viet Viet edt á 25910
Marbella a itor E A ES, 51120
Marblehead coo PES 10680
Marcus leas. hec lu a 94710
UE taa A 16700
Marettimo; Isola. Doo. lá 54420
Margaree: Harbor 12 . fet L 8550
Margaret, Cape (Canada)........ 4610

Margarita, Isla de (Venezuela) -_--

Marguerite Bay (Antarctica) _- 96130
Mania. Madre, Islas — — eee 15830
Maria Reigersbergen Bank....... 74400
Maria van Diemen, Cape. ....... 80800
MaranaJIs-.——— sam 94800

Maricás, Ilhas..

Marguereau, Pointe au
IMardquesas sspe 522 ET
Marsa- er e Rec c cep sal Ae
Marsden Point < =. ac
Marseille EE de -
Marshall s= 2 e a

Marshag, Ras TT ó

Marshfleld

Marteau, fle au.
IM arietes ee aces DS

Martim Vaz, Ilhas.........
Martin García, Isla. -----------.-
Martin Head (New Brunswick)... 9740
Martin, Kapp (Svalbard) ........ 2420
Martin, Río (Spanish Morocco)-- 59970
Martinique 23400
Maryland steiere, 11720, 11730, 11740
Mas a Tierra-- 2910
Mas Afuera 92920
Mas Palomas, Punta 32720
Masamirit 66110
T
Massachusetts. = = ` re 10600
Massacre Bay: es as aa 19120
E EE 66080
Massif KiatsoDe-.<ooos==iss=e= ¿de 68680
Masulipata0 =: ds S 70450
Matabao: Lesser sees 90010
Matagorda Ises ās as? - 25-2 13170
Mataja E 91230
Matakaoa Point Not 80650
Matakongy lle sa. ðn 62030
Matanzas Mss oss sE 21480
Matapan Cape: =" erm 56200
Matatani- Ep SIETE ES 30040
Maternillós--2..-....—.-90 7.402 21330
MAI K S Lecce SE 90410
MāatifoujCapēted-- es aa 59660
Matinicus Rocks. -. 22522-2222 10340
Matirre, Ponta------------------- 64440
Mütrüh €. A ET 58870
Matsu 1: (China) ea. S 82870
Ma-tsu Shan (China). ----------- 8287
Matsu Bo Korea) 0 0 Ð 83450
Mauger Cayo escasa 14010
Maüghold/Head: 22 37560
Mallu maar cedet rene 20200
Matnhane,:P.onta123 vu 22222 64520
Maüntania Le eroe aae 61500
Mauritius eene 67100
Maurizio PORTO = =L BEE ZE 53320
May, Isle EE 36370

Index
No.

May Point; Capel caidas 11510
Maya, dE 21470
Mayachnyy,, Mys ` m 84520
Mavaguang: o e - 2 eats 21140
Mayagūoz ne Be CE E tas 22740
Mayari, Punta (Cuba)----------- 21250
Mayor, Cabo (Spain)------------ 49540
Mayotte as s ES 68140
Maysi, Cape (Cuba) ----_--.____= 21210
Mazagan

McKean I

Meee Cape....
Mieati]Miarang Fó Ee
Médanos Punta. ss a 27210
Médas Islas Wee. 22022252) EN 51590
Mediterranean and Black Seas... 51000-
60000
Medway Head ser es 9350
Megalonisi (Aegean Sea)......... 57930
Megalo-Nisi I. (Bulgaria)-------- 57110
Meganom,
IMelidiā ss øðin s
Meiderts Reef, Pulau............
M'ononessM eae
Mel, Ilha do. E
Melangávi, Akra-
MEOE mear DD MR
Melchior Harbor.
Mele, Capo. rn sco aceite M M
Melékhas, Ara ET
Melilla EF =
Melinca?. F 25535. 22
Meloria, Secche della............. 53420
Melvill Reef (Indonesia). ........ 72430
Melville, Cape (Philippine Is.). 91140
Melville I. (Canada). ...........- 3630
Melville, Kap (Greenland)....... 1140
Memba, Balade ec 64510
MaN tetas O ee 43810
Menado SS SI EET 75720
Mendez Punta ees 27950
Mendires Capos aa 56920
Mendocino, Cape = Sm 16850
Mendro Rt v e 55760
Menier bon. 2-22 7570
íMenjawakstFulau ser re 73410
NÉE Tee ee 52200

Men’shikova, Mys (Novaya
Zemlya)
Men’shikova, Mys (USSR, east 1

CORSA Er 420
IVIGTAU S eel 92170
IMiercertHead femme 9 E 7150
Mercy, Capers) sees S 4360
Meredith Caper eee er 84010
Mi S a 70960
Merr sr sss SSS ES sd ot 95110
Menera, Punta o > 55490
Mers er KE Eege Ss 59770
Mersey Bluff. 6922: = a 79050
Morsin (Türkey) 222222222 St 58440
Mersing (Malaya) - -------------- 81020
WIOTSTADS seen S ege 43650
iMerundühpg;Pulauc--------2---—— 72020
Mesas Roldan 51210
Mosolóngidón ra e ti a 56050
Messina See ec A 54930
Mesurado, Cape" "C= 62230
Miēulābons m ms 72820
Mew TS as 38540
Mexico, east coast C = --— 13300
Mexico, West Tee 15700
Mexico, Puerto ccoo 13480
Minis q S 12310
et ee Ee 83120
Mibya yu se RM 70940
Midas eae 45780
Middelgrundjeeee es 45890
Midway io o enne 20900
HEES 86290

1116

Ml TT ER. S 70230
Mulo, Hrid
Mumbles Head. .......-

APPENDIX S
INDEX

Index

No.
Montauk Point. .-...-.-.---——. 11210
Monte. Belo: -z322---.-——- 64340
Monte-Carlo.--------- 52810
Monte de Cuyo.------ 13660
Monte Radford. .......... 29140
Monte.Somos-----——--——- - 49580
Montedor, Cabo. - -------- - 49910
Montego Bay. ------------ - 21840
Mionterey:-=-=tee-_-: - 16480
Montevideo 12222 a E - 27060
Montjuich, Castillo de. ..... - 51520
iMonitreal:s.-.-.--.-.3 € S55 - 7670
Montrose - 22223. 2-931 - 36430
Monts, Pointe des.---_---- 7630
IMIOHÉSerrat--..os=====e== - 23270
Montt, Puerto. ........- - 29270
Monze, Cape. 22235 - 69510
Moore Point: 220222 - 78250
IMiQosOnee sad ila tas - 4930
Morant Boint- ss 21810
Moreira, Ponta... ta 33740

Index
No.

Mikelbākar<= <a sd 43670
Miki Zaki coros fem d 85750
Mikomoto Jimna--.--23—— CE 93 85600
MIKONOS < des: sees na 56380
IMIR otahi e226 oes eee 80840
Milazzo, Capo di 221-2200 2212 54720
Mile ROCKS de. are MEE Y 16520
Milford Ha yen. Ss — 086 37850
MINI mr m ki
Miminegash
Mina Saud
Minas Channel
Mindanao
Mindanao Sea
Mindelo
Mindoro- -
NI coL PEA TE
Mine Head
Minorca
Minots Ledge a E6- ASIA 10730
Miquelon I

MAA E aes A
Misamis, Port
Miscou Lo meo TAN
Misoól.....
NESUuNIDDIL-—— c
Mississippi Rivers EE 12900
E AO m EE 86280
MMāitres Rockets =-: cce IN 92110
Mijrofanig EE aoc. E S 18650
Mitsi Shima eT ES S 86640
Miyako Jima- -2222 A 88100
Miyan o E 86910
Mizunoko Shima--——-----——-—— 222 86170
Mkumbiy Ras: 352 TER 64630
Moanda de cota os eae 63510
ING Dies 75 da Sevi ee m 12620
Mocambique--— S [D 0 m 64500
Mocāmedes E 63730
Mocha ((RediSea). c c 66020
Mocha, Isla (Chile). coca 29500
¡MOCaras EE ose er TN 75820
IVC glam Na o E 26580
HE se cach eee 45020
Moeraki 3 saat tee 80110
et MO 27-20 ES 64940
Litt 61290
IMogotes Puniat------ "m 27230
Moner au A EE 68120
Mohican, Cape..... E o de 19510
IMobnisaarp aR A E 43340
Monolmen e EE:
Moita Seca, Ponta de
MONEDAS eS eee
MORENO tee e eee
MOED OI ce geen = sees ee
INL OKC ORS sae een VAS
Miokt1O1S OS ee
Mokutoku To
Molas, Punta. .....
Mole n GSpIduN eee
e DEE

Molini, Capo (Sicily)...
Molino, Punta del (Spain)
iw ele eege Ze

Mombasa. ro- Sari ER
M

Monecron/Ostroyv -nm 84250
Monomoy Point). vesi 10820
Monrovia A 62220

Montagu TER 77300
Montara, Pont 16510

Moresby Point (Tanganyika).... 64630

Moresby, Port (New Guinea).... 92150
Moreton: Canes) <== = eae ee
Morguilla, Punta___

IMormugao AE =e de
Moros Tiree SEA
Morocco mmn 59900-60000, 61000-61330
MÓroni EEN A
Morris, Cape..........
Morris Jesup, Kap....

OITOS E D eae
Morro, Castillo del...
Morro Castle........ 21500
Morro Colchas. ....... 32720
Morro de las Torrecilla: 29510
Morro de Puercos.-------- 15120
Morro de São Paulo... 26250
Morro Gonzalo........ ---- 29420
Morro Nuevo. -------- -- 27470
Morro Pernambuco. ............. 6280
Morro, Punta (Mexico). ........- 13550
Morro, Punta del (Mexico) ------- 13370
Morups'Tāngēt cara = 41440
Morzhovets, Ostrov.............. 2830
Moses Oates; Cāpē-----..--- == 5030
Ree ES A 41220
Miossāmedes: cR 63730
IMosselbaal.-..-..- f eee
Mostaganem meneen e eee 59730
Mostardas, Ponta da
Motion I
Motodomari
Motsutano Saki
Moncas less c A 65140
NTould Bay = es E 3640
Moule a Chique, Cape___________ 23520
Moülmein S gar M 70910
Mount Carmel esr. I 58730
Mount Desert Rock -mEes 10290
Mount Sipler ss NN 96220
Mourepiane, Pointe de. 52550
Mouta Seca 3 2 T S REN
Mouton, Port...
Mozambique...
Mrlera Rio re ee

Mutou Hsu c EM 82750
MU yeh Tao- S A 83070
Muüaras: Reen oan NE 75820

Muari, Ras

Muckle Flugga..

Muckle Skerry 36610
Mucuripe, Ponte We Et 25980
Muggia.-.— EE NET 55380
Müglns.-. -— NEE 38350
Mui Rachbirang s me 81530
Muitāg 1 -—— RS 83070
Mujeres, Isla e SE ARS 13680
Muka Head RER 71210
Mulejé- eer ME 15900
Mulholland Point: — 7 10020
Mull'of Galloway, m 37350
Nee Ee 37170

---- 71560

---- 62800

=== 73130

4380

__ 76050

2650

---- 85100

Müuroto-Zaki---—--- ——- ---- 86140

Murro di Porco, Capo------------ 54880

MASCAT Een 69060, 69070, 69460

Musel, Puerto del" — ee 49600
Musick I

Musquash c 9790

Müsti Danes 83770

Mutji; Pulau, occ. 72310

Mürtou. Han. 22403 82750

Muūtsāmuduz.<_=_3- 9 ee 68130

Muisure Jima ¿CA 86810

Muttum Polnt-— S — "Xr 70050

Mu-yeh '(T530.------ ---- 83070

Muzon Cape -=< —— oc AINSI

Mwana Mwana......... ---- 64740

Myggenaes. S ES uoa A

Myken-- Sie m 40470

Mykdness- S ct 2220

Miylstrev ari... E 40910

Mys (cope, Point).
name.)
Nab Towót ee
Nachtigal, Cape
Nador, Punta.........
Nagasaki... :..~ccc sent
Nagasaki Bana......
Nagata Misaki......

Namalungo, Ponta..............- 64480
NampolShoto---—--——— AMEN 87500
Nan-p'eng Ch'ün-tao............. 82470
Nanaimo

iNanok-cec 2.

Nan-p’eng Ch'ún-tao.------------ 82470
Nanpo Shotó
Nansei Shoto-
Nantucket rn S SAD

Nao, Cabo'dejlā! co 51320
Nao Chou.. ciim EE e

Nao-chow, Ile...
Napakataktalik_-
Napier Harbor
Naples

Nassau

gad tid

1117

Index
No.

Natal, Cape (Republic of South
Africa)

Natal, Port (Republic of South
¿NIE A DU > end 64210
iNatashquan Point. - <=: 222< 7450

APPENDIX S
MARITIME POSITIONS
INDEX

Index

No.

Newport Beach (California) ______ 16140
Newport News (Virginia) ________ 11780
Newport Rock (Red Sea)........ 66250
iNba/Tranp Sees ae 81540
Nho Martinho, Ponta...
Nias, Pulau

Ee eng 52220
National City..... 16110
Natividad, Isla.... 16000

lattes le QUE. 25s ce ss sā 25422252 68520

Natuna, Pulau-pulau............ 72000
iNaturaliste, Cape. .—-.-........ 78160
Naufragados, Ponta dos.......... 26720

iNAusel Beach---..-..- sast - 10800
Nautla; R10-.—-- ===: 13360
Navalo, Port...... 48720
Navarin, Mys..... 84580
INS Varing 2s ss 56150
Nyassa A E 21910
INevinar Pont == salat 69620
iNavplion-.. — — 56260
Nawiliwili Bay.... 20730
Nayakhan........ 84470
Naze, The. ...-. 41050
iNXdeni*- o 92520
Docker EE Sets s 20830
Needles Ss og ee ee 35410
NERO Data EE 70370
Negra, Ponta (Azores)........... 31110
Negra, Ponta (Brazil)_--.-.------ 26420

Negra, Punta (Río de la Plata)... 27030
Negril Point, South (Jamaica).... 21850
Negro L., Cape (Nova Seotia).... 9430
Negro, Río (Argentina)_______-__ 27420
Negros (Philippine Is.) _- 90260, pem

10
Neil Har DORE lom o wernt 8620
Bel Polnbé- slan ii oa Es 37110
Nelson (New Zealand). .......... 80420
Nelson, Cape (Australia)......... 71660

Nelson Head (Canada)........... 3530
Nelson I. (South Shetland Is.)... 34420
Nelson, Port (Canada)........... 4020
Nemetskiy, Mys 2620
INemiours.....-..--- 59810
NOÓMUurot 29222. 85010
Neptune Isles..... 78040
Nera Point........ 55500
Nerva, Ostrov----- 43120
Ness Point........ 37110
INétherlan dS: 22-252 5.sss00 530202 47300
Netherlands New Guinea_ 92030, 92070,

92170, 92180
Neufahrwasser2=<- -- 222222282222. 44030
Nemand LA sassas ceo KE 44700
INTEL Werk:h2==3= ēdi LIO Y 46960
NOUTEN a taisses cilts šila ct 47510
NEVNT Sta so seo JE 95120
INGViS ER 23240
NOM Bedford-<=========oo=<esc==3 10920
INew-Britain 3512. 92240

New Brunswick------:.-..... 8000, 9700
New Galedonias--s--2.2. ume 92710
New Dungeness-.---.-..--.-.---1.2 17220
INewAGeO0rgla-------..J520.. 0092.5 92440
KEE RRE EEN 92000
New Hampshire- 72222222 RIE 10500
New y PA A 92220
AS A EE 11340
New Hebrides------2--—-—— e 92600
Now read 92230

Newsbondont^- sae ais =p cea 11320
New Orleans ti acoso 13000
New ely mou 80830

New Westminster_-

NeW4Y OTK E e -- 11100, 11390
New Zealand........ --- 80000-80880
Newbury ports... 22+ —— — 10610
Newcastle (Atstralia) "PT === ð = 77190

Newcastle (England) -------------
Newcastle (New Brunswick)-----
Newfoundland..............-

Newport (Rhode I.)-
Newport. (Wales) eee

NU Gin venison SSO E
Nieuweshi boh.

Nina KEE

Nikolayev (Black Sea)........... 57330
Nikolayevsk (USSR, east coast).. 84410
Ninfas, Punta 27490

IN TDDers TS PEA ee R
Nishinoomote Ko.
Nishi-notoro Misaki.....

Rey. rees
Nobbys Head
Noemfoor, Poelau...........
Nogas I
NOIA ZARIA
Nolloth, Port
INOISOy srs seas seca een es
Nombre de Dios. `

Nomo Saki.--
NONODSDa3- 22s emt ne tn
Noordwijk aan Zee_____-
Norah Head aa

Nordaustkāppsvssss Sa f
Nordborp sāns ras H
Noradori 222220233225
Nordenham. -
Norderney 522250 LL DES
Nordostrundingen. ..............-
NOordéyanizc.:niiiilm2-2:..10 7047
Nordre Hanner
Nordre Reie 222 2s 2se2se222222 283
Norfolk (Y ireinia)=2 ==. erer 1
Norfolk I. (South Pacific Ocean). 92720
Norman, Cape: =Y 2003 6230

Norra Udde, Ölands- ------------ 41830
NOETKODINE e e o ane 42040
Norskir AA oe ees 42700

Norte, Ponta (Cape Verde Is.)... 33410
Norte, Punta (Argentina)-------- 27450
North America, east coast... 6000-14780
North America, west coast. 15000-19700
NOD Barnard [ss ES Ee 78740

North Borneo "P ST 75840, 75880,

75890, 75920, 75940
¡North Brother- ces- masat 72420
North Canso: 2322226 ss 8480

North, Cape (Cape Breton I.).... 8580
North, Cape (Labrador) - -------- 6140
North’ Cape (New Zealand). 80780
North Carolina --:------—-—-—— 11900

North East New Guinea... 92080, 92100
North Foreland c = 3558

North Gigante I...
North Head...

North I. (New Zealand) 80500
North I. (South Carolina)........ 12010
North-Pont F e === ee 8270
North Quarken...-

North Reef---------

¡North Rock Se n M es

North Ronaldsay
¡North Saddle 1s m e —
¡North Sandy. 222.22 —— x
¡North Ubian [+237 ==========-=2=
NorthUnst V RR 4 4 AR 36850
North Watcher (Sumatra)....... 73440

Index

No.
North Watcher I. (Celebes)...... 75690
Northeast Foreland.............. 1590
Northern Ireland____-----________ 38500
Northern Two Cays.............. 14110
Northumberland, Cape. ......... 77670
Northwest Territories.----------- 3400
Norvegia, Capes ees at teens 96550
Norway res E E 40000
Norway, SEA ge dr 81770
INOSLEIDIDeS 22. aroha ocd 57130
¡Nos Galata m sen oases eee 57140
INOS: Kalakras tee ces 57160
iNOsappu Sakina. A 85020
Nosi Amambos a es 68770
INOS bal DG beep ege Ze 68760
NOSL nin Ee ee 68730
Nos Lava ēda PS 68720
NOSS Head E a e eee neh 36550
NOS A KAO Se Fco AK 68410
NOSY LANEOrO aM 68310
Notoro, Cape (Sakhalin)......... 84260
Notoro Misaki (Hokkaido)....... 87460
Noppmeliqni to eee o ee 5020
eps Be IO IRON 92710
ASPEN AER IER. 36760
Ret as E rid 8400, 9000
¡IIA 55960
Novaya Zemly asso o a 2900
INOVOroSsiysk- UA 57610
INOW Y'SE OF Gs. TS 253 aR 44030
Nūevosivlorrostese aga 27470
WIR A 80170
tes 93210
Denisa Koss 94120
oe ð 64750
S 18600
C 19500
O 42770
EXE hm pe 74200
DE ME 92090
B ELM E E 6020
adas 2460
E 86730
eee ae EE Se 45710
INivelisan Mys a eee En 84650
INighamnīes 2 a 42860
Nykøbing (Falster) -------------- 45140
Nykøbing (Sjelland)...-.......- 45480
Nysted == conce ee 45210
Nyundo paki ee 87230
Odata Shima enin 86340
Oman praes A 82640
O Shima (Goto Rettó)----------- 86520

O Shima (Honshū, south coast).. 85500
83

Oeean Cape..--.-========== e IB AS)
Ocean Falls aaa 18000
Ocean d aos ---- 94400
Ochiishi Saki 85040
et 83430
Ge e eR 2255: 82830
Ocós

Ocracoke I

O-date Shima

Odense

Odessa

Offer Wadham I----------
Ogami Shima- - ---------
Ogasawara Guntõ------

Osa A -.. 57950
Øhau Pon E SS 80510
Olean eret S e 80660

1118

APPENDIX S

MARITIME POSITIONS

Index
No

37120
_- 69640
.. 84430
Oki Guntē_- _- 86890
Okinawa Gunto -. 88000
Okinawa Jima -- 88020
Okino-daito Jima
Okino Shima (Kyūshū)
Okino Shima (Naikai)
Oks¢y
Okushiro Shima

Old Point Comfort.
Old Providence I
Oldensholm

E Île dr.

Olongapo
O-luan-Pi
Oliice Burun
Olympia

Omae Zaki-

Orang Dan

Orange Bay
Orangosinho, Ilha
Oranjestad (Aruba)...
Oranjestad (Sint Eustatius)
Orchilla, Punta
Ordaz, Puerto...

Oregon

Oregrund

Orfordness

Oriental, Punta
Orinoco, Río

Orkney Is

Orkney Is., South
Orlando, Capo d"
Orlov Mys

OD Cabo de
Orrengrund

Oskarshamn

Osmussaar

Ostergarn

55
Ostrov, Ostrova (Island, Islands).
(See proper name.)
Ostrovnoy, Mys

Ostrvo

(Island). (See proper
name.)

INDEX

Otago Harbor
Otake Zaki

Otway, Cape
Ouessant, [le d'

Ouro, Ponta do--..
Out Skerries

Ovoroū, Ākra
Oxelósund

Pachena Point

1
Pacific, Lesser Islands ofthe. 92000-

Packs Harbor
Padaran, Cap- -

Pahang, Sungei
Pai, Goh
Pai- chieh Shan

R Islas
Pajung, Pulau

Pak Nam Lang Suan
Pakchan River
Paker Ort

Pakhtusova, Ostrova....
Pakistan, east coast_____
Pakistan, west coast
Pakrineem

Palabuhan Ratu.

Palembang
Palenque, Punta

Palfrey Islet
Palinuro, Capo
Palliser, Cape
Palm Beach
Palm Isles
Palm Point

Palmaiola, Isola
Palmas, Cape (Liberia)
Palmas, Ilha de (Brazil)
Palmas,Punta (Mexico)
Palmeirinhas, Pontadas
Palmer Peninsula
Palmyra I

Palominos, Grupo de
Palompon

Palos, Cabo de

Panay
Panay Gulf

y
Pandan(Catanduanes)
Pandan(Luzon)
Pandang,Pulau

Pangkal, Pulau

Pangnirtung
Pankof, Cape. - --------

Pankosi, Akra
Panmurel

Pantelleria, Isola di----
Pantiñito, Isla

Panual, Punta...
Pan-yang Shan

Papan, Pulau

Pápas, Ákra (Aegean Sea)
Pápas, Akra (Greece)

Paramaribo
Paramushiru Kaikyo.

Parrsboro

Parry, Cape(Canada)............
Parry, Kap (Greenland)
Partridge I. (New Brunswick)...
Partridge Point (Newfoundland).
Pasado, Cabo

Pasajes de San Juan.

Paseagoula

Pascua, Isla de

Pasir, Tandjung
Pasitanete, Pulau. -
Paso Largo
Paso Tortuoso
Paspebiac
Pass I. (Newfoundland)
Pass, South (Mississippi River)... 12910
Pass, Southwest (Mississippi
12

Passamaquoddy Bay
Passaros, Ilhéu dos
Passero, Capo

Pata Point

Paxof

Paz, Ilha da

Peak I., High

Pearce Point 3450
Pearl Bank (Philippine Is.)_______ 91190
Pearl Harbor (Hawaiian Is.)______ 20640
Pearl I. (Nova Scotia)

Pechiguera, Punta

Peckford I

Pedra Branca (Malaya)
Pedras, Ponta de (Brazil)
Pedro Blanco (China)

Pedro do Sal, Ponta (Brazil)
Pedro, Point (Ceylon)
Pedro "Point, Little (Jamaica)
Pee, Goh

APPENDIX S
MARITIME POSITIONS

INDEX

Pegasus, Port.....

Pianosa, Isola (Italy, east coast)... 55230

Peggy Pont 9250 | Pianosa, Isola (Ital
y, West coast 53600
Sin KEE 81810 | Piao Chiao.__-- 20 7 Dad ķi 82440
PE a0---------------------- 82820 | Piave Vecchia, Porto di... 55340
er-yü Shan---------------------- 82920 | Picacho, Punta del 50230
I orulonpanss e (ET Ee 31400
Pelagie, ele 54600 | Picolet, Pointe 22220
LARA E 77 h5630 Preto 8460
Peleliu---------------------------- Pielou Tar NM eeart 8450
Pelepasan, Pulau................. Piedade, Ponta ds 50110

Below: Esso == 2

Piedra Point (Philippine Is.)__.-.- 89170
Piedras Blancas, Point (California) 16450

LN eee ees Piedras del Norte, Cayo (Cuba) __ 21460
DEE Piedras, Punta (Río de la Plata).. 27130
Relzerhaken c. ee Pierre. de?Herpin n co NN 48140
Pierres Noires, Chaussée des______ 48430
Pigeon Polnt«-9*--:— SE 16500

Pilar (Philippine Is.).
Pilar, Gabo (Chile) === 2

NO tio e
llene. ties

Peñas, Cabo de (Spain)-----------
Pencarrow Head

Pilot Point (Alaska)
Pilot Rock (Alaska) 1
Pine, Cape (Newfoundland) ______

Pine Islet (Australia)
Pingüino Isla: cer, Sess dð a
Pinos, Isla de (Cuba)
Pinos, Point (California) _________
Pinto, Ponta

Penífret, Tie dc ic RED Y: 48530
74120

Pengambengan, Tandjung.... ...
mrene-ehie HS... Ll. o ooi.
P'eng-hu Lieh-tao
ee 1 Tee
Penguin I. (Newfoundland)......
Penguin Is. (Newfoundland).....
Ponerini Islet eps Rc

Penguino, Isla......... E JR EOD

Reniscola Leo e Ripon c

Penmarc’h, Pointe de IBiraenste ies. 2o

Penna, Punta della............... ST Ee E

Penninis Head irm Ice AA
Rennsylyania øH -.-----—.- PPirotan ===.

Peñón de Velez de la Gomera... 30960, UE EE
Penrhyn, Cape (Canada)......... 4650 | Pisang, Pulau (Malaya)
Penrhyn I. (South Pacific Ocean). 93130 Pisang, Pulau (Sumatra)
Bensacolas s C A ée 12560 Pisco. VN e fan

Pentland Firth........
Pentland Skerries
SE Le e E en

Eitean Toss. sass
Pitsunda, Mys
Placentis 9. - Lc.

gs POM (arene ES ee Bjadda ĪSTS ee
epe TPS RIA EE .

Pera, VADO de: ===. ee 55 dee AETA MEAN

Percy Isles m AT ee EI t side

O pae ru A SU cra A A
Paria wet cere Tim Dino e
i«IBerlioat --—— = Pinuler LI due 3 sets
«Bermambbuco. D X. e. Plata, Puerto (Dominican Re-
Pernambuco, Morro.............. 26280) |Mirpüblig) EE 22510
Perpendicular, Point.------------ 77280 | Plata, Puerto de La (Argentina).. 27120
EewroduetiIss-- = e 1280 Plata RÍO dela o o ee 27000
kerlamculss 2 Lee 69100 | Plateau de Cordouan............- 49120
Borth e eee eee 78220 | Plateau des Triagoz..............- 48220
usado, EE 53000 | Platte Fougðre ===> 39410
Peru-__-----.---_----------------- S000) plate Eos se eee 7030
Pescador I. (Philippine Is.)......- 90820 | Plymouth (England)------------- 35290
EE Plymouth (Lesser Antilles) ------- 23270
Peschanyy, Mys Plymouth (Massachusetts) ------- 10750
Peter First T...--.--======:5======= ELE 76030

Pulau, Pulo (Island,
(See proper name.)

iBatersbūrg-- === eae ates

Poelau,
PotiiManan 0. == tests

Rock).

¡Petra ¡Branca === ips ..2 WEW Pro Ran Dong see eee rt
Wetropa VIOVSK=—--.- ~~ <2 ea 84510 | Põbja-Uhtju
IPelsSmonpuonoW ew o ces 2610 | Poiláo, Ilha..............-

Pezzo, Punta Poinsett, Cape

Phai, Ko < Point. (See proper name.)
Phan Rang, Baie de----------.--- 81510 | - Point-au-Fer Beet. 13030
Phan Thiet 81490 | - Point, East (Prince Edward I.)_ 8300
Phangnga------ - Point, North (Prince Edward L). 8270
Pharos I........ - Point of Ardnamurchan
Phassa, Cape--- = "Point Ol Avr sms
IBO O ES
Philadelphia - Point, Southwest (Anticosti I.)- 7560
Philip Broke, Kapsas!ss-gs=e 1570 | - Point, West (Anticosti I.)------- 7580
Philippeville (Algeria)....... 59560 | - Point, West (Prince Edward I.). 8250
Philippines c-r 89000-91240 | — Point, West (Tasmania) -------- 79300
Phillip, Port (Australia) ----.----- 77500 | Pointe (Point). (See proper name.)
iphleva.l e EE Ze 56320 | - Pointe-a-Pitre 23290
94900, Eesen ae 225-25 125

Phoenix Lorrie eN E:

1119

= Pointe de ]’Aiguille ___.._______
= Pointe de l’Espiguette____._____
= Pointe d'Itaperina. Va
- Pointe Noire, Baie de.
Poland

Bolo. Pont sees aur
Polonio, Cabo
RASO

Ponape s eee AA $

¡Pondichéry =
Ponente Point

Pont Géologie- 22 aes
Ponta (Point) (See proper name.)
- Ponta ta Delimara
Bonza Isola dis te 20032
Porbandar te si
Porcupine, Cape- -----

Port. (See proper name.) `
IBort-de=BOuei- to IRE EE
= Port Ercole: Tatta

- Port-Lyautey- ---------
= Port-of-Spain............
- Port-St.-Louis-du-Rhóne. ......

Portland (Iceland)....
Portland (Maine).....
Portland) (Oregon) 2=2-----eeseeee

Portland, Bill of (England). ----- 35330
Portland Harbor (England)...... 35340
Portland I. (New Zealand)....... 80600

Portland Point (Jamaica) ee

Bonto"Alegres2s. ass
Porto. Ambolmc........---.
«Porto-Aqmólia--------------
Porto de Leixões ........-
Porto Grandes
Porto Santa, Ilha de.......
Porto EE 228
Portoferfdio AmI eol. Reese T
Portofino, Punta di. .
Portsmouth (England)
Portsmouth (New Hampshire)...
Portsmouth (Virginia)
Ee eege Ee
Portugese Guinea. ----==-=-=-
Posesion, Galūr=++==es gare 18

61900
- 27920
56480
75600
57650
48610
- 81430
81560

NM Pointedes mms
Botlo:Condore==""=""""="="
Poulo Gambir------------===

Peulo Obi, Ile ` Ls. 81420
Povorotnyy, Mys-_--------- 83980, 84500
Prao oh... E ccelo 81150

¡Practicos, puntas: 22222 21310

Præstø - 45310
PAD Il 71300
Pida FØRDI. < ss M 33720
Praia da Vitoria 31630
Prap, Ko... 81150
Prasonisi, Akra-- 58130
iPrasoudhas--:-222-2:---::- 56... 56430
ENEE Reen islets 22-2322 s22s2 scene 56430
Preguica NA E E Se

1120

APPENDIX S
MARITIME POSITIONS

INDEX

Presqu'ile de Kermorvan Quita Sueño Bank..... Redonda, Punta
auna de Tien Sha.... Quobba Point Redwood City

Quoddy Head (New Brunswick). 1 Reedy bue
E i Quoddy Head, West (Maine). __- rT R E re reer
Prieta, Punta : yt
Prim Point (Nova Scotia) 9550 RM e
Prim Point (Prince Edward I.). . Ra, Ko Helles E pe
Prior kO A khir kaya t, Cap de eirson
Prince Christian Sound-
Prince Edward I. (Canada) 00 ecd Bay
Prince Edward I. (Indian Ocean) - 68000 esolu io ATE
Prince Harald Coast 96540 | Race, Cape (Newfoundland) Resurrec ion, Cape
Prince of Wales, Cape (Alaska). _ Race Point (Massachusetts) Réunion, Ile de la
Prinee of Wales I. (Northwest Race Rock (Block I. Sound) Feste R :

BEE Race Rocks (British Columbia)... Revellata, Pointe de_____________ 52940

Prince Patrick I Rachado, Cape Revsnes Puller
Prince Rupert Rachgoun, Īle
Prince’s I Reykjanes
Princesa, Puerto SN Revkiavücsit Wee i 2 AA
Príncipe, Ilha do Rhinns of Islay
Prins Karls Forland y Rhir, C
Prior, Cabo.
Prioriño Chico, Cabo Ragged Is. (Newfoundland)
Probolinggo..... Ragged Point (Lesser Antilles)... 23620
Procida, Isola di. Rag'sI Ribeirinha, Ponta da
Proclamation I 6530 Rájápur Riche Point

Rājpuri Point ichibucto
Proliv Yugorskiy Shar Rakahanga Richmond (California)
Promontory, Shantung Richmond River (Australia)
Promontory, Southeast Rico, Puerto
Prongs Reef E
Prģven

Prģven, South Rignys Bjerg

Rangas, Tandjung Riiser-Larsen Peninsula__
Rangasa, Tandjung
Rangiwha Raoma

Pubnico Harbor
Puerto SH Bay). (See proper

935: i 1
EE a Ras, Bas (Cape, Point). (See Rio, Río (River). (See proper
- Puerto Rico proper name.) name.)

Puget Sound -Ra's-e Jask

Pula (Yugoslavia) - 55460

Pula, Capo di (Sardinia) = ______ 53210

Pulau, Poelau, Pulo (Island,
Rock). (See proper name.)

pa (Islands). (See prop- 90371

0
0

7044
Pulau (Island,
(See proper name.)

Rizzuto, Capo... -
Road Town
Roatan, Isla...
Robbeneiland

Garam Wee. TE 69130
Qeys, Jazireh-ye

Quaco Head

Quarken, North

Quartermaster I

Cape
iU Roches Douvres. —
Raza, Ilha.. Roches Point...

Rebecca Shoal

Recife (Brazil) gases Ee 26170

Recife, Cape (Republic of South
64080
7290

Red Sea 66000-66270

Rodoni; Capo 22122201
[RSOdSkütu eec. MEE TA

1121

Index

No.
St.-Louis-du-Rhóne, Port... 52510
St. Lucia (Lesser Antilles)........ 23500

St. Lucia, Cape (Republic of South

APPENDIX S
MARITIME POSITIONS
INDEX

Index

No.
Sable, C
Sable cape times neo
BADON -Bonte du... ss M 52490
SUO Sho... E avis 82760
Sachs Harborīētomā Æ áb atajar 3520
Sacramento Ondian 70460

RolassHhéu dass 9e 3 PR
ROMAN ROCK- csc se e DIEN

Rompido, Punta del
Roms
«Ronaldssy,. ¡North EEE
Roncador Bank® i ei: at zos
Rond, Ca
Rønne (Denmark).......
Ronneby (Sweden)
BODBDSKÜP Str Es dlrs Esos vici kas
inne Bermejo ss <
Rosa, C

Rosen EE

Rose way. Cannes: E
Rosiers, Cap des.......
Røsnæs Puller..........

Ross, Fort (Oanada)-- Lot lar 4600
Ross I. (Antarctica)..-------.--=- 96300
ST ae M CEN edit. dee 92300
Rossello, Capo. ..... eres inst 54810
Ee Eeer 44440
Rostov Na Dom 2-0 «12 as 57550
NOS e 36350
Rota (Mariana Is.)............... 94870
Rota (Spain)

AD RA or
A o e II

Rotetsu San
ROMEU Ue: === e

LE AAA

Rotterdam ss SE
Rottnest I...

Rouene ts

Round Lene eet Au
Réversholmen

RONEN ees. loreet itte
Royin EE 4e
Royal, Port.-

Royale, Île

Royan Aese

Rozewie

Rt (Cape, Point).(Seepropername.)
Rubjierg Knude.-.c-2-. 209 k 0$ 46520
RG RG A ME. ols 36930
Iudkebingese Hob S 45910
RUO Point. coo 38590
A eee A 44300
Rügenwaldermünde............. 44160
Rumania RES 2e cc 57200
Rumeli Burnu-- 20232 ---- 57040
Ruml Gape: cb. ss 1 4 57040
RUN en ad 40780
iRyupert,.Isla----9-- eee. casos 29110
RUS P bulau-- een 72810
E me oo ete eet usi 42930
Russki Zavarot, Mys......... - 3000
RUSSKIY OSLTOV = i------.--- 52 3090
EE eege e TR 43020
KUVDUSU- M IA EET. 87130
IDA MEA 87130
Ryukyu isi (Japan) -e -se 87600
Ryukyu Sho (Taiwan)----------- 82650

Ryvarden ie ee ee ee dē
Ryvingen Ar E o A

Sabalana, Pulau
Sabang (Philippine Is.)---------- 89470
Sabane (Sumatra) 4330-2430 de 727

Sabang Point (Philippine Is.)---- 89790

Sabinal Punta del: eee ee el 51180
Sabine, "Cape (Canadas o... 4180
Sabine Pass (Texas)..>-======<==== 13110

Sacratif, Cabo
Sacrificios, Isla. -
Sada Misaki

Sagar ee. 04 Lentas AV
Sagres, Ponta de
Sagua la Grande
Sahara, Spanish
Bald»Port-— e

Sainte Anne-des-Monts
St. Anns Harbor (Cape Breton I.).
St. Anns Head (Wales)
St. Anns Point (New Zealand)...

Saint Anthony (Newfoundland).. 6250
St. Anthony Head (England).... 35250
St. Antonio I. (Cape Verde Is.)... 33100
SETA UCUSUNO eebe sech 12240
Saint Barbe Is. (Newfoundland). 6340
Ste. Barbe, Pointe (France)...... 49280

Saint-Barthelémy, fle
Sty Bees Head SSS eee
St Blaize: Cape me E
St. Catherines Point (England,

Isle of Wight). = see Ls 35420
St. Catherines Point (England,
south'eosst)see rd 3

St. Christopher
St. Clair, Mont
e O e rt ne
ar E a a
Sali Dennis
ON ere

St. Esprit I

Ek Francis, Cape (Newfound-
A LR 6760

sd Grannis: Cape (Republic of
Santh'ATrion) STS OM 64070
St. Francis I. (Australia)--------- 78090
St. George, Cape (Florida)....... 12520
St. George I. (Mozambique)..... 64490
St. George Reef (California)...... 16890
St. George's (Bermuda).......... 31020
Saint Georges (Lesser Antilles)... 23810
St. Georges (Newfoundland)..... 7260

Saint-Gildas, Pointe de
SAGES Sur Vio ce o

Saint-Jacques, Cap (Vietnam)....
St. Jacques I. (Newfoundland)...
St. James, Cape
St.-Jean-de-Luz_ ---------.------.
St Joe? EE
St. John (New Brunswick).......
StTobhndoacVirgmIs) eee
Saint Johns (Antigua)

Saint John's (Newfoundland).... 6770
St. John's I., East (Malaya) - - - --- 71510
St. Johns Point (Florida). - 12230
St. Johns Point (Northern Tre-

AI E 38520
St. Johns, Port (Republic of South

IAT TIGA) eee Se AR sc 64170!
Ss EI O EESE 23230
St. Lawrence, Cape (Cape Breton BS

[^

St. Lawrence Harbors (Newfound-
]arid)esee i E E 6950

St. LOL (Alaska) ie 222 =

St. Lawrence River (Canada) ----

Salnt- LOUS Se a TT ER anaa 6

Saint-Marc, Pointe...
Saint-Marcouf, Iles

Sainte Marie, Me wae. en
SUAM arks neraka

Saint-Martin, Île (Lesser Antilles) 23100

St. Martin, Pointe (France)...... 49260
St. Mary, Cape (Nova Scotia)... 9520
St. Mary Is. (Quebec) ------------ 430

St. Mary's (England). ----------- 35

St. Marys, Cape (Newfound-
land):% PAR e IPM 6850
St. Marys I. (England).......... 36100
St. Mathieu, Pointe de... -.. 48420
Si Michaela: ee --- 19620
Salnt;Nazalre"" ` TR 48810
St. Nicholas I. (Cape Verde Is". 33300
St. Nicolas Mole, Cape (Haiti)... 22240
Saint-Paul (Ile dela Réunion) ---- 67020
St. Paul, Cape (Ghana) ---. ------ 62490
Saint Paul, Ile (Indian Ocean).... 67820
St. Paul I. (Cape Breton I.)_____- 8590
St: Paul (Priboi IS.) - TT Ð 19210
St. Paul Rocks (Brazil) 25990
St. Pauls Hill (Malaya). --------- 71460
St. Peter Port (ChannelIs.)...... 39420
Saint Peters I. (Borneo) ---------- 76050
St. Peters I. (Prince Edward I.).. 8390
St. Petersburg (Florida).......... 12450
Saint-Pierre (Ile dela Réunion)... 67010
St. Pierre (St. Pierre and
Miquelon 13.) v t e =æ 1 7010
St. Pierre I. (St. Pierre and
Miquelon s.) ss A e eee 7000
St. Simons I 12130
St. Stephen 10120
St. Thomas I. (Sáo Tomé e
Príncipe). ts set 2 fl - 22 63200
St. Thomas I. (Virgin Is.) - - 22920
Dt roDēzs ss ee 52680
Saint Tudwals I. West... 37780
Saint-Valery-En-Caux........ 47830
St. Vincent (Lesser Antilles). .... 23700
St. Vincent I. (Cape Verde Is.)... 33200

pepan, dl A pd e c ipn

Sakhalin

Sakijang Pelepah, Pulau
Sakito...
Sakuntirr aM = qus
Sasha dodo T
Sal-Rei, let dosis
Sala y Gómez, Isla. -------.--
Salamaua
Salaverry
Salen

Salerund eee a es
Salina Cruz (Mexico)-.----------
Salina, sola (Italy)
Salinas, Cabo de (Balearic Is.).... 52110

Salinas, Ponta das (Angola) ------ 63710
Saline Point 2
Sálinopolis esee a ee see
Salmon Cove Point e ra e 6740
Salomapue v da cams 89090
Salou, Cabo..... 51480
Salskar lana 42810
Saltverholmen- 40850
Saluag I.....---. 91170
Salut, Des du.... 25710
Salvador: 7 ee 26240
Salvora D S S 49790
NLH EE 55410
Samaná, Cabo 22490

1122

APPENDIX S

MARITIME POSITIONS

Sams¢
San Ambrosia, Isla
SanAndrea
San Antonio (Chile)
San Antonio, Cabo (Cuba)
San Antonio, Cabo (Rio de la
Plata)
San Antonio, Cabo de (Spain) ----
San Antonio Oeste (Argentina)... 27440
San Augustin, Cape 90420
San Benito (Mexico)
San Benito, Islas (Mexico)
San Bernardino Islet
San Blas (Mexico)
San Blas, Cape (Florida)
San Carlos
San Cataldo, Punta
San Clemente I
San Cristobal (Solomon Is.)------ 92510
San Cristóbal, Isla (Archipiélago
de Colón)
San Cristobal, Punta de (Canary
Is.) 325
San Diego (California)
San Diego, Cabo (Argentina)
San Domino, I
San Elia, Capo
Saurbstebunt SE EN
San Fernando
San Francisco...
San Francisco Bay
San Francisco de Paula, Cabo.... 27600
San Francisco Solano, Punta
San-hsien T'ai
San Isidro, Cabo
San Jorge, Cabo
San José, Cabo (Argentina)
San Jose de Buenavista (Philip-
pineds)43 EE 91020
San José, Isla (Panama)
San José, Puerto de (Guatemala). 15610
San Juan (Puerto Rico)
San Juan Bautista (Chile)
San Juan, Cabo (Puerto Rico)...
San Juan, Cabo (Rio Muni)
San Juan del Norte (Nicaragua,
east coast)...
San Juan del Sur (Nicaragua, west

San Juan I. (Washington)
San Juan, Pasajes de (Spain)
San Juan, Punta (Peru)
San Lazaro, Cabo
San Lorenzo, Cabo (Ecuador).... 3
San Lorenzo, Isla (Peru)
San Lucas, Cabo
San Luis Obispo
San Marco, Capo
San Martin dela Arena (Spain)... 49550
San Martin, Isla de (Spain) 49860
San Miguel EE SE 31700
San Miguel de Cozumel (Mexico). 13720
San Miguel I. (Philippine Isi ` 89810
San Nicolas I. (California)
San D Shoals (Philippine

89

San Pedro (California)

San Pedro de Macorís (Dominican
Republic)

San Pedro, Isla (Chile)

San Pío, Cabo

San Sebastian
coast)

San Sebastian, Cabo de (Spain,
east coast)... É

INDEX

Index
No.

San Sebastian, Castillo de (Spain,
south coast)

San-tao Chao

San Telmo, Punta

San Vicente de la Barquera

San Vincente, Cabo

San Vito, Capo (Italy)

San Vito, Capo (Sicily)

Sanana, Pulau

Sanbore Cay

Sancho-Kaku

Sand I. (Alabama)

Sand I. (Midway Is.)-----

Sand Key (Florida)

Sand Point (Alaska). .......

SandPoint (Nova Scotia)

Sandakan

Sandalo, Capo

Sandhammaren

Sandhamn

Sandkaas Odde

Sandwich I. (South Pacific Ocean).

Sandwich Is.,South (South Atlan-
tic Ocean)

Sandy Cape (Australia)

Sandy Cape (Tasmania)

Sandy Hook (New Jersey). -

Sandy I., North (Australia)

Sangage Entrance, Rio

Sangamankanda Point. ...

Sanganeb

Sangch'uja Do

Sangihe, Pulau-pulau.....

Sangkapura

Sangley Point

Sanguinaire, Ile

San-hsien T'ai....

Sanibel I

Sankaty Head

Sansego, Isola

Sansendai I

Santa Ana

Santa Barbara (California)

Santa Barbara I. (California)

Santa Barbara Is. (California)...

Santa Catalina I. (California) ....

Santa Catalina, Punta (Spain)...

Santa Clara, Isla (Ecuador)

Santa Clara, Isla (Spain)...

Santa Croce, Scoglio

Santa Cruz (Argentina)

Santa Cruz (Azores)

Santa Cruz (California)

e Cruz de La Palma (Canary

Ss

Santa Cruz I. (California)

Santa Cruz I. (Solomon Is.)

Santa Elena, P

Santa Isabel (Fernando Póo)

Santa Isabel (Solomon Is.) __-

Santa Lucia

Santa Luzia, Ponta de___

Santa Magdalena, Isla.

Santa Maria (Cape Verde Is. )

Santa Maria, Cabo (Uruguay)...

Santa Maria, Cabo de (Portugal).

Santa Maria di Leuca, Capo
(Italy) 55130

Santa Mone Ilha de (Azores).... 31800

Santa Maria, Isla (Chile)

Santa Marta. (Colombia)

Santa Marta Grande, Cabo de
(Brazil)

15890
Santana, Ilha de (Brazil)... 25920, 26400
Santander

Santapilli

Santiago, Cape (Philippine Is.)... 89340
Santiago de Cuba (Cuba) 21720
Santiaguillo, Arrecife

Santo Agostinho, Cabo

Santo Antão, Ilha de

Santo António (Sáo Tomé e Prín-

ipe
Santo António, Ponta de (Brazil) 26230
Santo Domingo 22440

São Jorge (Azores)

São Jorge dos Ilheos (Brazil)

São Luís

São Nicolau, Ilha de

São Paulo, Morro de

Sáo Pedro e São Paulo, Rochedos

São Roque, Cabo de---------
São Sebastião, Ilha de
São Thomé, Cabo de (Brazil).... 26390
São Thomé, Ilha de (São Tomé e
Príncipe)
São Tiago, Ilha de
São Tomé (São Tomé e Príncipe). 63220
São Tomé, Cabo de (Brazil) 63
São Tomé e Príncipe
São Tomé, Ilha de (São Tomé e
Príncipe) 63
Sao Vicente, Cabo de (Portugal).. 50090
São Vicente, Ilha de (Cape Verde
EES oo oe T 33200

Sapiéntza
Süppi
Sapudi, Pulau

Sardáo, Cabo
Sardina, Punta
Sardinia
Sarich Point. .
Sarichef, Cape
Sark
Sürkküluoto
Saruyama Zaki
Sarych, Mys
Sasebo
Sassandra

Satelite, Punta...
Satumu, Pulau
Saüdade, Penedo da..
Saudhanes

749
Saunders, Cape (New Zealand). . 80160
Saunders, Cape (South GeorgiaI.). 34110
Savage I
Savannah

Savudrija, Rt

Sawazaki Bana
Sawu, Pulau

Scalambri, Capo
Sealpay

Scapa Bay
Searamia, Capo
Searborough
Scatari I

Sceic el Abu, Isola
Schanck, Cape
Scheveningen
Schiermonnikoog

APPENDIX S

1123

MARITIME POSITIONS

Index
No.

Sohlemmunde seed db 44760
Hohlfeswig tis ome E Site
SONON mr tum reae ree
ODO Went Aou e uo K
CIS VU a ras E or C dE
Scilly Isles. .......

Scoglio d' Africa

Scoglio Santa Croce. .............
Scoresbysund- ........

Scorno, Punta dello. -

ESC Gaps ede tum e
Grona Bayern Ne core eT

COL ANG vecors ccs 36200
CO CANO ente err m SS 17760
Seurdie Nee 2 P 36420
CANTA ues x MT ' 11420
ECON di A PEO 57500
SOMO a Lee 8540
ACO venea aia 8220
Seahorse Point (Canada)......... 4810
Seahorse Reef (Florida). ......... 12470
Seal I. (Nova Scotia) ------------- 9470
Seal Point (Nova Scotia)--------- 8450
Seal! Rocks (Alaska) .-.--=-==== Hs 18390
A A (so EE

Secche di Vada
Seguam I. (Aleutian Is.)......... 19050
Seguin I. (Maine)

Mee. Rungel-- eene E
Selasih, Tandjung
Sent? Badung uS s E
Selat Durian- t
Selat Riouw.........

Selat Walea---------

Selat:selat Gaspar-...-....--. =
Selatan, Tandjung
Seldovias tt E
EA Mc
Semau, Pulau
Sembilan r E
Nem bien Pane. costs ee th
Beni-Ostrovov. e
Ee Etage ds
Sened EE 58). asas sm das
Senetosa, Capo
Seniavin, Cape (Alaska).........
Sentinel I

29160
Senyavin Is. (Caroline Is.)....... 94920
7610

Sept-Iles (Quebec). ..........-...

Sept Iles, Les (France).....-...--
GE
A AR O
SORKORUOLO aam MA
Sermata, Pulau-pulau
Serpho I
Serrana Bank -..----..J:9000:.4
Serrat, Cap (Tunisia)
Serreta, Ponta da (Azores)-------
Serut Pulao cases 1
EE ME
Set'-Navolok, Mys

Seven Is

Sevilla

INDEX

Seward Mc sa = EIER
Seychelles Group------------
Seydhisfjórdhur.............

Shab Shakhs, Punta. .
Shadwan I
Shag Rocks
Shāhpūr, Bandar-e........

poaki Jazirat-------——-—-.
Shakotan.. NS LA SS TS

Shang-hai ee e

SAR Hou terca o S

Sharjah

Sholagskiy ¿Mys EE
Shelbuned sm. e
Bhomvalle cro E
Shepelevski-ct- a s 5 Rees
Shepstone, Port
AO 5-3 e

Sheringham Point--.-——-J— <.
Shetland Is

Shimo-kareki Shima..............
Shimonoseki i. nt cte
Shimonoseki KaikyOo.............
Siimushirubos ce:
Shinnecock Inlet
Shiokubi Misaki
Shiono Misaki
Shioya Misaki

Ship Harbor (Nova Sootia)....... 9170
Ship I. (Mississippi)... J2£2 2-2 12740
Ship Shoal (Louisiana)----------- 13020
Shipunskiy,Mys:--—-——— 3 84530
Shipwreck Pont pee 8290
Shimane clo A E 86360
Shirakami BAki....—--——-——. Es 85150
Shinya paki Sm a 85250
SITO SO esc cete EE 86550
Shoals, Isles Of ss sea Ļa 10520
Shoalwater, Cape... 17130
Shoalwater Is- enna 73230
Shokal’skogo, Ostrov------------- 3050
SHOP qoi oaa scan bites
Glen

Shoseiš Pos —-—---

Sbroud TE- es

Shumagin Is

Sialat Polnt--------

Sibago t...

Sibuyan Sea

SICH Vises ei eee os RS

Ek VE mt 58260
Sídhero, Akra (Greece) ore rue 55930
Sídheros, Akra (Crete)............ 58260

Sidi Mogdoul
Sidon____------------------------

pilelBurnus -----
Silleiro, Cabo

Index
No.

Sims. Cap ceste e 61310
Simao Grande RS 25840
Simarg Tete. Mise O ER. 89750
Simeulue; Pula ee 72840
Simonstown == 7 EE 64010
Simrishamn Aisn rn Spee 41630
Siímustir/Ostrov RR 84750
Ses Lë ere ca see 50070
Singapore a cer A ER 71540
SOTE a E eee Ó 72850
SINO Ba y A 62250
SMA 57720
SID Oren eee ene ona 83750
Sint Bustatiusseesses ee 23220
SINGINICOlaas A 24310
SUDA V o ca EET 208162250;
SUD Cape O ZO,
Siple Mount ee SE 96220
SGU) Ol eee ee S 90250
Sir J. Brooke Point --2. 91110
Siracusa

Skala Slvuchiya s ccc 84280
Skallingenses mad em Ec 46600
Skalmen ae ld 40680
ANA e 40870
SKelligeš Rocks SE" ---- 39030
kores MUNG see sees ae es eee 37730
BhentvvOlec-.--— .. = eee 37140
Sklnāris AkraMtsidesst melt. 56010
Skipjack fee ege nd hec e 17460
Bette wet. ---- 56440
Skjoldnss-.---.---.- ---- 46020
Skinned ceso ee ee 40520
skokholm Ia 37830
ISOM, OL raa eee ---- 40310
Skopelos: ceca ---- 56460
Skraven ---- 40350
Skroo... ---- 36820
Skrova ---- 40350
Skrypleva, Ostrov....... -... 83950
BESDOSOSE EE 56440
Slangkoppunt...-....... 5397
Sibus oyes eee

Sledge he MES ae
Slepikovskogo, Mys
A Tor
Sletringēns--=- =:

Sletterhage

Slidre Bay

Sligo Mo dei. inn pet

Slyne Head
Smals Phe n- Thm H

Smith I. (Canada). ....... 4960
Smith I. (Washington)...... 17410
Smoky. EEN e
Smygehuk....

SMT NG) Je E eju
Snake Cay, Kasims oue m EE 14220
Society Es Aenea Se Ege 93400
Socua - 49300
Socotra......- 65110
Sóderarm.... 42130
Sóderhamn 42230

1124

APPENDIX S
MARITIME POSITIONS

INDEX

Sóderskür Spain, Port-of- Struga, Rt
Södra Salskar.......- E Spanish Guinea Strumble Head
Sódra Udde, ólands Spanish Sahara

Spanó, Akra
Sohüksan Do 83 Seat Cap
Sol, Ponta do (Cape Verde Is. m Spartivento, Capo (Italy)

7 C Sardinia
rs VAR Spartivento, Capo (Sar )

Spathi, Akra

Solitary I., South. . A

Seller, Rei g Spáthi, Akra

Solomon (Alaska) __ Spear, Cape

Solomon Is. (South Pacific Ocean). 92400 | Spectacle I

Sélvesborg 41660 | Spencer, Cape (Alaska) ------
Spencer, Cape (New Brunswick).

Somali Republic Spencer, Cape (Northwest Terri-

Somaliland, French K tories) :

Sombrero (Lesser Antilles) Spencer, Point (Alaska) Sedest, tle

Sombrero Key (Florida) i Sudhuroy
Spitsbergen, West___- Sieste Point

Split (Yugoslavia) : S 66260

Split, Cape (Nova Scotia) 80 | Suez Canal 58810, 66260, 66270

SE Lon (Australia) Sugarloaf (New Zealand) 80750

pr i. Sugarloaf I. (China)
Sugarloaf Point (Australia)...
Suigen Tan

Sønderborg
Sondre Stromfjord

Sukhumiyskiy, Mys
Sena He Sukkertoppen
Staberhuk Sula, Pulau-pulau
Stack, South E Sule Skerry

Stamphani I
Standia
Stanley, Port
Stanton, Kap
Starbuck I Sumba (Indonesia)
Start Point (England) Sumbawa (Indonesia) IO
d Start Point (Orkney Isi — Sumbo (Faeroe: Is.) S P R 2010
Sórve Nina Stavanger Sumburgh Head
Sosnovets, Ostrov Steep Summerside
Sotsuko Zaki 87 Stefano Point_______-
Sottile, Punta Stein Ort Sunda Is., Lesser
Stenshuvud Sunda Strait
Stenskar Sunderland
Stephens I. (New Zealand)
Stephens, Port (Australia). ______ Sundsvall
: Stephenville Pond (Newfound- Sungai Gerong
South Africa, Republic of.. 63900, 64000 land) __ Sungei Kedah Entrance--
South America, east coast__ 25000-28030 | Stetti Sungei Pahang
South America, west coast_ 29000-30550 | Stevns Klint Sungei Selangor
South Atlantic, Islands of the... 33900 | Stewart I Sunnbour
South Bishop Stilo (Poland) Suno Saki
South Brother Stilo, Capo (Italy) Suqutrá
South Caicos------------ 50 | Stinking I Sür (Lebanon)
South Carolina 00 | Stockholm. ---------- Sur, Point (California)
South Foreland Stockton Sur-Sari, Ostrov
South Georgia I Stoer, Point of j
South I. Stokes Point Surgeon Cove Point

South Lima Islet Stokksnes S
ee poe ether ne urgidero de Batabanó

South Orkney Is S Stolpmiinde

Stončica, Rt Sušac, Ostrvo
Stor Jussaró.. Sušak
South Shetland Is..... au reet Sušak ja

Stora Karlsó
South Solitary I 7 Storbádan

S MOI
South-West Africa.. $ SE

South Wolf I Storjungfru

Southampton (England) Stórskjør 2

Southampton I, (Canada) Stralsundi see

Southeast Farallon I 310 | Stratford Point

Southeast Promontory 3070 | Straumnes

Southsea Castle Ð ARM 35520 | Streaky Bay

Southwest Head (New Bruns- Streymoy Sveagruva
wick) S as C Svendborg

Southwest Pass ssis 41160

Southwest Point (Anticosti 11. 7 i, Poen peers LÍA ees 42120

di rit Gayan 4 Strombolicchio, Isolotto Sverdrup, Ostrov

eA ND 1 e 90 | Strómmingsbádan Sveti Andrija, Ostrvo

SpadillosiEunta ee. li uomo Sveti Ivan na Pučini, Hrid

nu ee Ger Seed Sveti Ivan, Ue

Spam, northicoast o reani CNN 49400 i

Spain, south coast- T TENES 50200 | Stroomen Kaap

nom

1125

APPENDIX S
MARITIME POSITIONS

INDEX
E Index
Svörtuloft ai ind taad 1790 X 0.
Svyatoy Nos, Mys 2555] bon el a tl dl (ri presencia sie Renner aus 14430
Ewskopmund. s dlu We epe 63810 | Talise, Pulau... a onge, —— 69960
Swallow Head (Aleutian Is.) ____- 19070 | Tallinn ae TOME IUE Em 72650
Swallowtail (New Brunswick)... 9910 | Taltal ........- A IU EE 75580
Swan I. (Tasmania)-------------- 79020 | Ta-lu Tao. F ANE 75680
wan Is. (Caribbean Sea)........ 2 EE EE Y ie Mi simi E 0
Swansea : e Gr E el Eeer 73050
Malo I.e eros Ee Tema--------------------------=- 62485
TOS a oe T rRiver-..------------.-ess- meman EE 72890
Sweeper Cove.......-.-.--..-__- Damara, Reess S Memerosa,Bonta -= e 33730
AA Port... egen ol ei mendra Point. ----- anni 57350
Swtlllio:Polnt-------—----—-—-— 36620 Tamélos, Ákra endroyskiy c e eee 57350
Swnemünde 2 s ee 44200 | Tamerabel, Ensenada de......... Eer 57910
Ši GV N, socan A A AMA T t 12440 dE EE 32600
COUR AS AAA GE 13320 | rp nés, Cap-__--.----------------- 59710
Syðradalur 0 eee S e 2210 | Tampurung, Plan. 73530 Tenggaroh, Tanjong ss 81010
Sydney (Australia) --------------- 77229 | Tan-shui Ho-k'ou. ............... 82520 e Fulan EE 81050
Sydney (Cape Breton I.)...--.--- 8670 | Tanamo, Puerto An OG e A #1520
Sydpréwen 20 atea a2 1370 | Tanb-e Bozorg, Jazireh-ye.......- Bol e Ee 3810
“A Tanjong Tepa. Ada Br” E
ape, oint). E GREEN
RE E EE a
8 m EE EE Teriberskiy, Mm 2670
Syurkum, Mys name.) EE MS adi M S 47510
Shane. s n d s c o e AE um GEES 84310
Ta-hsing-tsan Yen Ee OUER Terrin tās mg jos P maki" v
PARC eee 1. Å TanegaShima A617 m EMS ae
datu l ivane ku EE Territories, Northwest----------- 3400
Ma-san-shan Tag” 5262-2222. Tanga ð ——- t Rer beling
oe Pao. ==. ee Pea Ceno EEE
a ee eegen hE 89 angasseri Point_-..------- ee
Tabarca, Isla de (Spain) --------- 51270 ss EA Testigo Grande, Isla. ...........- 23910
Tabarka (Tunisia) -------=====-- 60480 taco or o UNO pie, Panta 29900
IMabi Gen ef es opor datus. 94510 | Tanguingui Tiet. M c E E
Tablas, Cabo (Chile)------------- 29780 | Tanimbar, Pulau-pulau OL TAE
Tablas I. (Philippine Is.) ------- 89760 | Tanio, Pointe________- "elo Moni tate
Table Bay (Republic of South Tanjong, Tandjoeng, Tandjung Thailand east coast Mt ec uana
RT eT 63960 | ^ (Cape, Point). (See proper Thailand, west coast 71000
Table Bluff (California) ---------- 16860 | name.) Th: New Zealand s AN
Table Cape (Tasmania) ---------- 79070 | - Tanjong Hantu Thames, E du E: a Ee ur 80650
Table Head (Quebec). ----------- GE eat Tn T Piver Cela Seas 35600
Table I. (Andaman Ís.)---------- 706 a DPR The. (S arbor ES ane 1050
puabosdila elie ss E nee TS. | Tartan ākā yee pe ee name.)
Tabuan, Pulau...........-------- 73940 | Tan-shui Hokiong. Ge DE
Ta-ch'i Shan--------------------- 82090 pansu Harbor <<<. «eee Gids oe Shar
Tacking Point. ....-..----------- GE EE Three Hummock I...
Tacloban.....---.---------------- 90130 | Tapaktuan......----------------- Three Points, Cape...
dc ae RE SEH dophao Nol, KC — Thule (Greenland) ES
FDO ETRE 83320 Ge Ze Deus Sandwich Is.)... 16520
Taerorok To.........------------ 83460 | Tarābulus----- Ticio I 89820
feo ear se SE Ser Token, Tien ER 82030
Rar Punta dele ss" 55350 tt are GE ee SE 50
DE BEES 90280 RUE I RPO AN EE E NL ER
Tagomago, ISI do EN A tdi VA S ja T OO Isla Aa
of: eee se, O kās C vāji (se
Tagus Ķiver or Wei
Tahiti, Ile------------------ 93420, 93430 Tin EE 57370 | Tikus, Pulau (Malaya) - --------- 71220
Ta-hsing-tsan Yen _-------------- 82410 | Tarkhankut, Mys_--.------------ 57370 | Tikus, Pulau (Sumatra)..-.------ 72990
Tahuna-------------------------- 75410 | Tärnö-- Tillamook Rock
T’ai-tung------------------------- 82610 | Tarragona Timara ee ee
Taiaroa Head. ........----------- 80150 | Tarsi, Jezirat...- Timbué, Ilha.....
Tailon I___.---------------------- 89530 | Tarven.....-. Timmendorf_-----
DAMIT ARTA eee as 56200 | Ta-san-shan Tao MON rbd
Morada i NE m 85220. Rasman Lo raea ao cL 19 BIO) Min Rastet ea
toko eas 82610 || Dasmanis <a Tinaca Point......-
RED EE 82610 i katalan I Dian Fr
Mamani. te TE 82500 | Tateishi Saki.... Tino, Isola del. ----
E EE 55580 | Tateyama------- S Tiñoso, Cabo--.-- `
laka DEE EE Z5olDdcDathong Point n a z 'Tipara Reef--------
Takamatsu a enema SE Xen aea Phi taa d n Les eae ea eee er Mipasae caes ee
BUS OK On ee e e E 826604] Tayolara, Isola- + Ee
E CESE Oya spas Wa EN KEE
Takashima Mate 87390 Tawan Tok KOS m ses Mitan eec
BOW AN les Sees ee ae Pe 87720 | Ta-wang-chia Tao mumpar BEE
NA ga ONO eee Ie ee I O E eee ee eer ee HD
makhunaNnar se ae See SSeS 43100. tama IZM OEC eom EET ¿cla Pulau
Han tele DEE 729104 ERE Hora a e 80600 | Tjikoneng, Tandjung------------- 73520
EE GASON carac A 3001011 Biata p ea ase EE 73980
DECH EK GI Il ddr E 18250 I DMreDODE See ES 73130
Takur Eo Soe e E 71020 | Tehuantepec, Golfo de----------- 16720 | Mukuh Banding---—----—----—
Mara RR A0) en dar e 57000 | Tjukuh Belimbing

Talaud, Pulau-pulau------------- SACO NANA Sse Ne esas E 58740 MII EE

1126

APPENDIX S

MARITIME POSITIONS

Index
No.

(oc recrearse eee 23900
E A 95120
Mobruch vés. Scot cr Ss 58920
Tocdpilla. ccc <==icersci D 29930
(P6dBesd-POln ts sveta 36440
¡Nodo Saklz......5.. A See 85260
Modos Santos, Isla-—---— eer 16039
'Boenda Blanden sos 73600
MOCO). ege Sieger ELI A 62500
MoI Isaki.--2-eoec. IR os 86210
Tokelau Is- see ss 94100
'"Poküuyame.--:-:--23--...9 8 Sess 85980
PING FN RON NNNM NNNM T 85370
Bolbukhini <: cune A RE 43200
MROIStIKSUM.YS ces 2840
Borio nai sun ME 86530
Momi- Et orbe ee 94950
"omini Road. 2.222235 09.2.92 75540
Tomi Head. . recorra UMEN 9160
Tomoga Shima.--....--- 85820
IEODAJĀCE eeu te EE
Tondi
Tonga
Tongareva
Tongatapu
Tonki Cape i
(Donning. A c
PANS DETE c... EE 41190
Topo; Ponte do----....— ---- 31500
Topocalma, Punta. -...- 29710
Toporkova, Ostrov...... 84740
Toppershoedje- - ------2222 73530

Tor (Egypt). - 66210

Tor Bay (Nov a Scotia). 9100
Tor Ness (Scotland)... vus. 86780
Tl'orbjornskjser -------—----- 41270
Tordenskjold, Kap...... 1420
MO Vas mete a, 41490
berg Eege 41230
Morin 87540
Torigakubi Saki......... 87010
Morifana,, Cabos 49760
Tormentine Harbor, Cape este v
COLO -.-- 42610
Toro Point_- 25--214790
Toro, Punta. 22-2 14720
lte ee 49730
Torrecillas, Morro de las 29510
motes; Cabo de eue ET 49610
Torrox, Punta de 51150
(COSA yn nera Less t REN 2110
Morsy ar EA AC 40150
Tortola I 222050
Montosa Cabos see 25-2 01470

Nortuga (Hay NES
Tortuga, La (Venezuela)... 25180
Tortuga, Punta (Chile)...

Tossa, Cabo de............ --- 2051550
Mostonstbúntade rn 32830
Toulinguet (Newfoundland) ..___ 6460
Toulinguet, Pointe du (France). 48450
mMonion er DU POLOS y qe vdd 0] 52610
Morane es soos. Soe -- 81710
Tourgueness, Rass__- ---- 50310
Tower de Hercules ---- 49730
LOW Capas Sew TTC EE, 63950
Townsend, BOL. TOS 17230
Dow ee 78770
ira Zon ESE A 57710
Mracadigash Point on 7860
Trela Nosite cet er S, 46270
AC e e ROS ---- 40480
Mratalean (Cabo or 50290
AR (Xo SEE S A
rama da seen seme one eech
Traneker

Trang, Tanjong
braudy ies stekā AM
Tranguebar 70390
Tree eumd ce A 54780

INDEX

"Pravemünde-....——--..—. c3

HV eT sD 1G 2 Ale DO n eni eie CEA
‘Tree I. (Indonesia)... il
Tree Point (Alaska) ----_-
"I PreknOBGhe Sian
Trelde Nees
'Drelleborg:. Assam
Trengganu, Kuala........
AR Years noes ares
report sc
Tres Forcas, Cabo de...
Tres Puntas. ae

Triagoz, Plateau des-----
Triangulo Oeste Arrecife_
bestar 2 o S E S

Trimeson, Akra ` 2-1 =
¡Trincomalee: ss lt S
Trinidad

Ocean) oes ks sesto - es 33940
Trinité (Lesser Antilles).......... 23410
Trinity (Newfoundland)......... 6630
Trionto, GADOS sea AM 55080
Tripití, AÑO occ N 58230
Dripoli (Lebanon). A 58640
Eripoli'(Libya) e eee 58990
nistan [59 20 CIE 33950
ihniveandrum= ` m T 70040
(Drols;Riviēress SE 7660
Weg Ee Ge kr
A geteilt ee ee 40660
Droubridger shoals cas 77930
dE eeh 48000
'¡Druecial Coasts eges- senna 69120
Truk 1994 E 94930
Tryon,;Gape. E 8280
GË HE 83060
sint Ohads es EN 82310
ESTE bakas sia A 83050
IDSüken.Jlma.----..8 "ww 88010
sunoiShimacse TA NEE 86830
Tsurikaka Zaki remon 86250
Psurüupa Lo set. CO ANNE 86940
Tsurtel Saki Í CT 85450
dE onerosa ERN 86600
Tsyp-Navolok, Mys............. 2630
misning Pointe. 2-29...) RS 80620

Tuamotu Archipolago..
Tubbataha Reef. . .
'Tubigan Point

eee 393300
pep O (LA)

Tuguan, Pulau (Sumatra)
Tuktoyatuk
DUCATI eee pr NN
Tumaco PES ee
Tumba, Ponta de
Tumbes, Punta

Tumpat

Tunda, Pulau-.
A Vine Chait Hsu- ne
Tung-ch’ tian Tao
INS E ree sega
Tung Lung....
Tung-t'ing Shan
Tung-yin Shan
Tung Yung

Tung-kua Hsu

Tungkuen qM dew

Tung-t'ing Shan

Tung-yin Shan
i

Turlo, Cape
Turn Point

Turnberry. Fonit, =. 52 Tem
Turneffe Cays
'Duskar Rock ae

Tvingsbjerg
DWAIN B00 uc 230 on
Two SS Northern
Tybee I

Udbyhgj
Udjung Batumandi `` A
Velen, M ys. ss S
Ugashik ege e NN
Ujung Sungei Bramei
TON GH pat Seko a SE.

Undan, Pulau
Wndersten. =. Inte ay ae
Undu Point
Unga Spiti 0H eT EORR
Ungay Point
Ungeg lt VUELTAS: See LE
Unimak I

58800,
66210, 66220, 66260, 56276
USSR;6east.coast fm e eens 83900, 84400

,

USSR south consten: INDE
USSR, west coast
Unst, North: eo mann MM
Uomo Morto, Punta
Upernivik
UpDoluü-cuseiescieccec. M LEM
Uraga esi: In

57300

Urania T2995 ee EMEN

Uruguay v 26900, 27020, 27060, 27080
Urup, Ostrov- 847

Urupp

Ust'-Kamchatsk
us Isola d’
ua

Vache Hoan Onon
Vada, Secche di.
Vüderóbod..
Vado, Capo di
Vadsó

Vahsel Bay
Vaindlo ett 2s. E
Vakalapudi
Valassaari
Valdez

Valencia (Spain)
Valencia I. (Ireland)
Vallejo

Valletta

Valparaiso
Valsórarne

APPENDIX S

MARITIME POSITIONS

Vancouver (British Columbia)... 17810
Vancouver Pam cr setā 17040

Vancouver
Vanua Levu

Vasil'yeva, Mys
Vāstervik

Vejsnes Nakke
Vela, Cabo de la...

Vendres, Port-
Venétiko

Venus, Pointe...
Ver, Pointe de...
Veracruz

Verde, Cap (Senegal)
Verde, Cayo (Cuba)
Verde, Isla (Mexico)

. (British Columbia). 17600

Verde I. (Philippine Is.) . ........ 89590

Verde, Point (Newfoundland)...
Vernon I., East

Vert, Cap (Senegal)

Verte, Baie (Newfoundland)

Vesterálen.

Vestfold Hills

Vestmanna (Faeroe Is.)----------
Vestmannaeyjar (Iceland)

su e E

Victoria (British Columbia)
Victoria (North Borneo)
Victoria (Seychelles Group)

6860

Victoria I. (Northwest Territories) bad
22500

Viejo Francés, Cabo
Vieques, Isla de

Vierge, Ile

Villagarcia
Village Cove
Villano, Cabo

INDEX

Virgenes, Cabo___---
Virgin Is

Visakhapatnam
Visayan Sea
Visby

Vita, Puerto
Viti ‘Lev u

Vitória, Ilha da
Vizagapatam
Vladivostok
Vlakke Hoek
Vlaming Head_

Ze E Ae
Voronov, Mys
Vostochnyy

Vrakhonisís Kaloyéri.
Vrakhos Tourlos
Vrangelya, Ostrov
Vtoroy Kuril'skiy Proliv
Vulcano, Isola

Wada Misaki
Waifs, The

Wailangilala____-
Waingapu
Wainwright
Waipapa Point
Wajabula.-

Wakamatsu.
Wakayama
Wake E
Wakefield. `
Wakeham Bay
Wakkanai.
Walcott, Port

e e 75550
37700, 37930-37960
74

Wangerooge. -

W angiwangi, Pulau
Wan-jen-t'ui Pi_
Wan-shan Ch’ iin-tao
Ward Hunt I

Warden Head
Wardlaw, Kap
Warnemiinde
Warrnambool
Washington.

Washington (District of Colum-

bia)

Washington, Cape (Fiji) - -
Washington I. (North Pacific

Watch Hill Point...

Watcher, North (Sumatra)
Watcher I., North (Celebes)....
Waterford

Watling I....

Wauraltee I

17020, 17040, 17100

== 93910

Wedge I. (Australia)
Wedge I. Moya Scotia)
Wednesday I

Wei-chou Tao
Wei-hai-wei

Welles Harbor
Wellington
Welmaduwa I

West Point (Anticosti 1.).---_---.
West Point (Prince Edward I.)..
West Point (Tasmania)

West Quoddy Head

Westermarkelsdorf___
Western Arm
Westernport (Australia)
Westhoofd

Westkapelle

Westport (Ireland)
Westport (New Zealand)
Whaleback Reef

Whangaroa

Wharton Reef

Whidby Is

Whirlpool Point

Whitby

White Head I

White Point (Cape Breton I.)____
White Point (Labrador)
White Rock (Australia)...
White Rock (Malaya)....
Whitehaven.

Whitehead

Whittier

Whittle Caper
Wiekham, Cape-

Willapa Bay
Willemstad
Willemstoren
William Cape
Williamstown

Wilmington (California)...
Wilmington (Delaware)..........

1127

Wilmington (North Carolina)...
7l

Wilson Promontory

Windward Point
Winter Harbor

Wolf I., South (New Brunswick).
Wolf Rock (England)
Wollongong

Womens Bay

W onsan Hang

Wood I. (Maine)

Wood Is. (Prince Edward I.)
Woodman Point-----

Wrath, Cape
Wu-ch'iu Hsü
Wu-tao-kou Tsui-tzu

1128

Xicālango Puntata aan
Yakishirt Jima O

Yegorova, Mys....
Welizavety, MiySs<. ceo EE
Yelken Kaya Burnu
emer: . uds Se UMS
Vonikale Mys- onemi eae
Men al AE e A EES
Yerogómbos, Akra? =V
Yeşilköy Burnu.......
eure: dates es +.
Yevpatoriyskiy, Mys
Yin-k'uo-kou Lieh-tao------------

82900 | Za‘faranah, Ra’s

APPENDIX S
MARITIME POSITIONS

INDEX
Index
0.

XY okkaichi:-.::224-—2-222:2c2EEEL Zambezi River------. Hyon 64410
"Yokohama... cete Zamboanga FO r TAG he ae E 90510
Wokosuka= == SERERE VAM ZAR IES oe A 47380
Yonshu Gap. ------ Zunnone,lIsola----- 5 e 53880
York, Kap.-------- AZ DARA
KE Zapotitlán, Punta
Youghal....-------- Zarrugh, Ras
Y8tad- === Zaur, Basar
Ytre M¢kkalasset Zavodoski 1
Y'ttergrund-.----— ————— Závora, Ponta
Ytterholmen............-2-....-- Zav'yalova, Ostrov
kengt KE Jets aa C tes POR ee rS
Yttre Tistlarna--------- Zeebrugge
Yttre Vānnskār Zeegat Van Texol!---— 0 ES 47370
Yiūlin Zemlya Frantsa-Iosifa_----------- 2870
Yii-weng Tao.------- z Zenobia ee eed o s e d
Yugorskiy Shar, Proliv..........- yp E
Wille Osis viņs S AE 55400 a MYS r rat Ge
«Yukon Territory -a 3300 IMNegorskly, MyYs--------------
Aro EE Ram m 81920 | Zolotoy, Mys--------------------
Witeweng. Tao. . 2c! oq: Le EE
Yüzhno-Küribð sk SE OS 84790| Zourva, Akra__-
(ATS TE EE EE NE

88170! |:Zafann Iss 5 coc o eee
56210" Zafferano, Capo- <n
ZO Zakinthos: = nn ee

_—-”

APPENDIX T
EXTRACTS FROM TIDE TABLES

NEW YORK (The Battery), N.Y., 1958

Times and Heights of High and Low Waters

FEBRUARY

Dar Time Ht.

JANUARY

Ht.

©
E
E

. | Dax Time Ht. Dar Ti
5 À. m. ft. ë

Day Time Ht

Day Time Ht.

=
9
E
E
>
<
a

1200 is noon.

0000 is midnight.
Heights are reckoned from the datum of soundings on charts of the locality whic

Time meridian 75? W.

h is mean low water.

1129

1130 APPENDIX T: EXTRACTS FROM TIDE TABLES
TABLE 2.—TIDAL DIFFERENCES AND OTHER CON STANTS
POSITION DIFFERENCES RANGES
A F PE | Mean
N PLACE Hao Height Tide
O.
Lat. | Long. High ou High s Mean | Spring | Level
water water water | water
= ES i R | Rs N: feet feet feet feet feet
New YoRk— Continued on SANDY HOOK, p. 70
Long Island, South Side— Continued N w Time meridian, 769 W.
Hempstead Bay F
1501 Deep Creek Mendou 40 36 |73 32] +1 02| +1 09 *0. 52 0. 52 2.4 2.9 1.2
1503 Green Island... +=. í 3-223: 2226 235 40 37 | 73 30 +l 22 +l 29 WEN *0. 41 1.9 2.3 0.9
1505 Cuba Islands 5... eee 40 37 | 73 31 +1 08| +1 20 *0.50 | *0.50 2.3 2.8 II
1507 Bellmore, Bellmore Creek..... ....... 40 40 | 73 31 +1 29 +1 56 *0.43 | *0.43 2.0 2.4 1.0
1509 Neds Creek. -_.------- A tcd 40 37 | 73 33 +0 50 +0 52 —1.9 0.0 2.7 3.3 1.3
1511 Freeport Creeks. i252 `V 42 40 38 | 73 34 +0 34 | +0 27 —1.5 0.0 3.1 3.8 1.5
1513 Freeport, Baldwin Bay............... 40 38 | 73 35 +0 38 +0 53 —1.6 0.0 3.0 3.6 1.5
1515 Hong Beach: 32-20 - 53813 1— 40 36 | 73 39 +0 19 0 00 —0.7 0.0 3.9 4.7 1.9
1517 | Long Beach, outer coast................... 40 35 | 73 39 —0 29 —0 35 —0.1 0.0 4.5 5.4 2:2
Hempstead Bay— Continued
1519 East Rockaway.......... — O 40 38 | 73 40 +0 42 +0 45 —0.7 0.0 3.9 4.7 1.9
1521 Woodmere, Brosewere Bay .....| 40 37 | 73 42] +0 35 | +0 48 —0.7 0.0 3.9 4.7 1.9
1523 | East Rockaway Inlet.............. de 40 36 | 73 44 —0 06| —0 16 —0.5 0.0 4.1 5.0 2.0
Jamaica Bay
1525 Plumb Beach Channel............ ... 40 35 | 73 55 +0 03 —0 05 +0.3 0.0 4.9 5.9 2.4
1527 Barren Island, Rockaway Inlet.__.... 40 35 | 73 53 0 00 —0 06 +0. 4 0.0 5.0 6.9 2.5
1529 Beach Channel (bridge)............... 40 35|73 49] +0 38| +0 22| +0.5 0.0 5.1 6.2 2.5
1531 Motts Basin- +c Ee 40 37 | 73 46] +0 40 | +0 46 | +08 0.0 5.4 6.5 2:7
1533 Norton Point, Head of Bay........... 40 38 | 73 45] +0 39| +0 43 | +0.8 0.0 5.4 6.5 2:4
1535 New York International Airport..... | 40 37 | 73 47 +0 26 | +0 43]| +0.7 0.0 5.3 6.4 2.6
1537 Grassy Bay (bridge). ................. 40 39 | 73 50] +0 44 | +0 45 | +0.6 0.0 5,2 6.3 2.6
1539 Canarsie: 4538: D AA Co 3. T 40 38 | 73 53] +0 28 | +0 06 | +0.6 0.0 5.2 6.3 2.6
1541 Mill: Basin 3: See. ` JĀ 40 37 |73 55] +0 2| +0 02| +0.6 0.0 5.2 6.3 2.6,
NEw YORK AND NEw JERSEY
New York Harbor
1543 ["Coney island: "E e 4 40 34 | 73 59 —0 03 —0 19 | +0.1 0.0 4.7 5.7 2.3
1545 | Norton Point, Gravesend Bay ........... 40 35 | 74 00 —0 03 +0 01 +0.1 0.0 4.7 5.7 2.3
1547 | Fort Wadsworth, The Narrows........... 40 36 | 74 03 +0 02 +0 12 —0.3 0.0 4.3 5.2 21
1549 | Fort Hamilton, The Narrows............. 40 37 | 74 02 +0 03 +0 05 +0. 1 0.0 4.7 5.7 2.3
on NEW YORK, p. 62
155L.CcBayrRidge-—— EB SE S 40 38 | 74 02] —0 24 —0 2% | +0.2 0.0 4.6 5.5 2.3
1553 | St. George, Staten Island........... VES 40 39 | 74 04 —0 21 —0 18 +0.1 0.0 4.5 5.4 2.2
1555 | Bayonne, New Jersey... ... ............. 40 41 | 74 06 —0 19 —0 08 +0.1 0.0 4.5 5.4 2.2
16574 iGowanus Bayo. | ease. "E i-e 40 40 | 74 01 —0 19 —0 15 0.0 0.0 4.4 5.3 2.2
1559 | Governors Island ` `` SS -| 40 42| 74 01 —0 11 —0 06 0.0 0.0 4.4 5.3 2.2
1561 | New York (The Battery)......... ....... 40 42 | 74 01 Daily predictions 4.4 5.3 2.2
Hudson Rivert
1563 | Jersey City, Pa. RR. Ferry, N. J.......... 40 43,74 02] +0 07| +0 07 0.0 0.0 4.4 5.3 2.2
1565 | New York, Desbrosses Street |... |... 40 43 | 74 01 +0 10 +0 10 0.0 0.0 4.4 5.3 29
1567 | New York, Chelsea Docks -| 40 45 | 74 01 +0 17 +0 16 =0. 1 0.0 4.3 5.2 2.1
1569 | Hoboken, Castle Point, NI, 40 45 | 74 01 +0 17 +0 16 —0. 1 0.0 4.3 5.2 2.1
1571 | Weehawken, Days Point, NI, 40 46 | 74 01 +0 24 +0 23 —0.2 0.0 4.2 5.0 2.1
1573 | New York, Union Stock Yards... 40 47 | 74 00 +) 27 +0 26 —0. 2 0.0 4.2 5.0 2.1
1575 | New York, 130th Street. 40 49 | 73 58] +0 37 +0 35 —0.4 0.0 4.0 4.8 2.0
1577 | George Washington Bridge, 40. 51 1-73 .57 +0 46 +0 43 —0.5 0.0 3.9 4.6 1.9
1579 | Spuyten Duyvil, West of RR. bridge. `. 40 53 | 73 56 +0 58 +0 53 —0.6 0.0 3.8 4.5 1.9
16810 Yonkerse- see cw en 40 56 | 73 54 Í +1 09.| +1 10 —0.7 0.0 3.7 4.4 1.8
1583 |kDobbstkertyt S-98 1 ere 41 01|73 53] +1 29 | +1 40 —1.0 0.0 3.4 4.0 147
1585 “Tarrytown ee. 62 S03 Ee T 41 05 | 73 52] +1 45 | +1 54 —1.2 0.0 3.2 3.7 1.6
"Ratio.

{Values for the Hudson River above George Washington Bridge are based upon averages for the six months May to October, when
the fresh-water discharge is a minimum.

APPENDIX T: EXTRACTS FROM TIDE TABLES
TABLE 3.—HEIGHT OF TIDE AT ANY TIME

Time from the nearest high water or low water

.|h. Ih. m.|h. m.jh. m.
032 0 48

052

0 56

3

oz
->N

www NN BON O Nr
Ozna Wb
actio Sus

O DAD uuu (C) en MO es e P
w
GRD

35338 $233 $33 533 $253

Duration of rise or fall, see footnote

Correction to height

~

—-—-——000000o0000005000050000 00000 OO O0O OOOODOO:
q

e

AOA PPP PP RP RWWW WWWWW BO tO tO DO DO BO tO tà — Peer nmPoooo:
=

O 0 000000 Gali MOOD NM PPR IP W GO LI Q2 CO EO. BO DĪ tO DD ir DO:
<

TI GI GI BO DO DĪ DO DODOS GOOD GO NI NI RIO OO OY AUN Se CO CO LIDO BO BD = =O +
~<

(o U000-1 DD OTU ARAN N-===O O OO OO GO JANDO Ou LOCO NA AO:
=

DODAY NODO GOD OO IO 4 0» CONUS BO DIOS Octo: oo
=

LCUADAN CONTE VODNA Ge DOOM AW OO DANDO IO tO (oot
=

OG DUDA zl En Eat DOD DOD OOo Ot) ODO DD COMPLY OO CO bo"
=

e

p nme

* 25 5

ALAN Pre e

-
S 0 «5 oo oo

+

SONS ER Ra PAN HYNES IH Oo o8

ĪV D0 pt pt >

5
0
5
0
5
0
5
0
5
0
5
0
.5
0
5
0
5
0
5
0
5
0
5
0
5
0

Range of tide, sec footnote
esses coso EE 22000 95000 SOS POSO POSO M
esposo» cocos Sono ocooooocooooooooooooooooooon
OOoOooOo000o00o00000000000000500000co000o0oo0o0oooo0nu

OOoOOoOoo0ooococooooooooooooooooooooooooooooon
Pe pe mmm omnmne5oooooooooooooooooooooooooooohnhm
Dee ee epee unmmmmmpmomooooooopooooooooooooorn

NNNNN IDID EO IO NO. Pee ee See S DLL OLG. ODDS O00 000 ooooom

LD DO DO RO DO DO LO BO tO tO NNN Hipi pi im Im m E RRR mH MÁÍÓGmnROoOooocoooo
C» wa GO BO DO D DOWNY ONNAN OO to to CO DOVON O) OO da de GO GO DO Pi m
$0 gogo go NNNNN VNUNNN MIO IHR IH Ho 60000 ooooot
Cote C DOOM Ch MASNNY DO GO00 ADA BOB DO 00-1-10 0: Ke GI DO O m”
ERR po go co GO go o to £O. PLN NNNNN NN RRA Pee 0000 POSO
ro CEO sl OO ou CN Fans EPO, Gabi DO 000 Ou ot DOD Oria D bv ="
Tea Ra PPP Ro GO 00 £2 G0 £O. G9 CO IO IO PPNP I^ IIO LOS POPO
CDMA ANO OCH RO DO O 000» Ovi DD OD (CO 00 Ch NODO Oo DO
ANNAN DA A hu Par aw GO 00 CO CO CO. CO NO IO IO NN LO O00 0o
DDR DARAN mies A WHONN NN He OO ooo
NNNNN PPD cmo Dom mea PNNNN Neer r0 0 0 63
(00909000 NONNA PPPM incu RR RR Coco PUNO IIS II OSOS
esu ka MANO AOANHODO GARO NI Go DO 00 KONI NODO FON b”

popp par AUS S

—

Obtain from the predictions the high water and low water, one of which is before and the other
after the time for which the height is required. The difference between the times of occurrence of
these tides is the duration of rise or fall, and the difference between their heigbts is the range of tide
for the above table. Find the difference between the nearest high or low water and the time for

hi ight is required. 3 f
Ese table with the duration of rise or fall, printed in heavy-faced type, which most nearly
agrees with the actual value, and on that horizontal line find the time from the nearest high or low
water which agrees most nearly with the corresponding actual difference. The correction sought is
in the column directly below, on the line with the range of tide.

When the nearest tide is high water, subtract the correction.

When the nearest tide is low water, add the correction.

OPUNO OO Ch to C 06 ANDA t9 Oo GO t9. CO Oo zn Eo OO. PRNO Cn to O0 01 tóc UO On to^

1131

APPENDIX U
EXTRACTS FROM TIDAL CURRENT TABLES

THE NARROWS, NEW YORK HARBOR, N. Y., 1958

MAXIMUM
CURRENT

SLACK
WATER

Dar

Time Vel.

Time

160° true.

e —ebb, direction

340° true.

f — flood, direction

FEBRUARY

MAXIMUM

CURRENT

MAXIMUM SLACK
CURRENT | Day WATER

SLACK
WATER

Day

Time Vel.

Time

Vel.

Time

Time

JANUARY

MAXIMUM
CURRENT

SLACK
WATER

Day

Time Vel.

Time

o

Time meridian 75

1200 is noon.

0000 is midnight.

W.

1132

No.

1001
1003
1005
1007
1009

1011
1013
1015
1017
1019

1021
1023
1025
1027
1029

1031
1033
1035
1037
1039

1041
1043
1045
1047
1049
1051

1053
1055
1057
1059
1061
1063

1065
1067
1069

1071

1073
1075
1077
1079
1081

1083
1085

APPENDIX U: EXTRACTS FROM TIDAL CURRENT TABLES

TABLE 2.—CURRENT DIFFERENCES AND OTHER CONSTANTS

1133

MAXIMUM CURRENTS

POSITION TIME DIF- | VELOCITY
FERENCES RATIOS
PLACE Flood Ebb

Maxi- | Maxi- | Maxi- | Direc- 5 E d

Lat. Long. Slack mum | mum | mum tion rae E gs

water | current | flood | ebb | (true) | veloc- | (true) | veloc-

ity ity
5 les O KN O deg. | knots | deg. | knots
Hupson RIVER, Midchannel ! N: W. on THE NARROWS, p. 52
Time meridian, 75° W.
The Battery, northwest ot... 40 43 | 74 0297 +1 30 | +1 35 0.9 152 15 1.5 195 2.3
Desbrosses Streeti `T ac N tn el 40 43 | 74 01 | +1 35| +1 40 0.9 182 10 1,5) |5 2 ce 2.3
Cholon Dooks E MA E LI 40 45 | 74 OL} +1 30 | +1 40 0.9 132 10 1.6 2.3
Forty-second En AAA MESA E, 40 46 | 74 00] +1 35|+1 45 1.0 112 30 Um 2.3
Ninety-sixth Street_ 2-3 = nodos ee 40 48 | 73 59] +1 40 | +1 50 1.0 1.2 30 Max 2.3
Grants Tomb, Ue Ra 1. — 3 40 49 | 73 58] +1 45 | +1 55 0.9 1.2 25 1:6: | ee 2.3
George Washington Bridge. 40 51 | 73 587] +1 45 | +2 00 | 0.9 ital 20 16| 200 2.2
SpnyteniDuyyili-— EE 40 53 | 73 56] +2 00 | +2 10 0.9 171 20 IO AA 2.1
A IA A Enn 40 54 | 73 55] +2 05 | +2 20 0.8 1.0 15 1.4 200 2.0
DODDS Fary Cue a 41 01] 73 531 +2 25| +2 40 | 0.8| 0.9 10 ARSE es dk
Tarrytown AC A E MUT 41 05 | 73 53] +2 40 | +2 55 0.6 0.8 0 E 6s i 1.5
Ossining 772-8...) 9. +. -| 41 10/73 54] +2 55| +3 10 0.5 0.7 320 0:9 3-2 1.8
Haverstraw -| 41 12|73 577 +3 05| +3 15 0.5 HES 335 ONS E 1.3
PeskskHE m-i RO 8 Dele o. 41 17 | 78 57| +3 20 | +3 35 0.5 0.6 0 0.83 mer em 1.2
Bear Mountain Bridge. ................... 41 19 | 73 59] +3 25 | +3 0.5 0.6 0 0:8 |. --2 1.1
Highland Falls ege ere -| 41 22 | 73 58 | +3 35 | +3 0.6 0.6 5 1.0 185 1.2
West Point, off Duck Island -| 41 24 | 73 57 | +3 40 | +3 55 0.5 0.6 10 à ee lea ka
NOWDUIEH e EE 41 30 | 74 00] +3 55 | +4 15 0.5 0.6 5 0:97] e 1.1
[New ani A es e 41 35 | 73 57] +4 10 | +4 25 0.6 0.6 5 precem (ei)
Eemer keete EE E 41 42 | 73 57] +4 25 | +4 45 0.6 0.6 5 ¡AA Se 1.2
Hyde Park: Pe eaten ds adas 41 47 | 73 57] +4 35 | +4 55 0.7 0:7 5 SZ) ESTE 1.3
Kingston Point ? 41 56 | 73 57] +5 00 | +5 15 0.8 0.8 5 MA | eee 1.6
IBarrytown-e eg H 42 00 |73 56 1 +5 20 | +5 25 0.8 0.9 10 154 A IE
Saugertiesaceesec ei seat EE 3 42 04 | 73 56$ +5 35 | +5 40 0.9 1.0 0 AKB == =< 1.9
Silver Points ss S +. + 42 09 | 73 54] +5 55 | +6 00 0.9 1:0 30 1:5) SA 2.0
@atskill Eds: deen te de oe 42 13 | 73 51 | +6 10 | +6 0.9 1.0 355 A E 2.0
13: LO Bes S S e EN MEE Í 42 15 | 73 48] +6 20 | +6 0.9 1.0 30 VOL. 2.0
A EA O AA 42 21 |73 47) +6 50 | +6 50 0.9 0.9 350 15.64 sā 1.8
NewjBaltimore--L-—————-— oe see 42 27 | 73 47§ +7 10 | +7 05 0.8 0.8 355 14347 1.5
Castleton-on-Hudson. ...-........-.--.-..- 42 32 | 73 461 +7 25 | +7 20 0.5 0.6 15 Or EEES 1.2
IN O A ene a eee 42 39 | 73 45] +7 35| +7 40 0. 2 0.4 20 [US | ee 0.8
Troy (below the locks). .-------.--2--2-.— 491.44 MEA T X 5 AA A (3) (3) 190 0.7
NEW YORK HARBOR, Lower Bay
Pakso Hook Channel 2-12. e 40 28 | 74 00] —1 45 | —1 30 kal 0.7 320 1.8 135 1.4
Sandy Hook and South Channels (junction).| 40 29 | 73 59| —1 20 | —1 20 0.8 300 1.3 115 E
Sandy Hook Channel, off Sandy Hook
Point ASA a A. eee 40 29 | 74 01 $ —1 55 —1 55 1:1 0.9 255 1.8 55 1.
Sandy Hook Point, 2 miles W. of (channel).| 40 29 | 74 04| —1 45 | —1 50 0.3 265 0.6 85 0.6
New Dorp Beach, 114 miles south of......- 40 32 | 74 06] —4 25 | —3 55 0.2 0.2 225 0.4 30 0.5
New Dorp Beach, 1% miles SE. of........- 40 33 | 74 04 (4) (4) 0.3 03 Bassas 0:59 e 0.5
Hoffman Island, 1⁄4 mile west of. .........- 40 35 | 74 04 (5) (5) 0.5 0.4 20 0.9 210 0.8
Rockaway Inlet Jetty, 1 mile SW. of. ....- 40 32 | 73 57 Í —1 50|-—1 55 0.7 0.7 285 1:2 140 1.4
Coney Island Channel, west end. ........- 40 34 | 74 00| —0 50 | —0 45 0.6 0.6 295 11 100 172
SANDY Hook Bav?

Highlands Bridge, Shrewsbury River------ 40 24 | 73 59 | +0 25 | +0 25 155 1,3 170 PE es, 2.5
Seabright Bridge, Shrewsbury River. ----- 40 22173 581 +0 55 | +1 00 0.8 0.9 185 IA e 127

1 The values for the Hudson River are for the summer months, when the fresh-water discharge is a minimum.

2 In Roundout Creek entrance between lights, eddies on the flood make navigation difficult.

on the ebb.
3 Current does not flood.

4 Current is rotary, turning clockwise.

flood; SE. 114 hours after ““Slack, ebb begins”; and SW. 2 hours after maximum ebb.
5 Flood begins, —1h 45m; maximum flood, —1h 50m; ebb begins, —0h 15»; maximum ebb, —0 50m.
6 In Sandy Hook Bay (except in southern extremity) the current is weak.

Little difficulty will be experienced

It flows NW. at time of “Slack, flood begins” at The Narrows; NE. 1 hour after maximum

EXTRACTS FROM TIDAL CURRENT TABLES

APPENDIX U:

1134

CURRENT AT ANY TIME

OF

3.—VELOCITY

TABLE

Interval between slack and maximum current

No
“SS

Ns
Hdd

N +
“Ss

mie
“Ss

mu
“ss

v~
ss
ERS

00

eurn peirsep pu? ADB[S 199194 [8 AJ19JUT

in c r-
SS

oo t-
ooo

or
eco

«O r- oo
SSS

RI 00
ooo

00 >
SSS

00 o0 3
Ses

OAS
oor

ooo
os

DOS
on

oo
ri

o
m

'

i

1

1

1

[
1o
Ia
poa
TT
t
EMI
Wb
(H
d'r
nu
CI
ips
Tm
TET
TNT
ew
DIN
[ice

SRS
NNN

ooo
Son

noo
e ud

ooo
rr

ooo
rr

oo
no

o
=

'
[
1
1
1
1
1
1
[
1
1
D
1
1
1
1
[
1
1
1
1
1
i
1
1
1
1
i
|
D
'
1
1
1
D
i
1
1
1
1
H
1
1
i
[
1
'
D
1
1
1
'
'
D
i
'
D
1
D
1

1
D
1
1
1
D
Tos. al
Me il
ën
Eu
üe ^d
TE
ey)
(MR)
ihe a
(671
(EN
d. 2
Iren
TU
le 1%
nn
(E
T
NA
(US
(te
Ir za
VEER
(EE
Bag
e "o
HAR]
D aw)
MER
A
WAS
D
va
how
"Y
b-
[m
»-
poa
Dou
K Í
w
D m
Isi
Kn
EZ
VC
(JE)

SS SR
= <

m OD OD

=

TABLE B

Interval between slack and maximum current

ERS SRS SRS
Loo NAN SH A A

eur) pelrsep PUB xoe[s ueoAjeq [BA J9JOT

pe Cod Canal, Hell Gate, Chesapeake and Delaware Canal and all stations in |

places except those listed below for Table B.
Table 2 which are referred to them.

Use Table A for all
Use Table B for Ca

, and enter the top of !
d multiply the maxi-

ed, and enter the side of
be the approximate velocity at the time desired.

y agrees with this value.

ck water and the time and velocity of maximum current
g to the above two intervals an

, one of which is immediately before and the other after the time for which the velocity
e above slack and the time desir

t nearly agrees with this value.
st nearl
pondin

'The result will

2. Find the interval of time between the above slack and maximum current
A or B with the interval which mo
in the table, the factor corres

1. From predictions find the time of sla
Table A or B with the interval which mos

(flood or ebb)
is desired.
3. Find the interval of time between th

Table

4, Find,
mum velocity by this factor.

Northboung

APPENDIX U: EXTRACTS FROM TIDAL CURRENT TABLES 1135

CURRENT DIAGRAM NEW YORK HARBOR (via Ambrose Channel)
Referred to predicted times of slack water at The Narrows.

HOURS BEFORE | HOURS AFTER |HRS. BEI HOURS AFTER | HOURS BEFORE | HOURS AFTER
FLOOD BEGINS | FLOOD BEGINS |EBB BEGINS| EBB BEGINS FLOOD BEGINS FLOOD BEGINS
AT AT AT THE AT AT AT

THE NARROWS | THE NARROWS | NARROWS | THE NARROWS | THE NARROWS | THE NARROWS

spuvren au. 13? 2" 1^ 0” 1^ 2^g^2^.1^-. 0^ 1^:2^ 3^ gh 2^ 1^ o^ 1^ 2^.3^

264—121 1—41:51—90-0-4-r 0-0 ——1:5—4L2:11—41-5 1— 0-0
GEORGE WASHINGTON |
BRIDGE
pye 42.21 1. .0 —1:6 =S 6j—0:0
GRANTS TOMB
22-—2.3: -0— 1-6 — cmm
WEST 96th ST. |
20——23 1-61——2-3—— 1:6-1— 0-0
SPEEDLINES New York Harbor W. 42nd ST., PIER 83 |
m |
CHELSEA DOCKS 18 |4—2:3——34-6—1-0-0—1:1—1-6—1-1-40-0 6] —2:33—16——00
m | |
CANAL ST., PIER 34 Ley | S | |
2:3 1-6—]10-0]— 1:11 1:5 141-0 |—1-64—2:3-1—1-6 0-0
THE BATTERY | to j
M |
o STATUE OF LIBERTY m H
e 14 2:44 7--0:0—13-41.6—41:340:0 —}1-7 V 0-0 -1-1
S / a j
E |
5 | m |
a ROBBINS REEF LT.
125 41-1; 9-0 40:9 -11-3 4-0:9 —0-0--1-1 Gy 16—11 0:0 -}0-9-
| M
10 1 4 j—0:0—]1-24-17-11-21-070 —— 1:4 Hop 1:4 0-0-1-2— 1
THE NARROWS |
i !
EES 0 +1-4}-1-0+- 0-0 — 1-3 —]-81— 1-3--0-0 —1:0-1- 1:4
7 B 9 1011 12 13 14 15 15 14 13/12 11 10 9 8 7 6 OE SLAND 8 1:3 T OO ERD ET m d 2 +
KNOTS KNOTS | |
|
6 1:1— oo 1:7—1.0-- 1-7 40:07 — 1:1-—— 1:6 11—]0:0r— 1-7
WEST BANK LT. | | e
411 004 1:11—4-5 1:3 —0:0 4— 1-1 + 1:6 —1:14— 0:0 1:11 1
ROMER SHOAL LIGHT | | |
2i—1-41—0«0 41-1} 1-6 —1:1 —0:0 — 1-4 EZE 0-0 — 111.6
| | |
SEN SC 1-6 | 00 12 | 17 112 oo| 1-6 23 o9. Waj 17

1:6 ©
h 4h ghghgh 4h ph 1h5h qh 4h oh 4h gh qh 5h 4h
SAO 5n30209:09102 3199312" 1409005 243
HOURS BEFORE | HOURS AFTER |HRS.BEFORE| HOURS AFTER | HOURS BEFORE | HOURS AFTER
FLOOD BEGINS | FLOOD BEGINS |EBB BEGINS] EBB BEGINS | FLOOD BEGINS | FLOOD BEGINS
AT AT AT THE AT AT AT
THE NARROWS | THE NARROWS | NARROWS | THE NARROWS | THE NARROWS | THE NARROWS

OCT.-MAR.

APPENDIX V

EXTRACTS FROM NAUTICAL ALMANAC
ALTITUDE CORRECTION TABLES 10°-90°—SUN, STARS, PLANETS

SUN APR.-SEPT.

STARS AND PLANETS

App. Lower Upper

Alt.

Limb Limb

App. Lower Upper
Alt. Limb Limb

-22-7
+10:9 -22-6
+II:O — 22-5

+11 522"
I 4

+ 11:2 =22-3

+11-3 =22-2
+11:4 -22:1
+II-§ -22:0
+II:6-2r:
0 9

+12°5 -21-
8 5 -21-0

+12:6 - 20-9
+12-7 - 20-8

+12-8 - 20-7
2

+12:9 - 20-6
+13:0 -20:5
+I3:I -20:4
+13:2 -20:3
+13:3 -20:2
+13:4 - 20:1
+13:5 -20-0
* 3:6 - 19:9
+13:7 -19:8
+13:8 - 19:7
+13:9 - 19:6
+14:0 - 19:5

+I4:I - 19:
g uod

+14:2 - 19:3
+14:3 - 19:2

a +14:4 - 19:1

+14:5 - 19:0
+14:6 - 18-9
+14:7 -18-8
+14:8 - 18-7
+14:9 -18:6
+I5:0-18:5
+15:1 - 1844
+ 152 —18:3
*IS:3-18:2
+15:4 - 18:1

+15:9 - 17:6
+16:0 -17:5

+16:1 -17:
En T4

1136

App. Alt.

a +10:6 -22:4
+10°7 -22:3
03
15 +10-8 -22:2
+IO:9 -22-1
27
+II-O-22:0
+II:1 -21:9
54
+II:2 -21:8
o: +11
:3 -21:7
23 3 7
38 +11:4 -21-6
54 IIS 2105
+11-6 -214
ils 20-3
+11-8 -21:2
HTIO -21:1

0
5 +12:0-21-0

24
+12:1 -20:9
e +12:2 -20:8
30 +12:3 -20:7
+12:4 - 20-6
5 +12:5 —20:5
+12:6 - 20:4
Tt 12:7 -20:3
+12:8 - 20-2
+12:9 —20:1
+13:0 -20-0
+I3:I - 19:9
+I3:2 - 19:8
+13:3 -19-7
+13:4 - 19:6
+13°5 - 19:5
13:6 - 19:4
+13:7 -19:3
sr +138 -19:2
+13:9 - 19:1
53 +14:0 - 19:0
00
+14:1 - 18:9
+14:2 - 18:8
+14:3 -18-7
+14:4 - 18-6
ei +14:5 - 18:5
17 t 14:6 -18-4
+14:7 -18:3
26
t 14:8 -18.2
+14:9 - 18:1
+15:0 -18-0
+15:I -17:9
15:02 =17:8
ee
51 +15:4 -17:6
15:55 1705
+I5-:6-17:4
Mt
+15:8 -17-2
+15:9 -17:1

28

14

15

13

App. Additional
Corr®

Jan. I-Jan. 10

+0:5
+0:6
+0:7

Jan. 11-Feb. 14

+0:6
+0:7

12
+0:8

22

Feb. 15—Feb. 21

o
D

+0:5
+0:6
+0:7

+0:3
+0:2
+0-1

= Apparent altitude = Sextant altitude corrected for index error and dip.

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC 1137

ALTITUDE CORRECTION TABLES 0-10” —SUN, STARS, PLANETS

OCT.-MAR. SUN APR.-SEPT.

OCT.-MAR. SUN APR.-SEPT.
ARP: STARS

Lower Upper | Lower uU PLANE

ar E) ect

36 299
40 3:8 297
45 40 295
50 42 293
44 291
45 -29:0
05 47 288
10 49 286
I5 St 284
20 KE 28:3

Lower U
Limb Limb

+ 3I -29:9
3:3 297
RE CO
37 293
3:9 291
4I 28-9

+ 4:3 -28-7
45 28-5
46 28-4
48 28-2
5:0 28-0

25 5:4 281 S:I 279
430 | + 56 -279 5:3 -277
35 57 278 ss 275
40 $:9 27-6 5:6 27-4
45 6:0 275 5:8 272
50 6:2 273 59 21
4 55 6:3 2732. 6:0 270
5 00 + 6:4 -27:1 6:2 -26:8
05 6:6 269 6:3 26-7
I0 6:7 268 6:4 266
I5 6:8 267 6.6 26-4
20 6:9 266 6.7 26-3

71 264 6:8 26.2

8:0 25-0
8-1 249
8:3 247
8:5 245
+ 8:6 -24:4
8:8 242
9:0 24:0
9:1 239
9:2 23:8
9:4 236
KE EK
9:6 23:4
9:7 233
9:8 23:2
10:0 23:0
IO:I 229

8-2 253
8:4 251
8.6 249
8:7 248

7:2 -26-3 | + 6:9 -26-1

35 T3 262 70 260
40 T4 261 72 258 E
45 TS 260 14) ED 8:
50 T6 259 T4 256 8-
77 358 7S 2355 8
+ 7:8 -25:7 | 76 254 | — 8-
8-0 255 78 25-2 8:
8
7
7

GA vi HWA AJ OO

+ 8:9 -24:6
9:1 244
9:2 243
93 242
9:5 240
9:6 239

+ 9:7 -23:8

9:9 23:6
10:0 235
IOI 234
10:2 23:3
IO:3 232

+10:2 -22:8
10:3 22-7
10:4 226
10:5 225
10:6 22-4

10:6 224

+10:4 -23:1
10:§ 23:0
10:6 22-9
10:7 22:8

10-8 227

IO:9 22.6

+II:O -22:5 +10°7 -22:3

Additional corrections for temperature and pressure are given on the following page.
For bubble sextant observations ignore dip and use the star corrections for Sun, planets, and stars.

1138 APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

ALTITUDE CORRECTION TABLES—ADDITIONAL CORRECTIONS
ADDITIONAL REFRACTION CORRECTIONS FOR NON-STANDARD CONDITIONS

Temperature

Pressure in millibars
SIYIUL ur INSS d

wc OU AN SBAWWN NH MOO.

bai ba
"o

bá ba
on

Yu wv
Lët CG Lo e

>
o

MIS is SEU, with EE temperature and pressure to find a zone letter; using as arguments
er and apparent altitude (sextant altitude corrected for di ion i
j ter a k ip), a correction is taken fi h
This correction is to be applied to th i i iti | dr
e sextant altitude in addition to the correcti iti
ext ions for standard condit
(for the Sun, planets and stars from the inside front cover and for the Moon from the inside back Ke? +$

dā

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC 1139
CALENDAR, 1958
DAYS OF THE WEEK AND DAYS OF THE YEAR
3n Ex
„ | MAR. | APR. MAY 2:24] JULY Jas SEPT. OCT. | NOV. DEC.
S ni"
Monthy 8 dil ee Sy du [Se Elan O To E Senn e ye
e ren p ENSEM NT X Tcu Y EY
de AAA CI E EA LIA ALA ALEA Re
I |W. I|S. 32|S. 6o|Tu. 91|Th. 121 /Ð. rs2| Tu. 182| F. 21 jk
J . ? ; 3; M. 244| W. 274|S. 305, M. 33
2 Th. 2/8. 33| 3. 61|W. 92|F. 122|M. 153|W. 183|S. 214|Tu.245 | Th. 275 3. 306 Tu. 336
3|F. 3M. 34| M. 62| Th. 93 S. I23| Tu. 154| Th. 184| $. 215| W. 246|F. 276|M. 307 W. 337
4 S. 4 Tu 35|Tu.63|F. 94|8. 124|W. 155|F. 185|M. 216| Th. 247| S. 277| Tu.308| Th. 338
5/3. S|W. 36 W. 64|S. 95 M. 125|Th.156|S. 186|Tu.217|F. 248 $. 278|W. 309 F. 339
SIM 6|Th.37| Th.6s| $. 96|Tu.126|F. 157 š. 187 W. 218/S. 249|M
; > i A . 249 M. 279| Th. 310, S. 340
7|Tu. 7|F. 38|F. 66¡M. 97 W. 127|S. 158) M. 188| Th.219| 3. 250 Tu.280|F. 31II|& 341
8|W. 8 S. 39 S. 67| Tu. 98 Th. 128| €. 159|Tu.189|F. 220|M. 251| W. 281|S. 312| M. 342
9 Th. als 40|. 68|W. 99|F. 1I29| M. 160| W. 190| S. 221] Tu.252| Th.282 $. 313 | Tu. 343
10 |F. ro, M. 41|M. 69| Th. 100, S. 130| Tu. 161 | Th. 191 | š. 222|W. 253 |F. 283|M. 314| W. 344
II |S. i1 Tu.42| Tu. 7o|F. ror | €. 131/W. 162 F. 192 M. 223| Th.254| S. 284| Tu.315| Th. 345
I2 |$. I2; W. 43, W. 71|S. 102 M. 132| Th. 163, S. 193| Tu.224|F. 255| $. 285| W. 316|F. 346
13 | M. 13| Th. 44, Th. 72| $. 103|Tu.133|F. 164| €. 194 W. 225|S. 256|M. 286| Th.317|S. 347
I4 |Tu.14| F. 45|F. 73|M. 104| W. 134|S. 165|M. 195 Th.226| š. 257| Tu.287|F. 318 8. 348
15 |W. 15|S. 46|S. 74|Tu.105| Th. 135 | &. 166| Tu. 196|F. 227| M. 258, W. 288 S. 319 M. 349
16 | Th. 16| $. 47| 8. 75, W. 106|F. 136| M. 167|W. 197 S. 228 Tu.259| Th. 289 $. 320|Tu. 350
17 |F. 17| M. 48. M. 76| Th. 107, S. 137| Tu. 168| Th. 198 | $. 229| W. 260 | F. 290| M. 321 W. 351
18 S. 18|Tu.49|Tu.77|F. 108| 8. 138| W. 169|F. 199| M. 230|Th.261|S. 291|Tu.322|Th. 352
I9 | 8. I9| W. so| W. 78|S. 109| M. 139 Th. 170|S. 200 Tu.231|F. 262 Ð. 292| W. 323|F. 353
20 |M. 20| Th. st| Th. 79| & rro| Tu. 140|F. 171/35. 201| W. 232, S. 263|M. 293| Th. 324| S. 354
2I |Tu.21|F. s2|F. 80| M. 111 | W. 1i41|S. 172|M. 202| Th.233| & 264| Tu.294|E. 325 355
22 |W. 22|S. s3|S. 81|Tu.112| Th. 142| Ð. 173, Tu.203|F. 234| M. 265 | W. 295 S. 326 | M. 356
23 | Th.23| $. 54| &. 82, W. 113 F. 143| M. 174| W. 204 S. 235|Tu.266|Th.296|s. 327| Tu. 357
24 |F. 24| M. 55| M. 83| Th. r14| S. r44| Tu. 175 | Th. 205 | $. 236 | W. 267 F. 297|M. 328 W. 358
25 |S. 25| Tu.s6| Tu.84|F. 115) š. 145¡W. 176|F. 206 M. 237| Th. 268| S. 298| Tu. 329| Th. 359
26 5. 26 57|W. 85 S. 116|M. 146| Th. 177|S 207 Tu.238|F. 269 $. 299 W. 330 F. 360
27 |M. 27| Th. 58 | Th. 86| $. 117| Tu. 147| F. 178| &. 208| W. 239|S. 270 M. 3oo| Th. 331|S. 361
28 |Tu.28|F. 59|F. 87|M. 118 | W. 148|S. 179|M. 209| Th.240| $. 271|Tu.301|F. 332| $. 362
29 | W. 29 S. 88|Tu.119| Th. 149! š. 180| Tu.210| F. 241, M. 272| W. 302/ S. 333|M. 363
30 | Th. 30 $. 89|W. 120|F. 150|M. 181| W. 211,S. 242|Tu.273| Th. 303 | 3. 334] Tu. 364
31 |F. 31| M. 90 SST Th.212| $. 243| F. 304 W. 365
ECLIPSES
There will be three eclipses, two of the Sun and one of the Moon.
The maximum duration of the annular

I. An Annular Eclipse of the Sun, April 19. See map on page 6.

phase is 7" 073.

II. A Partial Eclipse of the Moon, May 3.
maximum eclipse 0:02 of the Moon’s diameter is obscured.

III. A Total Eclipse of the Sun, October 12.

ISS plies

The eclipse begins at 12" oo" and ends at 12" 26"; at the time of

It is visible from the western part of North America,
the Pacific Ocean, eastern Asia, the south-eastern part of the Indian Ocean, Australia, and Antarctica.

See map on page 7. The maximum duration of the total phase

1140 APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

1958 MAY 31, JUNE I, 2 (SAT., SUN., MON.)

ARIES VENUS MARS JUPITER
K A Be G.

UE keen Name

o

220 359 N 9 01:6| 251 Fees S73 270 "9 | Acamar
2235.95", 02-6 | 266 59:6 61 526 217 p *9 | Achernar
250 354 03-6 | 282 00-4 *6: 76.552 21:6 i "9 | Acrux
265352 < = 04-61297-01:20 5291 19105 7:8 srl '5 + + 509 | Adhara
280 34-9 05:5 | 312 02:0 21107 00:4 21% g Aldebaran
295 346 06:5 | 327 028 *5 | 122 03-0 215 R 50:8

310 34:4 N 9 07:5| 342 03-6 S "9| 137 056 S 7 21:5| 75 19:5 S21 508 | Alioth

325 341 08:5| 357 04-4 Ë b 214 | 90 22:2 50:8 | Alkaid

340 33:9 09.5! 12 052 : E 21:4 |105 24:8 508 | Al Na'ir

2359.3208 LOSE 27506:0 089.9 "4 ++ 213|120 275 ++ 508 | Alnilam
10 33:4 115| 42 068 R $ 21:3 | 135 301 50:8 | Alphard
25155» 12:5 || 57.07:6 $ E 213 |150 328 508

40328 N 9134| 72 084 S S S 7.21:2|165 354 S21 508 | Alphecca
144| 87 09-2 á 1 *2|180 381 50:8 | Alpheratz
15:4 | 102 10-0 2 ( 1/195 40-7 508 | Altair
* 164|117 108 ++ 44 9 ++ 211/210 4*4 ++ 503] Ankaa
132 115 $ D *1 | 225 460 50:8 | Antares
147 123 : ` :0|240 48-7 507

dE : ESA 2551512 S 2T 30y Arcturus
177139 B y 20-9 8 Atria

192 14:7 : $ 20-9 ú *7 | Avior
207415:5 m AO 209 3 ++ 50:7 | Bellatrix
222 163 : i 20:8 ` ‘7 | Betelgeuse
23717:

E o)

rīts mr US a
DOLIDO WSA

<PorzCAH>vw
o
VD PO Fäi zl P zl

uud BORDHS PEGNAIN HWOBRSDVJÓVREARJ PJVOVWDH PODOGE órnm-mdév|óiRounóo

Canopus
Capella
Deneb
Denebola
Diphda

138 07:8 S - Dubhe
153 10:4 d Elnath
168 13-0 E *6 | Eltanin
183 156 .. QUSS Enif

198 18:2 Ë È Fomalhaut
213 20:

228 23:
243 26:
258 28:
273131:
288 33:
303 36:

318 38:

I
3.
6:
B.
1:
3
6
8
0
3
5
8
0
3.
5.
ER
0
e
5
8.
0:
3.

un

166 39-1 S21 50:6 | Gacrux
181 41:8 50-6 | Gienah
196 44:4 50:6 | Hadar
211 47:1 + + 50:6 | Hamal
226 49:7 50:6 | Kaus Aust.
241 52-4 50-6

256 55-0 S21 50*6 | Kochab
271 577 50-6 | Markab
287 00-4 50-6 | Menkar
302 02-0 ++ 50:5 | Menkent
317 05:7 50:5 | Miaplacidus

130 24.9 N

145 246 333 41:

160 24:3 348 44:

175240 .- 3

190 23:8 s i 3| 18 49
237 36:3 6 T3254 332 08:3 50:5

220 232 N 9 488 347 11:0 S21 50:5 | Mirfak
49:8 + Ó d 2 136 50:5 | Nunki
50-8 . E 17 163 50:5 | Peacock
++ 518 5 eu 19 "2 ** 197| 32189 ++ 50-5] Pollux
52:8 E D d 7| 47 216 50:5 | Procyon
53:7 . . . 6| 62243 50:5

547 77 26:9 S21 50'5 | Rasalhagué

D : . < "Bi 92/290 50:5 | Regulus

567 E ; H "5 | 107 322 50:5 | Rigel
57:06 LITI 7 ++ 195|122 349 .. 50-5] Rigil Kent.

58:6 ? $ K 41137 375 50:5 | Sabik

59:6 e 2 s 41152 402 50:4

00-6 e H 167 42:8 S21 504 | Schedar

01:5 E d d 3 | 182 45:5 50-4 | Shaula
02:5 . D E 31197 482 50-4 | Sirius

+ 035 "ace 11s 2 +» 193|212 508 + + 504 | Spica
04.5 k E ^ "2 | 227 53:5 50-4 | Suhail
05:4 | 147 507 K : 2 | 242 56:1 50:4

06:4 | 162 51:5S 3 09: D 11|257 59:8 S21 204 Vega
07:4 |177 52:3 s " 1| 273 014 Zuben'ubi
08-4 |192 5311 : P "1 | 288 04-1

* 09:3 | 207 539 +. 07. "7 ** 19:0|303 068 --

10:3 | 222 547 +8, 2 0) 318 09:4 E Venus
11:3 | 237 55:5 D ` CONS Santee E Mars
Jupiter

Saturn

DEA O BOR OHS bhv
[^]

+
o
N
w
wW
`o

N
o
a
w
>
M
Ww
>
HOD BHD gqg]wrmogow

Lo

[94]
un

un
n

Mer. Pass.

172 467
176 348
149 461
328 478

84 33:3

137 17:2
14 19%
314 58:6
61
88

81 06:6
137 50.9

SHA

331 31 4
3 19:6
158 54-0
97 09:0

`

ZIM NN
Lab Cup P
cOn JO o
PA LD PA PM
DUNN OD
unm u zl PM

nnnzz

eU
DOr IOS
NF Own
BNP DIES
DON

nnzzz
EI NN
PROD
Ns Un Un
RAMUS:
Buu

ZZNNZ

Wor
“OOOO
NFR Mm UIP
PONIA
Orono

nzzzu
Hb BU)
DPN
H bouts
MORINA
Go U» do uo

uzzzz
N UNG
NOD DH Or
Un 4» n9 V9 Un
SEO OD
BOCW=S

nznunun
WIN Run
Ps Lui EN JO
n9 E E Iu
CODICI
NOC VH

nnzzz
DW Hu
OTLARA
wem
DEOD
VE Gs c Lu

zzzunvuz

NUD P
un 000.0
HONNA
uro
DC 0D 00 -

mnnnzz
U!' OMON
i

HO HH
SNOW
Horn

OMmnnz
> + w UN
MODO
FUI O
SP ORD
NO Yu

nz
alo
Sue
us
38165
: Ne

N
ooasos-

Ub
Uu oo

<rozcu «»g2caAa»o
Lad 1
N N

«X»0zozx
m
m

G.H.A.

H

165 36:3

180 36:3
195 36:2
210 361
225 36:0
240 35:9
255 358

270 357
285 356
300 35:5
315 354
330 35:3
345 353

0352
LD 235b
30 35:0

60 34:8
75 347

90 346
105 345
120 344
135 34:3
150 342
165 341

180 34:0
195 33:9

225 338
240 337
255 336

270 335
285 33:4
300 33:3
315.352
330 331
345 33:0

0:32:9
15 32:8
301327

60 32:5
75 324

90 323
105 32:2
120 32:1

150 319
165 318

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC
1958 MAY 31, JUNE |, 2 (SAT., SUN., MON.)
Twilight

hom hom
es | c

Civil

Moonrise

45 349 --

210 33:9

45 326 >>

135 32:07: :

568

N21 57:2 | 12 246 5-7 S17 263 5-1
575 | 26493 57 17314 49
579 | 41140 56 17 363 4-8
* 582 | 55386 5-7 17 411 4-7
58:6 | 70033 56 17458 4-6
58:9 | 84279 5.7 17504 44
N21 593 | 98 526 5-6 S17 548 43
21596 | 113 172 6 17591 4-2 Twilight
22 00:0 | 127 418 se 18033 4-1 Civil (| Naut
+ 00:3 | 142 064 5-6 18074 3-9 =
00:7 | 156 31:0 5:6 18113 3-8
01:0 | 170 556 56 18151 3-7
N22 01:4 | 185 202 5:6 S18 188 3-6
01:7 | 199 448 5-6 18224 3-4
02:0 | 214 094 56 18258 3-3
02-4 | 228 34:0 5:5 18291 3-2
027 | 242 58:5 6 18323 3-1
03:1 | 257 231 5-6 18 354 2-9
N22 024 | 271 477 5:6 S18 38:3 2-8
037 | 286 123 5:7 18411 2-6
04:1 | 300 37:0 5-6 18 43:7 2-6
+ 044 | 315 01:6 56 18 463 2-4
048 | 329 26:2 57 18 487 2-3
05:1 | 343 50:9 18 51:0 2-
054 | 358 155 5-7 $18 531 2-1
058 | 12 40:2 57 18552 1-9
061 | 27049 57 18571 17
- 064 | 41296 58 18 588 1-7
068 | 55544 57 19005 1-5
071 | 70191 5:8 19020 1-4
N22 07:4 | 84 43:9 5-8 S19 034 1-2
07:8 | 99087 5:8 19046 11
08:1 | 113 335 58 19 057 1-0
- 084 | 127 583 5:9 19 067 0-9
08:7 | 142 23:2 5:9 19076 0-8
091 | 156 481 59 19084 0-6
N22 094 | 171 13:0 6:0 S19 090 0-5
097 | 185 38:0 60 19095 o
101 | 200 03:0 6:0 19098 o
104 | 214 28:0 61 19101 o
10:7 | 228 531 61 19102 0
11:0 | 243 182 61 19101 o
N22 11:4 | 257 ae 6-2 eN 100 0- SUN
11:7 | 272 08:5 6-2 0- Å
120 | 286 337 6:3 19093 os 58 Eqn: of ime Mer, oier
12:3 | 300 590 63 19088 0-6 254 00h 12 B PP
126 | 315 24:3 63 19082 0-8 58: me syl AO P ttis-im
13:0 | 329496 64 19074 0-9 588 31| 02 34 | 02 30 | 11 58

357 599.

180 38:4 N21 48:6 | 26 24:6 64 S14 505 7-8 a
195 38:3 48:9} 40500 63 14583 7-6
210 38:2 493 | 55153 63 15059 7-5
225 38:1 ** 497 | 69406 6:2 15134 7:5
240 38:0 500 | 84 058 e» 15209 73
255 37:9 504 | 98311 62 15 28:2 7-2
270 37-9 N21 50:8 | 112 563 61 S15 354 7-1
285 37:8 511 | 127 214 61 15 42:5 7-0
300 37:7 515 | 141 465 61 15495 69
315 376 ** 518 | 156116 61 15564 es
330 37:5 522 | 170 367 60 16052 67
345 37:4 526 | 185 01:7 6:0 16099 ee
0373 N21 52:9 | 199 267 6:0 516 165 64
15 37:2 533 | 213 517 5-9 16229 6-4
30 37:2 536 | 228 166 5:9 16293 6-2
45371 * + 540 | 242 415 59 16355 61
60 37:0 544 | 257 064 58 16416 6-0
75 369 547 | 271 31:2 5:9 16476 5-9
90368 N21 551 | 285 561 5-8 S16 53:5 5-8
105 36:7 55-4 | 300 20:9 5-8 16593 5-6
120 366 558 | 314 45:7 57 17 04:9 5-5
135365 ** 561 | 329104 58 17104 5:5
150 36:4 565 | 343 35:2 s 17 159 5:

RD S.D: 16:4

1141

17 21:2

1| 02 25| 02 21 | 11 58
2|0216|0212| 11 58

16:1

16:3

1142

<KPOzCAHb>vo

260 48:0
275 50:4
290 52:9
305 5544
320 57:8
336 00-3

351 02:8

6 05:2
21 07:7
36 10:2
51 12:6
66 151

81 176
96 20:0
111 22:5
126 249
141 274
156 29:9

171923
186 34:8
201 373
216297
231 42:2
246 447

261 47:1

234
249
264
279
294

209
324
339
354
9
24

39
54
69
84
98
113

128
143
158
173
188
203

53
68
83
98
113

128
143
158
173
188
203

218
233
248
263
278
293

308
323
338
353
8
23

38
53
68
83
98
113

128
143
158
173
188
203

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

1958 JUNE 12,

05: 4
05:0
04:7
04:3
03:9

03:5 N13 40:4
03:2 413
02:8 42:2
024 - + 431
02:0 44:0
01:6 449

01:3 N13 45: 8
00:9
00:5
00-1
59:7
59.4

59:0 N13
58:6
58:2
57:8
57:4
Biel

567 N13
56:3
55:9
55:5:2 13,
551 14
547

543 N14
54:0
53:6
53:2
52:8
52:4

52:0 N14
51:6
51:2
50:8
50:4
50:0

49-6 N14
49:3
48-9
48.5 +
481:
477
47:3 N14
469
46:5
461
457

45:
44:
44:
44:
43:
43:
42:

3
49 N14
45

41

37

919,

2:9

42:5
42:1
417
41:3
40-9
40:5
0-0
9:6
9:2
8:8
8-4
8:0

40-
39.
39.
38:
38:
38:

N14

255151:9.S20127:5

270 52:7
285 55:5
300 54-4
sals) bey”
330 56:0

368
361

+ 354

34:8
341

345 20B sð 234

166 06:3
181 07:6
196 08:4
211 09:2
226 101
241 10:

76 41:6
91 42-4
106 43.3
121 441
136 449
151 45:8

166 46:6
181 47:4
196 48:3
211 491
226 49-9

S

wn

un

un

N

N

14 (THURS., FRI., SAT.)

G.H.A.

o ,

59 071NS 4:2

un

Lo

60 07:4 S
75 09:9
90 12:4
105 15:0
120 17:5
135 20:

150 22:
165 25:
180 27:
195 30:
210 32:
229935

240 37:
255 40:
270 42:
285 45:
300 47
315 50:

330 52:
345) 55:

0 57:
16 00:

BEARER AREAS eo errar bound omomnón O

141
141

+ 141

141
141
141
141
141

- 141

141
14-1
14:0
14:0
14:0

+ 140

14:0
14-0
14:0
14:0
14-0

* 140

14:0
14:0

SATURN 402
Dec.

G.H.A.
o

,

357 49:3

163 18:6

178 213
193 23-9
208 26:6
223 29:3
238 31:9
253 3%6

268 37:2
283 39:9
298 42:6
313 452
328 47-9

358 53-2

95905 Th
14 59-8
30 02:4
45 051
60 07-8
75 10:4

90 13-1

H

S21 48:8
48:7
48:7

+ 487
48:7
48:7

S21 487
48:7
48:7

+ 487
48:7
48:7

S21 487
48:7
48:7

+ 48:6
48-6
48-6

S21 48:6
48:6
48-6

Bed ES
48-6
48-6

S21 48:6
48-6
48-6

- 486

48-6

48-5

48-5

48-5

48-5

. 485

48-5
48:5

S21 48:5
48:5
48:5

* 48:5
48:5
48:5

48-5
48-4
48-4
- 484
48:4
48:4

S21 484
48-4
48-4
* 48-4
48-4
48-4

48-4
48-4
48:3
- 483
48:3
48:3

483
483
48:3
+ 483
48:3
48:3
48:3
48:3
48:3
+ 482

«1
N
[m

Lo
N
=

Name

Acamar
Achernar
Acrux
Adhara
Aldebaran

Alioth
Alkaid
Al Na'ir
Alnilam
Alphard

Alphecca
Alpheratz
Altair
Ankaa
Antares

Arcturus
Atria
Avior
Bellatrix
Betelgeuse

Canopus
Capella
Deneb
Denebola
Diphda

Dubhe
Elnath
Eltanin
Enif
Fomalhaut

Gacrux
Gienah
Hadar
Hamal
Kaus Aust.

Kochab
Markab
Menkar
Menkent

Miaplacidus 221 48"

Mirfak
Nunki
Peacock
Pollux
Procyon

Rasalhague
Regulus
Rigel

Rigil Kent.
Sabik

Schedar
Shaula
Sirius
Spica
Suhail

Vega
Zuben'ubi

Venus
Mars
Jupiter
Saturn

143 56:

Ww

+

>

un
Bo Oo
Daum P

96 44:
208 27:

81 06:5
137 50:9

S.H.A.
AE

318 08:7
355 237
159 19-4
98 05:2

ZN) NN
käbMO: un P
TONNO o
NUVNN f
WON o
Ore Won

nnnzz

PEW
Oi WG
NOW H
BSD
O O Un d ai

Loun
N_N
BM OO
RW E Un Un
EXPE VR
20 nun

zZZUNZ

Wore
- 0» vo OO
NENN
O lea
mo

Lë zu
Hep DU
009 P UN unn
rbonb
PB NG
OW OWA

NZZZZ
M UNO
OOF OF
Und NU
ee Ro
V» E cl Vi cl

nzununun
VR HU
BVO=NO
NP E I Un
uo
IRON

nnzz=z
Dw Hu
DC: PP
R unun+
Si UT 00 SD
Nr OOo

ZZUNDNZ

MUND
Un OO CO
HONNA
nom
Oo «9 Ou

nmnnzz
PO HH
Moonn
Parr lu
eebe
BHROND

Nnninz
q» 2m Uu
ORIO
PUIWOR
GO OEC OD
NOJA

N 38 44-7
5115522

Mer. Pass,

hom
9 25
6 55
19 56
0 04

ss T.

<> OPCA

G.H.A.

o

H

195 06:9
210 06:8
225 067

255 064

285 06:2
300 06:0
315 05:9
330 05:8
345 056

0 05:5
15 05:4
30 05:3
45 051
60 05-0
75 04:9

90 04:7
105 046
120 04:5
135 044
150 04:2
165 041

180 04:0
195 03:8
210 03:7
225 03-6
240 03-4
255 03:3

270 03:2
285 03-1
300 02:9
315 02:8
330 02:7
345 02:5

0 02:4
15 02:3
30 02:1
45 02:0
60 01:9
75 017

90 01:6
105 01:5
120 01:4
135 01:2
150 011
165 01:0

240 06:5

180 07:1 N23 06:2

270 06:3 N23 07:3

07:

* 068

APPENDIX V:

1958 JUNE 12,

241 41:3 14-8
256 151 14-7
270 48:8 14:7
285 22:5 14:6
299 56i 14-7
314 293 14-6

329 03:4
343 36:9
358 10:5
12 43:9
27 lT4
41 50:8

56 24:2

06:4
06'6

nd co

06:9
071

=m
CDD DODOODM®D O

OUBÐW mnmmnRouidd

14-5
14:6
14-4
14:5
14-4

07:4
07-6

07-9
08:1

08:2

m

084 | 70 57:6 10 310
086| 85309142 10393
* 08:7 | 100 04:1 14-3 10 475
08:9 | 114374 14-2 10 556
090 | 129 106 1431 11038
092 | 143 437 141 N11 118
094 | 158168 141 11199
095 | 172 499 140 11279
* 097 | 187 22:9 14-0 11358
098 | 201 55:9 14. 11 437

10:0 | 216 28:9

231 01:8

11 51:6
N11 594

245 34:7 12 07:1

104 | 260 07:5 13-8 12149
106 | 274 403 13.7 12 22:5
107 | 289 13:0 13.7 12301
+9 | 303 457 13-6 - 12377
318 18:3 13-6 N12 45:2

11:2 | 332 509 13-6 12527
11:3 | 347 23:5 1*5 13 00-1
4115 15601*4 13074
116 | 16284154 13147
: 31 008 13-4 13 22:0

Ú 45 33:2 13-3 N13 292
121 | 60 05:5 13-3 13 363
12:2 | 74 37:8 132 13 43-4
* 123 | 89100 13-2 13 504
125 | 103 42:2 131 13574
118 143 131 14 043

"8 | 132 464 13-0 N14 112
12:9 | 147 18-4 13-0 1418-0
13-0 | 161 50:4 12-9 14 247
13:2 | 176 223 12-9 14314
3] 190 54:2 17 14 38:0

205 26:0 14 44:5

180 00:8 "6 | 219 578 12-7 N14 510
195 007 137 | 234 295 12:6 14574
210 00:6 13-9 | 249 01:1 12-7 15 03:8
225 004 * + 14:0} 263 328 125 15101
240 00:3 14:1 | 278 04:3 12:5 15 163
255 00:2 14:3 | 292 358 125 15 22:5
270 00:0 N23 144 | 307 07:3 12-4 N15 28:6
284 599 145 | 321387 12-4 15 346
299 598 147 | 336 10:1 123 15 406
314 596 :- 148 | 350 41:4 122 15 464
329 595 14:9 S126 12-2) ENEE)
344 594 150 | 19428 12-2 15 58:0
359 592 N23 152 | 34 150 121 N16 03:7
14 591 153| 48461120 16093
29 590 154] 6317110270 16148
44 58:9 -- 155| 77481120 16 203
59 58:7 157 | 92191 11-9 16 257
74 58:6 15:8 | 106 50:0 1-8 16 31:0
89 58:5 N23 159 | 121 208 11-8 N16 36:2
104 58:3 160 | 135516 11-7 16414
119 58:2 162} 150 22:3 11-7 16465
134 581 -- 163] 164530 11-6 16515
149 57:9 16:4 | 179 236 11-6 16 564
164 57:8 165 | 193 542 1:5 17 013
S.D. 148 149

14 (THURS., FRI.,

Twilight
Civil

Naut.

Civil

SUN
Eqn. of Time
00h 12h

Twilight ,

Naut.

SAT.)

EXTRACTS FROM NAUTICAL ALMANAC

GER

23 44

00 14
00 30
00 43
00 54
01 03
0111

01 18
01 25
01 30
01 35
01 40
01 50

01 58
02 05
02 11
02 22
02 32
02 41

02 50
03 00
03 11
03 18
03 25
03 34

03 44
03 49

037551

04 01
04 07
04 15

14

hom
23 26
00 15
00 38
09 56
01 10

01 23
01 33

01 42
01 51
01 58
02 04
02 10
02 23

02 33
02 42
02 50
d 04
3 16
03 27

03 39
03 51
04 05
04 13
04 22
04 33

04 46
04 52
04 59
05 07
05 16
05 26

Moonset

13

14

1143

h m
18 34
18 04
17 41
17 24
17 10
16 59
16 49

16 40
16 32
16 26
16 20
16 14
16 02

15953)
15 44
15127
15 24
158129
15 03

14 53
14 42
14 29
14 22
14 14
14 04

113258
13 48
13 42
13 35
13 28
13 20

hom
20 29
2/99
19 07
18 44
18 25
18 10
17 58

17 47
17 38
17 29
17 22
WALS
17 01

16 49
16 39
16 31
16 15
16 02
15 50

15 38
15 24
15 10
15 01
14 51
14 39

14 25
14 19
14 12
14 04
19:55
13 44

MOON

Pass”

Lower

| Age | Phase

m

m s s
00 28 | 00 22

00 16 | 00 10
[00 03

00 04

h m d
20 30} 25

21115126

0
ee d

22 02

e

1144 APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC
STARS, 1958 JANUARY—JUNE
-H.A. Declinati
Mag Name and No. Sue l iu = =
Š Ë . | APR. A
p | JAN. | FEB. | MAR. | APR. | MAY | JUNE jano
3-1 |y Urse Minoris + |129|49:1|48-5 | 48-0 | 47-7 | 47:6 | 47:7 | N. 71 | 58-8
2:7 |8 Libre 131 | 18-8 | 18-5 | 18-3 | 18-2 | 18-1 | 18-1 | S. 9| 13-7
3:1 |y Trianguli Aust. | 131 | 15:4 | 14:9 | 14-4|14-0| 13-8 | 13-8 | S. 68 | 31-3
2:8 |B Lupi 136 | 03-3 | 02-9 | 02-7 | 02-5 | 02-4 | 02-4 | S. 42 | 57:8
2:2 |8 Urse Minoris 40 | 137 | 18-6 | 18-0 | 17-5 | 17:2 | 17-1 | 17-4 || N. 74 | 19:3
2:9 |a Libre 39 | 137 | 51:6 | 51-4 | 51-2 | 5I-O | 51-0 | 51-0 | S. 15 | 52-1
2:6 ¡e Bootis 139 | 12-7 | 12-5 | 12:3 | 12-1 | 12-1 | 12-1 | N. 27 | 14-8
2:9 ja Lupi 140 | I2:9| I2:6| 12-3 | 12-1|12:0|12:1| S. 47 | 12-4
oI |a Centauri 38 | 140 | 48-7 | 48:3 | 48-0 | 47-8 | 47:7 | 47:7 | S. 60 | 39-6
2:6 |n» Centauri 141 | 47:3 | 47:0 | 46:8 | 46-6 | 46:5 | 46-6 || S. 41 | 58-3
3:0 |y Bootis 142 | 24:2 | 24:0 | 23-8 | 23-6 | 23-6 | 23-7 || N. 38 | 29-2
0:2 |a Bootis 37 | 146 | 33:7 | 33'5|33'3| 33:2|33'2|33:2| N. 19 | 23:9
2:3 |0 Centauri 36 | 148 | 56-7 | 56-4 | 56:2|56:1|56:1| 56-1 | S. 36|09-7
0:9 |8 Centauri 35 | 149 | 47:0 | 46:6 | 46:3 | 46:1 | 46:1 | 46:1 | S. 60 | 10-0
3:1 |Ģ Centauri 151 | 46:1 | 45:7 | 45:5 | 45:4 | 45:4 | 454 | S. 47 | 04:8
2:8 |7 Boots ISI | 49:6 | 49:4 | 492| 49:1 | 49:1 | 49:2 | N. 18 | 36:3
1-9 [y Ursz Majoris 34 | 153 | 31-7 | 31-4] 31:2] 32-1 | 31-1 | 31-2 | N. 49 | 31-0
2:6 |€ Centauri + 155 | 4I:4| 41:1 | 40:8 | 40-7 | 40-7 | 40-8 | S. 53 | 15-0
1-2 |a Virginis 33 | 159 | 15:1 | 14:9 | 14:7 | 14:7 | 14:7 | 14:7 | S. 10 | 56-6
2:2 |Ë Urse Majoris 159 | 26-4 | 26-1 | 25:9 | 25-8 | 25-9 | 26-0 | N. 55 | 08-3
2:9 | c Centauri 160 | 26:2 | 26-0 | 25-8 | 25-7 | 25:7 | 25:8 | S. 36 | 29-4
3:0 |€ Virginis 164 | 58-5 | 58-3 | 58-1 | 58-1 | 58-1 | 58-2 | N. 11 | 10-9
2:9 |a. Canum Venat. 166 | 28:9| 28-6 | 28-5 | 28-4 | 28-5 | 28-6 | N. 38 | 32-4
1-7 [e Urse Majoris 32 | 166 | 57-1 56:8 | 56:6 | 56-6 | 56-6 | 56-8 | N. 56 | 10-9
1-5 |B Crucis 168 | 40-6 | 40-3 | 40-1 | 40-0 | 40-1 | 40-3 | S. 59 | 27-4
2:9 |y Virginis 170 | 06-8 | 06-6 | 06-5 | 06-4 | 06-4 | 06-5 || S. 1|13-3
2:4 |y Centauri 170 | II:7| 11:4| 11-2) 11-2] 11-2] II-4 | S. 48 | 43-6
2:9 la Musce 171 | 19:4 | 18-9 | 18-7 | 18-6 | 18:8 | 19-0 | S. 68 | 54-1
2:8 |8 Corvi 171 |57:0| 56:8| 56-7 | 56-6 | 56-7 | 56-7 | S. 23 | 09-9
1-6 |y Crucis 31 | 172 | 47:1 | 46-8 | 46-6 | 46-6 | 46-6 | 46-8 || S. 56 | 52-5
1-1 |a Crucis 30 | 173 | 55:5 | 55:2 | 55-0 | 55-0 | 55-1 | 55:3 || S. 62 | 51-8
2:8 |y Corvi 29 | 176 | 35:0 | 34:8 | 34:7 | 34-7 | 34:7 | 34-8 | S. 17 | 18-6
2:9 |ð Centauri 178 | 26-9 | 26-6 | 26-5 | 26-5 | 26-6 | 26-7 | S. 50 | 29-2
2:5 |y Ursz Majoris 182 | 05-3 | 05-0 | 04:9 | 04-9 | 05-0 | 05:2 | N. 53 | 55:3
2:2 |B Leonis 28 | 183 | 15:9 | 15-7 | 15.6 | 15.6 | 15-7 | 15-8 || N. 14 | 48-2
2:6 |ð Leonis 192 | 01:5 | 01:3|01:3|01-3|01:4|01-5 | N. 20 | 45-0
3:2 | Urse Majoris 193 | 10-0 | 09-8 | 09-7 | 09-8 | 09-9 | 10-1 | N. 44 | 43:3
2:0 ja Ursa Majoris 27 | 194 | 42:3 | 42:0 | 41:9 | 42:0 | 42:3 42:5 | N. 61 | 58:3
2:4 |B Ursa Majoris 195 | 09-8 | 09:6 | 09-5 | 09-6 | 09-8 | 10-0 | N. 56 | 36-1
2:8 |u Velorum* 198 | 45-0 | 44:8 | 44-8 | 44:9 | 45:0 | 45:2 | S. 49 II:9
3:0 |0 Carina*t 199 | 37:3 | 37-1 | 37-1 | 37:2 | 37:5 | 37-8 | S. 64 | 10-4
23 |y Leonis 205 | 34:7 | 34°5 | 34-5 | 34-6 | 34-7 | 34:8 | N. 20 | 03-0
1-3 |a Leonis 26 | 208 | 27:5 | 27:4 | 27:4 | 27-4 | 27:5 | 27-6 | N. 12 | 10-1
3:1 |€ Leonis 214 | 07:5 | 07:4 | 07:4 | 07:5 | 07-6 | 07-7 | N. 23 | 57:8
3:0 |N Velorum 217 | 30-0 | 30-0 | 30-0 | 30-2 | 30:5 | 30-7 | S. 56 | 51-0
2:2 ja Hydra 25 | 218 | 36-7 | 36-6 | 36-6 | 36-7 | 36:8 | 36-9 | S. 8 28.7
2:6 |K Ade 219 | 47:1 | 47:0 | 47-1 | 47:3 | 47:5 | 47:7 | S. 54 | 49-9
2:2 |+ Carine 220 | 59:7 | 59:6 | 59-7 | 59-9 | 60-2 | 60-5 | S. 59 | 06-0
1-8 |8 Carine* 24 | 221 | 47-6 47:6 | 47-8 | 48-1 | 48-6 | 48-9 | S. 69 | 32-7
2:2 |À Velorum* 23 | 223 | 22-6 | 22-6 | 22-6 | 22:8 | 23-0 | 23-1 | S. 43 | 15-8
3:I | c Urse Majoris 225 | 54:3 | 54:2 | 54:2 | 54:4 | 54:6 | 54:7 || N. 48 | 12-2
2:0 |ð Velorum* 229 | 06:1 | 06-1 | 06-2 | 06-4 | 06-7 | 06-9 | S. 54|33:4
AE es 22 | 234 | 34:4 | 34-4 | 34-6 | 34-9 | 35-1 | 35-4 | S. 59 | 22-6 | 22: t ; ;
1:9 [y Velorum 237 | 55-8 | 55:8 | 55-9 | 56-1 | 56-3 | 56:5| S. 47 | 12.9 | 13-111
P 5 3:2|13:2| 13-2 | 13-1
2:9 |p Puppis* 238 | 33:1 | 33-1 | 33-2 | 33-3 | 33-5 | 33-6 | S. 24 | 11-1 | 11-2 11-3 | 11-3 ns T
2:3 |Ë Puppis* | 239 | 27°8 | 27-8 | 27-9 | 28-1 | 28-3 | 28-4 | S. 5 ea! ; k
1-2 |8 Geminorum ` 21 | 244 | 18-2 18-2 18-3 | 18:4 | 18-5 18:6 | N šā 26 224 53:5 | 53:5 | 53:5 | 53:4
O:5 |a Canis Minoris 20 | 2 2-9 | 42:9 | 43: i See
" 45142:9142:9/43:0/43:1/43:2/43:3 | N. 5|19:8| 19-8 | 19-8 | 19-8 | 19-8 | 19-8

Formerly Argus

T Not suitable for use with H.O. 214 (H.D. 486)

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

POLARIS (POLE STAR) TABLES, 1958
FOR DETERMINING LATITUDE FROM SEXTANT ALTITUDE AND FOR AZIMUTH

L.H.A. | 240°- | 250°- | 260°- | 270°- | 280%- | 290°- | 300° i
ARIE o o : : 399— 320 -
S| 249 259% 269 | 279 289 | 299 309»
do do do ao ao d do
o |1 46:6 | I 41:0|1 340 I 26:11 17:3 1 07:9
I 461| 403 333 25:2] 163| 06-9
2 45:6| 397| 325, 244| 15:4] 06-0
3 451 3901031: 71023:5 145 | 05:0
4 445 38:3 31:0| 226 136| 040
§ |143:9|1 37:6!1 30:2|1 21:7|1 I26 I 03-1
6 434 | 369| 29-4] 209| 11:7| 02-1
7 42-8 36:2 28:6| 200 10:7 ori
8. 42:2 35:5 27:7 I9:I 09:8 | I 00-1
9 41:6 34:8 26:9 18:2 08:8 | 0 59:2
10 I 41:0|1 34:0 | I 26-I| I 173|1 07:9 | O 582
Lat a, ER a, a, a a, a, a, ER
o 0:4 0:3 0:2 0-2 DR ot o'I oI 0:2
10 :4 :4 3 2 2 +I “I 2 2
20 Wi :4 3 3 3 2 2 3 3
30 i5 éi E 4 3 3 3 :3 4
40 o5 os o5 os 0:5 0:4 0:4 0:5 0:5
45 6 ‘6 + 5 S 5 5 + 5
50 :6 :6 :6 :6 6 6 6 6 6
55 ‘6 7 Y. 7 g 7 7 7 7
60 7 7 :8 -8 8 8 8 8 8
62 0:7 0-8 0-8 0:9 og og 0:8
64 T :8 :9 0:9 1:0 1:0 0:9
66 8 9 oa 1:0 1:0 I'l 1:0
68 0:8 0-9 1-0 1:1 1-1 I2 II
Month| a, a, a, da ER ER ER
Jan. 0:5 0-5 0:5 0-5 0:5 0:5 0-6
Feb. 4 4 4 4 4 4 5
Mar. 4 4 3 3 3 3 "3
Apr. o5 0:4 0:4 0:3 0:3 0:2 0:2
June 8 “7 a ‘6 5 4 ES
July 0:9 o:8 o:8 0:7 0:7 o: 6 0:4
Sept. | -9 9 2 D 9 9 3
Oct. 0:8 0:9 0:9 0:9 0:9 0:9 0:9
Nov 7 7 -8 -8 -9 :9 1:0
Dec. os o:6 0:6 0:7 o:8 o:8 Lo
Lat. AZIMUTH
o 0:5 0-7 0-8 0-8 0-9 0-9 0'9 0:9 0-8
20 06,115 07 0:8 0:9 0:9 1:0 Lo 0:9 0:9
40 0:7 og 1-0 1-1 1-2 1-2 1-2 1-2 II
50 0:8 1-0 1-2 1:3 I:4 I:4 1-4 LA 1-3
55 0:9 I-I 1:3 1-5 1:6 I:6 1:6 1:6 1:5
60 I-I 1-3 1-5 1:7 r8 r:8 1:8 SM 1-7
6s PUE 1:3 15 E Srg EI-9 2:1 2:2 2:2 2:1 2:0

The table is entered with L.H.A. Aries to d
a, is taken, with mental interpolation,
degrees as argument; a,, a, are taken, without interpolation,
Go; du a, are always positive.

range of 10°.

330°-
339°

o

o
Ó 60 o Ó c A RU uU

O

0:7
o:8
1:0
1-2
1-3
I:S
1-8

o

o
wë 6 0 0 AA hun AAA

o

0:6
0:7
o:8
Lo
I-I
1:3
1:6

a

4
5
5
iS
ES
6
6
6
E
7
-7
8
8

o

o ©

n
Do

`

o o

o
ARU NNU FAY

mo 0
O `O oo

os
os
0:7
0:8
0:9
1-0
1-3

1145

Latitude = corrected sextant altitude —1° + Go + 4, + 4;
etermine the column to be used; each column refers to a

latitude and month respectively.

from the upper table with the units of L.H.A. Aries in
from the second and third tables with arguments
The final table gives the azimuth of Polaris.

1146 APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

CONVERSION OF ARC TO TIME

0°-59° 60°-119° 120°-179° o- 0-25 0'-50 0-75
, s m s m s m s
ojoo] 60| 4 00| 120| 800 o|o 00 |o of |o o2 |o 03
1loo4| 61 404 |121| 804 I | 0 04 | O 05 | 0 06 |o 07
2|008| 62 | 408 | 122 | 8 08 2/008 |o 09/010 |O II
3| 012] 63 | 4 12 | 123 | 8 12 ORAR AMORES
4|016| 64 |4 16 | 124 | 8 16 4|016|017|018 |0 19
5 | o 20 | 65 | 4 20 | 125 | 8 20 5|020|02I|022 |0 23
6 | o 24 | 66 | 4 24 | 126 | 824 6 | 0 24 | 0 25 | 0 26 |o 27
7|0 28] 67 | 4 28| 127 | 8 28 7 | 0 28 | 0 29 | 0 30 |0 31
8 | o 32 | 68 | 4 32 | 128 | 8 32 8 | o 32 |o 33 | O 34 |0 35
9 | 0 36 | 69 | 4 36 | 129 | 8 36 9 | O 36 | O 37 | O 38 |o 39
10 | O 40 | 70 | 4 40 | 130 | 8 4o I0 | O 40 |0 4I |O 42 |O 43
II | O 44 | 71 | 4 44 | 131 | 8 44 II | O 44 | O 45 | O 46 |0 47
12 | O 48 | 72 | 4 48 | 132 | 8 48 12 | O 48 |o 49 | O 50 |0 51
13 | O 52 | 73 | 4 52 | 133 | 8 52 13 | O 52 |0 53 |0 54 |O 55
14 | O 56 | 74 | 4 56 | 134 | 8 56 14 | O 56 | O 57 |O 58 |0 59
15 | I 00 75 | 5 00 | 135 9 00 IS | I 00 | 1 OF | I 02 |I O3
16 | 1 04 | 76 | 5 04 | 136 | 9 04 16 | I 04 |1 05 | I 06 |1 07
17 | 1 08 | 77 | 5 08 | 137 | 9 08 17 [108 | I 09 |I IO |I ir
18 | I 12 | 78 | 5 12 | 138 | 9 12 18 | 1 12 | 1 I3 | I 14 |I IS
19 | 1 16 | 79 | 5 16 | 139 | 9 16 19 I 16 |1 17 | I 18 |1 19
20 | 1 20 80 | 5 20 | 140 9 20 20 | I 20 |I2I |I 22 |I 23
21 | 1 24 | 81 | 5 24 | 141 9 24 21,1 24 |t 25 |I 2611.27
22 | 1 28 | 82 | 5 28 | 142 | 9 28 22 | I 28 |129 |1 30 |1 31
23 | 1 32 | 83 | 5 32 | 143 | 9 32 23 [1132 |T 3311 34 M35
24 | 1 36 | 84 | 5 36 | 144 | 9 36 24 | I 36 | 1 37 |1 38 |1 39
25 | 1 40 | 85 | 5 40 | 145 | 9 40 25 | I 40 |I 4I | I 42 |I 43
26 | 1 44 | 86 |5 44 | 146 | 9 44 26 |1 44 |1 45 |1 46 |1 47
27 | 1 48 | 87 | 5 48 | 147 | 9 48 27 | 1 48 | 1 49 |1 50 |1 51
28 | 1 52 | 88 | 5 52 | 148 | 9 52 28 | I 52 |1 53 | 1 54 |1 55
29 | 1 56 | 89 | 5 56 | 149 | 9 56 29 | I 56 |1 57 |1 58 |1 59
30 | 2 00 | 90 | 6 00 | 150 | IO 00 | 210 | 14 00 | 270 | 18 00 | 330 |22 00 | 30 | 200 |2 or |2 02 |2 03
31 | 2 04 91 | 6 04 | ISI | 1004 | 211 | 14 04 | 271 | 18 04 | 331 | 22 04 | 31 | 2 04 |205|206 |207
32 | 2 08 92 | 6 08 | 152 | 10 08 | 212 | 14 08 | 272 | 18 08 | 332 | 22 08 | 32 | 2 08 |2 09 |2 10 |2 II
33 | 2 12 | 93 | 6 12 | 153 | 10 12 | 213 | 14 12 | 273 | 18 12 | 333 | 22 12 | 33 | 2 12 |2 I3 |2 14 |2 15
34 | 2 16 | 94 | 6 16 | 154 | 10 16 | 214 | 14 16 | 274 | 18 16 | 334 | 22 16 | 34 | 2 16 |2 17 | 2 18 12519
35 | 2 20 | 95 | 6 20 | 155 | 10 20 | 215 | 14 20 | 275 | 18 20 | 335 | 22 20 | 35 | 2 20 | 2 21 | 2 22 |2 23
36 | 2 24 96 | 6 24 | 156 | 10 24 | 216 | 14 24 | 276 | 18 24 336 | 22 24 | 36 | 2 24 |2 25 |2 26 2 27
37 | 2 28 97 | 6 28 | 157 | 10 28 | 217 | 14 28 | 277 | 18 28 | 337 | 22 28 37 | 2 28 |2 29 |2 30 |2 31
38 | 2 32 | 98 | 6 32 | 158 | 10 32 | 218 | 14 32 | 278 | 18 32 | 338 | 22 32 | 38 | 2 32 | 2 33 |234 |235
39 | 2 36 99 | 6 36 | 159 | 10 36 | 219 | 14 36 | 279 | 18 36 | 339 | 22 36 | 39 | 2 36 | 2 37 |2 38 |2 39
40 | 2 40 | 100 | 6 40 | 160 | 10 40 | 220 | 14 40 | 280 | 18 40 340 | 22 40 | 40 | 2 40 | 2 41 |2 42 |2 43
41 | 2 44 | IOI | 6 44 | 161 | 10 44 | 221 | 14 44 | 281 | 18 44 | 341 | 22 44 | 41 | 2 44 | 2 45 | 2 46 |2 47
42 | 2 48 | 102 | 6 48 | 162 | 10 48 | 222 | 14 48 | 282 | 18 48 342 | 22 48 | 42 | 2 48 | 2 49 | 2 so |2 5I
43 | 2 52 | 103 | 6 52 | 163 | 10 52 | 223 | 14 52 | 283 | 18 52 | 343 | 22 52 | 43 | 2 52 |2 53 | 2 54 |2 55
44 | 2 56 | 104 | 6 56 | 164 | 10 56 | 224 | 14 56 | 284 | 18 56 344 | 22 56 | 44 | 2 56 |2 57 | 2 58 |2 59
45 | 3 00 | 105 | 7 00 | 165 | 11 00 | 225 | 15 00 | 285 | 19 00 | 345 | 23 oo 45 | 3 00 | 3 01 | 3 02 |3 03
46 | 3 04 | 106 | 7 04 | 166 | 11 04 | 226 | 15 04 | 286 19 04 | 346 | 23 04 | 46 | 3 04 | 3 o5 | 3 06 |3 07
47 | 3 08 | 107 | 7 08 | 167 | 11 08 | 227 | 15 08 287 | 19 08 | 347 | 23 08 | 47 3 08 | 3 09 | 3 10 |3 11
48 | 3 12 | 108 | 7 12 | 168 | 11 12 | 228 | 15 12 | 288 | 19 12 348 | 23 12 | 48 | 3 12 | 3 13 | 3 I4 |3 15
49 | 3 16 | 109 | 7 16 | 169 | 11 16 | 229 | 15 16 | 289 | 19 16 349 23 16 | 49 | 3 16 |3 17 | 3 18 |3 I9
so | 3 20 | 110 | 7 20 | 170 | I1 20 | 230 | 15 20 | 290 | 19 20 | 350 | 23 20 | 50 3.20 | 3 21 | 3 22 |3 23
SI | 3 24 | 111 | 7 24 | 171 | II 24 | 231 | 15 24 | 291 | 19 24 | 351 | 23 24 SI | 3 24 325 | 3 26 |327
52 | 3 28 | 112 | 7 28 | 172 | 11 28 | 232 | 15 28 | 292 | 19 28 352 | 23 28 | 52 | 3 28 | 3 29 | 3 30 3 31
53 | 3 32 | 113 | 7 32 | 173 | 11 32 | 233 | 15 32 | 293 | 19 32 | 353 | 23 32 53 | 3 32 | 3 33 | 3 34 |3 35
54 | 3 36 | 114 | 7 36 | 174 | 11 36 | 234 | 15 36 | 294 | 19 36 | 354 | 23 36 | 54 | 3 36 | 3 37 3 38 | 3 39
55 | 3 40 | 115 | 7 40 | 175 | 11 40 | 235 | 15 40 | 295 | 19 40 | 355 | 23 40 o I
56 | 3 44 | 116 | 7 44 | 176 | 11 44 | 236 | 15 44 | 296 | 19 44 | 356 | 23 44 36 : * å ds : 46 : A
57 | 3 48 | 117 | 7 48 | 177 | II 48 | 237 | 15 48 | 297 | 19 48 | 357 | 23 48 | 57 | 3 48 3 49 | 3 so |3 51
58 | 3 52 | 118 | 7 52 | 178 (i 52 | 238 | 15 52 | 298 | 19 52 | 358 23 52 | 58 | 3 52 | 3 53 | 3 54 | 3 55
$9 13 se 1:19 | 7 56 | 179 | 11 56 | 239 | 15 56 | 299 | 19 56 | 359 | 23 56 | 59 | 3 56 | 3 57 | 3 58 | 3 59

The above table

is for the conversion of longitude for application to L.M.T. (added if west,
versa, particularly in the case of sunrise, sunset, etc.

is for converting expressions in arc to their equivalent in time ; its main use in this Almanac
subtracted if east) to give G.M.T. or vice

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC 1147

24" INCREMENTS AND CORRECTIONS 25"

m v v v m v
moz DEDO a
s o , On ar o , D D D D ' , s [e 17 o0 o ' D D D D D D
00 | 6000 | 6 01:0 | 5 436 [0-0 0:0 | &o 25 | 120 4:9 *0 0+ d
01 | 6003 | 6 012 | 5438 [0-1 00| e1 25 | 124. 49
02 | 6005 | 6 01:5 | 5 44-1 ||0+2 01 | e2 25 |122 5:0

03 | 6008 | 6 017 | 5 44:3 [0-3 01 | 63 26 | 125 50
04 | 6 01:0 | 6 02:0 | 5 44:6 || 0-4 02| &4 26 |124 51

05 | 6013 | 6 02:2 | 5 448 || os 0:2 | 6-5 27 | 125 51
06 6 01:5 | 6 025 | 5 45:0 || 0-6 02| ee 27 | 126 51
07 6 018 | 6 02:7 | 5 45:3 [| 0-7 03 | 67 27 | 12.7 52
08 | 6 02:0 | 6 03:0 | 5455 || 0-8 0-3 | 68 28 | 128 52
09 | 6 02:3 | 6 03:2 | 5 45:7 || 0-9 04 | 69 28 | 129 53

10 | 6 02:5 | 6 035 | 5 46:0 || 1-0 04 | 7-0 29 | 13-0 53
11 | 6028 | 6 037 | 5 46:2 [| 1-1 04 | 71 29 |131 53
12 | 6 03:0 | 6 04:0 | 5 465 || 1-2 0:5] 7-2 29 |132 54
13 | 6 03:3 | 6 042 | 5 467 | r3 05 | 73 3:0 |133 54
14 | 6035 |6045 | 5 469 | 1-4 06 | 74 3:0 | 13-4 55

15 | 6038 | 6 047 | 5 47:2 | r5 06 | 75 31 | 1*5 55
16 | 6 04:0 | 6 05:0 | 5 4744 || 1-6 07 | 76 3:1 | 136 56
17 | 6043 | 6 05:2 | 5477 || 1-7 07 | 77 31 | 137 56
18 6 045 | 6 05:5 | 5479 | 1-8 0:7 | 78 3:2 | 1*8 5'6
19 | 6048 | 6 057 | 5 48-1 || 1-9 08 | 7-9 32 |139 57

20 | 6 05:0 | 6 06:0 | 5 48-4 || 2-0 0:8 | 8:0 33 | 140 57
21 | 6053 | 6 063 | 5 486 [| 2-1 09| 8-1 33 | 141 58
22 6055 | 6 065 | 5 48:8 || 2-2 09| 82 33 | 14-2 58
23 6058 | 6 068 | 5 491 || 2-3 0-9 | 8-3 3:4 |143 58
24 | 6 06:0 | 6 07:0 | 5 49:3 || 2-4 1:0 | 8-4 3:4 | 14-4 59

25 6063 | 6 073 | 5 496 || 2:5 1:0 | 8-5 3:5 | 1:5 59
26 6 065 | 6 07:55 | 5 498 || 2-6 l| 8-6 3:5 | 14-6 60
27 | 6068 | 6 078 | 5 50:0 || 2-7 1-1 | 8-7 3:6 | 147 60
28 | 6 07:0 | 6 08:0 | 5 50:3 || 2-8 11| &8 3:6 |148 6:0
6073 | 6 08:3 | 5505 [| 2-9 1:2 | 8-9 3:6 | 14-9 61

6075 | 6 085 | 5 50:8 || 3-0 1:2| 90 37 | 150 61
31 6 078 | 6 088 | 5 51:0 |31 13 | 91 37 | 151 62
32 | 6 08:0 | 6 090 | 5 51:2 || 3-2 13 | 9-2 38 | 152 6:2
33 | 6083 | 6 09:3 | 5 51:5 || 33 13 | 93 38 | 15-3 62
6 08:5 | 6 095 | 5517 || 3-4 1-4 | 9-4 38 | 154 6:3

6 08:8 | 6 098 | 5 52:0 | 3:5 14 | 95 39 | 155 63
36 6 09:0 | 6 10:0 | 5 52:2 || 3:6 1:5 | 9:6 39 |156 64
37 6 09:3 | 6 103 | 5 52:4 || 3-7 1:5 | 97 4:0 | 157 64
38 | 6095 | 6105 | 5 52:7 || 3-8 1:6 | 98 4:0 | 158 65
6 098 | 6 108 | 5 52:9 || 5:9 1:6 | 9-9 40 | 159 6:5

6 10:0 | 6 11:0 | 5 52:1 || 40 1:6 |10:0 4:1 | 160 65
41 | 6103 |6113 | 5 5344 | 41 17 |10-1 41 | 161 66
42 | 6105 |6115 | 5 536 || 4-2 17 |102 4:2 | 162 66
43 6108 | 6118 | 5 539 | 43 18 |10-3 42 | 163 67
6 11:0 | 6 120 | 5 54:1 || 44 18 |10:4 4:2 | 164 6:7

6113 |6 123 | 5 543 | 4-5 18 |105 43 | 165 67
46 | 6115 | 6125 | 5 546 || 4-6 19 |10-6 43 |166 68
47 | 6118 |6128 | 5 548 || 47 1:9 |10-7 44 | 167 68
48 | 6120 | 613:0 |5 55:1 || 48 2:0 |108 4:4 | 168 6:9
6123 | 6 133 |5553 | 4-9 2:0 |10-9 4:5 | 169 6:9

6125 |6135 | 5555 | 5-0 20 |11-0 45 |170 69
51 | 6128 | 6 138 | 5558 |51 21|ua 45 | 171 70
52 | 6 130 | 6 140 | 5 560 || 52 2-1 |11-2 46 |172 7:0
53 | 6133 |6143 | 5 562 || 5-3 22|1:3 46 |173 71
6135 | 6 145 | 5 565 | 5-4 2:2 |11-4 47 | 174 7:1

55 | 6138 | 6148 | 5 567 | 5-5 22 |[11-5 47 |175 71
56 | 6180 |6150 | 5570 || s6 23 |11-6 47 |176 72
57 6143 |6153 | 5 57:2 || 57 23|n-7 48 | 177 72
58 | 6145 | 6155 | 5574 | 58 2:4 |[11-8 48 |178 73
6148 |6158 | 5577 | 5-9 24 |11-9 49 |179 73

6 15:0 | 6 16:0 | 5579 || 6:0 2:5 |12-0 49

18°0

1148 APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

TABLES FOR INTERPOLATING SUNRISE, MOONRISE, ETC.
TABLE I—FOR LATITUDE

Tabular Interval Difference between the times for consecutive latitudes

10? 5° 2° |$m ro" 15" | 20" zen 30m | 35m 40" 45" | so" sam 60" | IP os" | 1^ ro" | 1^ 15m | 1^ 2om

o D o H o , m m m m m m m m m m m m h m h m h m h m
030 015 006|o O I T bil 1.42. 271) 22,2 rel N 0 02. tee ee et 2 OEO2
I 00 0 30 -0-12./ 0 PI). 14112 tea 3) 1 300 3984518 4 E 41S 05 o5 o5 05
1.30.,045: 0.18 | 1 krás 21534 936 0:41 14105045110 CAT 07 07 07 07
2/00, 1/00: 0,24.| 1.129 31 4 Ls Ms | 61.1 TETAS get IO IO IO IO IO
2.30 1116. .0:30,| 11122 41551625 7.12 SEO B0) T0 IS 12 13 13 13
3700791730. 0:36] T13 4 | 6 748% gv 10 #114125 13) 14 | o? 152] ORS PORTO ORIO
3730 1/45: 0'42 2713 s 77 8 ro") 112212 913/1142 16 17 18 18 I9 19
4.00 2/00: 0 48|2 '4 6|. 8 9 IT | 13. 14 15 165 18) 19 20 2I 22 22
4'30 215 054 | 2. 749 7 | 9 IE 13 |'15 16 181921 22 23 24 25 26
500 230 100|2 5 7|IO 12 I4 | I6 18 20 | 22 23 25 26 27 28 29
5:30 4245. 106)||3 |sē 8 [111 513016. |1820 92211124 26280 1072959 02398801319] 8 0832
600 300 112|3 6 9| 12 14 17,20 22 24 | 26 29 31 32 33 34 36
6/30 73115. 1183 16 TIO I3 816 Ig 220 24262983134 36 37 38 40
700 330 124|3 7 I0/14 17 20|23 26 29 | 31 34 37 39 41 42 44
730 345 130|4 7 II| 15 18 22,25 28 31 |34 37 40 43 44 46 48
800 400 136|4 8 12/16 20 23 27 30 34 | 37 41 44 | O 47 | O 48 | 0 §1 | o 53
830 415 I 42/4 8 13/17 21 25 | 29 33 36 | 40 44 48 | 051 | O 53 | O 56 | o 58
900 430 1 48/4 9 13/18 22 27 |31 35 39| 43 47 52 | O 55 | 0 58 | 1 or I 04
930 445 154|5 9 14/19 24 28 47 51.456. | 1:00:21. 104 I 08 IZ
1000 5 00 200|5 IO IS |20 25 30 0524 I 104 MI TSI S120

Table I is for interpolating the L.M.T. of sunrise, twilight, moonrise, etc. for latitude. It is to be noted
that the interpolation is not linear, so that when using this table it is essential to take out the reguired pheno-
menon for the latitude less than the true latitude. The table is entered with the nearest value of the difference
between the times for the tabular latitude and the next higher one, and, in the appropriate column, with the
difference between true latitude and tabular latitude; the correction so obtained is applied to the time for the
tabular latitude; the sign of the correction can be seen by inspection.

TABLE II—FOR LONGITUDE

Difference between the times for given date and preceding date (for east longitude)
or for given date and following date (for west longitude)

West Ih + In + |
IO" 20" 30" | 40" som 60^ | ro" 20" 30" | 40m som 6om | 22 rom | 2h 20m | 2h 39m | 2^ 49m | 2h som 3^ oom
o m m m m m m m m m m m m h m h m h m h m h m h m
0102907702 7012209707] £03 09901 20270290! f OYOOS SOTOO S NOTOO | O00 | 0 00 | o oo
10 |O I I TRG T 82) | 22:52 A 2325.3 293 04 04 04 04 05 05
20 | 19017 2172183 EAS 6887 07 o8 o8 09 09 IO
30 «| 1*:229.2 41731 7498 521 Be 7/9873 E83 o TO II I2 I2 I3 14 IS
40. Mr 7703717422678 77 | $829 E103 Tree I 2 T3 I4 16 17 18 I9 20
505 11553154116: 7722 8. IOS ITE I2A (148 1517) Kol 18 Koro on Fob 24 | 0 25
60 823 MS h 2722 8:103 1291399159 P1780818 te 22 23 25 27 28 30
e O 8 10 712. | T4 167172 0 198219823 25 27 29 31 33 35
80 |2 4 7| 9 11 13|16 18 20| 22 241827 29 31 33 36 38 40
90 (2357) LOR 12:56:15. 720220 [625827130 32 35 37 40 42 45
100 |3 6 8|1I 14 17|19 22 25| 28 31 33|0 36 | 0 39 | O 42 | 0 44 | 0 47 lo 50
110. 3-16 9 112815 18. 21124 2731534037 40 43 46 49 | O 52 | O 55
120 |3 7 10/13 17 20 | 23 27 30] 33 37 40 43 47 50 ISA NO ES 7 E100
130 |4 7 II|I4 I8 22 | 25 29 32 | 36 40 43 47 51 54 | 058 | I or | 1 os
140 | 4 8 12|16 19 23 | 27 31 35 | 39 43 47 SI S480 Ss T 028 T o6 LUTO
150 49973)! $17 21125 | 29 33 38 |42 46 so 0 54 | 0 58 | 103 | 1 OTELE TE ae lars
160 | 4 9 13 | 18 22 27 | 31 36 40 | 44 49 53150) 58 3150293 1 074 Terre I 161120
170 |5 9 14/19 24 28 | 33 38 42 47 52 57 | I OI | 106 | 111 | x 16 I 20 | I 25
180 | 5 IO 15 | 20 25 30 | 35 40 45 | so ss 60 | ros | I 10 | I IS | r 20] I 25 | I 30

Table II is for interpolating the L.M.T. of moonrise, moonset and the Moon's meridian passage for
longitude. Itis entered with longitude and with the difference between the times for the given date and for
the preceding date (in east longitudes) or following date (in west longitudes). The correction is normally
added for west longitudes and subtracted for east longitudes, but if, as occasionally happens, the times become
earlier each day instead of later, the signs of the corrections must be reversed.

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

Aldebaran

Alioth
Alkaid
Al Na'ir
Alnilam
Alphard

Alphecca
Alpheratz
Altair
Ankaa
Antares

Arcturus
Atria
Avior
Bellatrix
Betelgeuse

Canopus
Capella
Deneb
Denebola
Diphda

Dubhe
Elnath
Eltanin
Enif
Fomalhaut

Gacrux
Gienah
Hadar
Hamal
Kaus Australis

Kochab
Markab
Menkar
Menkent
Miaplacidus

Mirfak
Nunki
Peacock
Pollux
Procyon

Rasalhague
Regulus

Rigel

Rigil Kentaurus
Sabik
Schedar
Shaula

Sirius

Spica

Suhail

Vega
Zubenelgenubi

INDEX TO SELECTED STARS

Alpheratz
Ankaa
Schedar
Diphda
Achernar

Hamal
Acamar
Menkar
Mirfak
Aldebaran
Rigel
Capella
Bellatrix
Elnath
Alnilam

Betelgeuse
Canopus
Sirius
Adhara
Procyon

Pollux
Avior
Suhail
Miaplacidus
Alphard

Regulus
Dubhe
Denebola
Gienah
Acrux

Gacrux
Alioth
Spica
Alkaid
Hadar

Menkent
Arcturus

Rigil Kentaurus
Zubenelgenubi
Kochab

Alphecca
Antares
Atria
Sabik
Shaula

Rasalhague
Eltanin

Kaus Australis
Vega

Nunki

Altair
Peacock
Deneb
Enif

Al Nair
Fomalhaut
Markab

1149

1150

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC

ALTITUDE CORRECTION TABLES 0°-35°—MOON

10°-14°

1§°-19°

Corr»

I0 62.1
62-2
62:2
62:3
62:3
62:4

HI 62.4

62:4 |

62:5
62:5
62:5
62:6

12 62.6
62:6
62:6
62:7
62:7
62:7

13 62:7
62:7
62:7
62.8
62.8
62.8

14 62.8
62-8
62.8
62.8
62-8
62-8

Corr?
o

15 62.8
62.8
62.8
62.8
62.8
62:7

16 62-7

62-7
62-7
62:7
62-7
62.7

U 62.7
62.6
62-6
62:6
62-6
62.6

18 62-5

62-5
62-5
62.5
62:4
62:4

A 62:4
62:3
62:3
62.3
62:2

62-2
|

20°-24°

25°-29° | 30°-34°

Corr?

25 60.8
60:8
60:7

Corr^

3° 58:9
ECH?
58.8
5817
58-6
58:5

58:5
58:4
58:3
58-2
58-2
ECH:
58-0
37:9
57:8
57:8
57:7
57:6
$155
57:4
57:4
37:3
572
571

57:0
56:9
56:9
56-8

Alt.

LU

0:4 1:0
0:7 1-2
1-1 1-4
I:5 1:6
1-9 I:9
2:3 2:1
2:6 2:3
3:025
3427
3:8 2:9
4131
4:55 3:3
4935
5:2 3:8
5:6 4:0
6:0 4:2
6:4 4:4
6-7 4:6
7148
7:515:0
YES
8-2 5:4
8:6 5:7
9:0 5:9
9:4 6:1
9:7 6:3

DIP

: Ht. of, Ht. of
Host Corr? Eve Corr"| "Bye Corr?

MOON CORRECTION
TABLE

The correction is in two parts;
the first correction is taken from
the upper part of the table with
argument apparent altitude, and
the second from the lower part,
with argument H.P., in the same
column as that from which the
first correction was taken. Sep-
arate corrections are given in the
lower part for lower (L) and
upper (U) limbs. All corrections
are to be added to apparent alti-
tude, but 30’ is to be subtracted
from the altitude of the upper limb.

For corrections for pressure
and temperature see page A4.

For bubbie sextant observa-
tions ignore dip, take the mean
of upper and lower limb correc-
tions and subtract 15’ from
the altitude.

App. Alt. = Apparent altitude
= Sextant altitude corrected for
index error and dip.

m

APPENDIX V: EXTRACTS FROM NAUTICAL ALMANAC 1151
ALTITUDE CORRECTION TABLES 35?-90?9—— MOON

App. 35°-39° 40°-44° 45-49? 50-54? 55-59" 60°-64° 65-69" 70*- o o o ə o o o
74 |75°-79° | 80°-84° | 85°-89° | App.
e EE = Corre Set Corra Alt

Corr! Corral Corr:| Corr*| Corr

4° 537 14 50.5 | 5° 46-9 55 43:1 | © 339165 34:6 | 79 30-1 175 253 |80 205 | 85 15:6| 00
10 56-4) 536,| 5o4| 46:8) 42-9] 388| 344| 299| 252| 20-4] al 10

| 563| 535| 50-2) 467| 42-8) 38-7] 343| 297| 250| 202] 153| 20
30 | 562| 534| so I| 465| 427| 385| 341| 296| 249| 200| 151 30
40 562| 533| moi 464| 425| 384| 340| 294| 247| 199| 15:0| 4o
50 S61] 532| 499| 463| 42-4] 382| 33:8] 293| 245| 197| 148| so

I 6 6
56-0 4 $3:1 4 49:8 SI 46:2 5 42:3 ee 38:1 66 Aa Ja 29:I TE Šī 19:6 86 14:6| oo

10 55:9 53:0 49:7 46:0 42-1 37:9 33:5 29:0 24:2 19:4 I4:5| IO
20 558 52:8 49:5 45:9 42:0 378 33:4 28.8 24:1 I9:2 14:3 | 20
30 5557. 52:7 49:4 45:8 41:8 377 33:2 28-7 23:9 I9'I I4I| 30
40 55:6 52:6 49:3 457 41:7 SHAS) 33:1 28:5 23:8 18-9 140| 40
50 s5:5| 525| 49:2) 455! 41-6] 374| 32-9] 28-3] 23-6] 18-7] 13:8] so
oo |37 55:4| 52.414 49-1 |52 45-4 | 57 41-41 37.216 32-8 | 7? 28.2|77 23-4 | 82 18-6 | 87 13.71 00
10 55:3 52:3 49:0 45:3 413 37:1 32:6 28-0 23'3 I8:4 I3:5| 10
20 55:2 52:2 48-8 45:2 41:2 36:9 32:5 27:9 23:1 18:2 13:3| 20
30 55-1 ECH? 48:7 45:0 41:0 36:8 32:3 27:7 22:9 18:1 I3:2| 30
40 55:0 52:0 48:6 | 449 40:9 36-6 32:2 27:6 22:8 17:9 I3:0| 40
50 55:0 $1:9 48:5 44:8 40:8 36:5 32:0 27:4 22:6 17:8 I2:8| 50
38.,.143 51-8 45 8:4 53 44.6 ebe? 73 78 ,,..|83 88

IO 54:8 $1:7 48:2 44:5 40:5 36:2 31:7 27:1 22:3 17:4 I2:5| IO
20 54:7 51-6 48:1 44:4 40:3 36:1 31.6 26:9 22:1 17:3 I2:3| 20
30 54:6 515 48-0 44:2 40:2 35:9 31-4 26:8 22:0 I7-I I2:2| 30
40 54:5 51-4 47:9 44:I 40:I 35:8 31:3 26.6 21:8 16:9 12:0| 40
50 $44 51-2 47:8 44:0 39:9 35:6 31:1 26:5 21:7 16:8 II:8| 50

o o o

oo |39 54-3 | 51.114 47-6 | 54 43-9 | 59 39-8 | $4 35-5 |69 31.0 | 74 26.3 | 79 21-5 |84 16.6 | 89 11.7 | 00
10 542 51-0 4T:5 43:7 39:6 35:3 30:8 26:1 21:3 16:5 II-5 | IO
20 54:1 50:9 47:4 43:6 39:5 35:2 30°7 26-0 21:2 16:3 11:4| 20
30 540} 508| 473| 435| 394| 350| 305, 258| 21:0| 16-1] 11-2] 30
40 539| 50:7| 472| 43-3) 39:2] 349] 30-4] 257| 209! 16:0) 11-0} 40
50 s3:8| 50°6| 470| 432| 391| 34:7| 302) 25:5| 207| 15:8] 10-9] 50
Pee Ce On VISS e ECHO ELFU bm Ors heel LeU) (ZUS HP.
| L "ed «i
$40 | I-I 1-7 | 1-3 1-9 | 1-5 2-1 | 1-7 2-4 | 2:0 2-6 | 2-3 2:9|2:63-2|2:93:5|3:23:8|3:54:1|3:84:5 | 540
54:3 | 1-4 1-8 | 1-6 2-0 | 1-8 2-2 | 2-0 2-5 | 2-3 2:7 | 2:5 3:0 | 2:8 3:2 | 3:0 3:5| 3:3 3:8 | 3-6 4:1 | 3:9 4:4] 54:3
54:6 | 1-7 2:0 | 1-9 2-2 | 2-1 2-4 | 2-3 2-6 | 2-5 2-8 | 2-7 3-0 | 3 0 3-3 | 3:2 3-5 | 3:53:8|3:7 4:1 | 4:0 4:3 546
54:9 | 2:0 2:2 | 2:2 2-3 | 2-3 2-5 | 2-5 2-7 | 2-7 2-9 | 2-9 3-1 | 3-2 3-3 | 3:4 3:5 | 3-6 3:8 | 3-9 4-0 | 4-1 4:3 | 54:9
55:2 | 2-3 2:3 | 2:5 2-4 | 2:6 2-6 | 2-8 2-8 | 3-0 2-9 | 3-2 3-1 | 3-4 3:3 | 3-6 3:5 | 3:8 3:7 | 4040 4-2 4:2 | 552
55:5 | 2:7 2-5 | 2-8 2-6 | 2-9 2-7 | 3-1 2-9 | 3-2 3-0 | 3-4 3-2 | 3:6 3-4 | 3-7 3:5 | 3:9 3:7 | 4:1 3:9 | 4:3 4:1 | 55:5
55:8 | 3:0 2-6 | 3-1 2-7 | 3-2 2-8 | 3-3 3-0 | 3-5 3-1 | 3-6 3-3 | 3-8 3-4 | 3-9 3-6]. 4-1 3-7 | 4:2 3:9 | 4:4 4:0 | 558
56-1 | 3-3 2°8 | 3-4 2-9 | 3-5 3-0 | 3-6 3-1 | 3-7 3:2 | 3-8 3-3 | 4:0 3:4 | 4:1 3-6 | 4-2 3-7 | 4-4 3-8 | 4540 | 56-1
56-4 | 3-6 2-9 | 3-7 3-0 | 3-8 3:1 | 3-9 3-2 13-9 3-3 | 4:0 3-4 | 4-1 3:5 | 4:3 3:6 | 4-4 3-7] 4-5 3-8 | 4:6 3-9 | 56-4
56:7 | 3-9 3-1 | 403-1 | 4:1 3-2 | 4-1 3-3 | 4:2 3-3 | 4-3 3:4 | 4:3 3°5 | 4:4 3-6 | 4:5 3-7 | 4:6 3-8 | 4-7 3-8 | 56-7
57:0 | 4:3 3:2 | 4:3 3:3 | 4:3 3°3 | 4:4 3:4 | 4-4 3:4 | 4:5 3:5 | 4:5 3:5 | 4:6 3-6 | 4:7 3:6 | 4-7 3-7 | 4:8 3:8 | 57-0
57°3 | 4:6 3:4 | 4:6 3:4 | 4-6 3-4 | 4-6 3-5 | 4-7 3:5 | 4-7 3°5 | 4:7 3:6 | 4:8 3-6 | 4-8 3-6 | 4-8 3-7 | 4-9 3-7 | 573
57-6 | 4:9 3:6 | 4-9 3°6 | 4:9 3-6 | 4-9 3-6 | 4:9 3:6 | 4-9 3-6 | 4:9 3:6 | 4:9 3-6 | 5-0 3-6 | 5:0 3-6 | 5:0 3-6 576
57:9 | 5:2 3:7 |5237 | 523:7 | 5:2. 3:7 | 5:2 3-7 | 5:1 3:6 | 5-1 3-6 | 5-1 3:6| 5-1 3:6| 5-1 3-6 | 5-1 3:6| 57-9
58:2 | 5:5 3:9 | 5:5 3:8| 5:5 3-8 | 5:4 3:8 | 5:4 3:7 | 5:4 3:7 | 5:3 3:7 | 5:3 3:6| 5-2 3:6| 5:2 3:5 | 5:2 3:5| 582
58:5|5:940|5:84:0|5:83:9|5:7 3-9 | 5:6 3:8| 5:63:8|5:53:7|5:53:6|5:43:6| 5:3 3:5| 5:3 3:4| 58:5
58:8 | 6-2 4:2 | 6-1 4:1 | 6-0 4-1 | 6-0 40| 5:93:9| 5:8 3:8| 5-7 3:7 | 5:6 3:6 | 5:5 3:5 |5435 | 5-3 3:4| 58:8
59:1 | 6-5 4:3 | 6-4 4-3 | 6-3 4:2 | 6-2 4-1 | 6-1 4:0 | 6-0 3-9 | 5-9 3-8 | 5:8 3-6 | 5:7 3:5 | 5-6 3-4] 5:4 3:3 | 591
59:4 | 6-8 4:5 | 6-7 4:4 | 6-6 4:3 | 6:5 4:2 | 6-4 4-1 | 6-2 3-9 | 6-1 3-8 | 6:0 3-7 | 5-8 3:5] 5:7 3:4 | 5532 594
59:7 | 7:1 4:6 | 7-0 4:5 | 6-9 4:4| 6-8 4:3 | 6-6 4-1 | 6-5 4:0 | 6-3 3-8 | 6-2 3:7 | 6:0 3:5 | 5:8 3-3 | 5:6 3:2 | 59:7
60-0 | 7:5 4:8 | 7:3 4:7 | 7:2 4:5 | TO 4:4 | 6:9 4:2 | 6:7 4:0 | 6:5 3-9 | 6:3 3-7 | 6-1 3:5 | 5:9 3:3 | 5:7 3:1 | 60-0
60:3 | 7:8 5:0 | 7:6 4:8 | 7:5 4:7 | 7:3 4:5 | TI 4:3 | 6-9 4-1 | 6-7 3:9 | 6:5 3-7 6335/6032 | 5:8 3-0 | 60-3
60-6 | 8-1 5-1 | 7:9 5:0 | 7:7 4:8 | 7:6 4:6 | 7:3 4:4 | 7-1 4:2 | 6-9 3-9 | 6-7 3-7 | 6-4 3-4 | 6-2 3:2 | 5:9 2-9 | 60-6
60-9 | 8-4 5-3 | 8-2 5-1 | 8:0 4:9 | 7-8 4:7 | 7-6 4:5 | 7:3 4:2 | 7-1 4:0 | 6:8 3-7 | 6-6 3-4 | 6-3 3-2 | 6-0 2-9 | 60-9
61-2 | 8-7 5-4 | 8-5 5:2 | 8-3 5:0 | 8-1 4:8 | 7:8 4:5 | 7:6 4:3 | 7:3 4:0 | 7:0 3:7 | 6-7 3:4 | 6-4 3-1) 6-1 2:8 | 61:2
61-5 | 9:1 5:6 | 8-8 5-4 | 8-6 5-1 | 8-3 4-9 | 8-1 4-6 | 7-8 4:3 | 7:5 4-0 | 7:2 3:7 | 6:9 3-4 | 6-5 3-1] 6:2 2:7 | 61.5

APPENDIX W

EXTRACTS FROM AIR ALMANAC
INTERPOLATION OF G.H.A.

STARS, MAY—AUG., 1958

Acamar
Achernar
Acrux
Adhara
Aldebaran

Alioth
Alkaid
Al Na'tr
Alnilam
Alphard

Alphecca
Alphevatz
Altair
Ankaa
Antares

Arcturus
Atria
Avior
Bellatrix
Betelgeuse

Canopus
Capella
Deneb
Denebola
Diphda

Dubhe
Elnath
Eltanin
Enif
Fomalhaut
Gacrux
Gienah
Hadar
Hamal
Kaus Aust.

Kochab
Markab
Menkar
Menkent
Miaplacidus
Mirfak
Nunki
Peacock
Pollux
Procyon

Rasalhague
Regulus
Rigel

Rigil Kent.
Sabik

Schedar
Shaula
Sirius
Spica
Suhail

Vega
Zuben' ubi

1152

ji
$

9
10

315 50
335 58
173 55
255 45
291 37

166 57
153 31
28 35
276 29
218 37

126 46
358 26
62 48
353 56
113 17
146 33
108 55
234 35
279 17
271 46

264 15
281 36
49 59
183 16
349 37

194 43
279 05
91 05
34 28
16 09

172 47
176 35
149 46
328 48
84 38

137 18

14 19
314 58
148 56
221 49

309 40
76 49
54 24

244 19

245 43

96 45
208 28
281 52
140 48
103 00

350 28
97 18
259 10
159 15
223 23

81 07
137 51

o EN

S. 40 28
S207 27
S.62 52
$.28 55
N. 16 26
N.56 11

N. 49 31

S.47 10
S. 114
S. 8 29

N. 26 51
N. 28 52

N. 8 46
S.42 32
$.26 20

N. 19 24
S.68 57
S.59 23
N. 619
N. 7 24

S.52 40
N. 45 57
N. 45 08
N. 14 48
S. 18 13

N. 61 59

N. 28 34
N. 51 30
N. 9 41
S.29 50

S.56 53
S. 17 19
S.60 11
N. 23 16
S.34 24

N.74 20
N. 14 59
N. 3 56
S.36 10
S.69 33

N. 49 43
S.26 21
S.56 52
N. 28 08
N. 520

N. 12 35
N. 12 10
S. 8 15
S.60 40
S. 15 40

N. 56 18
S. 37 04
S. 16 40
S. 10 57
S 43 16

N. 38 45
S. 15 52

Increment to be added for intervals of G.M.T. to G.H.A. of:
Sun, Aries (Y) and planets ; Moon.

——

MOON

m s
06 52
06 56
07 00
07 04
07 08
07 13
07 17
07 21
07 25
07 29
07 33
07 37
07 42
07 46
07 50
07 54
07 58
08 02
08 06
08 11
08 15
08 19
08 23
08 27
08 31
08 35
08 40
08 44
08 48
08 52
08 56
09 00
09 04
09 09
09 13
09 17
09 21
09 25
09 29
09 33
09 38
09 42
09 46
09 50
09 54
09 58
10 00

“SUN, etc. MOON | SUN, etc. MOON | SUN, etc.
ua m "eis E e
o 9» 4 03 25 06 ape
Msc cie door rc
O OI O 5I ube
05 , 0006 25/2 eos 33 45 Tia
og °° 00 10 a9 22 03 37 4m 18
eet? 00 14 jue 03 41 53 I 44
DE 0018| 37 57. 0345/0657 |
21 ge: 00 22 41 Ge 03 49 | 07 OI I
25. E 0026... 45) 7^ Goa K tal
29 997 0031 49.20. 0358 gon S
o o8 o 58 1 48
33 S 00 35 53 aen 04 02 13 I 49
Vosa aste ae
joe it trie d al Pet oi 25 15!
4 O 12 do 5 T E eR A I 52
Seo 13 ELT. > 153
big 00 55 13 25.1 04.53 3,
00 57 | ^ or oo 17 * o4 27 37 E
oror 7 o1 04 2150 04 31 41 ee:
O 16 I 06 1 56
05 a 01 08 25 i 04 35 Ads 57
09 oig 9112 A 20439 AR 58
13 OI 16 33 04 43 53
17 9 19 or 20 37/519 od 48 (Og o7, 2099
o 20 I IO 2 00
21 OI 24 41 04 52 | 08 o1
O 2I Í TI 201
25 MUS 45 04 56 05
TEL 2 02
RA M E LO S3 49 05 00 09
3 TPES: 2 03
AAN or 37 37 05 04 EU
37 os OI 41 | 04 57 Tus 05 o8 VEER,
41 o eto 45 | 05 OI eg 05 12 21 E
1568; OI 49 05 117 05 17 25u
n SE 18 05 21 29 rae
53 020 OI 58 ELE 3,
OI 57 02 02 P EOS 29 S725 E
o 30 I 20 2 10
02 OI bes 02 06 21 05 33 41
05 "E 02 IO 25 vee 05 37 ages te
0907 02 14 29 05 41 dg tu
13 PE. 02 18 33. K 05 46 53 2113
17 a 02 22 37 DE os 50 | 08 57 7 14
21 gg 02 27 41 ES 05 54 | 09 OI Se
33 37:549. T esee
$ ag 02 39 33. «ris 06 06 1378
37 er EIER EE Ue LER
41 Si 02 47 0601 ` 3 06 15 2188 E
45 4 oe 5I 05 L3! o6 19 25 E
O 42 6 I 32 2122
49 DH 02 5 09 : 06 23 29
53 og SA A
02 57 pee 03 04 17 34 op 31 37 ip
03 OI tee 03 08 21 a 06 35 41 See
05 E mei 25 ^ S" o6 39 45 229
VARU 20 ca cadum cen
Lobe 03 20 ER 06 48 qué
17 oso E 00 dee
03 21 03 29 | 06 41 4° 06 56 | 1000 ? 3°
* Stars used in H.O. 249 (A.P. 3270).
1 Stars so indicated may be used with declination tables.
Tos aria following the names are those used in A.P. 1618

APPENDIX W: EXTRACTS FROM AIR ALMANAC 1153

CORRECTIONS TO BE APPLIED TO MARINE SEXTANT ALTITUDES
A piu mee eege

MARINE SEXTANT CORRECTIONS CORRECTION FOR DIP OF THE HORIZON
ERROR E
K To be subtracted from sextant altitude.
Sextant No. In addition to sextant
error and dip, corrections
are to be applied for:
Index Error Refraction i Tt El BE
Semi-diameter o ` 114 i 1,707 '
(for Sun and Moon) 2
2
Parallax (for the Moon) 6 3
Dome refraction if 12
applicable. ars
SH
43
SE
75
932 0
10

LIST OF CONTENTS

Pages
Inside front cover
Daily pages
AI—A3
A4—AI5
A16—4A17
A18—A21
A22—A47
A48—A49

Aso—A5I
A52

A53

A54

Under flap

A57 (flap)

A58 (inside of flap)

Inside back cover

Outside back cover

Contents

Star list and G.H.A. interpolation tables.
Ephemerides of Sun, Moon, Aries and planets.
Title page, preface, etc.

Explanation.

List of abbreviations and symbols.

Standard times.

Sky diagrams.

Semi-duration diagrams for rising and setting pheno-
mena in high latitudes.

Corrections for height to times of sunrise, etc.

Conversion of arc to time and interpolation of moonrise
and moonset for longitude.

Star index.

Explanation of star chart.

Star chart.

Star list and G.H.A. interpolation tables.

Polaris table, dome refraction, A.N.T. adjustment for
refraction.

Corrections for (total) refraction and Coriolis (Z) table.

Corrections to marine sextant observations.

1154

GMT

O suN ARIES | VENUS — 3.6 MARS 0.6
GHA Dec. GHA v GHA Dec. GHA Dec.
o LI o 1 o y o + o D o Z o +

0 35 N22 02
305

15 35 N22 02
18 05

20 35

23 05.
22155

28 05

30 35 N22 02
33 05

35135

38 05 .

40 35

43 05

45 35 N22 03
48 05

50 35

53 05.
55835

58 05

60 35 N22 03
63 05

65 35

68 05 -

70 35

73 05

75 35 N22 03
78 05

80 35

83 05.

85 35

88 05

90 35 N22 04
93 05

951535

98 05 .
100 35
103 05

105 35 N22 04
108 04

110 34

113 04 -

115 34

118 04

120 34 N22 04
123 04

125 34

128 04 -

130 34

133 04

135 34 N22 05
138 04

140 34

143 04 .

145 34

148 04

150 34 N22 05
153 04

155 34

158 04 -

160 34

163 04

165 34 N22 05
168 04

170 34

173 04.

175 34

178 04

APPENDIX W: EXTRACTS FROM AIR ALMANAC

GREENWICH P. M. 1958 JUNE 1 (SUNDAY)

O MOON Sun- | Twi-| Moon- |...
Lat| rise light| rise Diff.
GHA Dec.
o Li o + N

69 28
71 58
74 29
76 59
7930
82 00

84 30
87 01
89 31
92 02
94 32
97 02

99 33
102 03
104 34
107 04
109 34
112 05

114 35
117 06
119 36
122 07
124 37
127 07

129 38
132 08
134 39
137 09
139 39
142 10

144 40
147 11
149 41
15211
154 42
157112

159 43
162-13
164 44
167 14
169 44
172015

174 45
177 16
179 46
182 16
184 47
187 17

189 48
192 18
194 48
197519
199 49
202 20

204 50
207 21
209 51
21252
214 52
211822

219059
222 23
224 53
227 24
229 54
232/25

234 55
237.25
239 56
242 26
244 57
[247 27

40 27 N 9 38
42 56

45 26

47 56 +

50 26

52 56

55 26 N 9 39
57 56

60 26

62 56 -

65 26

67 56

70 26 N
72 56
75 26
77256 ES
80 26
82 56

85 26 N
87 56
90 26,
92 56.
95 26
97455

100 25 N
102 55
105 25
107 55.
110 25
112155

115 25N
11755
120 25
122155
125 25
127855

130 25 N
132 55
135725
137 55%
140 25
142 55

145 25 N
147 55
150 25
152 54.
155 24
157 54

160 24 N
162 54
165 24
167 54.
170 24
172 54

17524N
177 54
180 24
182 54.
185 24
187 54

190 24 N
192 54
195 24
197 54.
200 24
202 54

205 24 N
207 53
210 23
212159 7:
215 23
217453

9 40

9 41

9 42

9 43

9 43

9 44

9 45

9 46

947

9 48

7228 S 3 30
74 58

77 28
7958.

82 28

84 58

87 28 S 3 29
89 58

92 29

94 59 -
97:29

99899

102129 S 9:29
104 59

107 29

110 00 +

112 30

115 00

117 30 S
120 00
122 30
125 00 -
127 30
130 01

13213145
135 01
13781
140 01 -
142 31
145 01

147 32
150 02
152 32
155 02.
151052
160 02

162 32
165 02
167 33
170 03 -
17283
175 03

177 33
180 03
182 33
185 04 -
187 34
190 04

192 34
195 04
197 34
200 04 .
202 34
205 05

207 355
210 05
212 35
21505.
217235;
220 05

222065
225 06
227 36
230 06 -
232 36
235 06

231 3619
240 06
242 37
24507.
247 37
250 07

3 28

Nel

S

326

S

326

S

3125

S

324

324

2822

2122

JUPITER — 1.9
GHA Dec.

228 23 S
230 54
233 24
239599
238 25
240 56

243 26 5
245 56
248 27
250 57 -
253 28
255 58

258 29S
260 59
263 29
266 00 -
268 30
271 01

27595155
216 02
278 32
281 02 -
283 33
286 03

288 34
291 04
292195
296 05 -
298 35
301 06

303 36
306 07
308 37
311 08 -
313 38
316 08

318 395
321 09
323 40
326 10 -
328 41
331 11

333 42
336 12
338 42
341 13.
343 43
346 14

348 44
351 15
353 45
356 15.
358 46
116

347
6 17
8 48
11 18.
13 48
16 19

18 49S
21 20
23 50
26 21 +
28 51
3172)

SEKR
36 22
38 53
4123.
43 54
46 24

S;

S

S

S

S

720

720

7 20

7 20

720

1720

7 20

7 20

7 20

7 20

7 20

7 20

185 20 S18
187 44
190 08
192 32
194 56
197 20

199 44
202 09
204 33
206 57
209 21
211 45

214 09 S18
216 33
218 57
221 21
223 45
226 10

228 34 S18
230 58
233 22
235 46
238 10
240 34

242 58 S18
245 22
247 46
250 10
252 35
254 59

257 23 S18
259 47
262 11
264 35
266 59
269 23

271 47
274 11
276 36
279 00
281 24
283 48

286 12
288 36
291 00
293 24
295 48
298 13

300 37
303 01
305 25
307 49
310 13
312437

31501
2317.25
319 49
322 14
324 38
327 02

329 26 518
331 50
334 14
336 38
339 02
341 26

343 51 S18
346 15
348 39
351 03
353 27
295151

S18

19

26
27
27
28
28
29

29
30
30
31
32
32

33
33
34
34
35

Diff.

APPENDIX W: EXTRACTS FROM AIR ALMANAC 1155

GREENWICH A. M. 1958 JUNE 2 (MONDAY)

O sun ARIES | VENUS—3.6 | MARS 0.6 JUPITER—1.9 | O moon | Moon's
GHA Dec. |GHA T| GHA Dec. | GHA Dec. | GHA Dec. | GHA Dec, [^^^
o , o , o + o , o , o , o , o , o , o 4 o ^

GMT
h m

00 00/1180 34 N22 06/249 581220 23 N 9 49|252 37 S 3 22| 48 54 S 7 201358 15 S18 53
10,183 04 222 52 255 07 51225 0 39 54
20/185 34 225 23 257.37. 5295 3 03 54
30||188 04. 221.5342 (2600872 15 5626. <. 5:20 E
40||190 34 230 23 262 38 58 56 T52 55
50/1193 04 232.59 265 08 61 27 10 16 55

01 00/1195 34 N22 06 23523N 9 501267 38 S 321| 6357 S 7 20! 12 40 S18 55
10||198 04 237 53 270 08 66 27 15 04 56
20||200 34 240 23 272 38 68 58 17 28 56
30||203 04. 242053: 2 OS 7128 KO 19/52 02256

205 34 245 23 2638 713859 22 16 57

50||208 04 247 53 280 09 76 29 24 40 57
02 00||210 34 N22 06 250 23N 9 51|282 395 3 20| 79 00 S 7 20| 27 05 S18 57
10||213 04 252 53 285 09 81 30 29129 58
2011215 34 255 23 287 39 84 00 91753 58
30||218 04. 257832 2 9070 JSS o e lc MUSS

40||220 34 260 23 292/39 89 01 26 41 58
50/1223 04 262 52 295 09 91 32 39 05 59
03 00||225 34 N22 07 265 22 N 9 521297 40 S 3 20| 94 02 S 7 20| 41 29 S18 59
10||228 04 267 52 300 10 96 33 43 53 18 59

230 34 270 22 302 40 99 03 46 18 1900

30||233 04. 272923 (30510 51013477 |0487420 1700
40||235 34 215.22 307 40 104 04 51 06 00
50/1238 04 277 52 310 10 106 34 59250) 00
04 00||240 34 N22 07 280 22 N 9 53|312 40 S 3 191109 05 5 7 20| 55 54 S19 01

243 04
245 34

282 52 315 10 111935 58 18 01
285 22 317 41 114 06 60 42 01

30/1248 04 - 287452 S BRO dd nana 1613 019 2705863106501
40/1250 34 290 22 322 41 119 07 6531 02
50||253 04 292 52 32511 121737 67 55 02
05 00||255 34 N22 07 295 22 N 9 54|327 41 S 3 18|124 07 S 7 20| 70 19 S19 02
10||258 04 297 52 330 11 126 38 12 43 02
20/1260 34 300 22 332 41 129 08 7507 03
30||263 04 - SOLIS ZA LS EE, 1577-3177: 803
40|| 265 34 305 22 337 42 134 09 19:55 03
50||268 04 307 52 340 12 136 39 82 19 03
06 00|/270 34 N22 08 310 22 N 9 55/342 42 S 3 17/139 10 S 7 20| 84 44 S19 04
10/1273 03 951252 345 12 141 40 87 08 04
2011275 33 315 22 347 42 144 11 89 32 04
30||278 03 - II 9.50) T2 (A CA TI C1 56:204
4011280 33 320 21 352 42 149 12 94 20 04
50||283 03 322 51 355 13 151 42 96 44 05
07 00/1285 33 N22 08 325 21 N 9 56/357 43 S 3 17|154 135 7 20| 99 08 S19 05
10||288 03 327 51 013 156 43 101 33 05
2011290 33 330 21 2 43 159113 103 57 05
30/1293 03 - 332 5155 s Sido O Mes o 10692100805
40/1295 33 335 21 7 43 164 14 108 45 05
50||298 03 3237251 10 13 166 45 111 09 06
08 00||300 33 N22 08 34021N 9 57| 1244 S 3 16/169 15 S 7 20/113 33 S19 06
10||303 03 342 51 15 14 171 46 115257 06
20/1305 33 345 21 17 44 174 16 118 21 06
30||308 03 - ZATRE V Eo M2 OLA GE 120:46 44500
40/1310 33 350 21 22 44 17:9117 123 10 06
50/1313 03 352.51 25 14 181 47 125 34 07
09 00/1315 33 N22 09 355 21 N 9 58| 27 44 S 3 151184 18 S 7 19/127 58 519 07
10||318 03 357 51 30 14 186 48 130 22 07
20/1320 33 021 32 45 189 19 132 46 07
30/1323 03 - ils ree a jlbencero 2 (tēvi oc dun
40/1325 33 521 37 45 194 19 137 35 07
50/1328 03 y Epi 40 15 196 50 13959 08
10 00/1330 33 N22 09 10 21N 9 59| 42 45 3 15/199 20 S 7 19|142 23 519 08
10||333 03 12 50 45 15 20151 144 47 08
20/1335 33 15 20 47 45 204 21 147 11 08
30/1338 03 - ii) ē, | 50162000525 14925208
40||340 33 20 20 52 46 209 22 151 59 081
50/1343 03 22 50 55 16 21152 154 24 08
11 001/345 33 N22 09 25 20 N10 00| 57 46 S 3 14/214 23 S 7 19|156 48 S19 08
10||348 03 27 50 60 16 216 53 159112 09
20/1350 33 30 20 62 46 219 24 161 36 09
30/1353 03 - Ze Dirt 165165 221 54-51 165 00:15 AR
40/1355 33 35 20 67 46 224 25 166 24 09
50|1358 03 37 50 70717 226 55 168 49 09

1156 APPENDIX W: EXTRACTS FROM AIR ALMANAC

SEMIDURATION OF SUNLIGHT

N85

N80

SUN ABOVE
HORIZON

N75

N85

CONTINUOUS TWILIGHT
OR SUNLIGHT

N75

N70

MAY JUNE JULY AUGUST

APPENDIX W: EXTRACTS FROM AIR ALMANAO 1157

SEMIDURATION OF MOONLIGHT
|

12*
N85 Å

A N85
P \ MOON BELOW d Ë N N80
S HORIZON AN

N70

N75

N70

N85

N80 N80
MOON BELOW MOON ABOVE MOON BELOW
HORIZON HORIZON HORIZON
N75 N75
SEZ e à |

SÓ,

N70

4 N70

N85 N85

ay MOON ABOVE MOON BELOW SBD

HORIZON HORIZON

N75

N75

Ü N10

N70

N85

N85

Y N80

NEO Í MOON ABOVE MOON BELOW
HORIZON HORIZON

N75

N75

N70

AUGUST 5 10 15 20 25 30 1958

1158 APPENDIX W: EXTRACTS FROM AIR ALMANAC
CONVERSION OF ARC TO TIME INTERPOLATION OF
MOONRISE, MOONSET
m o i o h o h , m s
o e oo | 45 E 00 90 6 00 135 9 00 o | 0 oo FOR LONGITUDE
1 | o of | 46 | 3 04 91 | 6 04 | 136 9 04 I | 0.04 Add if longitude west.
2 | 0 08 | 47 | 3 08 | 92] © 08 | 137 993] 2] 0 08 Subtract if longitude east.
3 | 0 12] 48 | 3 12 93 | 6 12 | 138 | 9 12 331 © 12 | Diff.*
41016] 49 | 3 16] 94 | 6 16] 139 | 9 16] 4] 0 16 un
t
5|o20|50/320| 95|620]| 140| 9 20] 5|o020 WA 05 | IO | 15 | 20 | 25 | 30
6 | o 24] 51 | 3 24 96 | 6 24 | 141 9x2 6 | o 24 — eer pa A
70.28 | 52 | 3 28 | 9716.28 | 142 | 9/28 | 7 | o 28 eg B o = Ce LR
24.932.153 EETA | £43 E oa OI | OI | 02 | 02 | 03 | 03
6 6 6 30 | 1 6 o 36
9 | o 36 | 54 | 3 36 | 99 | 6 36 | 144 | 936| 9} 03 or hoz |03 04 | 061.67
io ono |53| 3: 491.100 Gna [14h oro O | odo 02 | 03 | 05 | 07 | 08 | 10
11 | O 44 | 56 | 3 44 | 101 | 6 44 | 146 | 9 44 | 11 | O 44 02 | 04 | 07 | 09 | II | I3
12 | 0 48 | 57 | 3 43 | 102 | 6 43 | 147 | 9 43 | 12 | o 48
13 | 0 52] 58 | 3 52 | 103 | 6 52 | 148] 9 52 | 13 | © 52 03 | 06 | o8 | I1 | 14 | 17
14 | © 56 | 59 | 3 50 | 104 | 6 56 | 149 | 9 56 | 14 | o 56 03 |07|10 | 13 | 17 | 20
15 | 1 00 | 60 | 4 00 | 105 | 7 00 | 150 | 10 oo | 15 | 1 oo 04 | o8 | 12 | 16 | 19 | 23
16 | 1 o4 | 61 | 4 04 | 106 | 7 04 | 151 | 10 04 | 16 | 1 04 04 | 09 | 13 | 18 | 22 | 27
17 | 1 08 | 62 | 4 08 | 107 | 7 08 | 152 | 10 08 | 17 | 1 08 05 | IO | 15 | 20 | 25 | 30
18 | I 12 | 63 | 4 12 | 108 | 7 12 | 153 | 10 12 | 18 | x 12 Diff *
19 | 1 16 | 64 | 4 16 | 109 | 7 16 | 154 | 10 16 | 19 | x 16 E
20 | I 20 | 65 | 4 20 | 110 | 7 20 | 155 | 10 20 | 20 | 1 20 35 | 40 | 45 | 50 | 55 | 60
21 | I 24 | 66 | 4 24 | 111 | 7 24 | 156 | 10 24 | 21 | 1 24 —Ý —— |_|
22 | 1 28 | 67 | 4 28 | 112 | 7 28 | 157 | 10 28 | 22 | 1 28 m| m| m| m| mj m
23|132|68|4 32 | 113 | 7 32 |] 158 | 10 32 | 23 | 1 32 oo |00 | 00 | 00 | OO | 00
24 | 1 36 | 69 | 4 36 | 114 | 7 36 | 159 | 10 36 | 24 | 1 36 03 | 03 | 04 | 04 | 05 | 05
25 | I 40 | 70 | 4 40 | 115 | 7 40 | 160 | 10 40 | 25 | 1 40 SO EA epo EO
26 | 1 44 | 71 | 4 44 | 116 | 7 44 | 161 | 10 44 | 26 | 1 44 2 lee a o
27 | 1 48 | 72 | 4 48 | 117 | 7 48 | 162 | 10 48 | 27 | 1 48 12 | 13 | 15 | 17 | 18 | 20
28 | 1 52] 73 | 4 52 | 118 | 7 52 | 163 | 10 52 | 28 | 1 52 15 | 17 | r9 | 21 | 23 | 25
29 | 1 56 | 74 | 4 56 | 179 | 7 56 | 164 | 10 56 | 29 | 1 56 18 | 20 | 22 | 25 | 28 | 30
30 | 2 00 | 75 | 5 00 | 120 | 8 oo | 165 | rr oo | 30 | 2 oo 20 | 23 | 26 | 29 | 32 | 35
31 | 2 04 | 76 | 5 04 | 121 | 8 04 | 166 | 11 04 | 31 | 2 04 2312745391033: 37 140
32 | 2 08 | 77 | 5 08 | 122 | 8 08 | 167 | 11 08 | 32 | 2 08
33 | 2 12 | 78 | 5 12 | 123 | 8 12 | 168 | 1x 12 | 33 | 2 12 26 | 30 | 34 | 38 | 41 | 45
34 | 2 16 | 79 | 5 16 | 124 | 8 16 | 169 | 11 16 | 34 | 2 16 29 | 33 | 38 | 42 | 46 | 50
35 | 2 20 | 80 | 5 20 | 125 | 8 20 | 170 | 11 20 | 35 | 2 20 31371 5 2
36 | 2 24 | 81 | 5 24 | 126 | 8 24 171 Tr 24117 368 62124 35 149 | 45 | 501 55 `
37 | 2 28 | 82 | 5 28 | 127 | 8 28 | 172 | 11 28 | 37 | 2 28 Diff.*
38 | 2 32 | 83 | 5 32 | 128 | 8 32 1731113211 382732
39 | 2 36 | 84 | 5 36 | 129 | 8 36 | 174 | 11 36 | 39 | 2 36 65 | 70 | 75 | 80 | 85 | 90
40 | 2 40 | 85 | 5 40 | 130 | 8 40 | 175 | 11 40 | 40 | 2 40 PES EE A ET
41 | 2 44 | 86 | 5 44 | 131 | 8 44 | 176 | 11 44 | 41 | 2 44 00 | oo | oo | oo | oo | oo
42 | 2 4 87 | 5 48 | 132 8 48 | 177 | 11 48| 42 | 2 48
43 | 2 52 | 88 | 5 52 | 133 | 8 52 178 | II 52 | 43 | 2 52 a 4 i šā Y: E
2 56] 8 6] 1 8 56 6 6 h
E: å visa 34 d lake coke. Lect hii IT 12) (12) (134140 BS
45 | 3 00 | 90 | 6 00 | 135 | 9 00 | 180 | 12 00 45 3 oo 14 | 16 | 17 | 18| 19 | 20
R | sog eg 46 | 3 04
47 | 3 08 I8 19 | 21 | 22 | 24 | 25
For angles greater than 180°, subtract 180° | 48 | 3 We 22.23 | 25 | 27 | 28 | 30
AOR St 25/27 | 29 | 31 | 33 | 35
and add 12^ t
O the result. Plos 29 | 31 | 33 | 36 | 38 | 40
The above table is for converting ex- | 5! | 3 24 32 | 35 | 38 | 40 | 42 | 45
À : 52 | 3 2
pressions in arc to their equivalent in time; | 53 | 3 32 36 | 39 | 42 | 44 | 47 | 50
its main use in this Alm is for th 54 | 3 36 ANAS AOH 40152. 155
anac is for the con- 43 | 47 | 50 | 53 | 57 | 60
version of longitude for application to L.M.T. a Å ho: 47 | 51 | 54 | 58 | 61 | 65
(added if west, subtracted if east) to give G.M.T. | 57 | 3 48 51 | 54 | 58 | 62 | 66 | 70
à ! i 8|3 52 54 | 58 | 62 | 67! 71 | 75
or vice versa, particularly in the c f 5
á y Olei EN EC A 58|62|67|71|76|80
Sunrise, sunset, etc. 60 | 4 oo 61 | 66 | 71 | 76 | 80 | 85
65 | 79 | 75 | 80 | 85 | 90

* When the Diff. is negative subtract correction if longitude west and add correction if longitude east.

AAA

APPENDIX W: EXTRACTS FROM AIR ALMANAC 1159

CORRECTIONS TO BE APPLIED TO SEXTANT ALTITUDE

REFRACTION
To be subtracted from sextant altitude (referred to as observed altitude in A.P. 3270).

Height above sea level in units of 1,000 ft.

^ EIA CNR EH pes Rer
j Sextant Altitude “lo-9 1-0 1-1 1-2
o + o D o , o + o + o + o + o , o , o + o € o €
90. .90 .90..|90 . 90 o -|90 90 go |90 go 90 ars Et *
o ojo o o o
: 63 59 55 51 46 41 36 31 26 20 17 13 aes g
d 33 29 26 22 I9 16 I4 II 9 7 6 4 A :
: 21 19 16 14 12 10 8 7 5 4 240 140 x b adds
16 14 12 IO 8 7 6 5 310| 220 130 040 SIMON
: I2 II 9 8 7 5 400 310 2IO| 130 039 +005 414 BEENA E
6 Io 9 7 550 450 350| 310 220 130| 049 +0II —019 A 3 z 5
810 650 550| 450 400 300| 220 150 110 024 —01I —0 38 i S À
: 650 550 500| 400 310 230| 150 120 038 +004 —028 —0 54 d te
600 510 410] 320 240 200] 130 100 019|-0 I3 —0 42 —108 4 Ri =
t 520 430 340| 250 210 I40| IIO 035 +003|—027 —053 —I I8 t d E hod:
o
—0 16 | — —108 —
S E AO sá lol Hin UE je adus
14 33 5 4 34 9 4 37 3 44 14113 14 15 17
x 250 210 I4O| IIO 037 +010|—013 —034 —053|—II4 —1 35 —I 56 DID
BS Oe. [ire RE
o = Se D in uf E = =!
20 x vg is V Y = 97 : 20|18 20 22 24
112 044 +0I9|—006 —028 —048|—109 —127 —142| SÉ —214 —2 30 EAS
E 034 +010 —0I3|—036 —055 —114|—1 32 —I 5I —206| —221 —234 —249 i E AL a
3 +006 —016 —037|—059 —117 —133|-151 —207 -223|-237 —2 5I —304 P ü d An
2 —0 18 —037 —0 58 | —116 —I 34 —149|—206 —222 -235|—249 -303 —316 pi 3604944 y
4 —0 53 —II4|—I31 —I 47 —203|—218 —2 33 -247|-259 —313 —325 BÐ s
45 —IIO —128|-144 —159 -215|-228 —2 43 -256|-308 —322 —333 sol45 50 55 60
P —I40|—I53 —209 —224|—238 —252 —304|—317 —329 —341 «log aeons
— — — — — — — - —3 48
R 203 —218 -233|-246 —30I -312|-325 —337 —34 60|54 60 66 72
2153" = 3.07 ES FON Be 431427 = 3,53
f o D 10 15 20 25 30 35 40 45 50 55 f 0-9 1-0 I-I 1-2
Temperature in °C When R, is
less than roi
AR ne ISI IO 3 Mig $
0-9 256 P roh ollis: 333 "2210 ed cmt 49 For these heights no '9 | or the height
1-0 4 temperature correction 1-0 iE C ud
+5 FÓ SG) += =f e». isnecessary:takef=1-0 | y an 835/000
1-1 claro FR ‘I | ft.takef=1-0
A —16 —25 —36| -46 —58 —71| —83 -95 9 1-2 and use
3345 El E EN R=R,

Choose the column appropriate to height, in units of 1,000 ft., and find the range of altitude in which the sextant
altitude lies; the corresponding value of R, is the refraction, to be subtracted from sextant altitude, unless
conditions are extreme. In that case find f from the lower table, with critical argument temperature. Use the
table on the right to form the refraction, R=R, xf.

CORIOLIS (Z) CORRECTION e
To be applied by moving the position line a distance Z to starboard (right) of the track in northern latitudes
and to port (left) in southern latitudes. The argument is given as T.A.S. (True Air Speed) in A.P. 3270.

G/S Latitude G/S Latitude

KNOTS o? Io? 20? 30° 40? 50? 60? 70° 80° go° KNOTS o? Io? 20? 30? 40? 50? 60? 70? 80? 90?
150 o I 1 2 3 3 3 4 4 4 450 OZ A O S292 ro PLE E72 T2
200 NANA 10/5575. [9.5 05 500 ZA A cw ues ose] ee one
250 o í a sh Hil © GS 7 550 CS RSS MOTTA 12 ayy TA TIA
300 DA AO le 7E MAESE 8 600 o 3| 5 8|10 12|14 15] 16 16
350 Opa sis RG [7-4 Burg 99 o! 650 onráx 6 NIIT 13) 1511641747
400 6 A ag V gi Seo 99e LO 700 | o 3| 6 9| 12 14 | 16 17 | 18 18

nm

APPENDIX X
LONG-TERM ALMANAC

This appendix is intended for use when a more complete almanac is not available.
It is based principally upon the fact that approximately correct values for the Greenwich
hour angle and declination of the sun, and the Greenwich hour angle of Aries, can be
obtained from an almanac that is exactly four years out of date. The differences in
these values at intervals of exactly four years can be largely removed by applying an
average correction to the values obtained from the tables of this appendix. The
maximum error in an altitude computed by means of this appendix should not exceed
2:0 for the sun or 1/3 for stars.

This four-year, or quadrennial, correction varies throughout the year for the GHA
of the sun (between about plus and minus one-fourth of a minute) and for the declina-
tion of the sun (between about plus and minus three-fourths of a minute). For the
GHA of Aries the quadrennial correction is a constant, (+)1'84. The appropriate
quadrennial correction is applied once for each full four years which has passed since
the base year of the tabulation (1956 in this appendix).

The tabulated values for GHA and declination of the sun and GHA of Aries are
given in four columns, labeled 0, 1, 2, and 3. The “0” column contains the data
for the leap year in each four-year cycle and the 1, 2, and 3 columns contain data for,
respectively, the first, second, and third years following each leap year.

The GHA and declination of the sun are given at intervals of three days throughout
the four-year cycle, except for the final days of each month, when the interval varies
between one and four days. Linear interpolation is made between entries to obtain
data for a given day. Additional corrections to the GHA of the sun of 15? per hour,
15” per minute, and 15" per second are made to obtain the GHA at a given time.
Declination of the sun is obtained to sufficient accuracy by linear interpolation alone.

The GHA of Aries is given for each month of the four-year cycle. Additional
corrections of 0%59!14 per day, 15?02/5 per hour, 15’ per minute, and 15" per second
are made to obtain the GHA at a given time.

The SHA and declination of 38 navigational stars are given for the base year,
1956.0. Annual (not quadrennial) corrections are made to these data to obtain the
values for a given year and tenth of a year.

À multiplication table is included as an aid in applying corrections to tabulated
values.

Sun tables. 1. Subtract 1956 from the year and divide the difference by four,
obtaining (a) à whole number, and (b) a remainder. Enter column indicated by re-
mainder (b) and take out values on either side of given time and date.

2. Multiply quadrennial correction for each value by whole number (a) obtained in
step 1 and apply to tabulated values.

3. Divide difference between corrected values by number of days (usually three)
between them to determine daily change.

4. Multiply daily change by number of days and tenths since 0* GMT of earlier
tabulated date, and mark correction plus (+) or minus (—) as appropriate.

5. (GHA only.) Enter multiplication table with hours, minutes, and seconds of
GMT, and take out corrections A, B, and C, respectively. "These are all positive.

6. Apply corrections of steps 4 and 5 to corrected earlier values of step 2.
1160

APPENDIX X: LONG-TERM ALMANAC 1161

Example.—Find GHA and declination of sun at GMT 17"13"49* on July 18, 1986.

Solution.—Steps 1 and 2: (1986—1956)+4=7, remainder 2. Use column 2,
and multiply quadrennial corrections by 7. Corrected values: GHA, July 16,
178°32/0— (70/23) =178°30/4; July 19, 1789280— (7X0/20)=17826/6. Dec., July
16, 21°29'2N—(7X0°35)=21°26'8N; July 19, 20589 N — (70/39) =20°56/2N.

GHA Declination
July 16 178?30'4 July 16 21%26/8 N
July 19 178?26'6 July 19 20%56/2 N
3-day change (—)3'8| Step 3 3-day change (—)30/6 | Step 3
daily change (—)1/3 daily change (—)10'2
days and tenths 2X Step 4 days and tenths DE Step 4
corr. (—)3:5 corr. (—)27/5
A 255°00/0 0" July 16 217268 N) Step 6
B .3915'0|| Step 5 d 20959/3 N
C 1272

0^ July 16 178?30/4) Step 6
GHA 76%54'1

Aries table. 1. Subtract 1956 from the year and divide the difference by four,
obtaining (a) a whole number, and (b) a remainder. Enter column indicated by re-
mainder (b) and take out value for given month.

2. Enter multiplication table with whole number (a) of step 1, day of month,
hours of GMT, minutes of GMT, and seconds of GMT, and take out corrections
D, E, F, G, and C, respectively.

3. Add values of steps 1 and 2.

Example.—Find GHA T at GMT 11506733* on November 28, 1979.

Solution.—Step 1: (1979—1956)+4=5, remainder 3. Use column 3.

GHA T

Nov. 38?33:0]) Step 1

D 9/2

E 217?35!9
F 165%27'1|) Step 2

Ger P2

C 812
GHAT 2332316) Step 3

Stars table. 1. Enter table with star name, and take out tabulated values.

2. Subtract 1956.0 from given year and tenth, and multiply annual correction by
difference. Apply as correction (+or—, as appropriate) to value of step 1.

Example.—Find SHA and declination of Spica on September 11, 1995.

Solution.—From decimal table, September 11, 1995—1995.7. 1995.7—1956.0=
39.7.

SHA Declination
1956.0 159°16/9} Step 1 1956.0 10955/9 S) Step 1
39.7X(—)0/79 (=)31!4 BO FD
w : CHITI "E Step 2
SHA 158%45/5 d 11%08/28

To determine GHA of star, add GHA T and SHA for given time and date.

LONG-TERM ALMANAC

APPENDIX X

1162

SUN

Date

Dec.

JANUARY

,

un un un un YN YA 02 LA UN YN
D-30000 t rr

ZSRÉSSSSZS

RANAAARAAR

QC» 010 NA QX cO 15 INO

Y YN YA YA YN YA Un UN UN YA
(LD hh ONDA O

SENSSSABSN
GEET

ao

„ri

NNNNNNNNNN
ri HA cw orodri.d

QSSSSSESRA

D. i + EE
Pi ri ri Pi ri ri A

nnnnnnnAaad&
Cur 0) co «f! C1 O» 00 VJ

ETA 6 Hs S
10 xf lo CY e OW e N E

Down M N ODO AN

NWOWN OO HOO

un un un Y Y Y Y YA YN 02

Ros!
SS A

(O O 19 H em ee)

aamnamamz ZZ
*f' oO «f co «o OO EH

om mm EE)

ZZZZZZZZZZ

DN ALDO ONO

ienes dosdads
SARs wud

HO DORIAN
rr

HOO DIN 10 00 xt C O» CO

ZZZZZZZZEZ

ve a EE e E
SE
ABRI

"ei Ve E SAS E
EE

ZZZZZZZZZZ

[> 00 10 00 HOO OOO
SSAHHAGHSO
tt O NC dl

ZZZZZZZZZZ

rm OQ» HH Nr MOD

RARARRARRĀR

AD ti C2 CN O CO e ti

DO DI 10 HR HO

O DAN H 1 1 V Ó O
e Nm QD u$ xf Co CY e

ZZZZZZZZZZ

NO O e 02 00 15 O 3
te OLOO:«:dxo
SRSSSSRĀRĀ

SARRAĀRRRRĀ

Do 00 00 OQ» «f i e à o5

un YN ua YN YN YN YA YA YN YA
A C4 OQ» cO «f 5 C C VA

ao
rr

SEET

FEBRUARY

un un un Un Y YN YN YN Y UN
KEE ooo

SRRSSRSROS

MARCH

eO ancor DOMO AN
EE
BSSARBSSBASS

NNNnnn Z Z Z
O N OD 10 00 E de oco
Serresetonnr
wf MON QD au ën om

OMD coc O Sra

APRIL

HATOCOMAMWNS

ZZZZZZZZZZ

C010 CH NANO 00
En b ti as
ASSSESSSSSS

"io b- 00 Or Nm
mmm

MAY

ZZZZZZZZZZ

Dio NOC
AIDA N
RS]

fac O E DÉI DÉI ER DO
rr RA

° RAAAAA

Na D OM o No

Un un un un un UN un ua UN UN
00:29 coco rco

EE Tas is As

ooo
rr

DO r- «f C Or N «à 05

Un un un YN un un dun un N UN
RON O CO pe Hob D

SsSawissaaars
CÓ ti HHH HOD CON

DICH ooo rot

UD un on ua ua oa ca Zi ZZ

SNN
FNN A OS co co vid

NONE N DOMS

10 OQ» OQ» ti LD 00 62 O =O

ZASSSZRSS

ZZZZZZZZZZ

DO M AD IO N HON
LORA HEN
EK
A SS E
==

E

ZZZZZZZZZZ

CX r- 00 «f «n co O3 CX f eo

JUNE

MAIL c DOI O AID

e NO $MN aA

ZZZZZZZZEZZ

CX c5 i2 O Dona
G ci ci Ó m OG d Ros
o

RRARRRRRRRĀ

ooo 10 ri hr Y

ZZZZZZZEZZZ

MN 00 r- Cat ee o0
SK sæl Úd
Sav on A NRAa+M

ARRARRRRRR

DOOM oc

SERZSSSSXI

1163

LONG-TERM ALMANAC

APPENDIX X

ZZZZZZZZZZ
MHI XH Ee KEE
da

NN N mam

ZZZZZZZZZZ

KE EE EH

ZZZZZZZZan
MON CO CO 00 OD e CO

00 N cO 00 O e e N 00

GO (o mmm DO e

1 00 CO «02 CO (Oo ch

ZZZZZZZZZZ

OOOONA AW DR
SĒSĀBABĀSS

RRRĀRARRĀS

ZZZZZZZZZZ

YH AH DO 00 « e MOL

wooo"

O00 t- (Oi «eo co NOD
AM M

ooo R GM
ec HO AO xf C co «ti

Kee

(00900009000
OD c 10 C9 «Hai a OD LH

QOO O00 (O xf — NO p-
"ad Or C CO CO ti ti H

N MA LR 00 5 a
rr

ANNNNNNNMNM
ON HONDO mo

Un uo 00 Y Y an on un UN Y
O «f Oi DN HHN O

DD do c» O» «t «OD cr cou

SSSNSRRRERE

LVOTYADVYDO YA

Y Y un un un YA on Y mu
ri DÉI rd ER EE CO e doi

HOSSAN
SSešaasduss3

No o 00D O y

Om OS m WOO
OO «f CO e 10 05 0

99 Y Y Y Y 02020202
Y Y 10000 D Or

cO Rm M D»
soc SANNA

SRAAARARRRA

NMMNDOOMO D

ZZZZZZZZZZ
ANO HG DIOBGOON

19 00 L- 5 C4 cO co

SSSSRRRSREZ

AUGUST

ZZZZZZZZZZ

0 ODIN e i
ŠAS$S 858GB

SEPTEMBER

ZZZZZZZZan

Wat NO co i pF

00 r- oio ceo eO n

OCTOBER

un un un un un YA YA Un Y YA
tO «0200 NOD +

e 00 > i5 CX 00 CX i5 tr
BESAR

Ni oo O DONA

NOVEMBER

Y YA YN Y YN YN YN UN UN UN
DIO CN V Die O 00 CO «t

SSRASSS

SRR

DECEMBER

10 (M0 © M 00 00 1D N A

Y ga Y Y Y Y Y Y 02 02
00 LO Xf C e DÉI CD AO O «t

MON C lt == Ó =H O
ND O NANA m

Sega

ZZZZZZZZZZ
PROPANO

O ASA
© CO e MCN mo

NAN N Eel oo
ARARNAR rr

€ Q» O i «tic p O
OOD HID OO e NOD

ZZEZZZZZZZZ
AWO O OO RN tH

AD OO Qn» OO 10 CD e C3 e 00
OD SH SH LO LO ACD H

00 E «Oi HN Nn 0S
AM rr

Leena o0 co O

RNA RA 00 «f C (Oo e He?
AN A N P AO e C P OH

ZZZZZZZZan
(O 00 CO» e (O 10 000 E

bb 10 1

0 DIN ODO

N CN SHH së 10 GO CO 0 NM

19 I Nr C02 00 «f CN e 00
SREZSSSSEZHS

MONO «n co «wn eo Oo

mammu ra Pa OD 00
N XP AO e 05 8 O =

9 Y Y Y 02 00 Y Y Y UO
Mc X EE

Y Y Y Y Y Y YA UN UN 02
MA 0 r- C ULoo io c e co

Lj OO CW «f «f C5 x ao co
ARS ssāšis

trio

SRASARGRRRRA

co f CO a N
NM HID i ©

1164 APPENDIX X: LONG-TERM ALMANAC

ARIES (T) MULTIPLICATION TABLE

HJ
a

~
~

SIA A
hV Ka O1 -100
Awo o
go
SSIS
NO POH
ISKYE O
asasa
EECH

greases
SiS 5

S88858|558585

BSN

© 00 00 00 N
DOD DO m
EISES
PENE
aN coo ct
$ ji po pod ba
9 Dan
Rn EE)
KREE
ESEER
> Co O 00

alos
BE | 35358

SS ES SES BBSES -

man] VO ROMA | Ono | GUIDO | moron
wH

e
RERERA| SSSRIS

O 00 1 SI [AN RR)
ORR ON | DO NI AG

2358
SSSRSS | RENER,

S

Wwwwr
LE
aon o
$2 od od ER
00 c1 to C 00
DSERS
0 00 (OD HN
J kr po po ki
eO DD O
SBEZZ
acon

EE

SBESS|56552

ph pi pa pi ERO o BRE
Wl DD OOD] Oi t0 | 00-10 | OO NIO

Cu Re
EE)
35858
Ap ae e
Sn o
E
gen ort
WOM
kä plo kä kä bh
ONDON

GERST

Acamar
Achernar
Acrux
Aldebaran
Alkaid

Alphard
Alphecca
Alpheratz
Altair
Antares

ODANA
DD or on gn
Voon

ES
©

TC

20
21
22
23
24
25
26
27
28
29

SE
Ct 0o c

Si mom oH |P

92
S
lllle|eeses | sera

Arcturus
Atria
Betelgeuse
Canopus
Capella

Deneb
Denebola
Diphda
Dubhe
Enif

SAS
OPARA | ro» ope E E IS

EE
Qo Cn to ooo

INEA

GI DO | RG OM | GO RG | FORDE

WOOO | CCW OAT | TIANA | Pannan | ee Ha aa | www | MODO D HH | HHOOO O
TAP.

MAA!
EJEA!

IS PA PE GS | DV ASS RRA AAA AOS SS

EI | SIRS

ono wowed va Va O =I tV Oe OO vn, Go 02-3 — 02 oo ooo Nooo tO o» 09 c» 06
zau|azanz|zZzzeu|zazza| zzuzz| ZZOZ | 072Z | zzuuo

Fomalhaut
Hamal
Kochab
Menkent
Mirfak

Nunki
Peacock
Pollux
Procyon
Rasalhague

Fa En
CAES

Poll) Ð
TSAR

s

no

Ute be

ERAS PA ER EPR

=

na

EAT se

mor
A

Regulus
Rigel
Rigil Kent.
Schedar
Sirius

235 | 53380
E Lo EM pa

DEE
Pee

SO C va

Spica
Suhail
Vega

SAND | DXNRODINDI
om EO | OTIS

one

Decimal 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Hour et ouz eer 2009 oat 1048 1312 1536 1800 2024 2248
0 o 0 to to to to t

Day 0112 4336 0600 0824 1048 1312 1536 1800 2024 2248 2400

w KSC "ds

APPENDIX Y
EXTRACTS FROM H.O. PUB. NO. 260

TRUE BEARING OR AZIMUTH.

LATITUDE 23°.

DECLINATION—SAME NAME AS—LATITUDE.

14°

15°

16°

17°

189

19°

20° | 21?

May.
12

Apparent 19

2

Apparent

Time.
A. M. October.

28

14

ovember.

Time. `
P. M.

29

122 130
127 59
134 46
143 16
` 153 45
XI 166 14

dee

79 33

Sun rises.
Sun sets .

Sun rises.
Sun sets.

Azimuth .

Azimuth.

In North latitude,
is setting or West of the meridian, t

when the body is rising or East of the meridian, the tabulated azimuths are reckoned from North tæ East; and when the body
he tabulated azimuths are reckoned from North to West.
s are reckoned from South to East; and when the body

In South latitude, when the body is rising or East of the meridian, the tabulated azimuth

is setting or West of the meridian,

the tabulated azimuths are reckoned from South to West.

1165

1166

APPENDIX Y: EXTRACTS FROM H.O. PUB. NO. 260

TRUE BEARING OR AZIMUTH.

LATITUDE 24°.

DECLINATION—SAME NAME AS—LATITUDE.

F

Dec.

Apparent
Time.
A. M.

23

12 2°

March.

| 23 | 26

js 18
September.

26 | 28

SES

28

=

16

4? 5? 6? (e 8° 9° | 10? | 11? Dec.
April.
31 3 ST 8 | II 13 | 16 | 19
September. August.
13 10 arro | gor "eager E Apparent
Time.
October. P. M.
4 6 9 league E: | 14 17 | 19 | 22
March. February.
20
F
or o t o 7 C.F or o + o , or h.

167 52 | 167 23 | 166 52 | 166 18 165 41 165 00 | 164 15 | 163 26 | 162 31 | 161 30 | 160 21 159 03 20
XI 50 173 52 | 173 38 | 173 22 | 173 04 | 172 44 | 172 23 | 172 00 | 171 34 171 O5 | 170.32 | 169 54 | 169 12 XII 10
e k.m.| h.m. | k.m.| h.m.| bal kal m. h.m.| h.m.| h.m ZS m.
Sun rises . 600} 558| 5 56 sie) S9 5 51 5 49 547] 546 5 44 5 42 5 40 || Sun rises,
Sun sets , 6 00 6 02 6 04 05 6 07 6 09 11 13 6 14 6 16 6 18 6 20 Sun sets.
À o 4 (šā 4 QI o 4 o 4 o 4 4 o di o 4 o 4 o 4 4 Y
Azimuth . 90 00 | 88 54 | 8749 | 8643| 85 37 | 84 32 | 8326| 8220| 8I 14 | 8008 | 7903 | 7757 Azimuth,

In North latitude, when the body is rising or East of the meridian,
is setting or West of the meridian, the tabulated azimuths are reckoned from North to West.

In South latitude, when the body is rising or East of the meridian,

is setting or West of

the tabulated azimuths a:

the tabulated azimuths a:

the meridian, the tabulated azimuths are reckoned from South to West.

re reckoned from N

orth to East; and when the body

re reckoned from South to East; and when the body

APPENDIX Y: EXTRACTS FROM H.O. PUB. NO. 260

TRUE BEARING OR AZIMUTH.

LATITUDE 24°.

1167

DECLINATION—SAME NAME AS—LATITUDE.
Dec. 12? | 13” | 14” | 15? | 16? | 17? | 18” | 19? | 20° | 21” | 22° | 23° Dec.
d
April. May. June,
22 | 25 | 28 I | 5 | 8 | 12 | 16 | 21 | 26 T | 10
August, | ul
Apparent R 3 Ld
16
rime | 9 | | 12 | 9 | 5 2 | 28 | 24 | 19 | 12 3 S
A. M. October. November, December. P E `
. M.
25 | 28 | 31 3 6 | 19 | 14 | 17 | 22 | 27 3 II
February. January.
18 15 12 | 9 5 2 29 | 25 | 21 | 16 10 2
h. m. o or o 7 ov or o.t or On 7 o, Eet Së o * h. m
D
v 20
EE Eeer Ses eae hos sees becuase) eelere rees 65 56 | 65 02 40
30 EE leede A la DE 71 28 | 7033| 69 39 | 68 45 | 67 50 | 66 56 | 6602 30
77 01 | 7607 | 7512 | 74 17 | 7323| 7228| 7133| 7038| 69 44 49 | 67 54 | 66 59 20
50 7801 | 7706 | 7611 | 7517 | 7421 | 73 26| 7231 | 7136 | 7041 | 6945 | 68 50 | 67 54 10
VI 00 79 01 | 7806 | 77 xo | 7615| 7519| 7424 | 73.28 | 7232 | 71 36
3 70 41 | 69 44 | 68 48 VI 00
De 79 59| 7904| 78 08 | 7712| 76 16 | 7520 | 74 24 | 73 27 | 7231 | 7134| 7038| 69 41 50
80 58 | 8001] 7904| 7808| 77 11| 76 15 | 75 18 | 7421 | 7324| 7226| 7129| 70 31 40
30 | 8r54| 8057 | 8000 | 7903| 7806) 7709| 76 11| 7513 | 74 15 | 7318 | 72 19 | 7121 30
40 | 8251 | 8154| 8056] 7958| 790 | 7802| 7704| 7605| 7507| 7408 | 73 8| 7209 20
50 || 8348 | 8250 | 81 sī | 8053| 7954 | 7855| 7756 7656 | 7557 | 7457 | 7357 | 72 56 10
VII 00 | 8444 | 8345 | 8246| 8147 | 8047 | 7947 | 7847 | 7747 | 76 46 | 75 45 | 744
3 | 7342 V 00
10 85 41 | 84 41 | 83 41 | 82 41 | 81 40 | 80 39 | 79 38 | 78 36 | 77 34 | 76 32 | 75 30 | 74 27 50
20 86 39 | 85 38 | 8436| 8335| 82 33 | 81 31 | 8028) 7925| 7822 77 19| 76 15 | 75 11 40
30 87 37 | 86 35 | 8532 | 84 29 | 83 26 | 8223 | 81 19| 8014 | 79 10| 7805| 7659 | 75 54 30
40 88 35 | 87 32 | 86 28 | 85 23 | 84 20 | 8314 | 8209 | 81 03 | 7957 | 7851 | 7744 | 7636 20
50 89 35 | 88 30 | 8725 | 86 19 | 85 13 | 8406 | 8259| 81 52 | 8044 | 7936| 7827 | 77 18 10
VIII 900 90 36 | 89 30 | 88 23 | 87 16 | 8608 | 8459 | 83 50 | 8241 | 81 31 | 8021 | 79 10| 77 59 Iv 00
10 9139 | 90 31 | 89 22 | 88 13 | 87 03 | 8553 | 8442 | 8330| 8218| 81 06 | 7953| 78 39 50
20 92 44 | 91 34 | 9023| 89 12| 8800 | 8647 | 85 34 | 84 20| 83 06 | 81 51 | 80 35 | 79 19 40
30 93 51 | 92 39 | 91 26 | 90 12 | 8858 | 87 43| 86 27 | 85 10 | 83 53 82 36 | 81 17 | 79 59 30
40 95 01 | 9346 | 92 31 | 91 15 | 89 58 | 88 40 | 87 21 86 02 | 84 42 | 83 21 | 81 59 | 80 38 20
50 96 14 | 94 57 | 93 39 | 92 20 | 9100] 8939 | 88 17 | 8654 | 8531 | 8407 | 8243 | 81 17 10
IX 00 97 32 | 96 11 | 9450] 93 28 | 9205| 90 40 | 89 15 | 87 49 86 22 | 84 54 | 83 26 | 81 56 mi 00
10 98 54| 9730| 96 94 40 | 93 13 | 91 45 | 90 16 | 8845 | 87 14 | 85 42 | 84 09] 82 35 50
20 100 21 | 98 54 | 97 26 | 95 56 | 94 25 | 92 52 | 91 19 89 44 | 88 08 | 86 31 | 8453 | 83 14 40
30 101 55 | 100 24 | 98 51 | 97 17 | 95 42 | 9405| 92 26 | 9o 46 | 8904 | 8722| 8539| 83 54 30
40 103 37 | 102 02 | 100 25 | 98 46 | 9704 | 95 22 | 93 38 | 91 52 | 9004 88 15 | 86 25| 84 34 20
50 || 105 29 | 103 49 | 102 06 | 100 22 | 98 35 | 96 46 | 9455| 9302 | 9107 | 89 11 | 87 13 | 85 15 10
x 00 107 33 | 105 47 | 103 59 | 102 08 | 100 14 | 98 18 | 96 19 | 94 18 | 92 16 | 90 rr 88 04 | 85 56 II 00
10 109 50 | 107 59 | 106 04 | 104 06 | 102 05 | 100 OI | 97 53 | 95 43 | 93 39 | 91 15 88 58 | 86 39 50
20 112 26 | rro 28 | 108 26 | 106 20 | 104 10 | 101 56 | 99 39 | 97 17 | 9453 | 92 26 | 89 56 | 87 25 40
30 IIS 23 | 113 18 | 111 09 | 108 54 | 106 34 | 104 09 | 101 39 | 99 04 96 27 | 93 45 | 91 00 | 88 11 30
40 118 47 | 116 36 | 114 27 | 111 53 | 109 22 | 106 44 | 104 00 | 101 II | 98 IS | 95 16 | 92 12| 89 04 20
50 122 47 | 120 29 | 118 03 | 115 27 | 112 44 | 109 52 | 106 51 | 103 43 | 100 27 | 97 04 | 93 35 go 02 10
XI 00 127 31 | 125 07 | 122 32 | 119 47 | 116 50 | 113 42 | 110 22 106 48 | 103 08 | 99 16 | 95 15 | 97 o8 I 00
10 133 09 | 130 42 | 128 02 | 125 08 | 121 59 | 118 33 | 114 51 | 110 52 106 37 | 102 06 | 97 22 | 92 25 50
20 139 55 | 137 31 | 134 52 | 131 54 | 128 35 | 124 57 | 120 51 116 20 | III 24 | 106 02 | 100 16 | 94 13 40
30 148 01 | 145 50 | 143 21 | 140 31 | 137 15 | 133 31 | 129 13 | 124 13 118 28 | 111 56 | 104 40 | 96 46 30
40 157 33 | 155 50 | 153 5I | I5I 29 148 41 | 145 19 | 141 10 | 136 07 | 129 50 | 122 03 | 112 30 | 101 18 20
XI 50 168 23 | 167 25 | 166 16 | 164 54 | 163 12 | 161 03 | 158 17 | 154 35 | 149 26 | 141 55 | 130 34 | 113 56 XII 10
Å h.m.| h.m. | h.m h.m.| h.m. | h.m.| h.m. | h.m. | h.m. | h.m h.m. | hom.
Sun rises . Ee ga eee ENEE e Suis S TS O AA rises.
Sunsets . 6 22 6 24 6 25 6 27 6 29 6 31 6 33 6 35 6 37 6 39 6 41 6 44 Sun sets.
Ë o 4 o 4 o 4 o 4 o 4 o 4 o 4 e 4 o d Di wf o 4 o 4 £
Azimuth . 76 51 | 7545 | 74 39 | 7333 | 72 26 | 71 20 | 70 14 69 07 | 68 or | 66 54 | 65 47 | 64 41 Azimuth,

In North latitude, when the body is rising or East
the meridian, the tabulated azimuths a:

when the body is rising or East of
is setting or West of the meridian, the tabulated azimut!

is setting or West of
In South latitude,

the meridian, t

of the meridian, the tabulated azimuths are reckoned from North to East; and when the body

re reckoned from North to West.
he tabulated azimuths are reckoned from South to East; and when the body

hs are reckoned from South to West.

APPENDIX Z

EXTRACTS FROM H.O. PUB. NO. 261
AZIMUTH OR TRUE BEARING.

=

LATITUDE 51%,

DECLINATION—SAME NAME AS—LATITUDE. LATITUDE 51%

Hour Angle.

480

59° | Hour Angle.

O HR ONTO
O HR Oo

In North latitude, when the star is rising or Hast of the meridian, the tabula
when the star is setting or West of the meridian, the tabulated azim

In South latitude, when the star is rising or East of the
when the star is setting or West of the meridian, the tabulated azimuths ar

When the latitude and declination are of different name, the tables are to be en
supplement of the tabulated azimuth is to be taken for the required true bearing,

1168

meridian, the tabulated azimuths are r

ted azimuths are reckoned from North to East; and
uths are reckoned from North to West.

eckoned from South to East; and

e reckoned from South to West.

tered with the supplement of the hour angle and the

APPENDIX Z: EXTRACTS FROM H.O. PUB. NO. 261 1169

AZIMUTH OR TRUE BEARING.

A o,
LATITUDE 520, DECLINATION—SAME NAME AS—LATITUDE. LATITUDE 520
Hour An o 5
Angle. | 48 490 509 51° 52° 53° 54° 55° 56° 57° 58° 59° | Hour Angle.
h. m. & A or OF DAI , ai CREE. or d
o 00 | 180 oo | 180 oo | 180 oo | 180 oo e Ce € be pu EN gne
105 Wasp di Ee e nd 9-80 di jesse ad asin tas esi) Kokos m M S S D 00
20 | 139 16 | 131 22 | 120 28 | 105 51 88 02 e 26 = 5 4 A E n EG 12 25 | 1025 10
30 | 126 45 | 119 13 | 110 or SPAR E GE M) 20
99 09 | 87 03 | 74 41 | 63 08 06 8 | 38
40 117 59 | 111 19 | 103 42 til 86 a 53 44 4 38 03 | 32 36 | 28 12 30
Bo (mūsos Sal 82/58 90/87 24 Se) 33 ue E
O 17
1 00 | 106 39 | 101 34 03 o 12| 8
10 102 42 | 98 12 2 24 és 20 85 = pi e de = ë = = 2 Sé aaa x is
$9 2 2 95 23 EN o8 a 44 | 8205 | 7723| 7239| 6755| 63 16 8 is 54 E so 17 20
92 57 9 09 5 II 8106 | 76 55 | 72 40 | 68 2 6. 60
40 S LA S 4 7 4 14 07 | 5606 | 52 13 30
BO $3 85 8 a2| 8227 | se se|nu| eese es c 4 50
2 4
2 a 2 2 87 93 = 08 | 81 o9 | 78 05 | 7456 | 71 44 | 68 30 | 65 15| 6202] 58 48 | 55 36 2 00
20 3 Ga ca 12 79 54 | 7704 | 74 10 | 71 13| 6814 | 6512 | 62 11 | 59 10] 56 10 10
Selten | E 7841 | 7603 | 7321| 7037 | 6749 | 6501 | 62 12 | 5922 | 56 31 20
Sei ook a 4| 7953 | 77 29 | 7501 | 7231 | 6957 | 67 21 | 64 43 | 6203] 59 23 | 56 44 30
BOE 53 | 8045| 78 33 | 76 18 | 7400 | 71 38 | 69 14 | 6647 | 64 19 | 61 49 | 59 18 | 56 46 40
121 | 7920| 7716 | 750 | 7258| 7044 | 68 29 | 66 11 | 63 50 | 61 29] 59 06] 56 42 50
3 00 | 79 SE 7756| 7559 | 73 59
5 5 71 56| 6949 | 67 42] 65 31 | 6318] Gro 8 6 3
10 78 23 | 76 35| 74 43| 72 49| 7053] 68 53 | 66 52 | 6448 | 6242 | Go S Ze R Ze 36 10
20 76 58 | 75 15 328 | 71 40 | 69 49 | 67 56 | 6600| 64 04 | 62 04 | 60 3 58 00 3 6 20
29 75 3⁄4 | 73 56 | 721 7o 32 | 68 46 | 66 58| 6508 | 63 16| 6122| 5926 5729 = p. 30
Ee 74 12 |. 72:38 | 75/02 23 | 67 42 | 6558| 64 14 | 62 27 | 60 39 | 5848 | 56 55 | 55 02 40
72 50 | 7120| 6948 | 68 14 | 66 37 | 6459| 63 18 | 61 37 | 5952 | 5807 | 56 19 | 54 31 50
4 00 130| 7004 | 68 35 | 67 04 | 65
32 | 6358 | 62 22 | 60 44 | 590 2 6 4
10 70 10 | 68 47 | 67 22 | 6555 | 64 27 | 62 56 | 61 24 | 5950 E + X à SENE: S 10
sa pa 50 9 31 | 6609| 6446 | 63 21 | 61 54 | 6026| 5856| 57 24 | 55 n EA Se Ë E. 20
732 14 | 64 56 | 63 36 | 62 14 | 6050] 59 26 | 57 59 | 5630] 55 OL 2 I 30
fo T 12 | 64 59| 6343 | 6226 | 61 07 | 5947 | 58 25 | 57 OI | 55 36 | 54 10 5 43 šī 1 40
4 54 | 63 43 | 62 29 | 61 1:5 | 5959 | 58 42 | 57 23 | 5603 | 5440 | 53 17| 51 52 | 5027 50
5 00 63 35 | 6226 | 61 15 | 6004 | 58 so 6
57 3 6 20 o
ae S a$ z = & x: 58 52 57 41 | 56 30 = 16 > o: 5 E = 28 = = 2 a ` 10
9 55 4 57 40 | 56 32| 55 22] 54 11 | 5300, 51 46| 5031 | 49 16 8 20
30 | 5938| 5835| 5732 | 5627 | 5521 | 5414] 5305 | SI 56 | 50 45 | 49 33 48 20 7 26 30
E s$ 18 | 57 18 | 56 16 | 55 14 | 54 10 | 53 05 | 5I 59| 5052| 49 44 | 48 34 | 47 23 | 46 10 40
56 59 | 56 or | 55 or | 5400] 5258 | 51 55| 5052 | 4947 | 48 40 | 47 34 | 46 25 | 45 15 50
6 00 | 55 39 | 54 41 | 53 43 | 52 45 | SI 46 | 50 45 | 4 8
9 43 | 48 41 | 47 36| 46 31 | 45 25 | 44 18 6 00
a3 54 16 | 5322 | 5227 | 5130| 5032 | 49 34 | 4834 | 4733 | 46 31 | 45 29 | 44 25 | 43 20 10
tg bg 58 | 5204 | 5109| 5014] 49 19 | 4822 | 47 24 | 46 25 | 45 25 | 44 25 | 43 23 | 42 20 20
Po S1 35 | 50 43 49 51 | 4858 | 4804 | 47 09 | 46 13 | 45 16 | 44 18 | 43 20 | 42 20 | At 20 30
* So II | 49 23 | 4831 | 4741 | 46 48 | 45 55 | 4501 | 44 06 | 43 10 | 42 I3 | 4116 | 40 18 40
5 48 49 | 4800| 47 11 | 46 23| 4532 | 4440 | 4348| 4256 | 4201 | 4108 | 40 II | 39 14 50
7 00 | 47 25 | 4638 | 4551 | 4503 | 44 15 | 4325 | 4234 | 4144 | 40
51 | 3959 | 39 06 | 38 10 7 00
10 | ¿600 | 4516| 4430 | 4343 | 4256| 4208 | 41 20 | 4031 | 39 40 | 38
38 50 | 3 o 10
ee 44 35 5 32| 43 08 | 4223 | 41 Se EK Ot | ae 17 | 38 28 | 37 39 36 p 35 E 20
2 4145| 41 02 | 40 18 | 39 33 | 3848| 38 03 | 37 16 | 3629 | 35 41 | 34 52 30
K 4I 43 | 41 02 | 40 21 | 39 40 | 38 58 | 38 15| 37 31 | 3647 | 36 02 | 35 17 | 34 30 | 33 43 40
40 15 | 39 37 | 38 57 |. 38 17 | 37 36 | 36 55 | 36 13 | 3531 | 34 47 | 34 94 | 33 20 | 32 34 50
8 00 | 3847| 38 10 | 37 31 | 36 53 | 36 14 | 3534 | 34 54 | 34 14 | 3331 | 3250| 3207 | at 24 8 00
SEE AE Sel 84) ES] Se) SS) Syl Se 28
14 31 3 30 5 3o 20 29 41 29 OI
76 34 E = T = II 32/374| 3203| 3h 284 30 53 3 D 2 41 | 29 04 | 28 26 27 48 30
2 43 31 II 30 37 30 04 29 30 28 5 26 21 27 47 ZI 26 34
50 31 13 | 30 43] 3013| 29 42| 29 11 | 2839 | 28 07 | 2734| 2701| 26 28 | 25 55 | 25 20 50
9 00 29 40 | 29 12 | 28 43 | 2814 | 27 44 | 2714 | 26:44 | 26 12 | 25 41 | 25 10 | 24 3 24 0; 9 00
10 28 07 | 2739 | 2712 | 2644 | 2616| 2548 | 25 19 | 24 50 | 24 20) 23 SI | 23 E 22 a 10
20 26 32 | 26 06 | 25 41 | 2515 | 24 48 | 24 21 | 2354 | 2326| 22 58 | 2230 2202, 21 32 20
30 24 57 | 24 33 | 2408 | 2343 | 2318 | 2253 | 2228| 22 02 | 21 36| 2109 | 20 43 | 2015 30
1n 23 20| 2258 | 2235 CN 21 48 21 a 21 or | 20 37| 20 12| 1948 | 19 22] 18 57 SR
21 43 2I 22 21 OI 20 40 20 I 19 5 19 34 19 I2 18 49 18 25 | 18 03 17 39 o
10 00 20 06 | 1947| 1927| 1907| 1847| 1827| 1806 | 1745| 17 24 | 1703] 16 42 | 16 19 10 00
10 18 28 | 18 10 | 1751 | 1734 | 17 15| 16 56| 1638 | 1619| 15 59 | 1540 | 1520 | 14 59 10
20 16 so | 1633 | 1616 | 1600 | 1543 | 1526 | 1509 | 1451 | 1434 | 14 16 | 13 57 | 13 40 20
30 15 IO 14 55 I4 40 14 26 14 IO I3 55 13 39 | I3 24 I3 07 12 52 12 36 12 I9 30
40 13.30 h 13 17 13 04 | I2 51 123374| 1223 1209 | II 55| II 4I 1101275113) (1058 40
50 {I S04] 11 39 |, TT 27 | IT 159] 11503 || ero351.]- -10:39!| 10°27) 10*15 | 10:62 9 50 9 37 50
11 00 IO IO | IO OO 9 5o 9 39 9 29 9 18 9 09 8 s8 847 837 8 26 8 15 11 00
10 8 28 8 21 8 11 8 o3 7 55 747 7 38 7 28 7 20 7 11 7 02 6 52 10
20 6 47 6 40 6 33 6 27 6 20 6 14 6 06 6 00 5 52 5 45 5 38 5 31 20
30 sel sol 455| 450| 445| 440] 434] 430] 424| 419) 413) 408 30
40 3.240) 3-204) 3.17) 3-24) 3.10) 3.07), 3:04. )--3)00,|, 2,50) 2.53.) 2:49] 2.46 40
50 I 42 I 40 HE 1037 I 35 I 34 I 32 I 30 1 28 I I 24 1 23 50
12 00 o 00 o 00 o 00 o 00 o 00 o 00 0 00 o 00 o 00 o 00 o 00 o 00 12 00

In North latitude, when the star is rising or East of the meridian, the tabulated azimuths are reckoned from North to East; and
when the star is setting or West of the meridian, the tabulated azimuths are reckoned from North to West.

In South latitude, when the star is rising or East of the meridian, the tabulated azimuths are reckoned from South to East; and
when the star is setting or West of the meridian, the tabulated azimuths are reckoned from South to West.

When the latitude and declination are of different name, the tables are to be entered with the supplement of the hour angle and the
supplement of the tabulated azimuth is to be taken for the required true bearing.

EL ('8S cI

ZLE G'SEEI
EL Liv €l

£,£9 P61 pl

24 €9 S'YS EI
zL €9 28€ VI

ZL €9 pet VI 2489 Y'El yl

06

Kal

Salka xy CO be CO O)

K-Keketck:
2 e

GOTT 14 99

0'80T 22 £9
0'60T 2 9
Q'OIT Un

P LOT 2 t9
v'80T c £9
€'60T Um
POTT 179
PILI 199

6 OTT 14 99
6 TTT 04 99
6'ZTT 02 29
O'PTI 69 89

6 OTT 12 99
€ TTT 12 99

PETT 049
Y VII 69 89
9'GTT 89 89
LOTT 89 69

9'0TT U 99
LITT 02 99
A'GTT 02 99

G "ETT 69 89
9'FIT 69 89

LTT 89 69
8'9TT 3904
0'SIT 49 IZ
6 6TT 99 14
POST 99 22

e

S'€IT 69 29
6 PIT 69 89

Z ATT 49 69
F'SIT 29 02

S'ZTT 02 99
9 SIT 69 99
A PIT 6929
6'STT 89 89

C OTT 89 69
TY AIT 4902

8'6IT 99 IZ

Y SIT 8989
9'OTT 89 69

OSL
992
694
694

GL

T84
HCH
664
662
$08
LIS
€ 16
036
976
686
OY6

EL £9 0'6€ ZI
£L £9 8 77 EI

£2 €9 805 VI

7139 9'£0 LI
7139 0"8p LI
7139 SZE 8I
PL 19 71161

SL 09 860 Z€
$409 [6b c£
SL09 Ct ££
SL09 9°61 VE
$209 L'h0 SE

TTIT 1299 y IE 0s
L'CTT0L29 SEL IS
TETT 02 89 ESG IS
TPIT 6989 8:98 ZS
Z'STT 6969 6
GOTT 8902 2'8S ES
GATT 2902 Ter
9'8TT 49 12 O61 SS
8'611 9932 98558
O'IZI 9984 9:16 95

SAN [16 Or OD

S LTT 29 69
6 SV T 9788

€ SPT Th 06
9'OGT S£ 26

e

Z OPT £v 68
SPI T 16
GOST 8€ 26

6 TST £t v6

GPP 9788 SIL 19
LOFT Ep 06 6"9€ 19
6 8YI OF 16 O10 89
C 191 8626 2782 89

APPENDIX AA

| Z EPT 97 28
PPT PP 68
2 LÆT b 06

C LPT 37 06
P OPT OF T6

O'PST FE v6

0'0ST 6€ 26

SOFT 2 06 p'yz c9
8"8pT OF 16 S"8p S9
OTST 8826 JIL 99
T'EST s£ & CZE 99
V "SST & 6 T7599

os
ee cus
NNN

£2 €9 0°02 I

EL e9 6 LP EI

.

dE?
OS |00 k= r-
b= h> I>

FLZ9 S"00 91

1129 G'GZ LI
voa TPL SI
#L Z9 288 81
SL 19 erte
21.09 g'S IE
21.09 OIE ZE
21.09 Cat
im €'I0 FE
SL 19 9'9Y p£l

TT 0229 € 1106
L'CTT0L89 EES 0S
LETT 6989 6HE IS
ARTI 6969 Z'91 26
8'9TT 89.02 11525
6 OTT 8902 L'LE ES
TSIT HU 61D YS
Z'611 ZL OLS FS
POZI 99 EZ 679t SS
L'IZI 9982 LSTI
E'LPI 2706 yIS V9
E'GPI OF 16 CIS S9
PIGT 2626 E
9'EGT se £6 S'O 99
8'GGT c£ 96 8'£7 99

Comm (io
oo
oor» ts»

O D O O O» |00 00

1
I
T
c
£
€
Y
I

[> |169 00 m H 00

G'EGT 98 €6 L'Y 89
O'OST ze +6 0'069
PRCT 6296 SIZ 69
Q'TOT 9:96 Z"LE 69
9'891 & 46 O'TS 69
6 991 0% 86 8°20 OL
6'891 91 66 SZI OL
Z'TZT EL 66 1°02 02
FELT 6001 967 OL
C LLT 9001 682 OL
0'08T co 0'1 0'0€ OL

O"EST 98 €6 ZI 69
G'GGT et 96

9'09T 4:96 T9002
ESOT &% 26 702 OL
0'99T 03 86 TZE OL

2897 2166 Tp OL
S'TZT€T 66 6'6y.0
6 YAT 600'TS"SS OL
c LLT 900 6'8G OL
0'081T c0 0'1 0°00 IZ

G "ZST 9€ £6
O'GST ££ 6
9"Z9T 08 96
c 091 Æ 96
6'C9T FC 26
SOT 03 86 9
S'89T 2166 ¿TI IZ
S'IZT£166 P6r IZ
SPLT OL OT YG IL
TLLT 900°T 8°82 IZ
0'08T 20 0'T 00€ IZ

"691 879 YS519
T'ZOT sc 26 Z 0189
G POLS Z EZ 89
O'LOT 61 86 FFE 89
9 69T S166 SEp 89
33113166 1°05 89
8 PLT 600'T 6'SS 89
"LAT 20 0'T 0766 89
"OST co 0'T 0700 69

S 691 82 96
L' TOT sc 46
C POL 2286 S75 89
8'99T 61 86 6'£0 69
P 691 91 66 C'tI 69
OGLI 3166 em 69
"PLT 60 0'T 8"SZ 69
€' LAT 20 0'T 6°82 69
0'08T 30 0'T 00€ 69

v'191 % 26
6'£91 ZZ 16 8"IZ 69
G'99T 61 86 £ft 69
Z GOT 91 66 6'Zb 69
6'"TZT 3166 Ce
9'pLT 60 0'T Lee
€ AAT 2001 685 69
0'08T 20 0'T 0°00 02

EXTRACTS FROM H.O. PUB. NO. 214

WGÜLLLVI SV ANVN 4WVS NOLLVNIIOSG

L LST 08 98 70129
0'09T 2 96 S"9Z L9
P GOT vc 26 TIP 29
8 POT IZ 86 6'£G L9
6 L9T 81 86 8'Y089
8'69I 97 66 8"ET 89
E'CLAT 31 66 6°02 89
6 FLT 80 0'T 6'Sz 89
PD LLT 20 0'T 0°62 89
0'08T 20 0'T Q'0£ 89

Of ët

0'89T 0€ 86 OIF 99
P 091 429 L'LS 99
L'C9T vc 26 Q'zI L9
T'GOT 12 86 9"pZ L9
G°LOT 81 66 €°SE 19
0'04T 9166 TYP L9
GCLT 2 66 TIS 19
O'GLT 80 0'T 0°95 79
S" LAT 20 0'T 0°65 19
0'08T 20 0'T 0°00 89
STEI- PVI o

00 GI

€L £9 6'£0 EL| 6

LED O'CE PL | Z
?.t9 Z9IST| 9.

#429 OSH 91 | v

on
Ke

M3 SR
EST oc grams

Sat RI ta

RSS 19 I~ 000

o

d

1170

1171

PUB. NO. 214

EXTRACTS FROM H.O.

APPENDIX AA

GOST 1992 6 SES

Z LCT 099 ZzI9
6'LZ1 099% T'8b 9
9871 69 LL YEZ L
€'6Z1 098. gel
TOETS 82 L'S8 8
EIST 2Z6 SIO IZ
7201 9826 672 IZ
ZEST 986 LER IZ
TFSI ES 878027
O'GST 2876 E'SZ ZC
O'OST 1836 (zy zz
6'9GT 08 96 1°00 £Z
61816296 9'LI EZ
8'8GT 8296 SPE EZ
8:6GT 2% 6706 £z
Soot 53 9 Cent

LT9T +3 26 102 vc
L'Z9T $216 GEE Vc
LET Æ 26 OLY Vc
A TOI 12 86 €°6S Vc

2'99T 6186 6'01 Sc
991 8186 L'IZ Sc
Z'L9T 2186 LTE Sc
L BOTST 0"Ip Sc
L69T PI 66 y"6p Sc
S'0OZT £166 T'LS Sc
SILT 11 68 0"p0 9c
8"22T 01 66 TOL 9c
8 8LT 60 0'T ESI 92
SPLIT 20 0'1 8°61 92
6'G4T 90 0T EZ 92
6'94T 20 0'T €°92 97
6 12T £0 0'T 782 92
O'6LT 20 OT 9°62 9c
0'08T 10 0'T 00€ 92
IV PV

G'OZI 29 SL

6 9cT 19 92

6931 1992

T IST 28 36
O'SGT 9€ 36
O'EST 28 £6
GEST PE £6
SPST ££ 6
8 GGT ct v6
L'OST 0€ 96
Æ AST 62 96
2891 8% 96
9'6GT 2% 96

QO LOT ^1 86 £'I0 9c
9'89T 91 66 9'01 92
2'691T #166 T'61 9c

LOLT £166 8°92 9c
LILI 2 66 8"££ 9c
LGLT 01 66 6°6E 9c
8 ELT 600 T Z'SP 9c
S PLT 80 0'T 26h 9c
8921 90 0'T HES 9c
6'92T 90 0'T €796 97
6 ALT 80 0'T CCGK
0'621300'19"65 92
0'08T 10 0'T 0700 LZ
IV PV

[2 14 gn
T'GcT 2992

S'GZT 1992

G'OZI 19 92
€°LZT 099.
O'SCT 09 LZ
L'SZT 69 42
v'6ZT 69 82
6 OST 2e c6
8'IST 98 26
8 2G, SE £6
LOGI Ye 86
9161 ££ 58
9'GGT c£ 96
9931 TE 96
G*LCT 63 96
G'8GT sc 96
Gei 229
C'O9T % 96
€ TOT 93 26
Got Z 16
"291 Æ 16
SPOT IZ 86 62S Sz
G'G9T 086 9°60 92
Q"9OT 81 86 9:07 92
G'29T 4186 g'0f 92
q'89T 91 66 Z'O 97
9'691 9166 gg
9'0LT £r 66 9°95 92
9'IZT 21 66 9'£0 22
L'ZLT 0166 1°60 12
L'ELT 6001 TSI 22
8'pL1 800'1 2°61 LZ
8941 9001 HET IZ
6:941 9001 £°92 LZ
6'LLT 2001887 LZ
O'6LT 200°T 9°62 LZ
0'08T 100'1 0'0€ LZ
o Kat pv D o

"ZV TV "ZV "ITV
08 LG ¿00 oTG. =

TEZISI res
SFZT 292 1909
G'GZT 2992 ger
TST 1992 ei
6'9Z1 1992 g9c L
LIZT9L 6288
Y SCI 69 LL $806
L'6Z1 6282 ere
LOST 88 26

O9'IGT 9€ 26

9'cGT SE £6

G'EGT 78 £6

G'YGT ee 16

SOOT ce 6:90 V7
FOCI 1896 £'ez yz
V'AG10£96 [eh Vc
€'891 82 96 7'00 Sz
£'691 129 9°91 SZ
£'O9T % 96 Z'Z£ SZ
€'T91 9226 Lire
€'C9r 9526 7:10 92
SLOT Æ 16 OI 9c
SPOT 13:86 712 92

P'G9T 0% 86 Q'6t 9c
P 991 81 86 TOS 9c
PLOT 4186 £'00 LZ
G'89T 91 66 8°60 LZ
S'69T F166 SST LZ
q'OAT ET 66 £'9z LZ
9'TZT 3166 DEE LZ
9"22T 01 68 9'6€ LZ
Æ ELT 600'T Q'sp LZ
A VAT 80 0'T 9"6p LZ
8"921 90 0'T EES JZ
8"92T 90 0'T 2°96 LZ
6'LLT FO 0'T £'8S 12
6'841 20 0'T 9°65 LZ
0'08T TO 0'T 0700 82
o IV PY , o

TEZI £9 92 GELS
SSSI £9 9L LISS
GPS 2992 7629
SGC 2992 ENL
6 SST 1992 ZEPL
9'9cT 1992 2618
ELST 09 24 6'S68
T8CT 09 2£ LIEG
8 SZT 6982 720 01

| OST se co

IGT 2£ c6
GST 98 £6
EEST vecs
SPST et 16
Z GST ct 16
6 9GT TE 96
Z LCT 08 96
ZBOT 62 96
C691 22 96

SGOT 0386 y"80 LZ
€'99T 6186 S61 LZ
SLOT 4186 6°62 LZ
P 89I9r66 p'6t LZ
Y69T 9166 18h LZ
GOLT $166 0799 L7
GILT 21 66 EO 82
9'ZLT 01 66 y"60 8c
9 ELT 600'T 6'pI 82
LVLT 8001 S'61 87
L'OLI 90 0'T € EZ 82
BOLT 9001 Z'97 87
6 LLT 2001 £87 82
6'8L1 20 0'T 9°62 82
0'08T 10 0'T 0'0€ 87

[A o

AGOLILVI OL AWVN AUVULNOO NOLLVNITIOWG

4/661 Y9 9.
PEST £9 v.
T'YGI £994
S vc T 29 92
9'GZT 39 94
€'9c T 19 92
O'LZT 1912
A'L6T 0924
G'8ZT 69 82
"OST 88 26
€ IGT 28 2
GC 6G] 9 £6
TEST $6 £6
T TST FE 6
0'GGT 2 6 £'£0 SZ
O'OGT T£ 96 IZZ Sc
O'LST 0896 TOF Sc
O'SST 6c 96. S 2G Sc
0'6S T 83 9 OFT 92
0'09T 9% 96 6°62 92
O'TOT sc 26 era
O'ZOL tZ 46 £'6G92
T'691 £ 26 621 LZ
LP9OT 12 86 2°S2 LZ

LIZ1 "982 LEIS
Y'CCI WL TESS
TEST 2972 7°99
SESI 8992 (VIL
SPST 2992 SIS f
ZOZI 299 9878
6'931 1992 Froë
2931 1922 616 6
YIZT9L 18101
7:83 1 0984 G'S 01
0'09T 8826 g'9y Ez
OTST 28% 16042
6'IGT 98 LOEIZ
6'Z9T sees LIS PZ
GEST 78 F6 0'Z1 Sz
6 FST E26 9'I£ SZ
8'991 1876 POS Sz
8'99T 08 96 9°80 92
8'L91 6296 1°97 92
8'891 8796 82h 9c

E 131 99€ LIS
O CGI WF 7079
LCST WE 1889
GEST £954 VL

IG PCT 992 OVS

6 YGI 992 F198
9971 2994 $826
6 9GI 1922 6'y0 01
1231 09 22 TIP Ol
81310982 ØLI ITY
SGPT 8826 CPI vz
8 08T 2826 L'9E pz
2"T9T 9 86 S"8S yc
LCST 9€ €6 9'6I Sc
LEST 26 OOF Sc
LYGT Se v6 865 SC
2'99T c£ v6 8'8I 9c
LOGT 1696 TLE 92
2"29T 6396 LYS 97
2 "891 87 9 SIL LZ

66ST 12% L389 92
6'09T 93 26 OPI LZ
6 TOT 13 26 Y87 Lc
6 GOT & 46 Teh Lc
0'Y91 Zz 86 OSS LZ

T'S9T 03 86 116 LZ
€ '99T 61 86 0'6p LZ
SLOT 1186 kel
€'89T 91 66 0°60 8c
€'69T ST 66 BLT 82
POLT 21 66 g'Gc 8c
PILT 21 66 6"2£ 82
G'ZLT TI 68 £"6£ 82
9821 60 0'T J^ yy 82
9"p.LT 80 0'1 FGF 8c
2921 90 0'T Z'£S 82
BOLT 20 0'T 2°96 82
6 LLT OT £"85 82
6 SLT 20 0'T 9°6S 82
Q'OST 10 0'1 0°00 62

O'GOT 03 88 T1082
T'99T 61 86 y"81 8c
T' LOT 81 86 6°82 82
C BIT 91 66 9'8t 82
C 69T 9166 GLb 82
€'OAT £166 ees
P 1213166 2°20 62
PCLT 11 66 1°60 62
GELT 60 0T OFT 6c
9"p2T 8001 £'6I 62
LGLI 90071 Z EZ 62
8'9Z4T 9001 2°92 62
S' LAT YOOTE'SC 62
6'821 20 0'T 9°62 6c
O'O8T 10 0'T Q'0£ 62

2691 Z% 927 L7
L'O9T 92 96 6'Zb LZ
S I9T 9c 26 S'S LZ
8'Z91 & 26 Z'I182
8'£91 Æ 86 pg
6'Y91 02 y'96 87
0'991 61 86 8'29 87
O'L9T 8186 y'8S 87
T'891T 91 66 2780 67
T'69T 91 66 1'21 62
C'OLT TI 68 ee
SILI 31 66 C'7£ 62
V'CAI 1166 688 67
G'ELT 6001 S'Y 62
PLT 80017'6h 67
9921 90 0'T T'ES 62
L'OLI 9001 1°96 62
8'LL1+00'1 £°85 67
6°SLT 200'T 9°65 62
0'081 100'1 0'00 0€

NO. 214

PUB.

EXTRACTS FROM H.O.

APPENDIX AA

1172

WH | 28g

4 4

HANLILVI OL ANVN AYUVALNOO AO SI NOLLVNITOSWG LVHL ALVOIGNI SOIIVILI NI SAUNDIA

"VH|ega|'v'H|eg|'v'H| eg veg | vH | 22a | -v-H| 0990

Ada LILIV

AId4VL NOLLVOIALENGAGI 8H ViLS

1173

PUB. NO. 214

EXTRACTS FROM H.O.

APPENDIX AA

— =

PIII pols | 7

8'ZZT £982 SEOS | IZZI 6575 | I'ZGI 992 EBPs | E

8'£21 2992 ERIS |S'231 2982 eors | SETI 2994 FEO |E ccr £994 6579 | E

SGZI 199. 2605 |6'p31 1994 CZES |ovcr 199 ZSSS | YZI 29% 6219 | 6821299 90r9 [9'EZT 299% TEOL | Z

9°9ZT 099. ZOOS [3931099 LETS |6:S31 0992 oops | 0931 19% 6809 [ESZI 199. 2189 [GFZ 199^ 94599 | 9'PCI 1992 VLIL | SPSL 799% zov? | 09
LTT 69 LL GSES |0 ZGI 0922 6855 | 9931 0944 07329 18901 0922 OSHI |0'9GI 0922 9802 |2'S31 1922 CIEL | E 97T 1922 OSL loost 6918 | 6
0871 6824 ZII 9 FL LS 6922 HHEO |P LSI 6822 9759 JOLSL 0922 LOTL | 2931092 GEHL [P 9ZT 0922 07208 | 1931 0942 TOES | 2931 192 Ess | 8
1871 8982 Z'9Y9 | v'8Z1 6984 S602 | 1831628. 8282 |S LTT 628 Z9GL | PLT 6282 S618 | T'LZ1 0984 8248 | 8'9ZT 0982 9906 |S'931 0982 E676 | 4
v'671 8982 gel | 16318282 CHL [8 8ZI 8282 ging |9871 828. TIES |Z STI 6982 1998 |6 22T 6282 1816 | 9231 6982 9166 | Z LTT 6384 05001 | 9
Z OST 2962 0552 | 6631 2962 L 9671 82 6. £Zp8 |Z 6ZI 8962 9906 |6 SZI 8064 9626 |9'831 82 62 TESE | SSI 6262 roror|O'ScT 6282 Copal 95
GIST 9826 g'8002| € 1ST 9826 S'98 07 | LIST 9826 Z0 IZ | GOST 4826 6'1£ IZ | 2001 2826 S65 IZ | GOST 28 26 122 ZC] € OGT 2626 89922 |O OST 8626 rectc | 6
PST 98 86 867 07 |S SST 98 86 9,502 | O ZST 98 86 YSZ 12 | 8 TOTEE ZES IZ |O IST 98 o OQ Iz zz | FIST 9886 8'8Y Cz] Z IG T 9 £6 991 £c JOIST 2666 Epy EZ | 8
GEST 6 [OS OZ | TEST PELS 181 IZļ6 29T 78 0'9 IZ|8'GGT Se es OPI ZCI OCCT ESO G' Ir ZZ | PSST 9886 8760 €Z| c GG I Se £6 LLE EZ [O "ZST 9 ES 950 PZ || A
€'PST LF 8760 IZ | TFSI ££ 96 67€ IZ |6'EST ee 6 07 LEST Et THEIS EST vero T7067 |g EST E ZOE EZ] TEST PE 86 Z'8G EZ |6 SCT 6 Z'9z PZ | 9
G:991 26 8'82 IZ | 0991 c£ 96 TLS Iz | SYST Ze vo 9'FGT?£*6 SEG ZZ | 0 FST 8836 L'Ic SZ | e PST ££ 99 Ger £2] D YET e76 OBI bZ |6 EST €e +6 ZOPVZ | SZ
T'981 1896 z'1y IZ] 0991 16 OSI ZZ [8991 18% GE 72 | 9991 1876 ezrez |y SST zero gorez c SST zer esovz| 1991 eH TLE bZ [6 TST ce m6 S90 sz | 7
T'ZST 0896 6077] 6'9S1 08 96 HEEZZ| LOST 0896 GI1OEZT]9'OST 0896 LOL EZ | HOST 08 96 g'sstz | G'9GI 1696 7:12 HZ} O'OGT 18 98 LSS pz |6 SCT 1ES6 [HZ Sc | 8
0'8ST 8296 61272 | 6 161696 SOS zc |L LST 6296 Fel ec|G 4916796 LLY Ez |P LOTES £90 yz |o LOTES Gry vc| O ZST 0896 DEI SZ |6 OST 0826 SIPS? | C
0'691 29 £'8£ ZZ |8'891 29 0720 EZ] 2891 82% LSEET| SRST 896 F OH |E SSTG LEE yc |o 8915296 SF 1OSZ] 0'8GT 83 SOE SZ |6281 6796 [65 S7 | T
6'691 9% 96 GES ZZ | 8'6ST % 9 822 EZ | 9691 9% 96 919 SZ] S'6GT 296 voz HZ | E'6ST 2396 Z 6r bZ | c OST 2296 081 SZ] OGTT 89 sz |6 89T 23 9 9'SE9z || 02

6 091 sc 96
6 TOT % 26 TEZ EZ
6 SOL 23 16 9'9t £z
8 891 1:26 FGF £z
SPOT 0386 p
8 391 6186 LI bz
8991 81 86 £'£z Vc
SLOT 91 66 T'EE yc
8891 91 66 er Vc
S'69T PI 66 p"0S 12
8'021 31 66 6 LS vc
SILT 1166 910 52
6'SLI 01 66 S01 SZ
6° ELT 600°T JST SZ
6 PLT 200'T [02 Sc
6 941% 0'1 9'£7 Sc
6'94T 90 0'T #92 SZ
0'84T 20 0'T y "82 Sc
0'62T 20 0'T 9°62 Sc
0'OST 10 0'T 070€ SZ
WV PV. o

8'091 92 96 BLE EZ
4197 vc 26 TZS £c
24391 €2 26 Lenk
LEQT 1226 9'8l vc
L POT 86 8"0€ vz

2"99T 6186 Ven vc
4'99T 8186 8"25 Vc
2"L9T 9166 9°20 Sc
2891 91 66 ZII SZ
L 691 FI 66 1'07 Sc

BOLT £t 66 922 Sc
SILT 11 66 y" pe SZ
SLT 01 66 FOr Sc
BELT 600'T 9'Gy Gc
S' PLT 20 0'T 0705 SZ
6 GLI 90 0'T 9'£6 SZ
6 92T 200'T 1796 Sc
6 LLT £00' 1 HBS Sc
0'621 20 0'T 9765 SZ
0'08T 10 0'T 0700 92
o pv_.

9 091 53 96 2°90 p7
9 TOT ve 26 cc vc
9'COT ez 46 6 HE vc
9'£91 7226 GLH Vc
9'T9T % 86 1"00 Sc
9'G9T 6186 SII Sc
9'99T 8186 £'Zz SZ
9 LOT 2166 c't Sc
9'89T 9166 VIb SZ
2'691 +1 66 8"6p Sc

LOLT £r 66 HLS Sc
Æ TZT 11 68 74092
Æ CAT 01 66 TOL 92
BELT 600'T SST 92
S' PLT 200'T 6'61 92
8921 9001 &'£z 97
6'92T 90 0'T EN
6 ALT £0 0 T 7°82 92
0:641 20 0'T 9°62 9z
0'08T 10 0'T 0'0£ 92
o 3V PV , o

S091 82 96 LSE vz
G TOT % 46 2°05 vc
SCOT £c 26 OHO Sc
S891 æ 26 121 Sc
Q POT 12 86 P62 SZ

G'G9T 6186 6 OF SZ
G'991 8186 IIS SZ
G LOT 2166 8°10 9c
9'89T 91 66 OIL 9c
9'69T +1 66 TGI 92

9'OAT £166 T'LZ 9c
OTLT 11 66 OVE 9c
Æ CAT 01 68 TOF 92
Æ EAT 60 0'T y"Sp 97
S' TAI 2001 g'6y 97
8'GAT 9001 SES 92
6'92T 20 0'T £95 92
6 LLT £00'T HBS 92
0'64T 20 0'T 965 92
0'08T 10 0'T 0700 LZ
o av o

0'091 % 96 y"Z0 9c
Q'T9T 96 16 CLI 92
TOL 12 26 PIE 9c
T'£91 22 26 Lbh 92
T'p9T 12 86 £7/S 92

SGOT 0386 1°60 LZ
c 991 8186 IO LZ
SLOT 1186 HOE LC
E 89T 9166 6'6€ LZ
E 691 F166 SBF LZ

P OLT £1 66 p'oc LC
GILT 3166 YE0 82
G`ZZAT 01 66 9°60 82
9621 600'T OST 82
9 PLT 80 0'T 961 82
LGLT 9001 EEZ 82
BOLT 90 0'T 2°92 8c
6`LLT £00'T £82 82
6 SLT 20 0'T 9°62 82
0'08T 10 0'T 0'0€ 82

6 691 9% 96 ETE 9c
6 O9T sc 26 7'9% 97
6 TOT 9c 26 y700 LZ
O'EOT % 26 GEL LZ
O' TOI Te 86 _ 9°92 LZ

O'G9T 03 86 S'8€ LZ
T'991 61 86 9'6p Ic
T LOT 2186 66S LZ
C 89T 91 66 $°60 82
€ 69T ST 66 TSI 82

€'OAT £T 66 192 82
PILT 3166 ZEE 87
S 321 01 66 p'6£ 82
G`ELT 600 T 6 vb 8c
9 PLT 80 0'T S'6h 82
L GLT 90 0'T EES 82
BOLT 90 OT 295 82
S'LLT TOOTE'SS 82
6'84T 20 0'T 9'66 8c
0'08T 100'T 0°00 62
IV PV 7

6 091 % 96 9'y0 Sc
€ TOT 9c 26 761 Sc
ESOT £ 26 TEE Sc
6 E91 23 46 £'9y Sc
P PT 12 86 18S SZ
POT 6186 E01 9c
FOOT 81 86 ZIZ 9c
PLOT AT86 £'I£ 9c
"891 91 66 9'0p 9c
S'69T Fr 66 16h 9c

S021 ET 66 6:95 97
9'TZT 21 66 920 LZ
Q°ZLT 01 66 6°60 LZ
L'ELI 600'TZSI LZ
L'ELI 8001 £'61 LZ
SGLT 00T FEZ LZ
8'921 900'1 £9 LZ
6'LLT 200'1 y 82 LZ
6'8LT 7001 9°62 LZ
0'081 10 0'T (0E LZ

7091 % 96 G"EE Sc
Z TOT sc 46 78h Sc
G COT € 46 7720 92
C 691 Æ 46
C Y9T IZ 86

SGOT 07 86 Leg
E 99T 8186 205 92
SLOT 2186 6'00 LZ
P 8979166 col LZ
y 69I*r66 8"81 LZ

S'021 £t 66 9°92 LZ
GILT 31 66 get LZ
9321 01 66 8'6€ LZ
9'ELT eoo't TSP LZ
A VAL 800'T ¿6h 22
LGLT 900'T PES Le
BOLT 0 0'T €°96 LZ
6 LLT £001 £"8S LZ
6'8ZT 20 0'T 9'65 LZ
0 TO 0'T 0700 82

e o

HACALILVI OL ANVN AUVA4LNOO NOLLVNIIOWG

1174 APPENDIX AA: EXTRACTS FROM H.O. PUB. NO. 214

ALTITUDE CORRECTION FOR D. R. LATITUDE

LATITUDE DIFFERENCE (minutes of arc)

[ As. EA A E a la tE See

180
179
178
177
176

Az.

0.7 "ei
[ Az

400 «ie co r- 00 C»

0.9

8
ili

.

0.4
0

0.
0.5 0.7 25|155
0.4 26|154
271153
28|152
29|151

0

0.0 | 0.1 | 0.1 | 0.1
0.0
0.1

0.4
0.4
0.3
0.1
0.0

S
0.

9
H
=
6
d
4
Ē
a
6
®
Ë
è
A
c

e
e
o
e
E
e
šā
e
de
e
K
e
m
e
H
e
m
=
Gel
à
=

j MEE i d

0.
0.

180
179
178
177
176
5/175
6|174
71173
81172
9|171
101170
111169
121168
167
166
151165
164
163
162
161
01160
159
158
157
156
25 |155 1 0.1
154
153
152
151

Te EA ele Eck
SAKS H LOOOO

0
1

ti [00 0000

9
6
4
1
9
6
3
1
8

KO a

3
3
3
3
2
2
2
2
1
1

SEESE
GI ri rr e
pel rd El pu, qu

=

E ME Sao lotto E
j ONNAN Nana a AANAN NODOJN N [C1 CN re rt | paa
O HH |A A FO O LR | 09 ed | Hi Op 1C o9 C00 o AH a
ANANAINAN Nari | weise RR mr

T r= rr pom | r= rH A | rm rm IM
a
=
E

m

itude, AL correction is minus; but for DR latitude less than selected tabulated latitude, the correction

ANNAN 1 dead
T

=| CoOoooo|mooocolooeocoo
vm rm rr

Lax]

DOODO|00000 00000 -b-««1 oio coc YAS AH OTRO | eS C31 A OH CD eO
DADOS |00 00 00 00 06 | 00 00 00 00 00 |00 00 00 00 06 OG OG Ó ee [HH H H NANA A Imi
DODOO|00000 0000000 OO AHL AH HOD er eO [DNA | orto | Heo 1000]...
0000000000 | 0 0b» E» E | be bw ES p [E ES RIN [ES RIED EE Pe Pw E be | 60600905 | d ii mimi O |00
cocoo|eeseoeo|eeoooo ODO «oto He co e CIC e osi Od || OS coi 69 aere oo p
REE [BB 00D DDD SID UDS SLDS [005050903 | im mii O O [te
Ce ERC AE «xoti et liegen [DONAR SNE ODOM.
«OOo «odo III ici IIA aciei |MAAAA HA ĀDOGSOLJO
20000 2 OOO NN OO AQAA HH OI lee MATO or |,
kk eeh E EE

2000020000 JOOP E | O O OWN 0202000 (DO AA obre

e$ c3 c3 c8 a tt (ededededes |Niriririr||H ooo loococo[w

eso A 22D] 000000t- NANN OO NAHH a hi Si HOD
Mana OANANAINANANAINANAAINAAAA |Hrrrir| DOSIS

ecoco|oocooooooooeooo|9o9oo |[wooor- (090220 yan eee eoeoeeaca
[lala laa] rt ri . . . . . + LU +

NANAN SAN An riririr | Hrirrir SS o o) n

esas jasssajsnccalacacalaaoaalo
SS a PAM aja]

0 | 1.
[í
6

DO MANO
o Ohh [te DO 2225
PLL n pee han pi | pu it A A A
o OO (ët DÉI CH Lee SANA
ANNAN

is plus.

han selected tabulated lat

Azimuth angle greater than 90°:
If DR latitude is greater t

o
at a than selected tabulated latitude, AL correction is plus; but for DR latitude less than selected tabulated latitude, the correction is minus.

APPENDIX AA: EXTRACTS FROM H.O. PUB. NO. 214 1175

10|170
11|169
12|168
13|167

14|166
79|101
80 |100

1|9.1| 0.1] 0.1] 0.2
0.1 |81
1
[0.17] 0.2'| 0.3] 0.4'| 0.57] 0.67 0.77] 0.87 0.9] Az. |

25

155
261154
271153
281152
291151

H
75 | 105
76 |104
71 |103
78 |102

51175
6/174
71173
81172
9/171
0
1
2

0.7

0.7

0.7

0.6

| «là SI

dH
1] 0.1] 0
0
0.1
0.0
0

100 0
09 0
98
97
96

1
2
3
84
Az.

0.1
0.0

LAT. DIFF. (tenths of minutes of arc)
0.4
0.4
0.3

0.1] 0.2/[ 0.37] 0.47] 0.5’[ 0.67] 0.77] 0.871 0.9" | Az.
RM ØR]

POPS LH HOA AH
WOOD «doudou
Sees

75 | 0.1
74
73
72
71

70

E SUE
TOO DO ARAN e |Ð DOMO] Ven

BRE BIS PSS a E

quA rr PV A | pm r= A kara ho! A | em m rm m m A re A A | pe rl per

j rA Oma OMOD| SANCHO OO FAO | Më

SC? NIT ed ea ERES ERES EE EE LERLE Sasa
"ATT AS io veo kl OO HINO WMO NOAA DIONA OGA LS CLE |

e| SSSCSSISSABASISASASSS! 05050505 HORNE EN Oð [uei xi eo c9 | rp Doi hi sti «eo co
RSSBARARAA SN Ne S aee remm

EE eelerer (90 Ort LO eO OE | i i O1 1o Cot
BOBO o6 00000000 |00 00 00 00 E | ES ES e cO Ud Rana] ES ES ODIO ti sti o c

eoocoo|oo)or-t- | DH OA |D AD OAD RATON [st Cd Obl | o TESCO | Nan | rt} AH
Ol sooo rz bere Bere [ES be bebe BS N 069 c0 OGG RR S 0909 NN | uu [shi «fco cO ON
ARRE EE ES ERES EE NINOS tx tos Ed Cd Cd COTA CR NON Fran

SOOO AAR (QH MA | HO OUN ANDO OOO 10000 i rbv 0900 | Dra = 1000900
FU cede a roedor coco NO | reci refl sl GGG
BNI IRLANDA AANA AAA | ret

160

8
3
7
2
7
2
7
2
7
1

5
3
1
8
6
5
1
7
3
8
0
5
1
6
2
5 7
2
6 8
2| 3.3
8
3

`

2
8
3
8
3
9
4
9
4
9
|27” 128" |29” |30"

lected tabulated latitude, AL correction is minus; but for DR latitude less than selected tabulated latitude, the correction is plus.

EI
a

tes of arc)

minu

ALTITUDE CORRECTION FOR D. R. LATITUDE

LATITUDE DIFFERENCE (

[ Az. _ ] 167 [177 [187 | 19 |20 [21 | 22" | 23" |

EEES ) ERES
INN Sas E
AANA NANNAN NANNAN ==
=

eerror
Dl 000000000 Ee Es
v rm rm rm rm

.

rn

If DR iatitude is greater than selected tabulated latitude, AL correction is plus; but for DR latitude less than selected tabulated latitude, the correction is minus.

If DR latitude is greater than se

Azimuth angle less than 90?:

HON r OTONO
lo Breese RE reOOowowo
SI imt rmm pl pd Soe

Azimuth angle greater than 90?

1176

MULTIPLICATION TABLE

DEC. DIFF. OR H. A. DIFF. (minutes of arc)

APPENDIX AA: EXTRACTS FROM H.O. PUB. NO. 214

CT x o
4 o <

ODO 010 «f 19 cob O»
SE
iic «c on jo Kéi o
ooo eo as ļo c e

cla
0.1

L Per

© ©

J e
19 Sr 190 Oo cro
EVEN DO o0 a SS nl HOL O D
TO ee Oen gen cerae ien cre) EG IE A R Ph =
SC sed Da beh Keele rn coto obs

o HA OMAHA
unn aa tl i joioogoooocoo
Le ri rA

OD HIDLO.00| PO ACOH [00 OR O DIO [IA HINO | ODO 05 | P 00 O ri N | io co b O

DEC. DIFF. OR H. A. DIFF. (tenths of minutes)

da
l
L
0.1
.
[0.1]

exeo

4
6
7
8
9
B R

3
4
5

=
ei ** '[e$eseseócó [có «1 rsd 5 05 [00000000 |O 9993 | 9 C O | Hi icd ed e |i cdi i edi ed

r=
ela o o EE E
A RRA o tdo ele 9 3| OO lan las] lan han ha Ja lan
Lan lon pl pl SSS

a

Sie
rt (NC «t | LO Ot 00 O | O ri NG ti [O ke ECK io pP 00 O | OMIA OD ti LD co E | Or N C9 YH 19 O b 00 O?
c ` ` '[eicicicici ededodedes [SSS SS (GS S GS rris QQ |oioioicioi|oicicioio

0. 1
2
4
5

0. 1
.3
.4
2.8
2. 9
3.0
3.1
3.2
3.3
3.4
3.5
3. 6
3. 7
6. 6
6. 7
6.8
6.9
7.0
"EP
7.3
7.4
7.5
7.6
4.4
7.8
7.9
8.0
8.1
8. 3
8. 4
8.5
8.6
8.7
9. 9
10. 0
10. 1
10. 2
0.3
0.5
10. 6
10. 7
10. 3
10. 9
11'

2
2
2
2
2
3.
3
3
3.
3
6.
6.
6
6.
6.
6.
6
6.
6.
6.
7
7
7.
di
7
7
7.
t
7
7
9
9
9
9
9.

See ` : q : ; ; ;
NAM omar qn or wn RA anna roo | O =r AA 9o 9 ona
e '' '[eieicicicileicicieici i iii iiie iðiðiðiðið RR SS] bin | ibis
ANM OCD MOO HAE «30900 «fio DNI |D OO PN ana icio EECH
$t P "leie icicicicd d Lil i ll fl qi (luc VE HLH BSS

0. 1
.2
.8
.4
3
3
4
5
6
2.7
2.8
2.9
3.0
3.1
5.4
5.5
5.6
5.7
5.8
5. 9
5.9
6.0
6.1
6. 2
6.3
6.4
6. 5
6.6
6. 7
6. 8
6. 8
6. 9
7.0
7.1
8.1
8.2
8.3
8.4
8.5
8.6
8.6
8.7
8.8
8.9

1

0.
1
1
1
2
2
2.
2
2
2
2
4.
4
4.
4.
4
4
5.
5
5

KARARAN

1

[ 4| 5] 6[ 7] 8] 9] 10’ ]11'[12/| 13' [ 14 15/| a]o.10.2[0.3'0.4'0.5"[0.6'[0.7"[0.8"|
0. 1| 0.1

EE Ë

4.

4

8.

8.

8.

8.

9

9

9

9.

9

9

9

9

0

0

0
. 8110. 5
10. 6
10. 8
10. 9
Viel
. 7/12. 6
12. 7
12. 9
13. 0
13. 2
13. 3
13. 4
13. 6
13. 7
13. 9

exe iecor-r- ooo ooo v? r«r-o000| DOO =r |A coco HH oic O ree | HDD OO mamma
mimmi mira (dedededes (dt ti ti qi] i Eee | Ei aiii VS S Šā

Nam +0 ha Vr [o 7-600090 uo ar |0000 0 AO nm ore

tot |i i ele) OS OS OD OOD ODES c3 66 c8 aaah araara IS

. 0
Sal
Si
.1
0. 8
.8
.8
.8
.9
0. 9
9
1.0
1.0
1.0
p 1.8
1.8
5 1.9
5 1.9
1. 9
2.0
2.0
2.0
2.0
2.1
5 2.1| 2. E
: 241122: d
2.2
2.2
2.2
2.3
2.3
2.3
2.3
2.4
2.7
2. 7
2.8
2.8
2.8
2. 9
2.9
2. 9
2.9
3. 0

1.0
1.0
1.1
1.1
1.2
.9| 12
-6| 29 1.2) 1.
.6 1.0) L3| 1.
JL LOL SHE
.7, 10| 1.4] 1.
1 .8| 2.4] 3.
1 2.4
1 2.5
1 2,5
1 2.6
1 2.6
1 2.6
1 2.7
1 2. 7
1 2.8
1 2. 8
1 2.8
1.4| 2.2| 2.9| 3. :
1.5| 2.2] 2.9] 3. ea pus
1.5| 2.2] 3.0| 3.7| 4.4] 5. S
1 3.0
1 3.0
1 3. 1
1 3.1
1 3.2
1 3. 6
1 3. 6
1 3.7
1 3.7
1 3.8
1 3.8
1 3.8
1 3. 9
2 3.9
2 4.0
[ 2’ | 3’ | 4’ |5| €.

0.0

Orar | 10 10 10 OSD | OCOD De | AN CID CD 09 09 CO ti H | HHEH AÐ UN LAD DOS E ET
2: Dag 40 Glo Gb ` «| AO qr era ae Jas qa jaa it di [a rg Ira es)
OO OOO VE EE EE LEE EE LOGO OO LED ERC Jj oo ooo
pia peo! dien Ob George 070-0-C us

CACO KE NC eg ECK WEE | O e

=

AL
0. 0
.0
.0
.0
Bw

01

99
mun

A
or
At

APPENDIX BB

0922-23 HI Ozz- HI 0z22-2 HI 0022-2 HI

oT V oT

8° Sz ds pP
4*90 Urb. Gen
(CA) TZS
$*90 8t 6*£T
M" Le 9T- M6'€€

221 (VOLUME ONE)

OU "1 8*'* 6
L* TT €T 6°9T

z geg CULO
Å €:00 st 2°90
S DAN St- WEE
[V
= "Es TE am
ri £ "TZ S
0*06 OC eee g tO
= L* 6% o 9°60
Q M9* 2S M6°2T
ES
--
z 8°85 0* 42
Q M9*80 02 MZ * 6€
4 e A o
= o1 o
=
E

08ZZ-Z HI 0922-2 HI Ozz- HT 02z22-2 HI 0022-2 HI

ga

i citu do t

NO. 221 (VOLUME ONE)

APPENDIX BB: EXTRACTS FROM H.O. PUB.

1178

ESA ag de L D NIO CI

09 T9 29 £9 +9 g9 99 49 99 69 04 t 0L oL
01 ter TI 29 cH A AA G (REVOIR IAS ieee 82
0 T t= 2- Ers G- 9- 6- TI- tī LT- Tē= tē= 82= Dës 62
KEE LOVaedtaas

g- Y 6 ST 9T- Te 92 Te 99 Tr 02
T+ Z= y et- SZ eg Tv 6t- Lo” TE
a WWesSa Te T- g 02- 62 Ot gs- Ze
ION Šā (74: Te T- TZ- 22 lt oe a H oe
Ge ESE 39 Se ‘b+ 6t- Ce Eër [25

TSA
Ee Kedā 68 G5. 6+ ZT. LZ tS- LON Gc
E CI iet "er Sw e o 6H IT CI” 9£- od 9g
«T Ll R 61 e+ sac VIII NI Ri ST+ |4= 99- L£
GUNDOIS T2) 92 TEE Lg vv- 29+ 69+ GG+ 82+ 8e
ST+ T+ 924 CC+ OF+ TS+ SC+ p+ 6€
Oc ve OF S89 6t+ : 9Y+ Ot
te 91 eet va pūt bi EL ER Tt
22 Lë Y v Gei ev
ce 92 99 Tb ZS+ SEA VA IA X & gp
T+ S24 OC+ Lët 9b+ G+ 69+ tt
aay GOS ON OA

e, E icon BS + SH+ £G+ 9G+ 94+ GY
ST _ 06 Eg Ae TE + Sg? Tb Stv+ 6Y+ 2S4 2S5 OG+ St+ Tt S24 $t
09) 19" 29 (95 99 eg 99 ¿9 89 69 DTI ÁL e) VI

DS TI OS'NIO-I

NOILOJUYOD HAVM ANS us

1179

APPENDIX BB: EXTRACTS FROM H.O. PUB. NO. 221 (VOLUME ONE)

£a 032095 VHT GIES Sheol ED OEI del GL OSS EL DOSS PRET

T V gt V 1 V 21

V

1

V

M GS ||TZT+ NS*T2 op | OLT+ N9*8S Sv | TOT+ N9*49 Gt | t6+ Ne°st St | 68+ NO*OO Sv
9S | STT S09 vei 50T L°Ov Sv |96 EOS S TOO SEI Sy A 9g'vv vv
LS | 601 6.0%, Sy. | COT cr Ce St | G6 TÜ SN 9*Sv vv | 08 T6 Pr
8S |vOI ATACAN 26 6°20 St | L8 Oia SV Vy viel 8 g*8c vv. SL 8° T vv
86+ NS*TO Sv |68* Mores by | T8+ NT°9C vv |94+ NS*OT vv | TL+ N6°SS ZV

09 || T6 A MA g'óo vv |9L Le DOV VIE NT Z ca A oo S*ge vv
GER CT vv | LL Se LOVE EA PRESS ee BEYs LS Ged eV
29 |84 Era vy EL St 6212 va 1159 OGG e Sie regs 0*20«€ Vv
KE AA A Æ OS oie agar NTS IEE LET
M v9 |v9- N»^90€?t |85+ Nb'vS Zv 69 Marek Zp |6b+ Neves cv |9v« NG'TC Cv

à o b o $ o 6 e D o

V LE V T V T V FH V E

V oT V oT V or y Ot V oT

Sc Re SE [PS um. She? Ot 600L. TE ee tom NOS PAS LO PM ov
ee AIDA ie ZA b EE LEO BOs ROL Pos. OF SE OL Ov cv
Tv G*€0 OL |8€ 94 TIMO J iS SLL whee e tog. DÄ CES bær db €p
8v v*z8 69 |v HS LOROT bit TOA e IB LOLA S 69507 o€ ev
86-. M2*O0v 69 |TS- M8%0S 6S Lë: MS'OO. OL |Sv- ISA LI Ar eed ba O PEN vv

H A o 6 [4] 4 © b T>

Buo'T 7 EN rri ol 7 Oo V Ort 7 Ø qe

1 d x
Ovc9-v HT 02£9-bv HT 00€9-v HT DËS
HS

087?9-v El 0929-v HT

APPENDIX CC

o
E
ei
O
Z,
ed
=)
po
O
m
=
z
Y)
E
e
<<
=
E
<
Æ

62€
oce
TEE
EE

bee
Stt
KA?
Lee
BEE

6£€
Ove
Tbe
tbt
bbe

£0€
Pü
S0€
90€
90€

LOE
80€
60€
OTE
TIE

ele
ELE
vit
SIE
9T£

LT€
BI
61€
oze
TZE

[441
EZE
bee
KAJ
Lee

8ze
62€
oce
TES
ttt

NOA20Yd

90 T£
62 1€
eS T€
bi ce
9€ C£

9S ZE
PUCE
SE €€
ESEE
OT be

Le ve
ev vt
LS v€
TESE
bZ SC

BIEL)

60 SZ
Lt SZ
S292
20 Le
8€ Le

ST 82
0S 82
9262
TO 0€
S€ 0€

60 TE
[4 T£
Se’
Lv C£
61 t£

NOA904d

0S €€
TZ be
TS be
WEE
6v S£

OK
sv 9€
TT LE
TES
20 8€

Le 8€
0S 8€
GO
St 6€
LS 6€

S9c
S92
992
192
192

892
692
692
Ole
oLz

VEZ
CLE
Ge
€le
VLC

Ob 61
Sc 0c
OT IZ
SSe
Tb zz

92 €2
Il tē
9S tc
ev Sc
Le9c

ete
LIL
tb 8c
8262
GO?

SuuS

Sle
Sle
9L2
LLZ
"He

81€
6L?
082
082
182

c8c
£8c
£82
v8z
S82

8S 0€
£t T€
82 ce
ET ee
8S EE

£t ve
82 SE
ERIE
ESE
[4 LE

92 8€
IT 6€
SS 6€
6€ Ob
22 Tb

SIS

982

L8c
882
882
682

062
Tec
262
toč
v6ec

S6c
962
L6c
86c
662
SNIYIS

90 Zv
0S ct
£€ Cv
91 bb
65 bb

Tb St
be 9b
90 Lb
8b Lb
6c 8t

OT 6b
TS 6b
TEOS
TT TS
TS TS

SJ VÆNA

Bez
8zz
BC
622

622
622
622
0€c
oez

oez
oez
Te?
TEZ
TEZ

60 S€
cb SE
919€
6b 9€
£c Le

IS LC
T€ 8€
90 6€
Ot 6€
ST Ob

6b Ob
be Ib
6S It
be cb
60€t

SNdONWS

TEZ
LEZ
eec
ce?
e€c

eec
eec
eec
EEZ
[117

EEZ
EEZ
EEZ
EEZ
EEZ

btt €b
02 bb
SS vb
Te Sb
909t

GE:
81 Lb
tc Lv
0€ 8b
906v

cb 6b
81 0S
bS 0S
0€ IS
90 cS

SNdONVI

EEZ
€ec
EEZ
EEZ
£€c

CEZ
EEZ
cez
EEZ
EEZ

EEZ
gel
EEZ
EEZ
££c

£t 26
6T £S
SS €S
ct bS
80 SS

St SS
12 96
LS 9S
be LS
OT 8S

9t 8S
€2 6S
6S 6S
S€ 09
TI T9

SNdONVI

DA
evi
evt
cv
Tot

Tol
Tot
Tel
Tol
Ort

WA
ObT
ObT
WA
ObT

Tv 8S
£T 8S
St LS
DU 45
6t 96

1296
cS SS
GH
SS tS
92 bS

¿SES
8c ES
6S ZS
0€ eS
TO es

EUELBISIEI

WA
ObT
OvT
ObT
OvT

ObT
ObT
Ott
WA
ObT

ObT
Obl
ObT
Obl
WA

T€ IS
20 1S
€€ 0S
€0 0S
be 6b

S06t
S£ 8t
90 8t
9€ Lv
L0 Lv

8€ 9v
809t
6€ Sb
WIEL)
Tb bb

"1N3X 1914

WA
OtT
ObT
Ort
WA

Tel
(A
IA
TbT
Tel

Tel
cvi
evi
cvi
DA

2T bb
Et Eb
bI €b
St zv
91 eb

Lv Tb
8T Tb
0S Ot
IZ Ot
€S 6€

ve 6€
9S 8€
8c 8€
00 8€
ce LE

"IN3X UY

860
660
660
00T

TOT
TOT
cot
[Aut
DO

£0I
bol
Sot
SOT
901

TI €€
922€
ev TC
LS 0€
[401

82 6c
£t 8c
65 LZ
SIZE
0€ 92

9v Sc
HOER
8r bz
SE €c
Is ec

SIGYVINV

850
650
090
190
290

€90
t90
S90
990
990

190
890
690
0L0
140

KRIER

ZLO
€L0
£10
vLO
SLO

910
910
LLO
820
610

610
080
180
280
280

VIIdS

bS Sb
91 Sb
LE bb
8S €t
BT eb

8t ev
LS Tb
LT Tb
9€ 0t
bS 6€

£T6€
Tc 8€
8v L£
90 L€
€29€

Ot Gr
LS be
bl ve
T€ €€
Lv ce

£0 c€
6l Te
SE 0€
Ts 6c
1062

cc 8c
8€ LC
ts 92
80 92
BASE

6€0
0v0
2b0
DA
tto

9v0
HA
8v0
0S0
150

250
€S0
Lët
550
150

KRIER

Sit
9v€
Loe
bbe
ose

IS€
ese
ESE
SSE
KE?

[4-11
85€
6S€
100
200

SNINDIY

£00
t00
900
L00
800

600
010
ZTO
€10
LAU

STO
910
LTO
610
020

Sn1n934

PERIANA

ec bS
ESES
ees
£S cS
2226

0S TS
LT IS
bb 0S
OT OS
S€ 6b

6S 8t
EZ 8b
Lv Lv
OT Lb
ee 9b

9€ SE
8b SE
BS S€
L09€
919€

be 9£
0€ 9€
9€ 9€
Tb 9€
HK

Lb 9€
6v 9€
0S 9€
0S 9€
6v 9€

Lv 9€
KE
Ot 9€
EK
62 9€

GK
ST9€
909€
LSS
9b SE

SESE
HAT
OTSE
SS t€
Tb ve

4
vH

LES
8€t€
6t
Ove
Ive

tbt
tte
Stt
9vt€
Ha

8vt
6v€
WEI?
TSE
ESE

62 62
9b 6c
200€
HI Or
EE 0€

Lv 0€
00 TE
elle
pele
be T€

bole
ESTE
TO Ze
80 2€
SUZE

Nvuv8301V

Lee
Loe
8tc
8b2
6vc

6vZ
osz
osz
TSZ

(ER

Cae
ESZ
ESZ
ER
EL

LS 81
6€ 61
IZ 02
£0 TZ
Sp TZ

1222
60€c
CNEL
St vc
LAETA

1092
bb 9c
Le Le
OT 82
ys 8c

LNVHIVWOJ4

ttt
bet
Stt
9€t€
9£c
LEE
BEE
6€€
Ove
Ive

evt
tbt
bre
Stt
9v€

St 0c
S0 IZ
Sé tc
bb TZ
2022

0222
LE ee
bS cc
60 €Z
bee?

8€ €c
es €c
S0 tc
LT be
82 vc

jewey

£92
092
t9z
odo
99€

992
L9c
892
892
692

692
01€
TLC
Tle
ele

LT 02
č0 Ic
Lv TZ
ce ec
LIET

20 vc
Lv vc
££ Sc
8192
CD LZ

8t LZ
be 82
61 62
to 0€
0S 0€

epudig

Seg
sel
sel
Scc
Sec

Scc
bec
vez
vez
pez

£cc
ele
tel
ZE
eec

TE bS
€0SS
S£ SG
L0 9S
6€ 96

TT 25
£t ls
vT 8S
9b 8S
LT 6S

6t 6S
0z 09
0S 09
IZ 19
[S209

YVNYIHIV

SSc
SSZ
KE
9S2
LSZ

LSZ
8S2
ETA
6S2
092

092
192
192
292
292

Le 6c
IZ 0€
S0 T€
6t 1€
€€ ce

LT t£
TO ve
9t v€
0€ SE
SES C

65 9€
tt LE
62 8€
DCH
8S 6€

1f vH1VWO3

Sec
Sec
Sec
Sec
Sec

sel
sel
Sec
Sec
Sec

Seč
Sec
sel
sel
sel

82 9b
00 Lb
ce Lv
t0 8b
LE 8b

60 6t
Tb 6b
£T OS
9t 05
8T IS

0S TS
ec CS
SS cS
LOC
6S £S

YVNY3IHIV

£91
v91
Gel
S91
S91

S91
991
991
L91
L91

891
891
691
691
OLT

be ST
TOSI
80ST
9S tī
bb vi

£€ VT
TZ vt
TT tī
00 tT
0S €T

Ot ET
TE €t
EEC
€T ET
SO€T

“IND 11914

eec
Teg
lee
ozz
ozz

612
612
812
Llc
912

IC
SIZ
tīz
BUG
¿te

ECiC9
cS 29
Te €9
TS €9
0c v9

6v v9
LUSI
Sy S9
£199
0t 99

9019
KE 19
8S /9
£c 89
8b 89

YVNY3HIV

LSI
EST
LST
8ST
8ST

6ST
6ST
091
091
091

tøl
TOT
291
291
£9I

82 61
OT6T
tS 8l
9€ 81
61 BI

20 8l
9t LT
0€ LT
LA LT
6591

bb 91
62 91
ST OL
TO 91
Lv SI

“INN 11918

9€l
Set
vel
cel
£€t

eet
Tel
TET
O€I
DT

621
621
eet
8et
821

etu
Tb 04
8004
S£ 69
2069

62 89
SG [9
TELS.
9t 99
2199

L€ 89
2069
9c v9
TS €9
SES

SNdONVI

821
8ct
Let
Let
Let

Let
Zen
Lët
Lel
Let

Let
Let
Let
Lel
LET

0t 29
v0 c9
8c 19
eS 09
9109

6€ 6S
£0 65
Lc 8S
TS LS
bT LS

8€ 9S
2095
Sess
6v bS
CT bS

SNdONVJ,

OTI
OTI
ITI
Ill
TET

TTT
ett
ett
¿tt
ETI

SLE
STI
tlI
vlt
vil

TS0
€S0
SO
Ei
1S0

850
650
090
190
290

€90
$90
990
190
890

890
690
020
1940)
eLo

£10
vLO
SLO
9L0
910

LLO
8/40
6140
610
080

SNIYIS

SNIYIS

S0 SS
£c bS
Ov £S
8S CS
Sires

tt IS
TS 0S
60 0S
126
9b 8t

t0 8b
el Lo
Tb 9b
6S Sb
8I Sb

ams

9296
0S SS
HT SS
LE bS
65 £S

Tees
et cS
£0 2S
bes
bb 0S

€00S
GH
cb 8b
00 8b
6T Lb

LE 9b
vS Sb
etse
62 bb
9t £t

£0 tp
61 Cp
9€ Tv
cS Ob
80 0t

bc 6€
Ob 8€
9S LE
TT L£
LE9S

920
820
0€0
e€0
veo

9€0
8£0
6€0
DA
€t0

tt0
9v0

Lto
6v0
050

9€ €9
SIDES
€S 29
0€ 29
S0 29

6t 19
er I9
tv 09
ST09
St 6S

tI6S
GES
60 8S
S€ LG
TO ZS

NES

tS€
SSE
KE
ESE
8S€

SE
000
200
£00
t00

S00
900
200
800
OTO

oz ze
se ce
8c C£
TE cC
Er c€

be ce
be ër
ARCAS
ce CE
62 zE

Sege
Te ce
912€
OT ce
€0 ZE

Nv4v8301V

TTO
rad)
D
vTO
STO

910
¿TO
810
610
020

eco
£c0
tzo
Sco
920

SS T€
9t T£
9€ T€
DATE
bite

c0 1€
6v 0€
S€ 0€
TZ 0€
S0 0€

6v 6c
e£ 6c
bl 6c
9S 8c
9€ 8c

NY4V89301V

1180

APPENDIX CC: EXTRACTS FROM H.O. PUB. NO. 249 1181

DECLINATION DS -29” SAME NAME AS LATITUDE LAT 41°
CÆÐ

1838 53
1903 54
1926 54

1950 55
2012-55 152116 32 -55

2034 55 153/1653 56
2055 55 154/1713 56 .
2116 56 15511732 56
2136 56 155/1751 56
2155-56 156|18 09-56

2214 57 157|1827 s7
1581844 57
159/19 00 57

161 (1931 -s8
162/1945 58

164/2012 59
165/2024 59
24 30 -59 2331 -58 2134-58 166/2036 -59

2442 59 2343 s9 2145 59 167/2046 59
2452 59 2353 59 2155 59 167/2056 59
2502 59 2403 59 2205 59 168/2106 eg
2511 59 2412 59 2214 60 169|2114 59
2520-60 2420-59 2222-60 170/21 22-59

2428 60 2229 60 171|2129 59
2435 60 2235 59 172|2136 60
2441 60 2241 eo 173|2141 59
2446 60 2246 60 174/2146 59
24 50 -60 2350-60 2250-59 175|2151 -60

2454 60 2354 60 2254 60 176|2154 60
2456 59 2357 60 2257 60
2458 60 2358 59 2259 ep 178|2159 60
2500 60 2400 60 2300 60 179/2200 60
25 00 -60 2400-60 180|2300-e0

OP NW WIG~00

1182

APPENDIX CC: EXTRACTS FROM H.O. PUB. NO. 249

TABLE Ill. —Correction to Tabulated Altitude for Minutes of Declination

NOU PWN OO OONOAW »huwun—0

— — — ` ` sch sch sesch sch sch
Ww NN==0 COD NNAOU UA AWW NN O

D
ND
— h sch sch sch sch ` sch
— — ` sch — sch —— — ` sch sch
PW WNN—== 00000 JJDOUO UA AWW ONO

ee SS
PP WWHND—| OOVOWO OUNOO OPPWW HONDO

29 | 15 15 16

30 | 16 16 16
SIA Red
32 | 17 17 18
33 | 17 18 18
34 | 18 18 19

35 |18 19 19
36 | 19 19 20
37 | 19 20 20
38 | 20 20 21
39 | 20 21 21

40 | 21 21 22
41 | 21 22 23
42 | 22 22 23
43 | 22 23 24
44 | 23 23 24

45 | 23 24 25
46 | 24 25 25
47 | 24 25 26
48 | 25 26 26
49 | 25 26 27

50 | 26 27 28
51 | 26 27 28
52 | 27 28 29
53 | 27 28 29
54 | 28 29 30

55 | 28 29 30
56 | 29 30 31
57 | 29 30 31
58 | 30 31 32
59 130 31 32

DU PRWWHY — — CO C OO JJOO OU d ROO ONO

16

19 20 20

20 20 21
2011822
21022027
22 22123
228730789

23 23 24
23 24 25
24 24 25
24 25 26
25 26 26

26 26 27
26 27 28
27 27 28
27 28 29
28 29 29

28 29 30
29/3031
29 30 31
30831827
315252

31 32 33
32 33 34
32 33 34
33 34 35
33 34 35

PAW NN=00 ODOND OYU1 OU) 4» 09 WHO

URWW N==00D (00000 -41O) OY f 4 0) WHO
esch — sch — — — — mb

15
5 16

— sch esch -— ` sch sech d scht ech ` esch sch esch esch esch?

8 18
18 19

18 19 20
19 20 20
20 20 21
20 21 21
21122 22

22 22 23
2282230253
23 23 24
23 24 25
24 25 25

25 25 26
25 26 27

WN==0 OWOONIN ORU COND —— O

— dl — sch — —
WNN=0O0 COWON OYU1U1 4-00 UNO

WWN=0 OLSN GOURR CO ND — — C

—— d d sm esch "ech

13 14 14
14 14 15
Tox Eus
15 16 16
16 16 17

17 17 18
17 18 18
18 18 19
19 19 20
19 20 20

20 20 21
22122
21522722
22/2323
23 23 24

23 24 24
24 25 25
25 25 26
25 26 27
26 27 27

27 27 28
27 28 29

26 27 27|.28 29 29

27 27 28
27 28 29

28 28 29
28 29 30
29 30 31
30 30 31
30 31 32

31832727
313233
32 33 34
33 34 34
33 34 35

34 35 36
35.35.36
SOS ON
36 37 38
36 37 38

29 29 30
29 30 31

305152
312132
316253
32 33 34
33 33 34

33 34 35
34 35 36
35 36 36
35896137
36 37 38

37 38 38
37 38 39
38 39 40
39 40 41
39 40 41

On 4.RUN — OOVOO -IOY UP GN NS —O0

17 18 18

18 18 19
19 19 20
19 20 20
20 21 21
212162 2

208022
2212323
23 23 24
24 24 25
24 25 26

25 26 26
26 26 27
27 27 28
27 28 28
28 29 29

29 29 30
29 30 31
30 31 32
313232
3213293

32 33 34
33 34 34
34 34 35
34 35 36
35 36 37

36 37 38
37837238
37 38 39
38 39 40
39 40 40

39 40 41
40 41 42
41 42 43
42 43 44
42 43 44

SO LP Pä “00.00 NAAM QU) h5h5-—C

NOU UAWN 0000 JOUNIN WHN-O
ee o de o

— — sch — — sch sch sch ——
NOD NPWWNH 00100 NOONE WNN—=0

18
18 18 18
18 19 19

19 20 20
20 20 21
21121122
2112222
2223123

23 24 24
24 24 25
25 25 26
25 26 26
26 27 27

27 27 28
28 28 29
28 29 30
29 30 30
308131

31:31:32
31 32 33
32 33 34
33 34 34
34 34 35

34 35 36
35 36 37
36 37 38
37 38 38
38 38 39

38 39 40
39 40 41
40 41 42
41 42 42
41 42 43

42 43 44
43 44 45
44 45 46
44 45 46
45 46 47

— — — — — e MÀ do
OURWM ==000 NNOUA COND ND O

— sch sch — — o —À
Om 00hND h2— OtO00 ONAN WNNDN—=0O

QYU) 0) NN 000 O NOU = GO CO h2 — C

i ot EN ere

16 17 17
17 18 18
18 18 19
19 19 20
20 20 20

20 21 21
2122022
22 22 23
23 23 24
24 24 25

24 25 26
25 26 26
26 27 27
27 28 28
28 28 29

29 29 30
29 30 31
30 31 31
31832892
32132299

33 33 34
33 34 35
34 35 36
3533.3037
36 37 37

37 38 38
38 38 39
38 39 40
39 40 41
40 41 42

41 42 42
42 42 43
42 43 44
43 44 45
44 45 46

45 46 47
46 47 48
47 48 48
47 48 49
48 49 50

w N=000 Oo OU. wWwWN—0O
w N==00 ONADVA =huwn-—0

— ` ` sch d sch —
P wWN—00 ONDUA PWUNMN—O

— —h- esch sch

16 17 17

17 18 18
18 19 19
19 19 20
20 20 21
21 21 22

22:22:22
23:23:23
23 24 24
24 25 25
25 26 26

26 26 27
27 27 28
28 28 29
29 29 30
29 30 31

30 31 32
318232
32433933
33 34 34
34 34 35

35 59136
36 36 37
36 37 38
37 38 39
38 39 40

39 40 40
40 41 41
41 42 42
42 42 43
42 43 44

43 44. 45
44 45 46
45 46 47
46 47 48
47 48 49

48 49 50
49 49 50
49 50 51
50 51 52

DOW wWWN=00 ONAADN UNO

— — — sch ` e — e do
NOU WH HOMO ONNOAW PWNH—-O

NOOR WH OO ONDU 4 COND — C

Ad IB sch eck ad «eh ww aedi
ee dd m qur e ee ol

17 18 18

18 1919
19 20 20
20 21 21
21 21722
22 22 23

23 23 24
24 24 25
25 25:206,
26 26 27
27 27 28

28 28 28
28 29 29
29 30 30
30 31 31
31482132

32193293
33 34 34
34 35 35
35 35 36
36 36 37

37 37 38
38 38 39
38 39 40
39 40 41
40 41 42

41 42 43
42 43 44
43 44 45
44 45 46
45 46 47

46 47 48
47 48 48
48 49 49
49 49 50
50 50 51

0551852
2185253
52 53 54
53 54 55

ES 31 32 a 34 35 S 37 38 s) 40 41 42 43 44 s 46 47 a 49 50 si 52:53 54 55 56 5 58 59 eg

RP PUN—-—O DHDOVOAVU P=un—0O

— ` sch h ði (di di
U PWH-O VOVNVOU AWN=O0O

EOS It
U «OON D— CO OONOU 4 C55 — CO

— ` geck seh e— em a

15 16 16
16 17 17
17 18 18
18 19 19

19 20 20
20 21 21
212222
22123123
23 24 24

24 25 25
25 26 26
26 27 27
27 28 28
28 29 29

29 30 30
30 30 31
31831832
323233
33 33 34

34 34 35
35 35 36
36 36 37
37 37 38
38 38 39

39 39 40
40 40 41
41 41 42
42 42 43
43 43 44

44 44 45
44. 45 46
45 46 47
46 47 48
47 48 49

48 49 50
49 50 51
50 51 52
51852368
52 53 54

53 54 55
54 55 56
55156157
56 57 58

51 52 531 54 55 561 57 58 59

7

TOV HIB CI dioit Hd Awer cdi

agit ht Iba nda dí Pih at
Rose aa Maret dora MR du JPA "
UL, or 1f MN ipf bip dj

e e

lidir í O stie A ATA

A. wi EN lacy thi Ud net: ^ Hate X BV SCA Ip

M ba s. i wn e = >= Zb:

Breatcivels Do uz rh» tudo of H retais st io DE ee ` `
b A i LE Aid Z "Y Side T ga de kka D
p ` < ` LD Ae i Uu u 4 | xit DI Wa) m
HM. Weide Nhs TRA faVi tot bide ere? a EGO

The Hal ""- e
rt WEN OF depéezeutédu t Dita Mas Taal qii oc feta

MPSS E AT I Nð.
PPR Ti t
7 D "
Ld 4 p Li

K X

"vi E "

yu j

i
11 i
Ny
A

ee:
ie | "
o»
=
vi
]
|
|
ER

(RARE le

TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE

TABLE 10.
TABLE 11.
TABLE 12.
TABLE 13.
TABLE 14.

TABLE 15.
TABLE 16.
TABLE 17.
TABLE 18.
TABLE 19.
TABLE 20.
TABLE 21.
TABLE 22.
TABLE 23.
TABLE 24.
TABLE 25.
TABLE 26.
TABLE 27.
TABLE 28.
TABLE 29.
TABLE 30.
TABLE 31.
TABLE 32.

TABLES

Explanation of Tables 34 2340.44 ZZ 32 m a KE A 1185
Conversion. Alle a ods ed Se se E 1198
Conversion of Compass Points to Degrees_-_---.----------------- 1217
‘Traverse Table:-4.2..d.3.2.28.2-5 MO 1100 _ a ES 1218
Conversion Table for Meridional Parts) = 2-2. € T S 1236

«Meridional Parts 1.7.2 S EE 1237
Length of a Degree of Latitude and Longitude. -----------2-2---- 1246
Distance. of an: Objeet by Two'Bearings. =a TTT C S 1248
Distance 6f the Horizon: Tø SS E r: SS S ee ee 1254
Distance by Vertical Angle”. ge m V 2.3 0 SS 1255
Direction and Speed of True Wind in Units of Ship's Speed-------- 1260
Correction of Barometer Reading for Height Above Sea Level. ____ 1262
Correction of Barometer Reading for Gravity FTTR 1262
Correction of Barometer Reading for Temperature... 1263
Conversion Table for Millibars, Inches of Mercury, and Millimeters

of Mercury.s.-...2. d ee o1 ee 1264
Conversion Table for Thermometer Scales_______.___.___-------- 1265
Relative Humidity ze +< SN vc 1266
Dew? Pont. ta va cM 1268
Speed Table for Measured Mile “TMO 1270
Speed; Time, and Distance 22 m N 1271
Conversion Table for Nautical and Statute Miles_ 0 1276
Conversion Table for Meters, Feet, and Fathoms_________________ 1277
Dip of thē.Šea' Short of the Horizon ec "TN 1278
Altitude Correction for Air Temperature________________________ 1280
Altitude Correction for Atmospheric Pressure____________________ 1281
Meridian Angle and Altitude of a Body on the Prime Vertical Circle.. 1282
Latitude and Longitude Factors 0 S 1286
Amplitudes... 2-44 90 09 SA AER TRA eee 1293
Correction of Amplitude as Observed on the Visible Horizon_______ 1297
Altitude Factor-£-- 52:5... S EM 1298
Change of Altitude in Given Time from Meridian Transit_________ 1308
Natural Trigonometric Functions A 1312
Logarithms’ of Numbērss-€ SE 30000 EES 1357
Logarithms of Trigonometric Functions HAR 1376

TABLE 33.
TABLE 34.

EXPLANATION OF TABLES

Table 1. Conversion Angle.--The angles listed in this table are the differences
between the great-circle and rhumb line (Mercator) directions between various points.
The table can be used either for converting rhumb line directions to equivalent great-
circle directions, as in great-circle sailing; or the reverse, as in converting radio bearings
to equivalent rhumb line bearings for plotting on a Mercator chart. The sign to be
used for each process is indicated at the bottom of the table. As indicated, the sign
given in the tabulation is reversed if the conversion angle is shown in italics.

The first one and one-half pages of the table, for differences of longitude of not more
than 4°5, and middle latitudes between 0° and 85°, is intended primarily for use in
converting radio bearings observed near a coast. In high latitudes it may be needed
for converting visual bearings of objects a considerable distance away (art. 2522).
This part of the table is entered with (1) the middle latitude between the craft and
radio station or object, and (2) the difference of longitude between these two points.
Do not use this part of the table if the latitudes are of contrary name (one north, the
other south), if the difference of latitude is more than 10°, or if the difference of longitude
is more than 4°5. Under any of these conditions, use the second part of the table.

For this part, select the page for the latitude nearest the latitude of departure in
the case of great-circle sailing, or the latitude of the receiver in the case of radio bearings.
On the selected page, the entering arguments are (1) difference of longitude (DLo)
between the two points involved, and (2) the latitude of destination in the case of
great-circle sailing, or the latitude of the transmitter in the case of radio bearings.
For 0° latitude of departure or receiver, there isa single table. For all other latitudes,
separate tables are provided for latitudes of same name and contrary name. For
accurate results, use triple interpolation, as explained in article P4.

Use of the table is explained in articles 821 (great-circle sailing), 1204 (radio
bearings), 1206 (consol), 2404 (azimuths by submarine periscope), and 2522 (visual
bearings in high latitudes).

The conversion angles on the first one and one-half pages of the table were computed by means

of the formula:

tan conversion angle=sin Lm tan % DLo,
in which Lm is the middle latitude, and DLo is the difference of longitude. This formula is based
upon the assumption that the plot of a great-circle track on a Mercator chart is symmetrical, the
axis of symmetry being the perpendicular bisector of the rhumb line connecting the two points. No
error of practical significance in ordinary navigation is introduced by this erroneous assumption over
the range covered by the first one and one-half pages of the table.

The remainder of the table was computed by means of the formula: conversion angle= initial
great-circle direction~rhumb line direction. The initial great-circle directions were computed by
means of the formula:

hav C=csc D sec L; [hav co L5— hav (D~co La
in which C is the initial great-circle direction, D is the great-circle distance in arc units, L, is the latitude
of departure (or receiver), and L; is the latitude of the destination (or transmitter). The distance D
was computed by means of the formula:

hav D=hav DLo cos L; cos L¿+hav (Lı ~L),

in which the notation is the same as above.
The rhumb line directions were computed by means of the formula:
tan c=PLo,
m
in which C is the rhumb line direction, and m= M, «M, the meridional parts of the two latitudes.
1185

1186 EXPLANATION OF TABLES

Table 2. Conversion of Compass Points to Degrees.—In this table the compass is
boxed to 128 quarter points and the equivalent angle is given in degrees, minutes,
and seconds. The naming of the quarter points, as given here, is one of several systems
that have been used. gi k

Table 3. Traverse Table.—This table provides the quantities needed for solution
of plane right triangles, arranged in a form for convenient solution of the problems
encountered in the various sailings (ch. VIIT). Two sets of column headings are given
to indicate the corresponding values in different problems. Thus, if DLo is used as
entering argument in the first column, p is taken from the second column, but if D
is used as entering argument in the first column, / is taken from the second column and
p is taken from the third column. When the top line of column headings is used,
the individual table is selected by means of the latitude. When the second line is used,
the table is selected by means of the course.

The entering argument can be multiplied by any power of 10, including negative
powers (art. O2), if the corresponding values taken from the table are multiplied by
the same power. Thus, using the table for course 205°, if D=6 miles, /=5:438, and
p=2.536 miles; but if D=600 miles, /=543/8, and p=253.6 miles; or if D=0.6 mile,
1=0'5438, and p=0.2536 mile.

In this table, DLo is difference of longitude, p is departure, D is distance, / is
difference of latitude, and m is meridional difference (difference of meridional parts at
two latitudes). In the solution of any right triangle, D can be considered the hypot-
enuse, and / and p the other two sides. The angle is that opposite side p. Also, if m
is one of the short sides of a plane right triangle, DLo is the other side if the given angle
is that opposite DLo. If the two short sides are known, the angle opposite one of them
can be determined from the tabulation on the right if the table is entered with the
quotient found by dividing this side by the other short side.

The use of this table in the solution of problems of the various sailings is given in
chapter VIII.

The top decimal in each individual table is a natural trigonometric function, the p, l column
being cosines, the p column being sines, the DLo, D column being secants, and the DLo column
being tangents. The decimals below the top line are multiples of the top value. The decimals in
the center column to the right of the double line are natural tangents at intervals of 0?1. For addi-
tional decimal places, use table 31.

Table 4. Conversion Table for Meridional Parts.—The meridional parts given in
table 5 are for the Clarke spheroid of 1866. The values given in table 4 can be applied
as corrections to those of table 5 to obtain the meridional parts for the international
spheroid, the Clarke spheroid of 1880, and the sphere. Data on these spheroids are
given in appendix D.

An additional decimal place is given in this table to provide greater accuracy for
interpolated values.

Table 5. Meridional Parts.—In this table the meridional parts used in the con-
struction of Mercator charts and in Mercator sailing are tabulated to one decimal
place for each minute of latitude from the equator to the poles. The use of the table
is explained in articles 307 and 817.

The table was computed by means of the formula:

L 4 6
M —a log, 10 log tan ESCHER (e sin LES sin? Ls sin? L-- .. aj
in which
M is the number of meridional parts between the equator and the given latitude,

a is the equatorial radius of the earth, expressed in minutes of arc of the equator, or
21,600 k
VE =3437.74677078 (log=3.5362738827),

.

EXPLANATION OF TABLES 1187

log. is the natural (Naperian) logarithm, using the base e=2.71828182846
loge 10=2.30258509299 (log=0.3622156886),
L is the latitude,

e is the ellipticity of the earth, or ¥2f—f?=0.08227185422 (log = 8.9152512855 — 10),

H

and

f is the flattening of the earth, or f= =0.00339006034 (log— 7.5302074283 — 10).

1
294.98
Using these values,

a log, 10— 7915.704468 (log— 3.8984895715)
ae? = 23.268932 (log— 1.3667764504)

4

g = 0.052500 (log— 8.7201593034 — 10)
6

=0.0002 13 (log=6.3283796034— 10).

Hence, the formula becomes
M —7915.704468 log tan (45°+3) — 23.268932 sin L—0.052500 sin L— 0.000213 sin5L . . .

The constants used in this derivation and in the table are based upon the Clarke spheroid of 1866
(app. D), the standard reference spheroid used for charting North America.

Table 6. Length of a Degree of Latitude and Longitude.—This table gives the
length of one degree of latitude and longitude at intervals of 1° from the equator to
the poles. In the case of latitude, the values given are the lengths of the arcs extending
half a degree on each side of the tabulated latitudes. Lengths are given in nautical
miles, statute miles, feet, and meters.

The values were computed in meters, using the Clarke spheroid of 1866 (app. D), and converted
to other units by the factors given in appendix D. The following formulas were used:

M=111,132.09—566.05 cos 2L+1.20 cos 4L—0.002 cos 6L+ ...
P=111,415.13 cos L—94.55 cos 3L+-0.12 cos 5L— ...

in which M is the length of 1° of the meridian (latitude), L is the latitude, and P is the length of 1°
of the parallel (longitude).

Table 7. Distance of an Object by Two Bearings.—To determine the distance of
an object as a vessel passes it, observe two relative bearings (right or left) of the object,
and note the time interval between bearings. Enter this table with the two bearings.
Multiply the distance run between bearings by the number in the first column to find
the distance of the object at the time of the second bearing, and by the number in the
second column to find the distance when abeam. Use of the table is explained in
article 910.

The table was computed by solving plane oblique and right triangles (art. 042).

Table 8. Distance of the Horizon.—This table gives the distance, in nautical and
statute miles, of the visible horizon for various heights of eye from 1 to 200,000 feet.
The actual distance varies somewhat as refraction changes. Also, the formulas used
contain an approximation which introduces an error of a few tenths of a mile at the
greatest heights tabulated. However, the error is generally less than that introduced
by nonstandard atmospheric conditions. Since the earth's ellipticity is not considered,
the table can be used at any place on the earth, without appreciable error.

Use of the table is explained in articles 916 (visibility of lights), 1208 (radar), 1606
(dip), and 1608 (wave height).

The table was computed by means of the formulas:
nautical miles: D=1.144 yh,
statute miles: D=1.317yh,
in which D is the distance of the horizon in miles, and h is the height above the surface in feet. The
constants 1.144 and 1.317 are based upon the mean radius of the earth according to the Clarke spheroid
of 1866 (app. D).

1188 EXPLANATION OF TABLES

Table 9. Distance by Vertical Angle.—This table provides means for determining -
the distance of an object of known height above sea level. The vertical angle between |
the top of the object and the visible (sea) horizon (the sextant altitude) is measured
and corrected for index error and dip only. If the visible horizon is not available
as a reference, the angle should be measured to the bottom of the object, and dip short
of the horizon (tab. 22) used in place of the usual dip correction. This may require
several approximations of distance by alternate entries of tables 9 and 22 until the
same value is obtained twice. The table is entered with the difference in the height
of the object and the height of eye of the observer, in feet, and the corrected vertical
angle; and the distance in nautical miles is taken directly from the table. An error
may be introduced if refraction differs from the standard value used in the computation
of the table. Use of the table is explained in article 905. Other references to its use
are given in articles 609, 4119, and 4127.

The table was computed by means of the formula:

tana \4 E tan a
D= ios) AR 0.74736 0.000246’
in which D is the distance in nautical miles, a is the corrected vertical angle, H is the height of the
top of the object in feet, and h is the height of eye of the observer, in feet. The constants 0.000246
and 0.74736 are based upon the mean refraction (0.0784).

Table 10. Direction and Speed of True Wind.—This table provides a means of
converting apparent wind, observed aboard a moving craft, to true wind. To use the
table, divide the apparent wind, in knots, by the vessel’s speed, also in knots. This
gives the apparent wind speed in units of ship’s speed. Enter the table with this
value and the difference between the heading and the apparent wind direction. The
values taken from the table are (1) the difference between the heading and the true
wind direction, and (2) the speed of the true wind in units of ship’s speed. The true wind
is on the same side as the apparent wind, and from a point farther aft. To convert
wind speed in units of ship’s speed to speed in knots, multiply by the vessel’s speed
in knots. The steadiness of the wind and the accuracy of its measurement are seldom
sufficient to warrant interpolation in this table. If speed of the true wind and
relative direction of the apparent wind are known, enter the column for direction of
the apparent wind, and find the speed of the true wind, in units of ship’s speed. The
number to the left is the relative direction of the true wind. The number on the same
line in the side columns is the speed of the apparent wind in units of ship’s speed.
Two solutions are possible if speed of the true wind is less than the ship’s speed. Article
3709 explains the use of this table, and also a graphical solution of the problem.

The table was computed by solving the triangle involved in a graphical solution, using the
formulas:

sin Ba
Sa—cos B4'
Br=Ba+a,
sin
S m Da
sin «

tan a=

H

in which a is an auxiliary angle, Ba is the difference between the heading and the apparent wind
direction, Sa is the speed of the apparent wind in units of ship’s speed, Br is the difference between
the heading and the true wind direction, and Sr is the speed of the true wind in units of ship’s speed.

Table 11. Correction of Barometer Reading for Height Above Sea Level.—If
simultaneous barometer readings at different heights are to be of maximum value in
weather analysis, they should be converted to the corresponding readings at a standard
height, usually sea level. 'To convert the observed barometer reading to this level,
enter this table with the outside temperature and the height of the barometer above

EXPLANATION OF TABLES 1189

sea level. The height of a barometer is the height of its sensitive element; in the case
of a mercurial barometer, this is the height of the free surface of mercury in the cistern.
The correction taken from this table applies to the readings of any type barometer, and
is always added to the observed readings, unless the barometer is below sea level. Use
of the table is explained in articles 3706 and 4119.

The correction was computed by means of the formula:

C=29.92126 | ! ; a |
anos Ursa eem
in which

C is the correction in inches of mercury,

H is the height of the barometer above sea level in feet, and,

T is the mean temperature, in degrees Rankine (degrees Fahrenheit plus 459267), of the air be-
tween the barometer and sea level. At sea, the outside air temperature is sufficiently
accurate for this purpose.

Table 12. Correction of Barometer Reading for Gravity.—The height of the
mercury column of a mercurial barometer is affected by the force of gravity, which
changes with latitude and is approximately equal along any parallel of latitude. The
average gravitational force at latitude 45°32’40” is used as the standard for calibration.
This table provides a correction to convert the observed reading at any other latitude
to the corresponding value at latitude 45?32/40", so that it will have maximum value
in weather analysis of an area. Enter the table with the latitude, take out the correc-
tion, and apply in accordance with the sign given. This correction does not apply to
aneroid barometers. Use of the table 1s further explained in article 3706.

The correction was computed by means of the formula:

C=B (— 0.002637 cos 2L 4- 0.000006 cos? 2L — 0.000050),
in which
C is the correction in inches,
B is the observed reading of the barometer (corrected for temperature and instrumental errors) in
inches of mercury. This table was computed for a standard height of 30 inches, and
L is the latitude.

Table 13. Correction of Barometer Reading for Temperature.—Because of the
difference in expansion of the mercury column of a mercurial barometer and that of the
brass scale by which the height is measured, a correction should be applied to the reading
when the temperature differs from the standard used for calibration of the instrument.
To find the correction, enter this table with the temperature in degrees Fahrenheit, and
the barometer reading. Apply the correction in accordance with the sign given. This
correction does not apply to aneroid barometers. Use of the table is further explained
in article 3706.

The standard temperature used for calibration is 32°F for the mercury, and 62°F for the brass.
The correction was computed by means of the formula:
m (T— 329?) —1 (T—62°)
tig P ifm (1-32) ?

in which

C is the correction in inches,

B is the observed reading of the barometer in inches of mercury,

m is the coefficient of cubical expansion of mercury = 0.0001010 cubic inches per degree F,

l is the coefficient of linear expansion of brass=0.0000102 inches per degree F, and

T is the temperature of the attached thermometer in degrees F.
Substituting the values for m and / and simplifying:

T—28°630 £
OE SONES

The minus sign before B indicates that the correction is negative if the temperature is more than
287630.

1190 EXPLANATION OF TABLES

Table 14. Conversion Table for Millibars, Inches of Mercury, and Millimeters of
Mercury.—The reading of a barometer in inches or millimeters of mercury correspond-
ing to a given reading in millibars can be found directly from this table. Use of the
various units is discussed in article 3702.

The formula for the pressure in millibars is:
BnDg
P
in which

P is the atmospheric pressure in millibars,
Bm is the height of the column of mercury in millimeters,
D is the density of mercury=13.5951 grams per cubic centimeter, and
g is the standard value of gravity=980.665 dynes. Substituting numerical values:

BET 33022 Bm)
and
P
Bm=1333227 0.750064P.
Since one millimeter = 0.03937 inches,
0.03937P

B:= 133322 ~ 0.0295300P,
in which B; is the height of the column of mercury, in inches.

Table 15. Conversion Table for Thermometer Scales.—Enter this table with tem-
perature Fahrenheit, F; Celsius (centigrade), C; or Kelvin, K; and take out the cor-
responding readings on the other two temperature scales. Temperature measurement
is discussed in article 3711.

On the Fahrenheit scale, the freezing temperature of pure water at standard sea-
level pressure is 32%, and the boiling point under the same conditions is considered
212°. The corresponding temperatures are 0° and 100°, respectively, on the Celsius
scale and 273°15 and 373°15, respectively, on the Kelvin scale. The value of (—)
273°15 C for absolute zero, the starting point of the Kelvin scale, is the value recog-
nized officially by the National Bureau of Standards of the United States.

The formulas for converting the reading of one scale to the corresponding values of the others,
derived from the figures given above, are:

C=2(F—32°)= K — 273215,
F= 0 +329= K — 459267,

K=2(F + 459%67) = C-- 278215,
in which all temperatures are in degrees.

Table 16. Relative Humidity.—To determine the relative humidity of the atmos-
phere, enter this table with the dry-bulb (air) temperature (F), and the difference
between the dry-bulb and wet-bulb temperatures (F). The value taken from the table
is the approximate percentage of relative humidity. If the dry-bulb and wet-bulb
temperatures are the same, relative humidity is 100 percent. Use of the table is
explained in article 3713.

The table was computed by means of the formula:

100e,
€w

in which
R is the approximate relative humidity in percent,
e is the ambient vapor pressure, and

ew is the saturation vapor pressure over water at dry-bulb temperature.
Professor Ferrel's psychrometric formula was used for computation of e:

SC | 0.000367P (&— t^) (1 Sa 2]

1571

‘a eV

EXPLANATION OF TABLES 1191

in which
e is the ambient vapor pressure in millibars,

e! is the saturation vapor pressure in millibars at wet-bulb temperature with respect to water,
P is the atmospheric pressure (the millibar equivalent of 30 inches of mercury is used for this
table),

t is the dry-bulb temperature in degrees Fahrenheit, and
t’ is the wet-bulb temperature in degrees Fahrenheit.

The values of e, were taken from the International Meteorological Organization Publication
Number 79, 1951, table 2, pages 82-83.

Table 17. Dew Point.—To determine the dew point, enter this table with the
dry-bulb (air) temperature (F), and the difference between the dry-bulb and wet-bulb
temperatures (F). The value taken from the table is the dew point in degrees Fahren-
heit. If the dry-bulb and wet-bulb temperatures are the same, the air is at or below
the dew point. Use of the table is explained in articles 3713 and 3715.

The values given in this table were obtained (1) by determining the saturation vapor pressure e”
for the given temperature T (in degrees Rankine) by means of the following formula:

T
671. ERA NS
d LUN 1 )+5.02808 logio $1167 1.316» 10-10 (mna) -1)

logio e’ = — 7.90298 (

671.67
(ym)
+8.1328x 1010 E —1/ 4-logio 1013.246,
(2) by determining the ambient vapor pressure by means of Ferrel's formula (see explanation to
table 16), (8) by substituting e for e' in the formula of (1) to obtain the temperature T of the wet
bulb when saturation occurs (to the precision of table 17), and (4) by converting the wet-bulb
temperature (T) to the dry-bulb temperature T’ by means of the equation:

T'— T4 (t—t^,

where (t—t’) is the depression of the wet-bulb temperature. Tables evaluating e'in terms of T for
use in steps (1) and (3) are given in International Meteorological Organization Publieation Number
79, 1951, and the Smithsonian Meteorological Tables, Sixth Revised Edition, 1951.

Table 18. Speed Table for Measured Mile.— To find the speed of a vessel travers-
ing a measured nautical mile in a given number of minutes and seconds of time, enter
this table at the top or bottom with the number of minutes, and at either side with the
number of seconds. The number taken from the table is speed in knots. Accurate
results can be obtained by interpolating to the nearest 0.1 second. Use of the table is
explained in articles 608 and 615.

'This table was computed by means of the formula:

3600
Bro"
in which $ is speed in knots, and T is elapsed time in seconds.

Table 19. Speed, Time, and Distance.—To find the distance steamed at any given
speed between 0.5 and 40 knots in any given number of minutes from 1 to 60, enter
this table at the top with the speed, and at the left with the number of minutes. The
number taken from the table is the distance in nautical miles. If hours are substi-
tuted for minutes, the tabulated distance should be multiplied by 60; if seconds are
substituted for minutes, the tabulated distance should be divided by 60. Use of the
table is explained in articles 608, 801, and P1.

The table was computed by means of the formula:

in which D is distance in nautical miles, S is speed in knots, and T is elapsed time in minutes.
Table 20. Conversion Table for Nautical and Statute Miles.—This table gives
the number of statute miles corresponding to any whole number of nautical miles from
1 to 100, and the number of nautical miles corresponding to any whole number of
statute miles within the same range. The entering value can be multiplied by any

1192 EXPLANATION OF TABLES 1

power of 10, including negative powers, if the corresponding value of the other unit is
multiplied by the same power. Thus, 2,700 nautical miles are equivalent to 3,107.1
statute miles, and 0.3 statute mile is equivalent to 0.2607 nautical mile. Hence, to
find the number of statute miles egual to 2463.2 nautical miles:

Nautical miles Statute miles
2400. 0 2761.9
63.0 D
0. 2 072
2463. 2 2834. 6

Use of the table is explained in articles 205 and 607.

The table was computed by means of the conversion factors of appendix D:
1 nautical mile=1.15077945 statute miles,

1 statute mile=0.86897624 nautical mile.

Table 21. Conversion Table for Meters, Feet, and Fathoms.—The number of feet
and fathoms corresponding to a given number of meters, and vice versa, can be taken
directly from this table for any value of the entering argument from 1 to 120. The
entering value can be multiplied by any power of 10, including negative powers, if the
corresponding values of the other units are multiplied by the same power. Thus, 420
meters are equivalent to 1378.0 feet, and 11.2 fathoms are equivalent to 20.483 meters.
Hence, to find the number of meters equal to 2163 feet:

Feet Meters

2100 640
63 19

2163 659.

These units of measurement are discussed in article 607.

The table was computed by means of the relationships given in appendix D:
1 meter =39.370079 inches,
1 foot —12 inches,
1 fathom=6 feet.

Approximately the same results would be obtained by using the direct conversion factors given in
appendix D.

Table 22. Dip of the Sea Short of the Horizon.—If land, another vessel, or other
obstruction is between the observer and the sea horizon, use the water line of the obstrue-
tion as the horizontal reference for altitude measurements, and substitute dip from this
table for the dip of the horizon (height of eye correction) given in the American Nautical
Almanac or other source. The values below the bold rules are for. normal dip, the
visible horizon being between the observer and the obstruction. Use of the table is
expluined in article 1606 and in the explanation of table 9.

The table was computed by means of the formula:
D,—0.4156d +0.56584,

in which D, is the dip short of the sea horizon, in minutes; d is the distance to the water line of the
obstruction, in nautical miles; and h is the height of eye of the observer above sea level, in feet.
Table 23. Altitude Correction for Air Temperature.— This table provides a correc-
tion to be applied to the altitude of a celestial body when the air temperature varies
from the 50? F used for determining mean refraction by means of the Nautical Almanac.
For maximum accuracy, apply index correction and dip to sextant altitude first,
obtaining rectified (apparent) altitude for use in entering this table. Enter the table

EXPLANATION OF TABLES 1193

with altitude and air temperature in degrees Fahrenheit. Apply the correction, in
accordance with its tabulated sign, to altitude. Use of the table is explained princi-
pally in chapter XVI, and especially in articles 1614 and 1632.
The table was computed by means of the formula:
$ 510
Correction=Rn( 1— ot :
in whieh R, is mean refraction and T is temperature in degrees Fahrenheit.

Table 24. Altitude Correction for Atmospheric Pressure. This table provides a
correction to be applied to the altitude of a celestial body when the atmospheric pressure
varies from the 29.83 inches (1010 millibars) used for determining mean refraction by
means of the Nautical Almanac. For most accurate results, apply index correction
and dip to sextant altitude first, obtaining rectified (apparent) altitude for use in
entering this table. Enter the table with altitude and atmospheric pressure. Apply
the correction to altitude, adding if the pressure is less than 29.83 inches and subtracting
if it is more than 29.83 inches. Use of the table is explained principally in chapter
XVI, and especially in articles 1615 and 1632.

The table was computed by means of the formula:
e B
Correction — Ra( 1 — Se

in which Rm is mean refraction and P is atmospheric pressure in inches of mercury.

Table 25. Meridian Angle and Altitude of a Body on the Prime Vertical Circle.—A
celestial body having a declination of contrary name to the latitude does not cross the
prime vertical above the celestial horizon, its nearest approach being at rising or setting.

If the declination and latitude are of the same name, and the declination is numeri-
cally greater, the body does not cross the prime vertical, but makes its nearest approach
(in azimuth) when its meridian angle, east or west, and altitude are as shown in this
table, these values being given in italics above the heavy line. At this time the body
is stationary in azimuth.

If the declination and latitude are of the same name and numerically equal, the
body passes through the zenith as it crosses both the celestial meridian and the prime
vertical, as shown in the table.

If the declination and latitude are of the same name, and the declination is numeri-
cally less, the body crosses the prime vertical when its meridian angle, east or west,
and altitude are as tabulated in vertical type below the heavy line.

The table is entered with declination of the celestial body and the latitude of the
observer. Computed altitudes are given, no allowance having been made for refraction,
dip, parallax, etc. The tabulated values apply to any celestial body, but values are
not given for declination greater than 23° because the tabulated information is gen-
erally desired for the sun only. Use of the information given in this table is discussed
in articles 2107, 2125, and 2306.

The table was computed by means of the following formulas, derived by Napier’s rules (art.
042):

Ge? approach (in azimuth) to the prime vertical:
ese h=sin d csc L,

sec t— tan d cot L.

On the prime vertical:
sin h=sin d esc L,

cos t=tan d cot L.
In these formulas, h is the altitude, d is the declination, L is the latitude, t is the meridian angle.

1194 EXPLANATION OF TABLES

Table 26. Latitude and Longitude Factors.— The latitude obtained by solution `
of an ex-meridian sight (art. 2103) is inaccurate if the longitude used in determining
the meridian angle is incorrect. Similarly, the longitude obtained by solution ofa
time sight (art. 2106) is inaccurate if the latitude used in the solution is incorrect,
unless the celestial body is on the prime vertical. This table gives the errors resulting
from unit errors in the assumed values used in the computations. There are two
columns for each tabulated value of latitude. The first gives the latitude factor, f, |
which is the error in minutes of latitude for a one-minute error of longitude. The
second gives the longitude factor, F, which is the error in minutes of longitude for a
one-minute error of latitude. In each case, the total error is the factor multiplied by
the number of minutes error in the assumed value. Although the factors were originally
intended for use in correcting ex-meridian altitudes and time-sight longitudes, they
have other uses which may suggest themselves.

The azimuth angle used for entering the table can be measured from either the
north or south, through 90°; or it may be measured from the elevated pole, through
180°. If the celestial body is in the southeast (090-1809) or northwest (270-3609)
quadrant, the f correction is applied to the northward if the correct longitude is east of
that used in the solution, and to the southward if the correct longitude is west of that
used; while the F correction is applied to the eastward if the correct latitude is north of
that used in the solution, and to the westward if the correct latitude is south of that
used. If the body is in the northeast (0009-0909) or southwest (1809-2709) quadrant,
the correction is applied in the opposite direction. These rules apply in both north
and south latitude.

The table was computed by means of the formulas:

x Gem 1 gesch
f=cos L tan Aas F’
1 1

ES S ee pem

in which f is the tabulated latitude factor, L is the latitude, Z is the azimuth angle, and F is the tabu-
lated longitude factor.

Table 27. Amplitudes.—This table lists amplitudes of celestial bodies at rising and
setting. Enter with the declination of the body and the latitude of the observer. The
value taken from the table is the amplitude when the center of the body is on the celestial
horizon. For the sun, this occurs when the lower limb is a little more than half a
diameter above the visible horizon. For the moon it occurs when the upper limb is
about on the horizon. Use the prefix E if the body is rising, and W if it is setting; use
the suffix N or 5 to agree with the declination of the body. Table 28 can be used with
reversed sign to correct the tabulations to the values for the visible horizon. Use of
table 27 is explained in article 2125.

The table was computed by means of the following formula, derived by Napier's rules (art. 042):
sin A=sec L sin d,
in which A is the amplitude, L is the latitude of the observer, and d is the declination of the celestial
body.

Table 28. Correction of Amplitude as Observed on the Visible Horizon.—
This table contains a correction to be applied to the amplitude observed when the
center of a celestial body is on the visible horizon, to obtain the corresponding amplitude
when the center of the body is on the celestial horizon. For the sun, a planet, or a star,
apply the correction in the direction away from the elevated pole, thus increasing the
azimuth angle. For the moon apply half the correction toward the elevated pole. This
correction can be applied in the opposite direction to a value taken from table 21, to

EXPLANATION OF TABLES 1195

find the corresponding amplitude when the center of a celestial body is on the visible
horizon. The table was computed for a height of eye of 41 feet. For other heights
normally encountered, the error is too small to be of practical significance in ordinary
navigation. Use of the table is explained in article 2125.

The values in the table were determined by computing the azimuth angle when the center of the
celestial body is on the visible horizon, converting this to amplitude, and determining the difference

between this value and the corresponding value from table 27. Computation of azimuth angle was
made for an altitude of (—)0°42/0, determined as follows:

Dip at 41 feet height of eye (—) 6/2
Refraction at (—)6:2 alt. | (—)35/3

Irradiation of horizon (—) 0/6
Parallax (value for sun) (+) 0/1
(—)42'0.

Azimuth angle was computed by means of the formula:
sin d+sin h sin L
cos h cos L ^?

in which Z is the azimuth angle, d is the declination of the celestial body, h is the altitude (—0°42/0),
and L is the latitude of the observer.

cos Z=

Table 29. Altitude Factor.—In one minute of time from meridian transit the
altitude of a celestial body changes by the amount shown in this table if the altitude
is between 6° and 86°, the latitude is not more than 60°, and the declination is not more
than 63°. The values taken from this table are used to enter table 30 for solving reduc-
tion to the meridian (ex-meridian) problems, explained in article 2103.

For upper transit, use the left-hand pages if the declination and latitude are of the
same name (both north or both south) and the right-hand pages if of contrary name.
For lower transit, use the values below the heavy lines on the last three contrary-name
pages. When a factor is taken from this part of the table, the correction from table 30
is subtracted from the observed altitude to obtain the corresponding meridian altitude.
All other corrections are added.

The table was computed by means of the formula:

a=1"9635 cos L cos d esc (Led),

in which a is the change of altitude in one minute from meridian transit (the tabulated value), L is
the latitude of the observer, and d is the declination of the celestial body.

This formula can be used to compute values outside the limits of the table, but is not accurate
if the altitude is greater than 86°.

Table 30. Change of Altitude in Given Time from Meridian Transit.—Enter this
table with the altitude factor from table 29 and the meridian angle, in either arc or time
units, and take out the difference between the altitude at the given time and the
altitude at meridian transit. Enter the table separately with whole numbers and
tenths of a, interpolating for t if necessary, and add the two values to obtain the total
difference. This total can be applied as a correction to observed altitude to obtain
the corresponding meridian altitude, adding for upper transit and subtracting for lower
transit. This problem is further discussed in article 2103.

The table was computed by means of the formula:

_at?

Geen

in which C is the tabulated difference to be used as a correction to observed altitude, in minutes of
arc; a is the altitude factor from table 29, in seconds of arc; and t is the meridian angle, in minutes of

time.
This formula should not be used for determining values beyond the limits of the table, unless

reduced accuracy is acceptable.

1196 EXPLANATION OF TABLES

Table 31. Natural Trigonometric Functions.—This table gives the values of `
natural sines, cosecants, tangents, cotangents, secants, and cosines of angles from 0° to _
180°, at intervals of 1^. For angles between 0° and 45° use the column labels at the
top and the minutes at the left; for angles between 45° and 90° use the column labels

D — 9

at the bottom and the minutes at the right; for angles between 90? and 135? use the `

column labels at the bottom and the minutes at the left; and for angles between 135? -

and 180° use the column labels at the top and the minutes at the right. These com- `

binations are indicated by the arrows accompanying the figures representing the

number of degrees. For angles between 180° and 360°, subtract 180? and proceed `

as indieated above to obtain the numerical values of the various functions.
Differences between consecutive entries are shown in the “Diff. 1^" column to

the right of each column of values of a trigonometric function, as an aid to interpolation.

These differences are one-half line out of step with the numbers to which they apply, as in

a critical table. Each difference applies to the values half a line above and half a line `

below. To determine the correction to apply to the value for the smaller entering angle,

AAT eil of the entering
angle. Note whether the function is increasing or decreasing, and add or subtract
the correction as appropriate, so that the interpolated value lies between the two
values between which interpolation is made.

The logarithms of values given in this table are given in table 33. The trig-
onometric functions are explained in article 039.

Table 32. Logarithms of Numbers.—The first page of this table gives the com-
plete common logarithm (characteristic and mantissa) of numbers 1 through 250.
The succeeding pages give the mantissa only of the common logarithm of any number.
Values are given for four significant digits of entering values, the first three being in the
left-hand column, and the fourth at the heading of one of the other columns. Thus,
the mantissa of a three-digit number is given in the column headed 0, on the line with
the given number; while the mantissa of a four-digit number is given in the column
headed by the fourth digit, on the line with the first three digits. As an example, the
mantissa of 328 is 51587, while that of 3.284 is 51640. For additional digits, interpola-
tion should be used. The difference between each tabulated mantissa and the next
larger tabulated mantissa is given in the “d” column to the right of the smaller mantissa.
This difference can be used to enter the appropriate proportional parts (‘‘Prop. parts”)
auxiliary table to interpolate for the fifth digit of the given number. If an accuracy of
more than five significant digits is to be preserved in a computation, a table of logarithms
to additional decimal places should be used. For a number of one or two digits, use
the first page of the table or add zeros to make three digits. That is, the mantissa of
3, 30, and 300 is the same, 47712. Interpolation on the first page of the table is not
recommended. The second part should be used for values not listed on the first page.

Additional information on the nature and use of logarithms is given in article 010.

Table 33. Logarithms of Trigonometric Functions.—This table gives the common
logarithms (+10) of sines, cosecants, tangents, cotangents, secants, and cosines of
angles from 0° to 180°, at intervals of 1/. For angles between 0° and 45° use the col-
umn labels at the top and the minutes at the left; for angles between 45° and 90° use
the column labels at the bottom and the minutes at the right; for angles between 90°
and 135° use the column labels at the bottom and the minutes at the left; and for angles
between 135° and 180° use the column labels at the top and the minutes at the right.
These combinations are indicated by the arrows accompanying the figures representing
the number of degrees. For angles between 180° and 360°, subtract 180° and pro-
ceed as indicated above to obtain the numerical values of the various functions.

multiply the difference by the number of tenths of a minute (or

EXPLANATION OF TABLES 1197

Differences between consecutive entries are shown in the “Diff. 1^" columns as
in table 31, except that one difference column is used for both sines and cosecants,
another for both tangents and cotangents, and a third for both secants and cosines.
These differences, given as an aid to interpolation, are one-half line out of step with
the numbers to which they apply, asin a critical table. Each difference applies to the
values half a line above and half a line below. To determine the correction to apply to the
value for the smaller entering angle, multiply the difference by the number of tenths of a

: seconds t NERO DN.
minute (or x) of the entering angle. Note whether the function is increas-
ing or decreasing, and add or subtract the correction as appropriate, so that the inter-
polated value lies between the two values between which interpolation is made.

Natural trigonometric functions are given in table 31. The trigonometric func-
tions, both natural and logarithmie, are explained in article O39.

Table 34. Haversines.— This table lists the common logarithms (+10) of haver-
sines, and natural haversines, of angles from 0? to 360°, at intervals of 1'. For angles
between 0? and 180? use the degrees as given at the tops of the columns and the minutes
at the left; for angles between 180? and 360? use the degrees as given at the bottoms of
the columns and the minutes at the right.

A haversine is half of a versed sine:
hav A=% ver A=% (1—cos A) —sin? M A.

It is further discussed in article O39. Examples of the use of haversines are given in articles 822 and
2109.

TABLE 1
Conversion Angle

1198

coooo

Correction sign

o On noc | Ht no

coococo|ocoocco

Radio bearings
Transmitter

2:5

Latitude receiver

Difference of longitude
90

1:5

Correction sign

Great-circle Sailing and Radio Bearings

1°

0°5

Great-circle sailing
Destination

Latitude departure

Spill dese

Eastward
Westward
Eastward
Westward

ZZan

II

Eastward
Westward
Eastward
Westward

1199

=
=
=
=
<
E

=
Ku
g
<
g
o
mk
m
-
E
>
S
©
O

Great-circle Sailing and Radio Bearings

Difference of longitude

Latitude of Departure—0°—Latitude of Receiver

Latitude of destination— Latitude of transmitter

Radio bearings

Great-circle sailing

Correction sign

Destination Correction sign Latitude receiver Transmitter

Latitude departure

Westward
Eastward
Westward

Eastward

Eastward
Westward
Eastward
Westward

e
=
N
-

TABLE 1
Conversion Angle
Great-circle Sailing and Radio Bearings

Latitude of destination— Latitude of transmitter

Latitude of Departure—5?— Latitude of Receiver

e 4. Se” AA.
DNP 7

"VT

50°

45°

40°

35°

Same Name

Radio bearings

os e M ae IES ASR NR, ames E Ame SSR RE = ah cS IDEE C
HSA + sg pcr ea SEKTA) AANA S6 o am a sā EES
o EADS |1010 er | HIDODS | MOHON | oi E SS HOD | N O > KR | DOD OLA | om | tone
SSHNG EAS ES A | a SS -ebe | o tus S | KROGS | HRs | BS
m mmm Hm NI ANNAN Z S LRH | RRR
AAA | NODON | ANNOAR IS | HANN > SS HAD | Dio Ot | 900] | 99 OO XO | osos
Godd | HSN | GO Gra [HSK | Hans ka EE EE IE
Før | ARAR | NANNAN a ER | BEERNS

ka
o am | OSHA | PI | ODA | 010 H re ww S's SHS | Roli | HHORS | OTH DA | OHHBOH
Godd | tas | No SH | N «duco SHNSH E SS mee eise AO SS
AR lane | ANNANN e AR lA Se
- Oi tr 0 a ND O FH NSONA | OOND Orta © Otona lÐ O o tO» 3c me 00000 | DH tort

Great-circle sailing

Correction sign

'Transmitter

Correction sign Latitude receiver

Destination

arture

Latitude dep:

+11+

Eastward
Westward
Eastward
Westward

Cece
ESES
Sia

BEBE
7 0t
ae Be
BERE
azaa

Reverse sign of correction for italic figures

1201

TABLE 1
Conversion Angle
Great-circle Sailing and Radio Bearings

E
o
=
o
o
o
pā
+
o
o
"a
=
+
sm
+
3
T
o
=
T
o
i=
5
+
E
c
a,
Do
A
—
o
c
ye)
=
+
Le
+>
3
H

Latitude of destination— Latitude of transmitter

Same Name

Contrary Name

g
SD
n
g
S ae it =
R
o
e
E
=
Ø
E H
EN sens
R c BSKS
3 EE
o A EROR
O [2 ISS
o a mono
2 a SS
a E asas
E] E
ER
-
e
ES
o
©
o
-
3 | ZZnn
5
=
2
a
H
g
i
n
3
= būri!
o
Q
-
EN
©
Q
g
= |8
=| S "gU
? $| 3288
$| 8| 2238
E n nono
S E Bo y
$ | A| SESE
w
H
S-
o
p^
[El
B
$
a
A
w
©
c zzna
5
=|
+
S
H

Reverse sign of correction for italic figures

pow Kādā AAA A A tb

|
o o &
H eio weu | Q eo|momos i$ O vi o Eu om emer | 2228288 | 28888 22228 Sp
A 9 228 | 88333 | Sesser | KDO Si a SAR | A888 | BEBER | LIDIA Sona (71
ri ri ri ri
|=|
o
3 | +11+
o
o oocooo|ooooo|ooooo|oocoo|ooooo o 99998 | 989089 ooooo|ooooo 399999 $
= ? sidðdidð leieieeice SSS | SSS [I I— cocooc|ocooocoloocooco|ooocoo|ooooo =
| oO
o OMOOGOH | «nono anon | oono | noso M | ats SS e im SHO DN
CO A AT | TA SAA ERAS IE Y OSEA RA A) PTO EEG "d IM qv. Ww. te M | VĒ R urat ili. Yeh set Te scar ARO cam VAL
acs ROB [DANA | SNODA | RO S [^ U =
B ASAS | Ste A ddsdd| gadā AR ER ege ee SR | NNNNÝ | e 99 9] e OP
e Ort | MON e t- 09 C «c5 , 99 SSS | SOSH | NLH: | Doa Bons e
(era Da TR V R Vē TĀ IESO Ad a. e Rh cde ce Pl p aas S opu ede S gem X EM PETS PEA MED ETICA
a rcd xar. SND Sm NO DORADA | NR | OROD | RR > O s
= SANO ein el (ee IN CW OSS B E 66 c6 = S OR | SRSĀR | RARR El 3 EE
+ == -
tu % o ET | ONDON AA | ooo | o o S99 MRO SiS see] eon MOD | Sis 40019 E E dēt
A E e | SA ibn leg IA: 2 dn ES 39 es Sestās as | ales g
` = SS EE ASI) Izd Sešus A b ER | ad ee NES EOS E E 223%
o
Q ES]
Kg s o ONDON | MOMWON Feet: | moon | DONNA o ER OTR o | 1S «t eto | ooo mo co to = S asas
EA tim LEGS EU, le, PE ir aa pore ` E EE
$ = Kee disp E BESA BEBE Sale a uad Sus|SSstE[SSESR | $ | E
n
= pā H o AS E | e r-ar-o | iSc ii o St MS SIA SS A | og stc m S
"silts I ele E eec A er Ee 5 EE NR E E dāmai VE ĒKAS
slsļš žē e EI IE Ss visis Sess a EEE ==
m
E o Ë o Reno | ALO | OANA | MAMA | ex ex eoi oo ¿AS SADA ARA | sten rt o6 NO 00 00 D
[aa] ø g 3 SHANG | oma or | NHN Sassy ANI SS NNR | Adios | SAHA | DANS Lee o ës Z
5 g NH | HAAN ANNAN Debe: KENNA | AA RRN g
ekl le m o cavcao | oamno | mnriso | onono | wooo om eneen | Looma | HOR Ka | soma | uo» E
aa + 3 19 o o EE
lee O El Meo Ce = AE der enr SRS AE uer R E:
E e E 3 15 Srada | dead | Addon GINS | ASS © SS NNN | RÓ] SFT] oo SIND | ISTDG E
© F 5
ri 5 g | B > £ E pores RO+WN | AMOR | mios E SSA A A id | BOUTS 2
SS A a o ieee DEE Tr Le SS GE | CARO cios =
K als = i = Sri | Sco Rc | CON RĒRĀS Z SS SNN | Rano | Hoon SSS 3
| g g 10 A [om Z MISS | vio coo | cnc ow | ow oro | «noo >| So». [oso |. [atole | arma.
ea "n q | 7 SA ES EIA ASES E E SS SSH | Res | SHES SA RO
2 a0 | 8 o Hm | HANARN | 6 OI 0$ e EI S
< c I = g
> B o = S E o Conan Joes OO | Occ O10 | HHMOO a 5 BES A | Neto | eos os | o Roze E
E ga, g H g + Un Sri | SNo | CHAT | CHSGHG lte zë SS SSS | NNNNA | RNS | Hg | NOS S R a
= e 5 e Am | HA ANNO OD 3 == g
+= =
O Y La 2 A ë SOMDO | GP | O D ONO | Üanqnnrnromyo | oo r- o0 cao A DH 95S | OO | Daraan | to BS | NO O ft E
S S = E dco | HSN | Scand luwërieeeilogwtzeei TN ETS EC ES El
o a KI Hmmm | HAoANN | ANNAN M =
V H
E A o EN o OZONO | voc en | m 96 | reos ois o Q99[.9*9* 99 [ua ao [one | OÐ e ©
R KS e SSHNG | HORA] Gora | dons | dt S SSISSS | SS SSS | SSSSH | NNNN | Ro O
D 5 ==
+ pes 5 mmm | rr ANNAN
` =
$ o 3 E S C Oc rao mor dao XH e co x 10 «C 00 ci c r= <í oD =H 00 o oo Omm Lenks Ke OD OD CO ti ti e MOA O Rat WO
R o =| e SSN | HAS SN | DASHA | RN | SASH oo dodóoo|ooooóo|coooo|odoooc|[sSsSsS-- Ep
5 o 3 co duoc rm e KE d tO 10 H =t =H =O 00 r «^ como Om NOY 10 00D) =H ke MIO Lt 0 C» O rr NANO = g BYGT
Ne a SOA | das dS | No Or SS AB D ee eieiei Lee eieiei | HH Lied eieiei |cicicicici a = 5558
= | ARAR leeë o = SESZ
Vë
H Së o SEND | MOR tr | Omit | NR | AGNA CN mor | OH OO | -maoo | moron | 150009 (5 = 8 ESES
E OSMANA | otis | CRASS | HANH | ROSNY ? SS Sd leede | SES | ei së | suivi ue € Y Seth
oda] T o = SE
5 ^ Reese
2 AS | DIEMOM | HOOH | OPDR | MONO 5 ON ro | MOCANS | PALEM | om | mn aa H 9 Ki
= IS AC | dons | SSHAH SRA SS SSH | HH | Nod | Hiðiðið | RENO 5
rH r rd r han i e e e N w
o 3 O YH 00 Oo ooo Rt moomo bioma N cou p. me Om OM RD D. C4 4 ccc = (O cm Pe et o OL 110 ES
Ka ASA OS | ASSHAN OA SEN ? SS ao | eieiei eis | druidas cci | SASHA =
mmn Oe hc kan AA 1 EE 5
> +
o a OMR EE INDIO A r4 (O NO ti 0010 MQ OG N + 5 Om ro no ono OMON | HOM NAN + a
> SSS | ANDY | asis HÓS ltiooiee | ANN HS SS Sriri | NOS | asas Ge | RARAS | Hartas a
Kl Las n n am gand cl — i e e D
GER »
| T | Aaa
N Š emo e Es
ws stets conono ao Ll Ll iÐ ac 15) cw e] I S19 Vi ea no
a) H o FAR | Sass | BEBER | KBS | SES IR H| 22" 228 | §83833 | BB88R | LRSRES!/SSS5R =
sej H

Reverse sign of correction for italic figures

1203

TABLE 1
Conversion Angle
Great-circle Sailing and Radio Bearings

Latitude of Departure—20°—Latitude of Receiver

Correction sign

o

Sao &
RDA R
As tas E

o

YN RNR R
RAIS =
Aou

Radio bearings
Transmitter

o

nom» V
SAAD oO)

MmOtR O
Magi a

o

Sone S
bere S

DNA=N >

Rede st +

Sy tO H
NRR oS

Latitude receiver

Same Name

Contrary Name

Latitude of destination—Latitude of transmitter

DON <>

Oww =

Correction sign

DLo

Great-circle sailing
Destination

Latitude departure

la

Eastward
Westward
Eastward
Westward

AZ NN

Sl

Eastward
Westward
Eastward
Westward

AZ RO

Reverse sign of correction for italic figures

o g
3 o SSR | RASS | BBSSR|LSBSE/SSSER |2| 7^8 58|88899 | BUSSE | C8388 | 33528 ü
g
B| +11+
o cocooco|jooooo|ooooo|,oooco|oococoo ooo oo | D os De | 909099 | S BS SS | 99998 Ej
ES * 3ssss|3ssss|sssss|sSssss|sss3ssS % S | SSSSS | eieiei | SS SSS |sasss E
: o Exeo | sagos | rneer leegen [mun d
3 Sinvs E ECC | SASAS | NASSE
2 2 Shere O da remi A
= bð | cage | inca | ARES | SASSS S |8| upon
% » noes | sours [amor [monos | once 5 E| PPP
9 = Sisse | cagas | SSSRi | JESAS | SASS 21215353
$ > LLL. E | 32382 e Eeer SEA
A | = Sisse E EEE | NAANS | SSSRS 3 E
a ES sa ateos (sosa [nes jasmas
āļaļž Savs | nos | stad | Hangs | di
lol AO oo Bes | 29395 E
algia Sidi | cegas | idoga | SANNE | SASAS A
E Te : $2353|23223 "PRESE Yevas E
Ged En SE Srads | rasa | isrss | digas lis | o A acts
= fel TT E | Ë 3
< of i]s 2 | E | "Sus ó6570 | wanes ds leases | ž 3
REA E SE XC CHERCESIEEEEPIEREESIEFAEN I1
A A| y Z| o| s59*5|9-sssisssssissusW SSSES | &
«sSsll|iig|s oa osos z &
Bea] E 2 | AERE EEELCIEEECEE | S 4
eko IKEA . 23255 | 22825 | 32332 ra reper Li SEO?
Sats |* Sided | Crécy | idee | Satan leese E
$l&lsis& 82325 | 32232 ET d Beer a E
"agg 75 Sis] SSeS ASAAN | ARNAS | ASHER
< e CE > 89523 | 28238 Sa
abe [05 L8 sh | Sores |addās |ŠšaNā | SĀSšē x
3 & e 32232 | 32:222 | 25333 are: kee? 3 | ste?
Z Songe Sends | Sad | SARRA TE 2) 3| 5253
4 % A O | Sarat edes emen £ | å | 3338
= SAD SES ESE EEE IEA ae $ SERE
" pase [sanan [mano [anos | ormer E
z Soris E |sgidd | Honda | NASAS S
2 sakām O dt. Sones | eons 2
x Sóc |ddissr|dogrd |ddgūs | SNAKK 5
o orto O x ec O hr 10 10 ti «ti HO AN MA O 00 =
e Í SSHad | ci idco roo uH SASN | Ran F E
ka
9| zzaw
+ Q 3 Q €
E a o PEER | RESSS | SESER Kassi |[SESES | Á E
A E

Reverse sign of correction for italic figures

1205

Q | e E
o 19 O 1Q 19 Q 19 0D cw no 10 ac O 1Q C» uci Caci 19 CS i; C5 i ooo no AC) CO 15 C5 i no WQ 0
H o 238 | III | BESER | KIRA | SS SNS = || EECHER | EI | Sos Šā a
o
3 Seif iss
o ,999oo0|oococo|oocoooo|ooooo|ooooc „ 99988 | 999298 | 299 90 | 929922 |999 99 Ð
= ooódcoo|occodoo|ooooco|coooo|oocooc SSSSS | SSSSS | SSS SS | SS SSS | SSS SS E
©
% y € wo l|onan- | mowo |mr-co | 1ooon o & 99s | eer | NnS | mats | Re M mo o
quie ES a! oe En A CANC CINC x
Sues [ss | wanes ANNAN | REIS Sees | issus k ssi | sees | SSY šā
ES o DOA 28838 HOOHO | MORMO | RH HOW o RUNAS | coso xo Sa» NO | BONDS | ARS o
Sods | RADAR | air is SOS | Amos Serge egeo (sms | OSH HY kn
EEBISESSE|SGN | 99009 IRR OP SA | ASSE ARR RK El NS
^ = R H
A =A [ROSANA | cenas | novo | mono IN SSI SS 5 s ages
ee ese | arn cues AA ao MA OO e she lores S EM Ya
~ - o or Cd ep 10 Oo N ot or Out 00 CD his oo a] o
SS 2
o o
E = SSA EE Sy DEPO | adde e o SNA | o => to mola RO | DOWD | RON RK 3 8 Zë
a UI | CR ts a P ^— | exe ādas | sista uec NEG
e AO SZIA £5238 | ARASS | RRE SN | SS | PII SNS 2 E
n o
56] c E % met | wawoem | moma | oo | DOONAN ISE SS | BRM HS | 2 | «o to
E 2 E EE, mas ln E 1 | eaea ele EE aoe e
KS + x SMS eZzSzE|S5SSNSSISSSSSISSSSS SS SIUS ES SES PI SS v
1 ®
E 3 g A g CHOON | recon | r- nor. | HANNA ES o SANO j ORLO | cao | enwn | mt Ha e 5
g © Sredd j| RIASAH | SNS | SLS | edna | | SSSSS | Nunne | RRS SY! as as ada joS E
fan) "d F mm m | nr a aN| AAND | MON FH E à
r$ o
o => E os g CSS | CANAD | «0o | A HORA | mao ar $ 2
oz Kei 2 i Zei 64d | Radar | CRASH | HLØSV | nodar s
= Se E o [A RU PON | SESRA | ARRSS | DR E o ES R
TV H
= s Øg m 3 2 g A a anti Ron lomos E E o
lira V NS i str A ede asi a V Eee Se eS er NM ^
= = ið | = judas So lados +
= < ð | = = Seen CSOs | ASAS | ARRAS | IE Z E 3
= = = T p Z g 26000 | onion | mao [Nooo | mona R >
Ka F aitas | md om | HORA aðar AS) lær] o
ea 2 ww eo g > V Sim exuti, SAS 1285235 | NINA |a 35 8 B
e
< 2. 5 | = 2 E o € 0 [PARAR | NRO | awm v Loo woo = & S
= As dram Na CES Cu NACION Kr ere r A de
E Adis | Gooina SNo Ci «God | Arad (7)
EA E z Ë El + Ka or LAÉEIXSEESISASSSISSS5SS Í g z
=
O Ke 2 = 9. o & re | POHON | NAWHS | DONWS | OOH aD 2 5
© 3 B e Sii | SHISHA | idos | RES | io S a
£ A < E MET ere NANNAN | anna E EA
LR
E V D 2 o € eco | MOONE | HONAN | omo | OHWHA o D
CA 4 | 2 Sucia | Crags | icra | HASH | Saas O E
E: E ae | SARA | NANANA | od E
+= kel
S o K & o DONAN | omoon | covon|oaoroo!rowxor
SANA | SNG | ASSO mmn | BATS
Ë E- H K a PEE SANSN | SASES El
=>} 2 o 99095 | -o coc EL NOIR | OO 3 g gua
2 a Sia | sas iaa 89888 | | sod [aras | SSK WS aras a | 3 E RH
P ATA | HANNA | AMAN D = SESE
=
3 $% o SAN | MONON | MOMMA maana | N co ro S E BEES
= Sins | dnas | oA dodas [Rains | | SSA eros | dis 9 | 2 | deās
= m m m rr rr AN N Neo cc 2 E E
A "jā
% o 22900 | ON | rocn«o [memos | oo ro o & LIO | momo | re 1010 | DOORN | Orn v 9
= Sav SN | ods IAS E AS | mas dd | roo dH | cie ir | OSH Gs Ó
rr rr a OD co co nl rr — NAN

Latitude departure

1206

o
"eb
==
Rog
ENS
n
=
EZ
o
O

D
a0
E
*-
ku
3
O
A
o
Ll
yo)
a
E
Ð
E
g
50
=
=
x
Y
[^
Leed
o
E
©
1
+
a
O
H
O

Latitude of Departure—35?— Latitude of Receiver

Latitude of destination—Latitude of transmitter

Same Name

Contrary Name

7.6 13.5 | 9,1 | 4.5 E 9.5 13.7 17.6 |20.8 |23.0 23.6 | 0.0

35.6 [33.3 |30.8 |28.0 |24.8 |21.4 |1

Radio bearings

Great-circle sailing

Correction sign

'Transmitter

Destination Correction sign Latitude receiver

Latitude departure

Eastward
Westward
Eastward
Westward

Eastward
Westward
Eastward
Westward

Reverse sign of correction for italic figures

1207

TABLE 1

Conversion Angle
Great-circle Sailing and Radio Bearings

Latitude of Departure—40°—Latitude of Receiver

g
bb
E
n
g
Q del |48
5
o
o
-
E
o
o
D A
Ele ese
= = Baia
D B SESE
HB SEHE
o 8 Q8
= =
"d H BERE
a E
D
E
E
2 3
: E
o
B $
+ -
3 = An
S © E z ZZ
E E E =
3 S d a
5 Z Z H
H o >»
| E A
3 = =
= un zi &
E E z
= g
ES = Par!
= ES
e E
Q 9
ð
3 AA o
=
+
3 ESA
H oo
H
E 5 sera
2 ss Raka
< 3 BER
g g dE
St šās
d o
2 | Å | SES
w
H
o
o
R
3
=
ka
d
Ei
3
V NM
E ZZ
5
Ð
E
ES
Q
El

Reverse sign of correction for italic figures

šā niks U EA ú a >

Correction sign

MN M eee A e ere, LIZA Fs BS ] AJ TASAS A E

ees tt E E

Transmitter
Eastward
Westward
Eastward
Westward

Radio bearings

Reverse sign of correction for italic figures

R
o
>
a]
o
o
m o
= Ki El 9 o SH di | ooo ona: | Sages MES >
d CU ER E a E D Y a E ies = cea ae re as SACH
R = - Søn Ed PEBETDELBEECEEREXLELI z
B o : 3 FRA Akt ¿en S
A Xu ds A Pirie D bm A MEN E Soc ood eran sin nr AAA osque =
ri SI o o so
A R H Sme | PANS | ARANA EEE 8
+
iS R4 Ki > SS NOOO D | OOOOD | DONND | HOOOAN o EL 5
[eb] "y + ESI MI o Pci ws Ee a | d "ed dd BES SAS A AS SS Tra (DSS SC
m d 3 3 SAA ESE |9RARĀ Re | RASH © g
2
= 3 A T B > = | 82552 | 32852 SE Leed ees E o 2. E
E daag A E kn ya AES r d EE ee ue ce Kee Ree =
or oOoNVWHIMD O oo
El g * o 3 a A mee ARARAS ASS AS tik SD Ka =R
kel o d MS | > z o SRS DNOM | NNM | Ron | HNM >| ME :
= = cs 0d I ECE ES O ES ss ir asis as E Ga a die ME Ehe
= 2 24 | g o kel ES | ARANA EE | FIAT E
< = DN
9 = o a 3 E o SOLANO | MOHAN 23588 acne, DANDO = o 99 &
E stiprā | cd ne (1% Mdsl | a | ero io || Eo eot pE a Es 145 SEA! A ON IRA A AS Poin DRA d
E SE | oos SS a
a a = A un Suma PPK SS | S9 SSS 8 d
+ a
Ø o D E SOMSH | 13e 500 | ooon | onoo | OADMO y > = CEEI
2 3 Sie es ks CEN sis: sss | | V S e 5
o R E E
KE o o 5
RENE os aurae. a da bør NER M —3 d O ute rrr. rrr | Gece ne ere | cece we O
eina B| 8 | |*35sse|asdss | sega leáis Sadus | | ° 9285|99959 O
SE + =
g E =
o g
H o VJ ek Se a Ge Eme ab A r OA A a a e |5 da 3
O 3 g
=
E g
dl rā a Ee asā rð BEER UB TEE le Zare po rr DRESS" 3 3 esere
+ = = Baks
o 3 3 a
3 & = ESPE
Eesen EE EE Ee Mem mere M — T TO A r (| eer rt ce Jee e ee ae E s 2828
> | 2 | seat
+
3 A
o
BREUI i ed MW WEE. M A QO ode". eð. f eTe— Fee E IDU fus ele is Mí ele. v. e.» R
o
o
PRONTI Að V dec Rare enn MO AU o unies leue eu a A m: SI H
=
KH
LE
3
a O a a a eh) EE e bs o: rr ef Ss sae ee £g
3
o ZZN
O
o 3 s Ë
H cnong | nonon | OKWONMO | LONDON | Rono Si ew ono luewe leweaelweewewlewaewe R
C o HEN | NM [DIDIER | RADO | DOHA o AMA | coo cox | DANDON | AO a | SO QA +
a mmn A A AAA 3
CH Gi
r=

1209

e o =]
vi o SPONDS luewe | ororo | omos | SVWOØLR Ð) En
BAA | ABRIR | DODEN | DDIS | ŠONA a
a Tm nnm a
5
A
o ,999eecoooo|ooooo|cooooo|oooco =
= css | oscoss|osess¡sSsescos | cocos Ë
o
o meega | DONON | CONDH | ovcoow | ore mios o
00 Guo | Goran ESA | SRDS | A Min SO
ARR | a RR | ANAND | Co c5 CÓ 06 668
a o SOOM | AMIS | mama | aman | Ar oom
Gi SAR | SAR | ER Leoeecizä | GOD Gi M
araa | ARANA | ANDAN | Momo El = STE
E = H H
Es o CARO | ec if oo | ON LON | 1010191015 | «co r-o000 8 = Raks
E N SHS | SLO | GSN E jg xd | OSA D H SEEE
o mmm | HANA MAA | co SH xti SH SH 2 G Stadt
= Qo
= a o CAME E | coco coco s | HOND | noir o E S Bed
dat Soe ee nee CM tt Pa ER RM NEVERA = =
R ri mn odiada | dodi S | Gross | SASS
S ØKI HARA | ANNAN |o oco | RARAS £ E
n
sol e E % o € 99 | roo | CONDA | ona | HHDH
a 3 ei Gedas | sr Leed Gut | SAYSH | ri Oe
"= = = FRS | ANNA | Bromas | WHA
S o E E: o COIRA | cr-r-r-r- | roo on | miom | 0N co 5
d keet Porekāem = EE EE E R
A E E Samer | CBOs | AREA | ADS | S SE SIG T
o
o = = 25 o CORDO | rrr rr | ODHA | ror. | ANO 2
Cr. Ras + e i Soma iresm| IAB | SABES | ARAS
fens 3 o MOR | POSEN ERARA| 383398 | RAR o 3 zzaan
7 ya]
= SZ Øg A B gc 9| ,cowwer|odoododo)|reoon | meno | «ono E =
AA ES] ee hs ES Ba MES Se NES | cape RK a
< | = 5 E SASN | arods | do nos Gorg | dada 3 B
Ð a Ze , a mmm | ANGA 6960 00 60 | «tk tajās Ka S
o kl
E = g e H o Ka o PASO | 01001919 ES A ono A
= Ve | c SHOE | GHOSE leede | SNOKSD | ASr SH La
[aa] 2 ep g o ar | ANNANN | RRE | i vas E
i D
< S E | z 2 E „ea re | esce | eo mio t- | 00900 | too = &
= E E RE ICAO Eesen as || eius pe dere | A | md at act ems av xL
= Ë Feist | sR | dnis | SAVN SS
g 3 = £ un Sia FARA ŠAANA | Ronan | ERE e E
o +
O Ke = a o o 20000 | NAH HO | Haro | DADOS | nar o O S EE
D © ETH SN MISS Ao EE 5
= 3 = SC SC EGR Nome | Y ARI 3
R
¿ES o E os oC 6 | HORON | 0000 c9 | AREA | ora wot a
o 5 ed e rz same | occur je dog | HHS
KR A 2 Ho Es pp he Rae A SES CO C0 C0 | HH HID ID e
e ke
= O * o o DOON AA SIS | Ie ies
Zei GO E SSNS | oógGc xd SiO | mro
ó 8 H S = SEE IEZIN NA mmm | M SB uma E
5 o ONONO | MEHMAN | HAHAHAH | ORAR | DROOGO ES g EM
Ð R IO PAP AS PR | Sadan 8 | 8 | es?
d RAR | ARNAR $505 08 00 | HA HID ES E EEETS
3 ER o Che | emo | ra | ONONO [moon 5 B 2335
TA r on e a
iGO | oó D Ama | ro e ci SAO | SHON "e iA nouo
= Ki Saas | SAAR $569 c8 00 | SP HP a > A Sese
+
a o eege | MOOH | NANNAN | MOOMO | OMON MO S a
= rimas | asias |rodocgG!|mÓgcudo!sgciod elas i|-uGo9 cci æl
Aran | ARANA | ANDAN EET AA o ERA EN ens o
= o $9099 | nonno | ron | RADO | tm ES | ONWH | VIOMAM | HAM GO ESSE
Hu SHH | oo uou | GSN SOS | oci MEE oda ¡ORO sø ris SR) E
= mes | SYNG | RASS | BEA SAS PONT ANNAN | GRR RS | BSUS 5
+
S o COTE |owneo|moooo|oneoen | HHA o Em | A A | Adm On | + Mm =
> RS | GG Sm SS ESA | | E NS ES E AE Vø Nið ES
SKD Sr E ANAD | co mt RS SS SVR [AAS EE, E
S ZZN
S Snows] ROMS | ororo | mono. 12 O10 3 onon 92290900 | OMORS | VOV OW ee 3
H o 228 | 3333%% | BESSBR | EDS | BOÐAR H | o 228 | ASSSS(SESER | RRS 88 | ēšanā 2
H

Reverse sign of correction for italic figures

1210

m
20
E
E
a
o
[ea]
o
2s
eo S
= E D
< s
Æ oe
nos
m a
WE
> ms
Bos
9 Q
eTe
o
std
o
45
ei
o
R
o

Latitude of Departure—55°—Latitude of Receiver

Latitude of destination— Latitude of transmitter

Same Name

Contrary Name

9.6. |t
4

3 |36.
1 |39,

6 |38
4 |41
4 |44

39
5 |42
5 |45

51

7

6 |40
5 |43
5 |46

1

41
44
47

105
110

54

Radio bearings

Great-circle sailing

Correction sign

Transmitter

Correction sign Latitude receiver

Destination

Latitude departure

astward
Westward
Eastward
Westward

E

Eastward
Westward
Eastward
Westward

Reverse sign of correction for italic figures

1211

TABLE 1
Conversion Angle

Great-circle Sailing and Radio Bearings

Latitude of Departure—60°—Latitude of Receiver

DLo
o
0
5
10
15
20

DLo

100
105
110
115

120

©
S
e
Se
=
`+
S
>
~
m
oi
5 oS & camoo 0D r4 mio b ON 1 00 H YO OHD HO SOOHN CO oma DRISXDS D ti 0010 ODO O
= O SNATCH | SAVNA ass S | circ rod. Sona La as dm | NG Do Or | ARS | OSS Ó
= HES | ANNAN | 000060 HH | HH zu mun mmm maar ra
S o a CO cip. | DAM: | OMODA Conan DIO coco DO DOD co occ O NN wafer. 0
g 3 SASH | mata | NEG | BSHSH | SHS SANNA | as SRA | SASHA | ADOS | SHANG Æ
g mnm m r Rm NANN | 600060 P | H H 10 10 19 Anne HAHAHA ANNAN
= es S C C ci r O» moo CX ic 00 CX cO Stato ONDO + SAN Pac Oo ON + «e o0 C C ic 00 10 O) ep DD "Hr 00 ©
o 15 eieiei |cdoeiro!|cuced!|uwcdoomun-!ucouxt SAA fido GOS | Hava dd | no Sand | SSS A
o non rd rr NANO GO OD c9 OD xri zi «txt 190 10 1D o = — e r e n HANANAN NANN M
Ð
5 e 9 a ON MO rt DH ho N (0D NA 00 + m 00 O bi CH E C mia 00 r4 He Co» OHIO Cw 00 «f HO Onn
E 7 E SEEM Eb oo do El a SHNS | SN eer | GASO | SHARE | GSN” N
= 3 m r on Ron r NN NAN eS c C «ti SH ti =H 10 10 10 Ka ae mr NANA ANA NAMM a
S
H o Z SON Mia tr DD ucc N «c C YO Moton HN O ao O x uo AM ONT CX r- 0» O i M © 00 00 GO Qr ir O
| = ? SASH |dwdEdg|cdunged!|ucgcosu!|mcedo B SAT | SH GAN | HidrdS | ÁTD Ð SD d
= d ~ = =
O
= e a e e C eor Cedom cn CN ic O en 00 MDI NODO ONH = conomo HO Mr Mo +A ooo ca DORI Oo
SIS wu Savia | Sara duda león Nodod = dub | no da AR RTS | Hea is
= rr ANN eo MOON sp SH =H 19 19 19 10 e rr ANO NA CY Ma MORA xh
=
8 pm E QC rm 05 Hr oO C N 16 00 m 10 00 M 00 MDI CVD b= Q O O pr i coo-rt ce Did Hm C4 c 00 co cO Ot Oo H DINA Oo
© e Sada | onson RD | Hogt | noo LARES EAS SE | Gods O
= KEE NANN C C0 C H H tH 10 10 19 10 aod mcm 0l NANO CÓ EG CO on H
D e A C n ccc ro eub omnino rb. tr O IR Ø Oro eoo odo mo ro C o» 00 r- oo Qc cor. oo cca rp. C
S es SÁ GL | SAVNA ALLER A ASIN |RD Sods | GS view | ASES | EVANG lost: a
5 rr ei rd A ANN m C OD OD SH SH ti 10 19 19 10 m mc rd HANNAN | N NM OO SH eH SH 10
=. j
a > > OANA OBONW GO H uo O) xf DINO t- C O OI O oso ont NOOO t> >= t- t- 0 comort Hoo c
e Gode | SNN | tggi | aeo | Snee Smag | GS AHH | Noa | IDEAR | SHSH m
H A A rd ra A AANN OD OD CO CO x SH 10 uo 10 Ø S A A HANNA NN Ma "ef së zz Vi
10 O) 0600 DON AN I~ O b= 10 ei zb 10h CR C Er rA Mma O10 H HH 19 «O 00 O «M 00 HO GC m
ai too OI ELE ER nodos Sima | AS AHS | ASNO | HÁÐA H
nn on nl NN CX AN EE OD ep =t 10 19 uo O m ed rd rn ANNAN CN c cd C2 60 ei si SHLD O
HOF Oo moo +00 moto HO mm Naio 00 care a coco SOSNO OD 00 «t CH coco c

ASAS

58.6 [57.9 [57.1 |56.

Radio bearings

Great-circle sailing

Correction sign

Transmitter

Latitude receiver

Correction sign

Destination

Latitude departure

+1 14+

Eastward
Westward
Eastward
Westward

ZZAN

ltl

Eastward
Westward
Eastward
Westward

zzana

Reverse sign of correction for italic figures

ais
V pr

Correction sign

Radio bearings
Transmitter

Latitude receiver

TABLE 1
Conversion Angle
Great-circle Sailing and Radio Bearings

Contrary Name

Correction sign
Reverse sign of correction for italic figures

=

o

2

=

B

N

g

«g

E

B

bd

o

o

E V

E E

a 3

7 z
o

8 E

Z

E a

&8 Y

S

n

o

©

ās

o

o

"d

r3

=

=

o

8

Latitude of Departure—65°—Latitude of Receiver

Eastward
Westward
Eastward
Westward

Great-circle sailing
Destination

8 |34
5 |86

|

Latitude departure

1212

1213

o o g
SHOws | never» | creo | menes» | romo o cio o Iewen | QWO190 | noron | DPO NMS bb
H 9 MAAN | Coco Leet | DDIS | SSHAR d SSR | ARFA | BIDER | ERES | SERNA Ki
a HAHA A Nr
3
E (COR 0QPKÓEÓEQ_ KR o». o »QarR-LáEIROOO o Dam OO S Sei +l |+
E ,999eco|occoo|ocoooo|coooo|ocooc o 399989 | 99088 | 99998 | 99988 | S9999 E
e SSS SSS SSS SSS SSS SSSSS | SSSSS | SSSSS | SSSSS | SSSSS E
©
95 o CAMHS | OHMAN | Geo | we oo | OS IBM o 99998 |--99-|5-.o-eo|oxoo9|ooeeom o
Ó Srimiði ja mae | GSAS IAS | | CIO SS SS | SSN NN | aseos lee
Bann | HANAN BVD ARES SESSS S22 Aa MEN > a"
| EES
en o CAMHS | OONN | HONDO | AMONG | ONHE o CHO | PHONE | PMODAN «ooo | AD H oo
[rs] SNAGS | SABES | ARES | NASOS | WSNS SSHAN OA SES SRA AOS E Së
rdc cnn INANN | MANR | HHH PO g g HØRT
ei = H R
2 o € 0n | coo | WANS | HOHO | HADNA o CAHOON | CIO MMA | MOO | NONWO | HOMO 5 2 ROHS
E N Sanda | dios Leite | Noon | SES a Sorin | HSS | SSS N | PAHS | SNNN o g EERE
< mrmrm m ts ANN e C9 C0 CO SH SH AHI aac aed KSE KEES E Q 2 414
ao
Ge es o SERA ocio ome | room | OMAAN | A 0009 H o Qe RO | HMDS | MONON | oo | OMDR 9 S Zë
(5) = SHOES | HASO | GS OS |o | anos Sii | Gnador | aida | donam | SSS = B e?
m Ee rcc cC | ANA | CO CO HHH | PO 101010 m | Hm | HANAN | NANAMN È
Ed cá & 25 o CHOND | Diao | MOMON | MOON | o eoi o € Oo | ANANA | r- 100 6 | omo ii eo oe
omy Së = eS Sano | NASS | RUDA GSN | OAKS SHNA | SOS | ASNS | ASNS E
R o = Ar ANNM MMN H xt HAD 190 19 © TA TA A A ON NANA OD OD OD OD FH
S o S a o & 9 eo | ANANA | r- 06000 O | ONDON | Oman a o CONDO | oio io | c wo oo | ooo: | COOH 5
g D Coro | NANSEN ing dið | rc oii o6 e$, oS cl eieiei eg | oso | CHSAG | BEBER | Sondre >
[sal E g AFSANA ANA EECHER Soa SAN | ARANA | ÁNANN | OOH “a
s P
Oo Ð cn 95 o emo o o | Brown o PR 9n | oro | AMAA | oco | ODA E
«D. re = e i Coro | NANSA | SR SNS |o codo | nn od Gear TS E | OSAHS ASIS AS | SHSIN o
tb 3 3 3 SHAHN | ANDAN | OHHH | 191019 D Ó o mim rn | ANNAA | Amma | HH ruo "d
= 5 Øg H E Ce 9 o PHO | moore o0 o00 | weno | nro tt E MASA A a ai | |919 mt E
URL Au ees EE GR Et LL M PES AIS OR Moe a | MEAM E hz
< ð | E 5 = SAGES | ÁVRSA | ISES GS | Ori dS | Nido 3 SAMA | DARRO | SR SASAS | Ainas B
g B- B A = a F| HARRAN | ANNDAN | M HF | 191510 O Ó Z Hanm | ANNA PNF | HAH IO 1S 3
fa. 8 e Y 23 Ka See | OMANO | Hm 010A Dio | ANANA >| o 222022 | SKAM | ONOMA | noo | Doma
"a h> bul SASS | NSN | SHSHS | dmn | SSSA Di SAHA | SAMS | SASS | NFSA | HON WHO
= B = g 9 S| ARRAN | ANS | CO Sn SR RD | ISO CO cO = Hen | AÑNANA | HMOFA | HOD
< E La
E Ez | 3 g E o DRONN | Carmo | OADOH | NOO DD | ODO "= o CHAN | vieron | MOMO o | DONO &
= om + SASS | AREA | SoSe | SAKES | BSBA SASH | ORD | HOSS | PSG | N o Ki
8 = H g un r4 | ARRAN | ANDAN | comi | ibo nod e rm mmn | NANA | (mom | Kibo oo E
EZ
165 šā 5 A y Sege cooowo|dcoorio|eanoo!|oednavo O o CAMHS Leen | OAKS o | MOM E
E 3 = e Gerd | ira | darias | Sado | oss Goo | maca laura | eo dos oooo 9
o A, = m | HARRAN | ANNAN | OMS | ADD mm nnn | ANNAN | Mmmm lang 2
H
3 o = = o € 89 n | ONOHO |OMODWO | HONAN | ooo n o SN woo | Mec oc | ANAG | OMAAN | i00 o o0 5
` A 5 E? SIRO | AGKSH | SHAS | SNO | demo Geiaeëoi | ARS | ASE SON | id | Gori O
= ae 5 R | n nO | AANMNAN | cox io aig ouo HARRAN | dd | o0 m | Bidioo
=
E o Es SE o TIPS | ONNO omo | ammam | «co 75 o SIO | MOMO | NONAVD | te ee | Ino coo
E o H Ei Gaismā j| NSN | SOn | SNG | nS Go 4Go | ados | Miðlon | doo | t o oing bo
© rð = | cen dc oed | HYH io | ioio D OÓ O HARRAN | AÑADA | 0560 t P XP | 1115 Co Ó a
“a
= o EM ODA | LONA | MRNA | OPOPO | MA E g Cad
€] |a| | Ssn |gs | SSS | SAO | Hee SAYS | Heus dead | ESAS | auna | 2 | ESES
dc rmm [CO Oeo | Ma | ias i coc d 8 SESE
3 =
Ð o SORDO | ONOHO | eire 600 | Dio io r- | AMDOTN A BSES
so | Sn | acne | oao | He ios SANS ECN ET ESAS | Nggon 9| S d d
HA NANN | OMA | ic a a Ó Ó D o E =
SEU
o OTONA | SHAM] o | OORON | KONAD ES
PUES E, h Sct A V TØ o i) ie Aa cA d Le e Sadna dudan - ro oa GANS adan E
vc m ROI | ANNAN | NARRO | 15 15 ooo
MS | eo con SSA | vno SS es
e ariete p e QN. E a Rie de A | RS EE eae g
REESE AMO | NARRO | idio ooo 3
=
o SYANDO | ANO | Geo o | 000 | P900 Ë
e LU ect cies ccc atico DN ORNA Ed E Inc ES Eee v rogue sep njā &
mmm C4 | CU Cd GO CO CÓ | OHH HID | 15 159 O c Ó 2
S Zu
o O
kl o onono | POMS | ororo | nonon leese B
BAAN | NDF | SHESR | N 0 ŠO | SSSAAA =
A rr +
a
H

Reverse sign of correction for italic figures

1214

Y MIA ti

Correction sign

[RAS co

Eastward
Westward

Radio bearings

Transmitter
Eastward
Westward

| M5 D- Co CN iS

Latitude receiver

70.1

Same Name
Contrary Name

m
Ep
A
B
ci
O
A
S
os
GË
= A
* ei
Ð gg
Ð Ë à
H ap
< 9 RH
ES
a 3
O m
Og
[5
P
B
o
1
+
3
O
H
O

63.3 |62. 2
67.1 |66.1

Wal

Correction sign

60
64.1

69.5 |69.5 |69.4 [69.2 |68.9 |68.5 |67.

73.1 (73.2 |73.2 (73.0

Reverse sign of correction for italic figures

Latitude of destination— Latitude of transmitter
57.5 |56.

72.8 |72.4 |71.9

Latitude of Departure—75°—Latitude of Receiver

65.5 165.2 164.7

Destination
Eastward
Westward
Eastward
Westward

Great-circle sailing

62.3 |62.3 |62.1 |61.9 |61.5 |61.1

58.9 |58.8 |58.6 |58.3 [58.0
65.9 [65.8 [65.7

Latitude departure

1215

TABLE 1
Conversion Angle
Great-circle Sailing and Radio Bearings

Latitude of Departure—80°—Latitude of Receiver

Latitude of destination—Latitude of transmitter

50°

45°

40°

Same Name

Contrary Name

% sedana lāsē ddšas leon Ge car sadukļēkss a nues | weep
Es EEE EEE ERES EEE IEA
2 qa esr Peers [nena sexos oa al ome LEAR
S Soda | SIJAN | 23539 d | dere SARAF
% 3295 zudug dēkas deans | 83242 e sage. HERS Aib Sētu
S ERE ELE EE E
2 SER BEL LEE re is
s Sasad | Sedan | S8SSs SISSE |sseex Sacer | Stade | LESA BEEE
% suya [esque | Casas |(tēaca | sana 2228 Pech cipe ed lesa
A Socia didas | SBSSS|SSSES|SSSER Saison | Sinan |Sesee MEA

Radio bearings

circle sailing

Great

Correction sign

Transmitter

Latitude receiver

Correction sign

Destination

Latitude departure

+11+

Eastward
Westward
Eastward
Westward

LIDO

lāsē.

Eastward
Westward
Eastward
Westward

zzaan

1216

Correction sign

Radio bearings
Transmitter
Eastward
Westward
Eastward
Westward

+ t> = t [>
O O ll >

Latitude receiver

E
o
>
H
o
o
o
D
—
o
o
O
=>
42
H)
+
S
PN
o
10
oo

Kal MRO
COE EEG ES

D

TABLE 1
Same Name

Conversion Angle
Great-circle Sailing and Radio Bearings

Contrary Name

Correction sign

|
|
|

Latitude of destination— Latitude of transmitter

Latitude of Departure

Eastward
Westward
Eastward
Westward

Great-circle sailing
Destination

ZZAN

Latitude departure

NE by EIgE......

EAST TO SOUTH

SE by EME.

TABLE 2
Conversion of Compass Points to Degrees
Points Angular Poi Angular
4 measure oints measure
QURE y SOUTH TO WEST NUM.
0 0 00 00 Souths ona. SAT 16 180 00
1⁄4 2 48 45 S14 Wii A en ` 161⁄4 | 182 48 L
19 5 37 30 So Wate Mi Ae. 1619 | 185 37 30
34 8 26 15 S34 Wi eee. UN. Me 1634 | 188 26 15
1 11 15 00 OY (Wt Ba X "keep 17 191 15 00
11% 14 03 45 S by WIZW....... 1714 | 194 03 45
1% 16 52 30 S by W16W_------ 1714 | 196 52 30
134 19 41 15 Sby WAWE See 1734 | 199 41 15
22 30 00 BOW 8 Æ Co». "m. Am. 18 202 30 00
214 25 18 45 SS 1814 | 205 18 45
214 | 28 07 30 SEW. Ir 1814 | 208 07 30
234 30 56 15 SAVAA S 1834 | 210 56 15
3 33 45 00 S WDY 5 AO 19 213 45 00
34 | 36 33 45 SW SE 1914 | 216 33 45
3% 39 22 30 SWISS NEM 1914 | 219 22 30
334 42 11 15 SW 14 See S Ee 01934818222 11715
4 45 00 00 SWE s. M ¿Me 18. Mh. 0 225 00 00
414 47 48 45 SW1⁄4 W 1 ee 20144227 48 45
41% 50 37 30 SWW 201548230 37 30
434 53 26 15 SWW DN. See . 2034 | 233 26 15
5 56 15 00 DWiby We. R. eH. 21 236 15 00
54 59 03 45 SW by W24W----- 2114 | 289 03 45
5% 61 52 30 SW by WKW___-_- 2119 | 241 52 30
534 64 41 15 SW by W AV 21% | 244 41 15
67 30 00 WOSMES MT et GE 22 247 30 00
614 70 18 45 WSW1¿W--------| 22% | 250 18 45
61% | 73 07 30 WSWÁÍZW........ 921% | 253 07 30
634 dos WSW%W Br. || 2254 (1255 56 15
7 78 45 00 WD yr Do dā. m 3 258 45 00
71⁄4 81 33 45 WS JE. fte 2314 | 261 33 45
7% 84 22 30 Wissen. 2. iw 231% | 264 22 30
734 87 11115 WISE ME EEE 232402 007 1115
WEST TO NORTH
8 90 00 00 Westi =. Me TES V 24 270 00 00
84 92 48 45 WI4Nf 285 mt 2414 | 272 48 45
814 | 95 37 30 W⁄2N HUN. 2414 | 275 37 30
834 98 26 15 eeneg eg 2434 | 278 26 15
101 15 00 IEN e NS F wu F. 25 281 15 00
914 | 104 03 45 WANWAN ee eee 2514 | 284 03 45
914 | 106 52 30 WN W216 W ee D 251% | 286 52 30
934 | 109 41 15 WNWÁÍ4W........ 2534 | 289 41 15
10 112 30 00 M d BS 26 292 30 00
1014 | 115 18 45 NW by W34W.... 2614 | 295 18 45
101% | 118 07 30 NW by Wi4W....| 2614 | 298 07 30
1034 | 120 56 15 NW by Wi4W....| 2634 | 300 56 15
11 123 45 00 NW by WE 1⁄2 M4. x. 27 303 45 00
1114 | 126 33 45 NWAWS NH He |1 2714 | 306 33 45
11% | 129 22 30 NW1⁄4We_ AE wr 2719 | 309 22 30
1134 | 182 11 15 Mr Me M 4. + 2734 | 312 11 15
12 135 00 00 UW D. do »*» Hoe. 28 315 00 00
1214 | 137 48 45 NW AN e ee 2814 | 317 48 45
1214 | 140 37 30 NWN- SU STE - 281% | 320 37 30
1234 | 143 26 15 NWA Ne Eki 2834 | 323 26 15
13 146 15 00 INV Var Nooo eee 9 326 15 00
1314 | 149 03 45 NN WSA VV EEE S 2914 | 329 03 45
1319 | 151 52 30 NNWLSW +H PR: 291% | 331 52 30
133⁄4 | 154 41 15 NNWAW E EE: 2934 | 334 41 15
14 157 30 CO NIN We ee E m ae 30 337 30 00
1414 | 160 18 45 N by W34W......| 3014 340 18 45
1419 | 163 07 30 N by Wl2W-_------ 843 07 +
E J 9

1217

1218

TABLE 3

Traverse Table
A A A ee ee

0°—180°—180°—360° = Å

(17 CSS pn j

DLo p NH — e DLo HEATED EBERT I 180° DLo+m 359°

D L p l D m DLo 0.0 0. 000 1.0 <

1 i 0. 000 1 1. 000 1 0. 0. 1 0. 002 0. 9 i
2 2. 0. 000 2 2. 000 2 0. 0. 2 0. 003 0.8
3 3. 0. 000 3 3. 000 3 0. 0. 3 0. 005 0. 7

4 4. 0. 000 4 4. 000 4 0. 0. 4 0. 007 0. 6
5 5. 0. 000 5 5. 000 5 0. 0. 5 0. 009 0.45
6 6. 0. 000 6 6. 000 6 0. 0. 6 0. 010 0. 4
7 de 0. 000 7 7. 000 fí 0. DSZ 0. 012 0.3
8 8. 0. 000 8 8. 000 8 0. 0.8 0. 014 0:2
9 9. 0. 000 9 9. 000 9 0. 0. 9 0. 016 0. 1

1°—179°—181°—359° POT

1? p+l 178°

DLo p MÀ p DLo WI TTE 181? DLo+m 358°
D 1 p l D m DLo 0. 0 0. 017 1.0
1 1. 000 0. 017 1 1. 000 1 0. 017 0.1 0. 019 0.9
2 2. 000 0. 035 2 2. 000 2 0. 035 022 0. 021 0.8
3 3. 000 0. 052 3 3. 000 3 0. 052 DES 0. 023 0.7
4 3. 999 0. 070 4 4.001 4 0. 070 0.4 0. 024 0. 6
5 4. 999 0. 087 5 5. 001 5 0. 087 035 0. 026 0.5
6 5. 999 0. 105 6 6. 001 6 0. 105 0. 6 0. 028 0.4
7 6. 999 0. 122 7 7. 001 7 0. 122 0. 7 0. 030 0.3
8 7. 999 0. 140 8 8. 001 8 0. 140 0.8 0. 031 0. 2
9 8. 999 0. 157 9 9. 001 9 0. 157 0. 9 0. 033 OAI

2°—178°—182°—358° =
2° = 177°
DLo p MMMM DLo AB M$ 182° DLo+m 357°
D L p Ü D m DLo 0.0 0. 035 150
1 0. 999 0. 035 1 1. 001 1 0. 035 0. 1 0. 037 0. 9
2 1. 999 0. 070 2 2. 001 2 0. 070 0. 2 0. 038 0.8
3 2. 998 0. 105 3 3. 002 3 0. 105 0.3 0. 040 (057
4 3. 998 0. 140 4 4. 002 4 0. 140 0. 4 0. 042 0.6
5 4. 997 0. 174 5 5. 003 5 0. 175 075 0. 044 0. 5
6 5. 996 0. 209 6 6. 004 6 0. 210 0. 6 0. 045 0. 4
7 6. 996 0. 244 7 7. 004 7 0. 244 0. 7 0. 047 0.3
8 7. 995 0. 279 8 8. 005 8 0. 279 0. 8 0. 049 0. 2
9 8. 995 0. 314 9 9. 005 9 0: 314 0. 9 0. 051 0. 1

3°—177°—183°—357° NU
3? p+ 176°
DLo p MMMM DLo LL 183° DLo+m 356°
D i p l D m D Lo 0.0 0. 052 10
1 0. 999 0. 052 i +] 1.001 1 0. 052 0. 1 0. 054 0. 9
2 1. 997 0. 105 2 2. 003 2 0. 105 0. 2 0. 056 0. 8
3 2. 996 0. 157 3 3. 004 9 0:157 0. 3 0. 058 02
4 3. 995 0. 209 4 4. 005 4 0. 210 0. 4 0. 059 0. 6
5 4. 993 0. 262 5 5. 007 5 0. 262 Dk 0. 061 0.5
6 5. 992 0. 314 6 6. 008 6 0.314 0.6 0. 063 0. 4
tü 6. 990 0. 366 7 7. 010 y 0. 367 0. 7 0. 065 0. 3
8 7. 989 0. 419 8 8. 011 8 0. 419 0. 8 0. 066 0. 2
9 8. 988 0. 471 9 9. 012 9 0. 472 0.9 0. 068 0. 1

LE | e

4°—176°—184°—356° Course
- TEE de O E DE 1760
5 | P VME p | D Lo E EHE LÀ M 1842 DLo=m | 355%
2 p SÄI D m DLo 0.0 0. 070 150
1 0. 998 0. 070 1 1. 002 1 0. 070 0. 1 0. 072 0. 9
2 1. 995 0. 140 2 2. 005 2 0. 140 (082 0. 073 0. 8
3 2. 993 0. 209 3 3. 007 3 0. 210 (053 0. 075 O
4 3. 990 0. 279 4 4. 010 4 0. 280 0. 4 0. 077 0.6
á) 4. 988 0. 349 5 5. 012 5 0. 350 ORS 0. 079 0.5
6 5. 985 0. 419 a | 6. 015 6 0. 420 0. 6 0. 080 0. 4
7 6. 983 0. 488 i 7. 017 f 0. 489 0. 7 0. 082 0. 3
8 7. 981 0. 558 8 8. 020 8 0. 559 0. 8 0. 084 0. 2
9 8. 978 0. 628 9 9. 022 9 0. 629 0. 9 0. 086 0. 1

TABLE 3

Traverse Table

5°—175°—185°—355°

Course

1219

o

p+l

174°

5
DLo p TT es DLo MN 185°. | DLo=m | 354%
D l Dn» n Le D m DLo 0. 0 0. 087 1.0
1 0. 996 0. 087 1 1. 004 1 0. 087 0.1 0. 089 0. 9
2 1. 992 0. 174 2 2. 008 2 0. 175 0. 2 0. 091 0. 8
3 2. 989 0. 261 3 3. 011 3 0. 262 0.3 0. 093 0. 7
4 3. 985 0. 349 4 4. 015 4 0. 350 0. 4 0. 095 0. 6
5 4, 981 0. 436 5 5. 019 5 0. 437 0.5 0. 096 0.5
6 5. 977 0. 523 6 6. 023 6 0. 525 0. 6 0. 098 0. 4
7 6. 973 0. 610 7 7. 027 7 0. 612 0.7 0. 100 0.3
8 7. 970 0. 697 8 8. 031 8 0. 700 0.8 0. 102 0. 2
9 8. 966 0. 784 9 9. 034 9 0. 787 0. 9 0. 103 0.1
Course
6°—174°—186°—354° = = =
DLo p MMM > D Lo THT 186° DLo=m 353°
D l d p l D m DLo 0. 0 0. 105 ils 0)
1 0. 995 0. 105 1 1. 006 1 0. 105 0. 1 0. 107 0. 9
2 1. 989 0. 209 2 2. 011 2 0. 210 0. 2 0. 109 0.8
3 2. 984 0. 314 3 3. 017 3 0. 315 0. 3 0. 110 0. 7
4 3. 978 0. 418 4 4, 022 4 0. 420 0. 4 0. 112 0. 6
5 4. 973 0. 523 5 5. 028 5 0. 526 0. 5 0. 114 0.5
6 5. 967 0. 627 6 6. 033 6 0. 631 0.6 0.116 0.4
7 6. 962 0. 732 7l 7. 039 if 0. 736 0. 7 0. 117 0.3
8 7. 956 0. 836 8 8. 044 8 0. 841 0.8 0. 119 092
9 8. 951 0. 941 9 9. 050 9 0. 946 0.9 0. 121 0.1
Course
7°—173°—187°—353° TS
DLo p MAN > DLo EBERT TTL 187° DLo+m 352°
D l p l D m DLo 0. 0 0. 123 1.0
1 0. 993 0. 122 1 1. 008 1 0. 123 0.1 0. 125 0.9
2 1. 985 0. 244 2 2. 015 2 0. 246 0. 2 0. 126 0. 8
3 2. 978 0. 366 3 3. 023 3 0. 368 0. 3 0. 128 0. 7
4 3. 970 0. 487 4 4. 030 4 0. 491 0. 4 0. 130 0. 6
5 4, 963 0. 609 5 5. 038 5 0. 614 0. 5 0. 132 0.5
6 5. 955 0. 731 6 6. 045 6 0. 737 0. 6 0. 133 0. 4
7 6. 948 0. 853 7 7. 053 7 0. 859 0.7 0. 135 0. 3
8 7. 940 0. 975 8 8. 060 8 0. 982 0.8 0. 137 02
9 8. 933 1. 097 9 9. 068 9 1. 105 0. 9 0. 139 0.1
A A A AAA | a
Course
8:—172:—188:—352* — Ium
DLo p PIP DLo HH HILL L| — 1882 DLo+m 351°
D l Ë p KS D ol DLo 0.0 0. 141 1.0
1 0. 990 0. 139 1 1. 010 1 0. 141 0.1 0. 142 0.9
2 1. 981 0. 278 2 2. 020 2 0. 281 0. 2 0. 144 0.8
3 2. 971 0. 418 3 3. 029 3 0. 422 0. 3 0. 146 (D 7
4 3. 961 0. 557 4 4. 039 4 0. 562 0. 4 0. 148 0.6
5 4. 951 0. 696 5 5. 049 5 0. 703 0.5 0. 149 0.5
6 5. 942 0. 835 6 6. 059 6 0. 843 0.6 0. 151 0. 4
7 6. 932 0. 974 7 7. 069 7 0. 984 0.7 0. 153 0. 3
8 7. 922 1. 113 8 8. 079 8 1. 124 0.8 0. 155 0. 2
9 8. 912 1. 253 9 9. 088 9 1. 265 0. 9 0. 157 0.1
9 1892 || _ MÁ
Course
9°—171°—189°—351° J TI
D D Lo HL) 189? DLo=m 350°
nis p | P aS m n do 0158 1-0
1 0. 988 0. 156 1 1. 012 1 0. 158 0.1 : S
2 1.975 0. 313 2 2. 025 2 0. 317 0. 2 0. 162 ez
3 2. 963 0. 469 3 3. 037 3 0. 475 0. 3 0. 164 og
4 3. 951 0. 626 4 4, 050 4 0. 634 0. 4 0. 166 4
5 4. 938 0. 782 5 5. 062 5 0. 792 0. 5 0. 167 B5
6 5. 926 0. 939 6 6. 075 6 0. 950 0. 6 0. 169 0. 4
7 6. 914 1. 095 7 7.087 7 1. 109 0. 7 0. 171 0. 3
8 7. 902 1. 251 8 8. 100 8 1. 267 0.8 0. 173 0. 2
9 8. 889 1. 408 9 9. 112 9 1. 425 0.9 0. 175 0.1

1220

TABLE 3
Traverse Table
C
10°—170°—190°—350° = =P =
DIS RULLT P DLo TNT | 190* DLo+m 349°
D I p l D m DLo 0.0 0. 176 1.0
1 0.985 | 0.174 | 1 10187171 0. 176 0.1 0.178 | 0.9
2 1.970 | 0.347 | 2 2.031 | 2 0. 353 0. 2 0.180 | 0.8
3 2.954 | 0.521 | 3 3.046 | 3 0. 529 0. 3 0.182 | 0.7
4 3.939 | 0.695 | 4 4.062 | 4 0. 705 0. 4 0.184 | 0.6
5 4.924 | 0.868 | 5 5.077 | 5 0. 882 0. 5 0.185 | 0.5
6 5.909 | 1042 | 6 6.093 | 6 1. 058 0. 6 0.187 | 0.4
7 6.894 | 172169 | 7 7.108 | 7 1. 234 0. 7 0.189 | 0.3
8 7.878 | 1389 | 8 8.123 | 8 1 411 0.8 0.191 | 0.2
9 8.863 | 1563 | 9 9.139 | 9 L 587 0.9 0.193 | 0.1
11°—169°—191°—-349° pr
11? e 168?
DIS SS s DLo Vmr 199 DLo+m 3480
p D m DLo 0. 0 0.19 | LO
1 0.982 | 0.191 1 1.019 | 1 0. 194 0.1 0.196 | 0.9
2 1.963 | 0.382 | 2 2.037 | 2 0. 389 0. 2 0.198 | 0.8
3 2.945 | 0.572 | 3 3.056 | 3 0. 583 0. 3 0.200 | 0.7
4 3.927 | 0.763 | 4 4.075 | 4 0. 778 0. 4 0.202 | 0.6
5 4908 | 0.954 | 5 5.094 | 5 0. 972 0.5 0.203 | 0.5
6 5.890 | 1145 | 6 6.112 | 6 1. 166 0.6 0.205 | 0.4
7 6. 871 1336 | 7 7.131 | 7 1. 361 0.7 0.207 | 0.3
8 7.853 | 1526 | 8 8.150 | 8 L 555 0.8 0.209 | 0.2
9 8.8385 | 1717 | 9 9.168 | 9 1. 749 0.9 02117 071
12°—168°—192°—-348° Gë
12° D ?
DIS p — Imm s Do O CT aes DIM Mis
p ZER m DLo 0.0 0. 213 1.0
1 0.978 | 0.208 | 1 1022 | 1 0. 213 0.1 0.214 | 0.9
: 1 956 0.416 | 2 2.045 | 2 0. 425 0. 2 0.216 | 0.8
3 2 934 0.624 | 3 3.067 | 3 0. 638 0.3 0.218 | 0.7
4 3. 913 0.832 | 4 4.089 | 4 0. 850 0. 4 0.220 | 0.6
5 4. 891 1. 040 | 5 5,1120 [95 1. 063 0.5 0.222 | 0.5
6 5. 869 „247 | 6 6.134 | 6 1. 275 0.6 0.224 | 0.4
7 6. 847 1 455 7 7.156 [|7 1. 488 0. 7 0.225 | 0.3
Å i 8 8.179 | 8 1. 700 0.8 0.227 | 0.2
9 8/803 51-1: 8719] 9 9201 | 9 L 913 0. 9 0.229 | 0.1
13°—167°—193°—347° gora
14-13: pt 2
DIS D "mmm p Dro ÇN is Dlo+m 3460
m DLo 0.0 0.
1 9 974 0.225 | 1 1026 | 1 0. 231 0.1 0. zE Gs
ASH ee a eet E IE
. 07 e 0.236 | 0.7
4 3 897 o. 900 4 4 105 | 4 0. 923 0. 4 0.238 | 0:6
5 182 | 1.195 | 5 5. 132. GE 1. 154 0.5 0.240 | 0.5
6 5. 846 1.350 | $ 6 158 | 6 L 385 0. 6 0.242 | 0.4
7 osar | iarsi ii? 184 | 7 1, 616 0.7 0.244 | 0.3
8 ; 8.210 | 8 1. 847 0.8 0.246 | 0.2
8.769 | 2.025 | 9 9.237 | 9 2. 078 0.9 0.247 | 0.1
14°—166°—194°—346° ees
149 +1 o
DIS D T D Dre ÇM O 194 Die 3460
=! m DLo
1 0.970 | 0. 242 1 1. 031 1 0. 249 o i dier ata
2 1941 | 0.484 | 2 2. 061 2 0. 499 0.2 i em Gs
2.911 | 0.726 | 3 3.092 | 3 0. 74 j l
4 S ||; 3. 0925 11 3 | 748 0.3 0.255 | 0.7
0. 997 0. 4 0.257 | 0.6
5 4. 851 1.210 | 5 5.153. [1.5 1 i
; ` 247 0. 5 0.259 | 0.5
6 58:22 | “TI 6.184 | 6 |
` 1. 496 0. 6 0.260 | 0.4
7 6.792 | 1693 | 7 72148 | 7,
1. 745 0.7 0.262 | 0
8 7.762 | 1935 | 8 8245 | 8 | 3
¢ 1-2 1005 0.8 0.264 | 0.2
9 >
Sak 276 9.276 | 9 2. 244 0.9 0. 0.1

y" SN

1221

TABLE 3

Traverse Table

15°—165°—195°—-345° 17 1 ØKI A.

Dell E laa A ri S A or A E E 15° p o
DLo p MIMI, p DLo TTA TTL! 195° DLo+m 3440
D l p l D m DLo 0.0 0. 268 150
1 0. 1 1. 085 j 0. 268 0.1 0. 270 0. 9
2 0. 2 2. 071 2 0. 536 0. 2 0. 272 0.8
ð 0. 3 3. 106 3 0. 0.3 0. 274 0. 7
4 if 4 4. 141 4 |: 0. 4 0. 275 0. 6
5 d 5 5. 176 5 e 0.5 0. 277 0.5
6 Ae 6 6. 212 6 1; 0.6 0. 279 0. 4
7 (E 7 T AAT 7 1. 0. 7 0. 281 0.3
8 2 8 8. 282 8 2. 0.8 0. 283 0.2
9 2 9 9. 9 2: 0. 9 0. 285 0. 1

16°—164°—196°—344° OT IO

162 Pos 9
DLo p (HH p DLo HEBR LL 196° DLo+m, 3430
D 1 p l D m D Lo 0.0 1.0
1 0. 9 0. 1 1. 040 1 0. 0. 1 0.9
2 1. 923 0. 2 2. 081 2 0. 0. 2 0. 8
3 2, 884 0. 3 3. 121 3 0. 0. 3 0. 7
4 3. 845 ils 4 4. 161 4 tk 0. 4 0. 6
5 4. 806 Es 5 5. 201 5 ils 0. 5 0. 5
6 5. 768 d 6 6. 242 6 ils 0. 6 0. 4
y 6. 729 1. 7 7. 282 Y 2. ORT 0.3
8 7. 690 2. 8 8. 322 8 2. 0. 8 0. 2
9 8. 651 2. 9 9 9 2. 0. 9 (RI

17°—163°—197°—343° TES —

172 = 162°
Lo p TT > DLo HOI 197° DLo+m 342?
D l p l D m DLo 0.0 0. 306 1.0
1 0. 956 0. 292 1 1. 046 1 0. 306 0.1 0. 308 0. 9
2 1. 913 0. 585 2 2. 091 2 0. 611 0. 2 0. 310 0.8
3 2. 869 0. 877 3 31317 3 0. 917 0.3 0. 311 0. 7
4 3. 825 1. 169 4 4. 183 4 225 0. 4 02318 0. 6
5 4. 782 1. 462 5 5. 228 5 1. 529 0. 5 0. 315 0. 5
6 5738 1. 754 6 6. 274 6 1. 834 0.6 0.317 0. 4
I 6. 694 2. 047 Tí 7.320 7 2. 140 07 0. 319 0.3
8 7. 650 2. 339 8 8. 366 8 2. 446 0. 8 0. 321 0. 2
9 8. 607 2.6831 9 9. 411 9 234152 0. 9 0. 323 0. 1

18°—162°—198°—342° "n

D Lo ARR VETT (87 DLo+m 341°

DLo p mM We
D l p Ú D m DLo 0. 0 0. 325 1.0
1 0. 951 0. 309 1 1. 051 1 0. 325 0. 1 0. 327 0.9
2 1. 902 0. 618 2 2. 108 2 0. 650 0. 2 0. 329 0.8
3 2. 853 0. 927 3 3. 154 3 0. 975 0. 3 0. 331 QE ff
4 3. 804 1. 236 4 4. 206 4 1. 300 0. 4 0. 333 0.6
5 4. 755 1. 545 5 5. 257 5 1. 625 0. 5 0. 335 0. 5
6 5. 706 1. 854 6 6. 309 6 1. 950 0. 6 0. 337 0. 4
7 6. 657 2. 163 7 7. 360 7 2. 274 0. 7 0. 338 0. 3
8 7. 608 2. 472 8 8. 412 8 2. 599 0.8 0. 340 0. 2
9 8. 560 2. 781 9 9. 463 9 2. 924 0. 9 0. 342 0. 1

19°—161°—199°— 341° qn
is a AES o oom 19° E p+l 160°
Lo p TT ae DLo TTT 1999 DLo=-m 340°
D l p l D m DLo 0.0 0. 344 1.0
1 0. 946 0. 326 1 1. 058 1 0. 344 0. 1 0. 346 0.9
2 1. 891 0. 651 2 2115 2 0. 689 0. 2 0. 348 0.8
a) 2.831 0. 977 3 axo 3 12083 0.3 0. 350 0.7
4 3. 782 1. 302 4 4, 230 4 il Sie 0. 4 0. 352 0.6
5 4, 728 1. 628 5 5. 288 5 12722 0. 5 0. 354 0X5
6 5. 673 1. 953 6 6. 346 6 2. 066 0. 6 0. 356 0. 4
Y 6. 619 2. 279 7 7. 403 7 2. 410 0.7 0. 358 0.3
8 7. 564 2. 605 8 8. 461 8 286155 0. 8 0. 360 0.2
9 8. 510 2. 930 9 9. 519 9 3. 099 0.9 0. 362 0. 1

1222

TABLE 3

Traverse Table

20°—160°—200°—340°

Course
A Ee

DLo p MMMM DLo ee 200° DLo+m 339° 4
D 1 p i D m DLo 0. 0 0. 364 1.0
d 0. 940 0. 342 1 1. 064 I 0. 364 0. 1 0. 366 0. 9
2 1. 879 0. 684 2 2. 128 2 0. 728 0. 2 0. 368 0.8
3 2. 819 1. 026 3 3. 193 3 1. 092 0.8 0. 370 0.7
4 3. 759 1. 368 + 4. 257 4 1. 456 0.4 0. 372 0. 6
5 4. 698 ib TO 5 5. 321 5 1. 820 0.5 0. 374 0.5
6 5. 638 2. 052 6 6. 385 6 2. 184 0. 6 0. 376 0. 4
7 6. 578 2. 394 7 7. 449 7 2. 548 0.7 0. 378 0.3
8 (ADS 24780 8 8. 513 8 2. 912 0. 8 0. 380 0. 2
9 8.457 | 3.078 | 9 9.578 | 9 3.2764 || 0.9: | . 0.982, | da Y

Course
21°—159°—201°—339° - = =

DLo p HI > DLo (1111111111 e 201° EE 2
D l p H D m DLo 0.0
1 0. 934 0. 358 1 1. 071 1 0. 384 0. 1 0. 386 0. 9
2 1. 867 OR eld 2 2. 142 D 0. 768 0. 2 0. 388 0. 8
3 2. 801 1. 075 3 3. 213 SIM 13152 0. 3 0. 390 0. 7
4 8. 784 1. 433 4 4. 285 ara 15935 0. 4 0. 392 0. 6
5 4. 668 1. 792 5 5. 356 5 1. 919 0.5 0. 394 0. 5
6 5. 601 2. 150 6 6. 427 6 2. 303 0.6 0. 396 0. 4
T 6. 535 2. 509 Ji 7. 498 if 2. 687 0. 7 0. 398 0. 3
8 7. 469 2. 867 8 8. 569 8 3. 071 0.8 0. 400 0. 2
9 8. 402 91225 9 9. 640 9 3. 455 0. 9 0. 402 0. 1

Course
22°—158°—202°—338° Kap sepu

DLo p TT pn DLo ABT ETT I 202? DLo+m 337^
D l p H D m DLo 0. 0 0. 404 1.0
1 0. 375 1 1. 079 l 0. 404 0. 1 0. 406 0.9
2 0. 749 2 23151 4 0. 808 0. 2 0. 408 0.8
3 1. 124 3 3. 236 3) 1. 212 0.3 0. 410 0.7
4 1. 498 4 4.314 4 1. 616 0. 4 0. 412 0. 6
5 1.873 5 5. 393 5 2. 020 0.5 0. 414 0.5
6 2. 248 6 6. 471 6 2. 424 0.6 0. 416 0.4
d 2. 622 of 12590 7 2. 828 0. 7 0. 418 0.3
8 2. 997 8 8. 628 8 3. 232 0. 8 0. 420 0. 2
9 3. 371 9 9. 707 9 3. 636 0. 9 0. 422 0. 1

23°—157°—203°—337° pot
23° EN 156°
2 R MALL Á DLo APT VT B T 203° DLo+m 336°
p D. miim DLo 0. 0 0. 424 1.0
1 0. 921 0. 391 1 1. 086 1 0. 424 Oxi 0. 427 0.9

2 1. 841 0. 781 2 21113 2 0. 849 0. 2 0. 429 0. 8
3 2162 1. 172 3 3. 259 3 1. 273 0.3 0. 481 0. 7
4 8. 682 1. 563 4 4. 845 4 1. 698 0. 4 0. 433 0. 6
5 4. 608 1.954 5 5. 432 5 2. 122 0:5 0. 435 0.5
6 5. 523 2. 344 6 6. 518 6 2. 547 0.6 0. 437 0. 4
Y 6. 444 227195 Y 7. 605 Y 2. 971 037 0. 439 0. 3
8 7.364 3. 126 8 8. 691 8 3. 396 0.8 0. 441 0:52
9 8. 285 3. 517 9 9. 777 9 3. 820 0.9 0. 443 0. 1

24°—156°—204°—336° > Ë
24° pos S
e T WITH V V VUL LI > D Lo BT VETT T 1 204° DLo+m dt
5 p D m DLo 0.0 | 0. 445 1.0

1 0. 914 0. 407 1 1. 095 144 0. 445 0. 1 0. 447 0.9
2 1. 827 0. 813 2 2. 189 2 0. 890 ($2 0. 449 0. 8
3 2.741 1. 220 3 3. 284 3 1. 336 0.3 0. 452 0.7
4 3. 654 190277 4 4. 879 4 1. 781 0. 4 0. 454 0.6
5 4. 568 2. 084 5 5. 478 5 2. 226 Dech 0. 456 0:35
6 5. 481 2. 440 6 6. 568 6 2. 671 0. 6 0. 458 0.4
if 6. 395 2. 847 7 7. 662 7 3. 117 0. 7 0. 460 0.3
8 7. 308 3. 254 8 8. 757 8 3. 562 0. 8 0. 462 0. 2
9 8. 222 3. 661 9 9. 852 9 4. 007 0. 9 0. 464 0. 1

$e A II SI S S

1223

TABLE 3
Traverse Table
25°—155°—205°—335° ponse
KO pc o
= P WA T s be /7/////1111|11/11111711111111111117] 205° DLo+m gads
p m DLo 0. 0 0. 466 1.0
1 0. 906 0. 423 1 111038 1 0. 466 0. 1 0. 468 0. 9
2 1813 0. 845 2 2. 207 2 0. 933 0. 2 0. 471 0. 8
3 2. 719 1. 268 3 92910 3 1. 399 ONS 0. 473 (07
4 8. 625 1. 690 4 4. 414 4 1. 865 0.4 0. 475 0.6
D 4. 532 22h23 5 58510 5 22992 0. 5 0. 477 0. 5
6 5. 438 2. 536 6 6. 620 6 2. 798 0. 6 0. 479 0. 4
7 6. 344 2. 958 7 TA 24. T 8. 264 0. 7 0. 481 0.3
8 7.250 3. 381 8 8. 827 8 at Hed) 0. 8 0. 483 0. 2
9 8. 157 3. 804 9 9. 930 9 4. 197 0. 9 0. 486 OE
26*—154*—206*—334* pu
26° x 153°
== p MMMM A D Lo yy MT I LT LI I 206? DLo=m 333°
p Ú D m DLo* 0.0 0. 488 1.0
1 0. 899 0. 438 il 15113 1 0. 488 0. 1 0. 490 0. 9
3 1. 798 0. 877 2 2.225 2 0. 975 042 0. 492 0. 8
3 2. 696 11315 3 3. 338 3 1. 463 03 0. 494 037
4 3. 595 1: 753 4 4. 450 4 1. 951 0. 4 0. 496 0. 6
5 4. 494 2. 192 5 5. 563 5 2. 439 0.5 0. 499 0. 5
6 5. 393 2. 630 6 6. 676 6 2. 926 0. 6 0. 501 0. 4
7 6. 292 3. 069 7 7. 788 7 3. 414 0.7 0. 503 0.3
8 7. 190 ouod] 8 8. 901 8 3. 902 0.8 0. 505 032
9 8.089 | 3.945 9 10. 013 9 4. 390 0. 9 0. 507 oi
e
27°—153°—207°—333° a oe
DLo p MNT m DLo P7 207 DLo+m 332°
D l p l D m DLo 0.0 0. 510 1.0
1 0.891 | 0.454 1 13122 il 0. 510 om 0:512 0. 9
D 15782 |. 0:908 2 2. 245 2 1. 019 0. 2 0. 514 0. 8
3 2.673 1. 362 S 3. 367 3 1. 529 ONS 0. 516 037
4 324856048 1128156 4 4. 489 4 2. 088 0. 4 0. 518 0. 6
5 AAD SM | 2.270 5 5. 612 5 2. 548 0. 5 0. 521 0. 5
6 5. 346 2. 724 6 6. 734 6 3. 057 0. 6 0. 523 0. 4
7 6. 237 3. 178 7 7. 856 7 3. 567 0. 7 0. 525 0. 3
8 7. 128 334632 8 8. 979 8 4. 076 0.8 0. 527 0.2
9 8. 019 4. 086 9 10. 101 9 4. 586 0. 9 0. 529 on
©
28°—152°—208°—332° guo
D Lo p ih p D Lo TET I 208? ī” kā
D l | p l D m DLo 0. 0 0. 53: d
1 0. 883 0. 469 1 ilc 31555 1 0. 532 0. 1 0. 534 0. 9
2 1.766 0. 939 2 2. 265 2 1. 063 052 0. 536 0. 8
B 2. 649 1. 408 3 3. 398 3 1. 595 0. 3 0. 538 0357;
4 3532 1. 878 4 4. 530 4 23127 0. 4 0. 541 0. 6
5 4. 415 22044 5 5. 663 5 2. 659 ORS 0. 543 0. 5
6 5. 298 2. 817 6 6. 795 6 3. 190 0. 6 0. 545 0. 4
7 6. 181 3. 286 Y 7. 928 Y 93422 08 0. 547 0.3
8 7. 064 8. 756 8 9. 061 8 4, 254 0. 8 0. 550 0. 2
9 7. 947 4, 225 9 10. 193 9 4. 785 0.9 0. 552 omi
Course
29°—151°—209°—331° ` om
DLo p III p = 11111111111 CATT Wa 0 56d ta
D l p l Tm o | Ë Ó
1 0. 875 0. 485 1 1. 143 1 0. 554 0.1 0. 557 0.9
2 1. 749 0. 970 2 22281 2 1. 109 0. 2 0. 559 0. 8
3 2. 624 1. 454 D 8. 430 8 1. 663 0. 3 0. 561 0.7
4 3. 498 1. 939 4 4.573 4 222171 0.4 0. 563 0. 6
5 4.373 2. 424 5 im. Wt 5 286772, ORS 0. 566 0.5
6 5. 248 2. 909 6 6. 860 6 3. 326 0862 0. 568 0. 4
7 6. 122 3. 394 7 8. 003 of 3. 880 DAA 0. 570 ONS
8 6. 997 3. 878 8 9. 147 8 4, 434 0. 8 04573 0. 2

1224

TABLE 3

Traverse Table
Course
o
30*—150»—210*—330 IR
DLo p TT pn ` o. MM a ut DLo+m 329°
D l p l m I
1 0. 866 0. 500 1 12155 1 0. 577 0.
2 1. 732 1. 000 2 2. 309 2 l. E "
3 2. 598 1. 500 3 3. 464 3 GE E
4 3. 464 2. 000 4 4. 619 4 Ser "
5 4. 330 2. 500 5 5. 774 5 rn 4
6 5. 196 3. 000 6 6. 928 6 Āri o
3 |698 | žūo | 8 | 9238 | 8 | e | o
8 ; : ;
9 7.794 4. 500 9 10. 392 9 5. 196 0.
Course
31°—149°—211°—329° ES c
DLo p AM > ` 5 11111111111 A 5 - ~ =
D 1 p 1 m o i
1 0. 857 0. 515 1 1. 167 1 0. 601 0. 40
2 1. 714 1. 030 2 2. 333 2 1. 202 0. 8
3 2-072 1. 545 3 3. 500 3 1. 803 0. a
4 3. 429 2. 060 4 4. 667 + 2. 403 0. . 6
5 4, 286 23545 5 5. 833 5 3. 004 0. Gë
6 DUIS 3. 090 6 7. 000 6 3. 605 0. . 4
Of 6. 000 3. 605 ff 8. 166 7 4. 206 0. Lä
8 6. 857 4. 120 8 9. 333 8 4. 807 0. 22
9 7. 715 4. 635 9 10. 500 9 5. 408 0. AT
32*—148*—212*— 328? = Si r“
DLo p TT > cs LL LT S AT x S dE =
D l p 1 m 0 0. Á e
1 0. 848 0. 530 1 1. 179 1 0. 625 0. 1 0. 627 0. 9
2 1. 696 1. 060 2 2. 358 2 1. 250 0. 2 0. 630 0.8
3 2. 544 1. 590 3 3. 538 3 1.875 0.3 0. 632 0.7
4 3. 392 2. 120 4 4. 717 4 2. 499 0. 4 0. 635 0. 6
5 4. 240 2. 650 5 5. 896 5 3. 124 0. 5 0. 637 0. 5
6 5. 088 3. 180 6 7. 075 6 3. 749 0. 6 0. 640 0. 4
7 5. 936 3. 709 7 8. 254 7 4. 374 0. 7 0. 642 0.3
8 6. 784 4. 239 8 9. 433 8 4. 999 0.8 0. 644 0. 2
9 1. 632 4. 769 9 10. 613 9 5. 624 0. 9 0. 647 (5 il
C
33*—147*—213*—327* [ea
DLo p INĀ — p Dia ` WULLI 2332 — | ^ DLocm 326°
D Ú p l D m D Lo 0. 0 0. 649 1.0
1 0. 0. 545 1 1. 192 1 0. 649 0. 1 0. 652 0. 9
2 i 1. 089 2 2. 385 2 1. 299 0. 2 0. 654 0. 8
3 2i 1. 634 3 3. 577 3 1. 948 0. 3 0. 657 0. 7
4 3 2.179 4 4. 769 4 2. 598 0. 4 0. 659 0. 6
5 4. 2. 723 5 5. 962 5 8. 247 0.5 0. 662 0.5
6 5. 3. 268 6 7.154 6 8. 896 0.6 0. 664 0. 4
7 5. 3. 812 7 8. 347 7 4. 546 O 0. 667 0.3
8 6. 4. 357 8 9. 539 8 5. 195 0.8 0. 669 0. 2
9 Vë 4. 902 9 9 5. 845 0.9 0. 672 0.1
Course
34°—146°—214° 326° =
34° xb Jr que
DLo p JIL P D Lo (7010101111 VB 214? DLo+m 325°
D i p y D m | Die 0.0 0. 675 1.0
1 0. 829 0. 559 1 1. 206 1 0. 675 0. 1 0. 677 0.9
2 1. 658 LMS 2 2. 412 2 1. 349 0. 2 0. 680 0.8
3 2. 487 1. 678 3 3. 619 3 2. 024 0.3 0. 682 ON
4 3. 316 29291 4 4. 825 4 2. 698 0. 4 0. 685 0. 6
5 4. 145 2. 796 5 6. 031 5 3.373 0. 5 0. 687 0.5
6 4. 974 3. 955 6 1.237 6 4. 047 0.6 0. 690 0. 4
Jl 5. 803 3. 914 Y 8. 444 7 4. 722 0. 7 0. 692 0.3
8 6. 632 4. 474 8 9. 650 8 5. 396 0. 8 0. 695 0. 2
9 7. 461 5. 033 9 10. 856 9 6. 071 0. 9 0. 698 0. 1

1225

TABLE 3

Traverse Table

35°—145°—215°—325°

Course

o p+l o
m H TUE p a MUU 215° DLo+m 3240
i DI DLo 0.0

1 0. 819 0. 574 1 1. 221 1 0. 700 0. 1 0 703 0
2 1. 638 1. 147 2 2. 442 2 1. 400 0. 2 0. 705 0.8
3 2. 457 13721 3 3. 662 3 2. 101 0. 3 0. 708 0. 7
4 3.217 2. 294 4 4. 883 + 2. 801 0. 4 (> gibi 0.6
5 4. 096 2. 868 5 6. 104 5 3. 501 0.5 0. 718 0. 5
6 4. 915 3. 441 6 7.320 6 4. 201 0. 6 0. 716 0. 4
7 5. 734 4.015 tú 8. 545 7 4. 901 0.7 0. 719 0. 3
8 6. 553 4. 589 8 9. 766 8 5. 602 0. 8 0. 721 0. 2
9 7.372 5.162 d 10. 987 9 6. 302 0. 9 0. 724 OR

36°—144°—216°—324°
36° Pr o
R p TATTLE DLo LL, LL 216° DLo+m 3230
p D m DLo 0. 0 0. 727 1.0
1 0. 809 0. 588 1 1. 236 1 0727 0. 1 0. 729 0. 9
2 1. 618 1. 176 2 2. 472 2 1. 453 0. 2 0. 732 0. 8
3 2. 427 1. 763 3 3. 708 3 2. 180 0. 3 0. 735 (0 74
4 3. 236 2. 851 4 4. 944 4 2. 906 0. 4 0. 737 0. 6
5 4. 045 2. 939 5 6. 180 5 3. 633 0. 5 0. 740 0. 5
6 4. 854 3. 527 6 7. 416 6 4. 359 0. 6 0. 743 0. 4
7 5. 663 4.114 ri 8. 652 7 5. 086 0. 7 0. 745 0. 3
8 6. 472 4. 702 8 9. 889 8 5. 812 0. 8 0. 748 0. 2
9 7. 281 5. 290 9 (le als 9 6. 539 0. 9 0. 751 0. 1

37°—143°—217°—323°

ES p MMMM DLo AMET EB :
] p l D m DLo 0. 0 0. 754 1.0
1 0. 799 0. 602 1 1. 252 1 0. 754 0. 1 0. 756 0. 9
2 1. 597 1. 204 2 2. 504 2 19507 0. 2 0. 759 0. 8
8 2. 896 1. 805 8 3. 756 3 2. 261 0. 3 0. 762 0. 7
4 3. 195 2. 407 E 5. 009 4 3. 014 0. 4 0. 765 0. 6
5 3. 993 3. 009 5 6. 261 5 3. 768 0. 5 0. 767 0. 5
6 4. 792 3. 611 6 75513 6 4. 521 0. 6 0. 770 0. 4
7 5. 590 4. 213 Il 8. 765 T Do 0. 7 0. 773 0.3
8 6. 389 4.815 8 10. 017 8 6. 028 0.8 0. 776 0. 2
9 7. 188 5. 416 9 11. 269 9 6. 782 0.9 0. 778 0. 1

38°—142°—218°—322°

38° : 141?

DLo p HAD P Da ADAM 2187 DLo+m 321°
D l H Ú D m DLo 0. 0 0. 781 110
1 0. 788 0. 616 1 1. 269 1 0. 781 @ il 0. 784 0. 9
2 1. 576 1. 231 2 2. 538 2 1. 563 0. 2 0. 787 0. 8
3 2. 364 1. 847 3 3. 807 3 2. 344 0. 3 0. 790 0. 7
4 3. 152 2. 463 4 5. 076 4 3. 125 0. 4 0. 793 0. 6
5 3. 940 3. 078 5 6. 345 5 3. 906 0. 5 0. 795 0. 5
6 4. 728 3. 694 6 7.614 6 4. 688 0. 6 0. 798 0. 4
7 5. 516 4. 310 7 8. 883 7 5. 469 2 o 0. 801 0.3
8 6. 304 4. 925 8 10. 152 8 6. 250 0. 8 0. 804 0. 2
9 7. 092 5. 541 9 11. 421 9 7. 032 0. 9 0. 807 0. 1

E mg

[e] o o o Course

39*—141*—219*—321 TE

D Lo p AAA TI D DLo AB HT LINI 219? DLo+m 320°
D l p l D m D Lo 0. 0 0. 810 IBO
1 0. 629 1 1. 287 1 0. 810 (0% 1 0. 813 0. 9
2 1. 259 2 2. 574 2 1. 620 0. 2 0. 816 0. 8
3 1. 888 3 3. 860 3 2. 429 0. 3 0. 818 0x7
4 28517 4 5. 147 4 3. 239 0. 4 E 0.6
5 3. 147 5 6. 434 5 4. 049 095 0. 5
6 SO 6 TE PA 6 4, 859 0. 6 0. 4
y 4. 405 7 9. 007 it 5. 668 ( 7 0. 3
8 5. 085 8 10. 294 8 6. 478 0.8 0. 2
9 5. 664 9 115531 9 7. 288 0. 9 021

1226

TABLE 3
Traverse Table 4
Course
o
40°—140°—220°—320 + € =
DIO mt P D = jo TR ar x Se E -
R ET 0. 643 1 1. 305 1 0. 839 0. 1 842 0. 9
2 1. 532 1. 286 2 2. 611 2 1. 678 0. 2 0. 845 0. 8
3 2. 298 1. 928 3 3. 916 3 2. 517 0.3 0. 848 0.7
4 3. 064 2. 571 4 5. 222 4 3. 356 0. 4 0. 851 0.6
5 3. 830 3. 214 5 6. 527 5 4. 196 0. 5 0. 854 0. 5
6 4. 596 3. 857 6 7. 832 6 5. 035 0. 6 0. 857 0. 4
7 5. 362 4. 500 7 9. 138 7 5. 874 0. 7 0. 860 0. 3
8 6. 128 5. 142 8 | 10.443 8 6. 713 0.8 0. 863 0. 2
9 6.894 | 5.785 DER 11.749 9 7. 552 0. 9 0. 866 0. 1
Course
41?—139*—221*—319? =: 51 =
DLo p MT, p DIC BI EDI =a = =
D l p E m o i y 5
5 1 1. 325 1 0. 869 0.1 0. 872 0.9
2 ne ee 2 2. 650 2 1. 739 0. 2 0. 875 0. 8
3 2. 264 1. 968 3 3. 975 3 2. 608 0.3 0. 879 0. 7
4 3. 019 2. 624 4 5. 300 4 3. 477 0.4 0. 882 0. 6
5 3. 774 3. 280 5 6. 625 5 4. 346 0. 5 0. 885 0. 5
6 4. 528 3. 936 6 7. 950 6 5. 216 0. 6 0. 888 0. 4
7. 5. 283 4. 592 7 9. 275 7 6. 085 0.7 0. 891 0.3
8 6. 038 5. 248 8 10. 600 8 6. 954 0.8 0. 894 0.2
9 6. 792 5. 905 9 11. 925 9 7. 824 0.9 0.897 0. 1
Course
42°—138°—222°—318° a e
DLo D M E DIS V = Dieter ar
D l p l m [9 E à
1 0. 743 0. 669 1 1. 346 1 0. 900 0. 1 0. 904 0. 9
2 1. 486 1. 338 2 2. 691 2 1. 801 0. 2 0. 907 0. 8
3 2. 229 2. 007 3 4. 037 3 2. 701 0. 3 0. 910 0.7
4 2. 973 2. 677 4 5. 383 4 3. 602 0. 4 0. 913 0. 6
5 347168 72:248 5 6. 728 5 4. 502 0. 5 0. 916 0. 5
6 4. 459 4. 015 6 8. 074 6 5. 402 0. 6 0. 920 0. 4
7 5. 202 4. 684 7 9. 419 7 6. 303 0.7 0. 923 048
8 5. 945 5. 353 8 10. 765 8 7. 203 0.8 0. 926 0.2
9 6. 688 6. 022 9 12. 111 9 8. 104 0.9 0. 929 0. 1
a A E ER LT CEA
Course
43°—137°—223°—317° He o.
Dio pnp DLo PMI 2238 DLo+m 316°
D H D l D m DLo 0.0 0. 933 1. 0
1 0.731 0. 682 1 1. 367 1 0. 933 0. 1 0. 936 0. 9
2 1. 463 1. 364 2 2. 735 2 1. 865 0. 2 0. 939 0.8
3 2. 194 2. 046 3 4. 102 3 2. 798 0. 3 0. 942 0. 7
4 2. 925 2. 728 4 5. 469 4 3. 730 0. 4 0. 946 0. 6
5 3. 657 3. 410 5 6. 837 5 4. 663 0. 5 0. 949 0.5
6 4. 388 4. 092 6 8. 204 6 5. 595 0. 6 0. 952 0. 4
7 5.119 4.774 7 9. 571 7 6. 528 (7 0. 956 0. 3
8 5. 851 5. 456 8 10. 939 8 7. 460 0. 8 0. 959 0.2
9 6. 582 6. 138 9 12. 306 9 | 8 393 050. | 1-0:069 0. 1
———— ——— I V
(e d
449 — 1369 —2249*— 3162 € i
44° EM CE 135?
DLo p (HEH > DLo MM TTT 2240 DLo+m 315°
D L Kees Ep D m DLo 0.0 0. 966 1.0
1 0. 719 0. 695 1 1. 390 1 0. 966 0.1 0. 969 0.9
2 1. 439 1. 389 2 2. 780 2 1. 931 0.2 0. 972 0.8
3 2. 158 2. 084 3 4. 170 3 2. 897 0.3 0. 976 0.7
4 2. 877 2.779 4 5. 561 4 3. 863 0. 4 0. 979 0.6
5 3. 597 3. 473 5 6. 951 5 4. 828 0.5 0. 983 0.5
6 1. 316 4. 168 6 8. 341 6 5. 794 0.6 0. 986 0. 4
7 5. 035 4. 863 7 9. 731 7 6. 760 0. 7 0. 990 0. 3
8 5.755 5. 557 8 11.121 8 7.726 0.8 0. 993 0.2
9 6. 474 6. 252 9 12. 511 9 8. 691 0.9 0. 997 0.1

1227

TABLE 3

Traverse Table

45°—135°—225°—315° m

45° p+l 134°
DLo p DOUT E DLo WU ` 225° DLo+m 3149
D 5 p l D m DLo 0.0 1. 000 1.0
1 0. 707 0. 707 1 1. 414 1 1. 000 1 003 0.9
2 1. 414 1. 414 2 2. 828 2 2. 000 0.2 1. 007 0.8
3 2, 121 2. 121 3 4, 243 3 3. 000 0.3 1. 011 0.7
4 2. 828 2. 828 4 5. 657 4 4. 000 0. 4 1. 014 0. 6
5 3. 536 3. 536 5 S 07 5 5. 000 0. 5 1. 018 0. 5
6 4. 243 4. 243 6 8. 485 6 6. 000 0. 6 1. 021 0. 4
ri 4. 950 4. 950 7 9. 899 7 7. 000 0. 7 1. 025 0.3
8 5. 657 5. 657 8 11. 314 8 8. 000 0.8 1. 028 0.2
9 6. 364 6. 364 9 12. 728 9 9. 000 0. 9 1. 032 0.1
46°—134°—226°— 314° e LP
DLo D TIP DLo RR UII] | 226 DLorm | 3132
D l p l D m DLo 0.0 1. 036 1.0
1 0. 695 0. 719 1 1. 440 1 1. 036 0. 1 1. 039 0.9
2 1. 389 1. 439 2 2. 879 2 2. 071 0. 2 1. 043 0. 8
3 2. 084 2. 158 3 4. 319 3 3. 107 0.3 i 0.7
4 2.779 2. 877 4 5. 758 4 4. 142 0.4 1 0.6
5 3. 473 3. 597 5 7. 198 5 5. 178 0. 5 8 0. 5
6 4, 168 4, 316 6 8. 637 6 6. 213 0.6 i 0. 4
y 4. 863 5. 035 y. 10. 077 7 7. 249 0. 7 1. 0.3
8 5. 557 5. 755 8 11. 516 8 8. 284 0.8 1 0. 2
9 6. 252 6. 474 9 12. 956 9 9. 320 0.9 Y 0.1
47°—133°—227°—313°
bio D ITT P DLo TTT
D 1 D i D m DLo 0. 0 1. 072 1.0
1 0. 682 0. 731 1 1. 466 1 1. 072 0. 1 1. 076 0. 9
2 1. 364 1. 463 2 2. 933 2 2. 145 0. 2 1. 080 0.8
3 2. 046 2. 194 3 4. 399 3 3, 217 0.3 1. 084 0. 7
4 2. 728 2. 925 4 5. 865 4 4. 289 0. 4 1. 087 0. 6
5 3. 410 3. 657 5 74531 5 5. 362 0. 5 1. 091 0. 5
6 4. 092 4. 388 6 8. 798 6 6. 434 0. 6 1. 095 0. 4
7 4. 774 5. 119 7 10. 264 7 7. 507 0.7 1. 099 0.3
8 5. 456 5. 851 8 11. 730 8 8. 579 0.8 1. 103 0. 2
9 6. 138 6. 582 9 13. 197 9 9. 651 0.9 1. 107 0.1
1-99 | 615 | 658219 EE E E, M
48°—132°—228°—312° Tua E
DLo p TI _P DLo TUN 228 DLo+m 311°
D 1 7 7 D m DLo 0.0 GA 1.0
1 0. 669 0. 743 1 1. 494 1 1111 (i 1.115 0. 9
2 1. 338 1. 486 2 2. 989 2 2. 221 0. 2 RIS 0.8
3 2. 007 2. 229 3 4. 483 3 3. 332 0. 3 1. 122 0.7
4 2. 677 2. 973 4 5. 978 4 4. 442 0. 4 js
5 3. 346 3. 716 5 LSD 5 5. 553 0.5 1. 130 0.5
6 4. 015 4. 459 6 8. 967 6 6. 664 0. 6 TIO 0. 4
7 4. 684 5. 202 7 10. 461 7 TATA 0.7 1. 188 e
8 5. 353 5. 945 8 11. 956 8 8. 885 0.8 1. 149 0. 2
9 6. 022 6. 688 9 13. 450 9 9. 996 0. 9 : Å
49°—131°—229°—311° E as
DL V E DLo AT LL 229 DLorm sv
a ct | DR
1 0. 656 0. 755 1 T 3 : i
2 19512 1. 509 2 3. 049 2 2. 301 0.2 K 169 0.8
3 1. 968 2. 264 3 4. 573 3 3. 451 0. 3 1. 163 0. 7
4 2. 624 3. 019 4 6. 097 : e oy Ze We
` da de. i 9. 146 6 6. 902 0. 6 th 0.4
^ 4. 592 5. 283 ij 10. 670 7 8. 053 0. 7 1. 179 E
12. 194 8 9. 203 0. 8 1. 183 0.
8 5. 248 6. 038 8 Ke dE GE
9 5. 905 6. 792 9 13. 718 9 10. 353 :

1228

TABLE 3

Traverse Table

Course
o
50°—130°—230°—310 = x =
7 DLo ` HUTT 230° DLo=m 3090
Dia P JULI p 1 m TT a D e
1. 556 1 1 192 0.1 1. 196 0.9
z Y E 1 E 2 3. 111 2 2. 384 0. 2 1. 200 0. 8
3 1.928 | 2.208 | 3 4.667 | 3 3. 575 0. 3 1. 205 0.7
4 2. 571 3. 064 4 6. 223 4 4. 767 0.4 1. 209 0.6
5 3.214 | 3.830 5 7. 779 5 5. 959 0. 5 1. 213 0. 5
6 3.857 | 4596 | 6 9. 334 6 7. 151 0. 6 1. 217 0. 4
7 4. 500 5. 362 7 10. 890 7 8. 342 0.7 1. 222 0.3
8 5. 142 6. 128 8 12. 446 8 9. 534 0.8 1. 226 0.2
| 9 | 5.785 | 6.894 | 9 | 14002 | 9 | 10.726 | 0.9 1. 230 0. 1
Course
51°—129°—231°—309° ae LEE.
DLo p Qmm > DLo WII TID z ; 2e =
D l p m , 4 Á
| Tt 1 1. 589 1 1. 235 0. 1 1. 239 0. 9
5 S 259 " 257 2 3. 178 2 2. 470 0. 2 1. 244 0.8
3 1. 888 2. 331 3 4. 767 3 3. 705 0. 3 1. 248 0. 7
4 2. 517 3. 109 4 6. 356 4 4. 940 0.4 1. 253 0. 6
5 3.147 | 3.886 5 7. 945 5 6. 174 0. 5 1. 257 0. 5
6 3. 776 4. 663 6 9. 534 6 7. 409 0. 6 1. 262 0.4
7 4. 405 5. 440 7 11. 123 7 8. 644 0.7 1. 266 0.3
8 5. 035 6. 217 8 12. 712 8 9. 879 0.8 1. 271 0.2
9 5. 664 6. 994 9 14. 301 9 11. 114 0.9 1. 275 0.1
Course
52°—128°—232°—308° meri
DLo p Wm P D E mu III 239 | Diosm ` le = ās
D l p l m o 0.0 ` :
1 0.616 | 0.788 1 1. 624 1 1. 280 0.1 1. 285 0.9
2 1. 231 1. 576 2 3. 249 2 2. 560 0.2 1. 289 0.8
3 1. 847 2. 364 3 4. 873 3 3. 840 0.3 1. 294 0.7
4 2. 463 3. 152 4 6. 497 4 5. 120 0.4 1. 299 0.6
5 3.078 | 3.940 5 8. 121 5 6. 400 0.5 1. 303 0.5
6 3.694 | 4.728 6 9. 746 6 7. 680 0.6 1. 308 0.4
7 4.310 | 5.516 7 11. 370 7 8. 960 0. 7 1313 0. 3
8 4. 925 6. 304 8 12. 994 8 10. 240 0.8 1. 317 0.2
9 5. 541 7. 092 9 14. 618 9 11. 519 0.9 1. 322 0. 1
Course
53°—127°—233°—307° T
53° T o
DLo D VN, p DLo WU Dm 2330 pi 306°
D l p l D m o 0.0 1. 327 1.0
1 0. 602 0. 799 1 1. 662 1 1. 327 0.1 1 332 0.9
2 1. 204 1. 597 2 3. 323 2 2. 654 0.2 1 337 0.8
3 1. 805 2. 396 3 4. 985 3 3. 981 0.3 1 342 0.7
4 2. 407 3. 195 4 6. 647 4 5. 308 0. 4 1. 347 0. 6
5 3. 009 3. 993 5 8. 308 5 6. 635 0.5 1.351 0.5
6 3. 611 4. 792 6 9. 970 6 4. 962 0. 6 1. 356 0. 4
7 4, 213 5. 590 7 11. 631 7 9. 289 0.7 1. 361 0. 3
8 4. 815 6. 389 8 13. 293 8 10. 616 0.8 1. 366 0. 2
9 5. 416 7. 188 9 14. 955 9 11. 943 0.9 1371 0.1
In——————————————————————————M— 7 ES AAN A cl
C
54°—126°—234°—306° a ee
DLo D VT p DLo PMN äus DLo+m 305°
D l D i D m DLo 0.0 1. 376 1.0
1 0. 588 0. 809 1 1. 701 1 1. 376 0.1 1. 381 0.9
2 1. 176 1. 618 2 3. 403 2 2. 753 0.2 1. 387 0.8
3 19763 2.427 | 3 5. 104 3 4. 199 0. 3 1. 392 0.7
4 2. 351 3. 236 4 6. 805 4 5. 506 0.4 1. 397 0. 6
5 2. 939 4. 045 5 8. 507 5 6. 882 0. 5 1. 402 0. 5
6 3. 527 4. 854 6 10. 208 6 8. 258 0. 6 1. 407 0.4
7 4.114 5. 663 7 11. 909 7 9. 635 0.7 1. 412 0.3
8 4. 702 6. 472 8 13. 610 8 11. 011 0.8 1. 418 0. 2
9 5. 290 7. 281 9 15. 312 9 12. 387 0. 9 1. 423 0.1

1229

TABLE 3

Traverse Table

55°—125°—235°—305°

TMN DLo MEN TLL
D DLo
. 428
856
284
713
141
569
997
425
853

o

ele
en A

OO NO Gra GO DD
NOP PWN HS
EE EE EE E El

CO HO RI 02 01 4 02 DO |5
Kolo cs Keri SV Šo iem)

p
l
1
2
3
4
5
6
ti
8
9

KE

— bech

56°—124°—236°—304°

WAN DLo mmm 111101011111111111111171
O

483
965
448
930
413
895
378

g
E
BB

D

p

l

1 788
2 577
3 365
4 153
5 . 941
6 730
7 518
8 306 860
9 095 343

57°—123°—237°—303° REESE

p+l
TT > DLo ABE EL DLo+m
p 1 D DLo
839 1 1. 836 1. 540
677 2 3. 672 3. 080
516 3 5. 508 4. 620
355 4 7. 344 6. 159
193 5 9. 180 7. 699
032 6 11. 016 9. 239

7 12 10

8 14 12

9 16 13

DONDA ON -
NOP PWNS
O O RI C Ov 4 02 ND | B
EE EE E EE E E S Ba
O 00 NIO OUR GO NO O
ncm e Be
spees EE EE EE
m N Ww 4 OUO 0o

E

Ee
So
wre
ow
Nw
oo

e

871 . 853 . 779
709 „689 . 319
548 . 525 . 859

A mg

Course
58°-—122°—238°—302° |
BUT LLLI DLo RHET VETT LI INI
p
848
696
544
392
240
088
936
784
632

00 RIO Or GO D y
a bo 02 4 OO» -100 EE E

EE EE KEE KEE S Ha
g
PPP ba ba ba pi pupu

NØDVUR BO O
«500-10» JT 0» to E
O 0 TO OH NO
oocooooooor

o

o
wor
on
=
o o

o

tú
g

oo

Ge 99
o

1
3.
4,
6
8

Fk P
MVU 4 OO» -1000 c

OO RO GW HH
ooooooooooc
«coo-Ioc»o0wu»o0 Šo am)
EE EE E EECH

1
3
5
7
8)
11.
13
15
16

DODOS GO O ÐI
O O RIO EN e WN Ra D

GER EN OUR NINE

Course
pel

t2
e
Ka

o

TT, DLo ET
p D Lo
. 857

. 664
. 329
. 993
. 657
. 921
9. 986
. 650
. 314
. 979

«600-10» cv O2 to | B
oooobpcoooc
CDs CD On, Duke
E te e ar E
SE EE EE ENEE
RN 0? 00-100 DO

0 1
1 3
2 5
3. 7
4, 9.
5 I
6 13
6 15
7 1⁄7

1230

TABLE 3
Traverse Table
Course
o o o o

60°—120°—240°—300 ERI

DLo p AR np DLo ABE VIT TEL 240? DLo+m 299
D E p y D gm (tk DLe NOOO 1732 |F 100
1 0. 500 0. 866 il 2. 000 1 IBY 0. 1 1. 739 0. 9
2 1. 000 19782 2 4. 000 2 3. 464 Qu» 1. 746 0.8
3 1. 500 2. 598 3 6. 000 3 5. 196 0.3 1. 753 0.7
4 2. 000 3. 464 4 8. 000 4 6. 928 0. 4 1. 760 0.6
5 2. 500 4. 330 5 10. 000 5 8. 660 0. 5 19767 0.5
6 8. 000 5. 196 6 12. 000 6 10. 392 0. 6 196775) 0. 4
7 3. 500 6. 062 " 14. 000 7 12. 124 0.7 1. 782 0.3
8 4. 000 6. 928 8 16. 000 8 13. 856 0. 8 1. 789 0. 2
9 4. 500 7.794 9 18. 000 9 15. 588 0.9 1. 797 dei

o o o o Course

61°—119°—241°—299 = ae

DLo p V > DLo TN TTT 241% DLo+m 298°
D i p l D m DLo 0.0 1. 804 1.0
1 0. 485 0.875 1 2. 063 1 1. 804 opi 1.811 0.9
D 0. 970 1. 749 2 4. 125 2 3. 608 0.2 1. 819 0.8
3 1. 454 2. 624 3 6. 188 3 5. 412 073 1. 827 0. 7
4 1. 939 3. 498 4 8. 251 4 7. 216 0. 4 1. 834 0. 6
5 2. 424 4. 373 5 10. 313 5 9. 020 0. 5 1. 842 0.5
6 2. 909 5. 248 6 12. 376 6 10. 824 0. 6 1. 849 0. 4
7 3. 394 6. 122 7 14. 439 7 12. 628 0591 1. 857 0. 3
8 3. 878 6. 997 8 16. 501 8 14. 432 0.8 1. 865 0:2
9 4. 363 7. 872 9 18. 564 9 16. 236 0.9 1. 873 0.1

62°—118°—242°—298° aos
DLo p LL Vas DLo TMM MMM) 2428 DLo+m 297°
D 1 p l D m DLo 0.0 1. 881 1.0
1 0. 469 0. 883 1 2. 130 1 1. 881 0. 1 1. 889 0. 9
2 0. 939 1. 766 2 4. 260 2 3. 761 0. 2 1. 897 0. 8
3 1. 408 2. 649 3 6. 390 3 5. 642 0. 3 1. 905 0.7
| 4 1. 878 3. 532 4 8. 520 4 7. 523 0.4 1. 913 0.6
5 2. 347 4, 415 5 10. 650 5 9. 404 0.5 1. 921 0.5
6 2. 817 5. 298 6 12. 780 6 11. 284 0. 6 1. 929 0. 4
7 3. 286 6. 181 7 14. 910 7 13. 165 0. 7 1. 937 0. 3
8 3. 756 7. 064 8 17. 040 8 15. 046 0.8 1. 946 0. 2
9 4. 225 7. 947 9 19. 170 9 16. 927 0.9 1.954 0. 1
——— E DS ERUN DOMS I ASR” d

63°—117°—243°—297° ei
63° ai 116?
DLo p iii WS DLo MMMM 243° DLo+m 2969
D l p l D m | DLo 0.0 1. 963 1.0
1 0. 454 0. 891 1 2. 203 1 1. 963 051. 1. 971 0.9
2 0. 908 1. 782 2 4. 405 2 3. 925 0. 2 1. 980 0. 8
3 1. 362 2. 673 3 6. 608 3 5. 888 0.3 1. 988 0.7
4 1. 816 3. 564 4 8. 811 4 7. 850 0. 4 1. 997 0. 6
5 2. 270 4. 455 5 lī 018) 5 9. 813 0.5 2. 006 0. 5
6 2. 724 5. 346 6 13. 216 6 11. 776 0. 6 2. 014 0. 4
7 3. 178 6. 237 7 15. 419 7 13. 738 0.7 2. 023 0.3
8 3. 632 7. 128 8 17. 622 8 15. 701 0.8 2. 032 0. 2
9 4. 086 8. 019 9 19. 824 9 17. 663 0.9 2. 041 0.1

id Pj EIL ll AMA

64*—116*—244*— 296» =
64° Dt o
D En p TMT p Do MMMM AM 2442 + Dlorm — 205°
D D m DLo 0.0 2. 050 1.0
1 0. 438 0. 899 1 289281 1 2. 050 0. 1 2. 059 0.9
2 0. 877 1. 798 2 4. 562 2 4. 101 099 2. 069 0.8
3 1.315 2. 696 3 6. 844 3 6. 151 0. 3 2. 078 0.7
4 1. 753 3. 595 4 9. 125 4 8. 201 0. 4 2. 087 0.6
5 2. 192 4, 494 5 11. 406 5 10. 252 0.5 2. 097 0.5
6 2. 630 5. 393 6 13. 687 6 12. 302 0. 6 2. 106 0. 4
Y 3. 069 6. 292 7 15. 968 7 14. 352 0.7 2.116 0.3
8 3. 507 7. 190 8 18. 249 8 16. 402 0.8 20195 0. 2
9 3. 945 8. 089 9 20. 531 9 18. 453 0. 9 2. 135 0. 1

TABLE 3

Traverse Table

65°—115°—245°—295°

1231

65° pz 114°
DLo p (HH v DLo TORTA 245° DLo+m 294°
D á p l D m DLo 0.0 2, 145 1.0
1 0. 423 0. 906 1 2. 366 1 2. 145 0.1 2. 154 0.9
2 0. 845 1. 813 2 4. 732 2 4. 289 0. 2 2. 164 0. 8
3 1. 268 2. 719 3 7. 099 3 6. 434 0. 3 2. 174 0.7
4 1. 690 3. 625 4 9. 465 4 8. 578 0. 4 2, 184 0. 6
5 2. 113 4. 532 5 11. 831 5 10. 723 0. 5 2,194 0.5
6 2. 536 5. 438 6 14. 197 6 12. 867 0.6 2, 204 0. 4
7 2. 958 6. 344 7 16. 563 7 15. 012 0.7 2. 215 0.3
8 3. 381 7. 250 8 18. 930 8 17. 156 0.8 2. 225 0.2
9 3. 804 8. 157 9 21. 296 9 19. 301 0.9 2. 236 0.1
Course
66*——114*—246?— 294? ss SE 718
DLo D TT» De TT TI em Do m
D l p l D m 0 j i :
1 0. 407 0. 914 1 2. 459 1 2. 246 0.1 2. 257 0. 9
2 0. 813 1. 827 2 4. 917 2 4. 492 0.2 2. 267 0.8
3 1. 220 2. 741 3 7.376 3 6. 738 0.3 2. 278 0.7
4 1. 627 3. 654 4 9.834 | 4 8. 984 0. 4 2. 289 0.6
5 2. 034 4. 568 5 12. 293 5 11. 230 0.5 2. 300 0.5
6 2. 440 5. 481 6 14. 752 6 13. 476 0.6 2. 311 0. 4
7 2. 847 6. 395 7 17. 210 7 15. 722 0.7 2. 322 0.3
8 3. 254 7. 308 8 19. 669 8 17. 968 0.8 2. 333 0.2
9 3, 661 8. 222 9 32. 127 | 9 20. 214 0.9 2. 344 0.1
: Course
67°—113°—247°—293° = = =
DLo PVN? De — pi mmm a > a = um
D l p l m 0 1 7 "
2. 559 1 2. 356 0.1 2. 367 0.9
3 de d j 5. 119 2 4. 712 0.2 2. 379 0. 8
3 1. 172 2. 762 3 7.678 | 3 7. 068 0. 3 2. 391 0.7
4 1. 563 3. 682 4 10. 237 4 9. 423 0. 4 2. 402 0.6
5 1. 954 4. 603 5 12, 797 5 11. 779 0. 5 2. 414 0.5
6 2. 344 5. 523 6 15. 356 6 14. 135 0. 6 2. 426 0. 4
7 2. 735 6. 444 7 17. 915 7 16. 491 0. 7 2. 438 0. 3
8 3: 126 7. 364 8 20. 474 8 18. 847 0.8 2. 450 0.2
9 3. 517 8. 285 9 | 23.034 9 21. 203 0. 9 2. 463 0.
Course
68°—112°—248°—292° ia
DLo p mmm E DIS NINI TIR = D ES = an
Ë 0 m 0.927 1 2. 669 1 2. 475 0.1 2. 488 0.9
0. 749 1. 854 2 5. 339 2 4. 950 0. 2 2. 500 0.8
= 1. 124 2. 782 3 8.008 | 3 7. 425 0.3 2. 513 0.7
: 1. 498 3. 709 4 10.678 | 4 9. 900 0. 4 2. 526 0. 6
` 1. 873 4. 636 5 13. 347 5 12. 375 0.5 2. 539 0.5
: 2. 248 5. 563 6 16. 017 6 14. 851 0. 6 2. 552 0. 4
7 2. 622 6. 490 7 18. 686 7 17. 326 0.7 2. 565 0.3
4 2. 997 7. 417 8 21. 356 8 19. 801 0. 8 2. 578 0.2
9 3. 371 8. 345 9 24. 025 got 022. 2708 || 069, | 2582: | 0.1
Course
o
69°—111°—249°—291 - su =
J| ADOS 2902
DLo p mn $ ES On AIT = z 3 = n
D l p l h 09
. 790 1 2. 605 0.1 2. 619
: n j + 2 5. 210 0.2 2. 0.8
l Sal 3 7.815
a EON A aS 4 10. 420 0.4 2. 0. 6
5 4. 668 5 13. 952 5 13. 025 0.5 2, 0.5
à 5. 601 6 16. 743 6 15621 0. 6 2. 0. 4
: 6. 535 7 19. 533 7 18. 236 0.7 2, 0.3
4 7. 469 8 22. 323 8 20. 841 0.8 2. 0.2
9 8. 402 9 25. 114 9 23. 446 0.9 Å |

1232

TABLE 3

Traverse Table

Course
70°—110°—250°—290° PET d:
e | DLo-m | 289
DIS p — WD Dia A D = 2 = =
T 0 940 1 2. 924 1 2. 747 0. 1 2. 762 0. 9
; ee 1. 879 2 5.848 | 2 5. 495 0. 2 2. 778 0.8
i ; : 0.3 E7 à
3 1.026 | 2.819 3 8. 771 3 8. 242 0.3 = kor
4 1.368 | 3.759 4 11. 695 4 10. 990 E
13. 737 0.5 2. 824 0.
; 0. Ē 038 S EE 6 16. 485 0.6 2. 840 0. 4
: E 6. 578 7 20. 467 7 19. 232 0.7 2. 856 0. 3
a 2.736 | 7.518 8 23. 390 8 21. 980 0.8 2. 872 0.2
9 3.078 | 8 457 9 26. 314 9 24. 727 0. 9 ;
Course
71*—109:—251:—289* IE BE
DLo p. mmm $ Dia A E a =
l m p R $
Í 0.326 | 0 946 1 3. 072 1 2. 904 0.1 2. 921 0.9
2 0. 651 1. 891 2 6. 143 2 5. 808 0.2 2. 937 0.8
3 0.977 | 2.837 3 9. 215 3 8. 713 0.3 2. 954 0.7
4 1.302 | 3.782 4 12. 286 4 1j. 617 0. 4 2. 971 0.6
5 1.628 | 4.728 5 15. 358 5 14, 521 0.5 2. 989 0.5
6 1.953 | 5.673 6 18. 429 6 17. 425 0.6 3. 006 0.4
7 2.279 | 6.619 7 21. 501 7 20. 329 0.7 3. 024 0.3
8 2. 605 7. 564 8 24. 572 8 23. 234 0.8 3. 042 0. 2
9 2.930 | 8.510 9 27. 644 9 26. 138 0.9 3. 060 0.1
72°—108°—252°—288° FS
ga + a
DLo PVN, 9 DLo ` ROU 2529 | Dior 287°
D 1 p i D m DLo 0.0 3. 078 1.0
1 0.309 | 0.951 1 3. 236 1 3. 078 0. 1 3. 096 0.9
2 0. 618 1. 902 2 6. 472 2 6. 155 0. 2 3. 115 0. 8
3 0.927 | 2.853 3 9. 708 3 9. 233 0.3 3. 133 0.7
4 1.236 | 3.804 4 12. 944 4 12. 311 0. 4 3. 152 0. 6
5 1.545 | 4.755 5 16. 180 5 15. 388 0. 5 3. 172 0.5
6 1.854 | 5.706 6 19. 416 6 18. 466 0. 6 3. 191 0. 4
7 2. 163 6. 657 7 22. 652 7 21. 544 0. 7 3. 211 0. 3
8 2.472 | 7.608 8 25. 889 8 24. 621 0. 8 3. 230 0. 2
9 2. 781 8. 560 9 29. 125 9 27. 699 0.9 3. 251 0. 1
73°—107°—253°—287° Des
73° p= 106°
DLo DWN DLo PMI 253° DLodE 2869
D I p 1 D m DLo 0.0 3. 271 10 1
1 0.292 | 0.956 1 3. 420 1 3. 271 0. 1 3. 291 0.9
2 0. 585 1.913 2 6. 841 2 6. 542 0. 2 3. 312 0.8
3 0.877 | 2.869 3 10. 261 3 9. 813 058 3. 333 0.7
4 1. 169 3. 825 4 13. 681 4 13. 083 0. 4 3. 354 0. 6
5 1.462 | 4.782 5 17. 102 5 16. 354 0. 5 81/376 0.5 |
6 1.754 | 5.788 6 20. 522 6 19. 625 0. 6 3. 398 0. 4
7 2.047 | 6. 694 7 23. 942 7 22. 896 0. 7 3. 420 0. 3
8 2, 339 7. 650 8 27. 362 8 26. 167 0. 8 3. 442 0. 2
9 2. 631 8. 607 9 30. 783 9 29. 438 0.9 3. 465 0.1
SS
74°—106°—254°—286° =
fae pē 105%
DLo PVN. p Da 77/777) 254° DLo+m 285°
D l p l D m |- DIS 0. 0 3. 487 1.0
1 07276 £ | 0. 961 1 3. 628 1 3. 487 0. 1 3. 511 0. 9
2 0. 551 1. 923 2 7. 256 2 6. 975 0. 2 3. 534 0.8
3 0.827 | 2.884 3 10. 884 3 10. 462 0. 3 3. 558 0.7
4 1. 103 3. 845 4 14. 512 4 13. 950 0.4 3. 582 0. 6
5 1.378 | 4.806 5 18. 140 5 17. 437 005 3. 606 0.5
6 1.654 | 5.768 6 21. 768 6 20. 924 0. 6 3. 630 0.4
7 1. 929 6. 729 7 25. 396 7 24. 412 0.7 3. 655 0.3
8 28205 | 7. 690 8 29. 024 8 27. 899 0. 8 3. 681 0. 2
9 2. 8. 651 9 32.652 | 9 31. 387 0. 9 3. 706 0. 1

1233

TABLE 3

Traverse Table

75°—105°—255°—285° 00126 Bens >

p+l
NNN DLo MAN VETT PSIDLoZinz—
D

DLo 732
. 864 "TS: 758
24217 . 464 785
. 591 . 196 812
. 455 . 928 839
. 319 . 660 867
. 182 . 992 895
. 046 . 124 923
. 910 . 856 952
m . 588 981

76°—104°—256°—284° SE

p+l
TT DLo (7011111111 LLLA DLo=m
D DLo 011
. 011 041
. 022 071
. 032 102
. 048 134
. 054
. 065
. 075
. 086
. 097

o

oono wn HgS

ONOOPWNH OS

(O O TO CT 02b H|-l'2
cO 00 RIO OV i Q2 bo | B
oooooooooo
OOSIJIOQUOUIRWNHO
92 Q2 9o W 93 po Qo po Qo Oo
EE EE EE E
ka bi DV, a A DD ECH ©

o

p

l

1 . 134
2 . 267
3 . 401
4 . 534
5 . 668
6 . 801
7 . 935
8 . 069
9 . 202

77°—103°—257°—283°

JI DLo WOON
D DL

974

949

c0 -10 cou ote [o

DNS prue po ES
O 00 1D) VT V to kal
ASP PP PPP ge
oceoocccocor
m. bà Q2 H4» OO» -1 00 cO ©

9
E
E

D

l

1 . 445
2 . 891
923 3 . 336
897 4 . 782
872 5 . 227
846 6 . 672
821 7 S
795 8 . 563
; 769 9 . 009

78°—102°—258°—282°

ALLL DLo AIT HE I
p D m DLo
978 . 705
956
934
913
891
869

D
1
2
3
4
5
6
7
8

WNP Pr O
O O RIO o0 4 WINE
oooooooooo
OOSIOQOOBRW NHO
EE E EE EE Et:
H-NWKRBRUIOSVUJIOOO

o

NJ
EE
Ho
o

=
o
=

o

ei
y

. 810
2610
. 429
. 239
. 049
. 858
847 . 668
825 . 478
: 803 . 288
TS A A A ea

79°—101°—259°—281°

TT > DLo VULLA LLL HI
p l DLo
982 1 . 145
963 2 . 289
945 3 . 723 . 434
927 4 . 963 „578
908 5 . 204 . 428
6
7
8
9

=

HO RIO Os WN Ay
OO NO GT GO DO

BOSS SS OS 55
OO NODOT N-O
cooooooooc
HNDNIMBUIOQSJIODOO

«o0o-Ic»01 o0 rb.z-A-|-/'3

A TET

o

t2
00
©

o

. 241
. 482

890 . 445 . 867
871 . 686 . 012
858 . 927 . 156
835 . 168 . 301

EE EE EE EE EN
CHM OVA OU NS
ooooooooorc
PNWHEODNOOS

O O RO Ga GOD HS

SUS SU IS

1234

gegen

TABLE 3

Traverse Table

80°—100°—260°—280°

Course

83°—97°—263°—277°

80° p=l 999
L Ui I|. p DLo WANN 260° DLo+m 279°
= p 1111111 e D E IS TET 3 671 1. 9
0. 174 0. 985 1 5. 759 1 5. 671 0. 1 5. 5
2 0. 347 1. 970 2 11. 518 2 11. 343 0. 2 5. 789 0.8
3 0. 521 2. 954 3 17. 276 3 17. 014 0.3 5. 850 0. 7
4 0. 695 3. 939 4 23. 035 4 22. 685 0. 4 5. 912 0. 6
5 0. 868 4, 924 5 28. 794 5 28. 356 0. 5 5. 976 0.5
6 1. 042 5. 909 6 34. 553 6 34. 028 0. 6 6. 041 0. 4
7 1. 216 6. 894 7 40. 311 if 39. 699 0. 7 6. 107 0.3
8 1. 389 7.878 8 46. 070 8 45. 370 0.8 6. 174 0. 2
9 1. 563 8. 863 9 51. 829 9 51. 042 0. 9 6. 243 0. 1
Course
o op CE o
819— 999 261—279 ES
DLo p MAUL > DLo MAH EET II __ 2019 DLo+m 278°
D l p l D m DLo 0.0 6. 314 1.0
1 0. 156 0. 988 1 6. 392 1 6. 314 0. 1 6. 386 0.9
2 0. 313 1. 975 2 12. 785 2 12. 628 0. 2 6. 460 0. 8
3 0. 469 2. 963 3 19. 177 3 18. 941 0.3 6. 535 0. 7
4 0. 626 3. 951 4 25. 570 4 25. 255 0. 4 6. 612 0. 6
5 0. 782 4, 938 5 31. 962 5 31. 569 0.5 6. 691 0.5
6 0. 939 5. 926 6 38. 355 6 37. 883 0.6 6. 772 0. 4
7 1. 095 6. 914 a 44. 747 7 44, 196 0. 7 6. 855 0. 3
8 1. 251 7. 902 8 51. 140 8 50. 510 0. 8 6. 940 0. 2
9 1. 408 8. 889 9 57. 532 9 56. 824 0. 9 7. 026 0. 1
82°—98°—262°—278° da
829 p+l 97°
DLo p MMMM DLo AO 262° — DLo+m 277°
D l p i D m DLo 0. 0 7. 115 1.0
1 0. 139 0.:990 1 7. 185 1 7. 115 0. 1 7. 207 0. 9
2 0. 278 1. 981 2 14. 371 2 14. 231 0. 2 7. 300 0.8
3 0. 418 2. 971 3 21. 556 3 21. 346 0.3 7. 396 0. 7
4 0. 557 3. 961 4 28. 741 E 28. 461 0. 4 7. 495 0. 6
5 0. 696 4. 951 5 35. 926 5 35. 577 0. 5 7. 596 0. 5
6 0. 835 5. 042 6 43. 112 6 42. 692 0. 6 7. 700 0. 4
7 0. 974 6. 932 7 50. 297 Y 49. 808 (e 7 7. 806 0.3
8 1.113 7. 922 8 57. 482 8 56. 923 0.8 7. 916 0. 2
9 1. 253 8. 912 9 64. 668 SEN 64. 038 0. 9 8. 028 0. 1
—§—§—§—$—§—§—ݧ—(——

84°—96°—264°—276°

= 83° p+l 96°

DLo p MMMM DLo MM LN) 268° DLo+m 276°

D H D l D m DLo 0.0 8. 144 1.9

1 0. 122 0. 993 1 8. 206 1 8. 144 0. 1 8. 264 0. 9

2 0. 244 1. 985 2 16. 411 2 16. 289 0. 2 8. 386 0. 8

3 0. 366 2. 978 3 24. 617 3 24. 433 0. 3 8. 513 0.7

4 0. 487 3. 970 4 32. 822 4 32. 577 0. 4 8. 643 0. 6

5 0. 609 4. 963 5 | 41.028 5 40. 722 0.5 8. 777 0.5

6 0. 731 5. 955 6 49. 233 6 48. 866 0.6 8. 915 0. 4

Y 0. 853 6. 948 Y 57. 439 7 57. 010 Ära 9. 058 0.3

8 0. 975 7. 940 8 65. 644 8 65. 155 0. 8 9. 205 0. 2

9 1. 097 8. 933 9 73. 850 9 73. 299 0. 9 9. 357 0. 1
3 AI ss

849 pc o

DLo p MILII] np DLo ATH M V IL 264° DLo+m 275°
D l —LD l D m DLo 0.0 9. 514 1.0
1 0. 105 0. 995 1 9. 567 1 9. 514 0. 1 9. 677 0. 9
2 0. 209 1. 989 2 19. 134 2 19. 029 0. 2 9. 845 0.8
3 0. 314 2. 984 3 28. 700 3 28. 543 0. 3 10. 019 0. 7
4 0. 418 3. 978 4 38. 267 4 38. 057 0.4 10. 199 0. 6
5 0. 523 4. 973 5 47. 834 5 47. 572 035 10. 385 (05 f
6 0. 627 5. 967 6 57. 401 6 57. 086 0. 6 10. 579 0. 4
7 0. 732 6. 962 7 66. 967 i 66. 601 0. 7 10. 780 0. 3
8 0. 836 7. 956 8 76. 534 8 76. 115 0.8 10. 988 (0) 9
9 0. 941 8. 951 9 86. 101 9 85. 629 0.9 11. 205 0. 1

šai oe

1235

TABLE 3

Traverse Table

85°—95°—265°— 275°

Course

859 pc 94°

DLo p Te p DLo MMMM TIT __ 265° DLo+m 2742
D l p l D m DLo 0.0 11. 430 1.0
1 0. 087 0. 996 1 11. 474 1 11. 430 0.1 11. 664 0.9
2 0. 174 1. 992 2 22. 947 2 22. 860 0. 2 11. 909 0.8
3 0. 261 2. 989 3 34, 421 3 34. 290 0.3 12. 163 0.7
4 0. 349 3. 985 4 45. 895 4 45. 720 0. 4 12. 429 0.6
5 0. 436 4. 981 5 57. 369 5 57. 150 0.5 12. 706 0.5
6 0. 523 5. 977 6 68. 842 6 68. 580 0. 6 12. 996 0. 4
7 0. 610 6. 973 7 80. 316 7 80. 010 0.7 13. 300 0.3
8 0. 697 7. 970 8 91. 790 8 91. 440 0. 8 13. 617 0. 2
9 0. 784 8. 966 9 103. 263 9 102. 870 0. 9 13. 951 0. 1

86°—94°—266°—274° t Course
86° p+l 93°

DLo p TMM — DLo VI TU us Dra = =
D 1 p l D m o 0. p 3
1 0. 070 0. 998 1 14. 336 1 14. 301 0. 1 14. 669 0. 9
2 0. 140 1. 995 2 28. 671 2 28. 601 0. 2 15. 056 0.8
3 0. 209 2. 993 3 43. 007 3 42. 902 0.3 15. 464 (D), 77
4 0. 279 3. 990 4 57. 342 4 57. 203 0. 4 15. 895 0. 6
5 0. 349 4. 988 5 71. 678 5 p 303 » 5 v 259 n 5
6 0. 419 5. 985 6 86. 014 6 1 f : ;
7 0. 488 6. 983 7 100. 349 7 100. 105 0.7 17. 343 0.3
8 0. 558 7. 981 8 114. 685 8 114. 405 0.8 17. 886 0. 2
9 0. 628 8. 978 9 129. 020 9 128. 706 0. 9 18. 464 0. 1

Course
87°—93°—267°—273°
879 p+l AN, 929

DLo p TIT, p D us DAT DI 2 Dec =
D 1 p l m o i ! :

1 0. 052 0. 999 1 19. 107 1 19. 081 0. 1 19. 740 0. 9
2 0. 105 1.997 2 38. 215 2 38. 162 0. 2 20. 446 0. 8
3 0. 157 2. 996 3 57,322 3 57. 243 0. 3 21. 205 (7
4 0. 209 3. 995 4 76. 429 4 76. 325 0. 4 22. 022 0. 6
5 0. 262 4. 993 5 95. 537 5 95. 406 0. 5 22. 904 0. 5
6 0. 314 5. 992 6 114. 644 6 114. 487 0. 6 23. 859 0. 4
7 0. 366 6. 990 7 133. 751 7 133. 568 0. 7 24. 898 0. 3
8 0. 419 7. 989 8 152. 859 8 152. 649 0.8 26. 031 0. 2
9 0. 471 8. 988 9 171. 966 9 171. 730 0. 9 27074 Och
Course
88°—92°—268°—272° |

88° Vs | ge

DLo p TI p D a TIMI TT n E E = (5

D i p m i à 3
! 0. 999 1 28. 654 1 28. 636 0.1 30. 145 0.9
2 al 070 1. 999 2 57. 307 2 57. 273 0. 2 31. 821 0. 8
3 0. 105 2. 998 3 85. 961 3 85. 909 0. 3 33. 694 0. 7
4 0. 140 3. 998 4 114. 615 4 114. 545 0. 4 35. 801 0. 6
5 0. 174 4. 997 5 143. 269 5 143. 181 0.5 38. 188 0.5
6 0. 209 5. 996 6 171. 922 6 171. 818 0.6 40. 917 0. E
7 0. 244 6. 996 ri 200. 576 Gi 200. 454 0.7 44. 066 i
8 0. 279 7. 995 8 229. 230 8 229. 090 0. 8 47. 740 0. 2
9 0. 314 8. 995 9 257. 883 9 25727260 ||+0+0' ap 210 1010.10)
Course
89°—9 1°—269°—271° = E
89° Douce. 90
DLo TIMI MITTIN _ 269° DLo=m 270°
Bro P VIII p I i Tn Ze E 200 à o
1 57. 299 1 57. 290 0.1 63. 6
2 i SCH 5 UU 2 114. 597 2 114. 580 0. 2 71. 615 0. 8
3 3. 000 3 171. 896 3 171. 870 0. 3 81. 847 o. 7
4 3. 999 4 229. 195 4 229. 160 0. 4 i a:
5 4. 999 5 286. 493 5 286. 450 0.5 o ;
6 5. 999 6 343. 792 6 343. 740 0. 6 a
T 6. 999 "i 401. 091 7 401. 030 0.7 E
7. 999 8 458. 390 8 458. 320 0.8 0. 2
S : 515. 610 0. 9 0. 1
9 8. 999 9 515. 688 9 5. Jt

1236

TABLE 4

Conversion Table for Meridional Parts

Latitude Pes ion Sphere || Latitude sinters T Sphere || Latitude Aree Sphere i
RERO ER d `
o 00 | 0.00) 0.00 ooch 30 00 |+0. 08|—0. 06 +11. 64]| 60 00 —0. 10|+20. 19
030| 0.00 0.00 +0. 20l| 30 30 |0. 08 —0. 06/+11. 82]| 60 30 — 0. 10| +20. 29
100] 0.00] 0.00] +0. 41|| 31 00 |+0. 08|—0. 06| +11. 99|| 61 00 —0. 11|+20. 39
130] 0.00] 0.00] +0. 61ll 31 30 |+0. 08|—0. 06 +12. 17]| 61 30 —0. 11| +20. 48
2 00 |+0.01| 0.00! +0. 81|| 32 00 |--0. 08 —0. 06 +12. 34|| 62 00 —0. 11|-- 20. 58
2 30 |--0. 01|—0. 01| +1 02|| 32 30 |+0. 09 — 0. 06 +12. 51|| 62 30 — 0. 11/+20. 68
3 00 |+0.01|—0.01| +1. 22ll 33 00 |--0. 09 —0. 07/+12. 68|| 63 00 —0. 11|+20. 77
3 30 |+0.01|—0.01| +1. 42ll 33 30 |+0. 09|— 0. 07/+12. 85|| 63 30 — 0. 11 +20. 86
4 00 |+0. 01|—0. 01| +1. 62]| 34 00 |+0. 09/—0. 07/+ 13. 02ļ| 64 00 —0. 11 +20. 95
4 30 |--0. 01|—0. 01| +1. 83ll 34 30 |+0. 09/—0. 07/+13. 19|| 64 30 —0. 11| +21. 04
5 00 |--0. 01|—0. 01| +2. 03|| 35 00 |+0. 09/—0. 07/+13. 36|| 65 00 —0 11/+21 13 IN
5 30 |+0. 02/—0. 01| +2. 23|| 35 30 |+0. 09 —0. 07 +13. 52|| 65 30 201142191
6 00 |+0. 02/|—0. 011 +2. 43|| 36 00 |+0. 09|—0. 07|+13. 69|| 66 00 — 0. 11|-- 21. 30
6 30 |+0. 02/—0. 01| +2. 63|| 36 30 |+0. 09|—0. 07|+13. Sall 66 30 — 0. 11|+21. 38
7 00 1+0. 02/—0. 01, +2 84|| 37 00 |+0. 10/—0. 07/+ 14. 01|| 67 00 — 0. 11 -- 21. 46
7 30 |+0. 02.—0. 02| +3. 04|| 37 30 |+0. 10,—0. 07/+ 14. 18|| 67 30 —Q. 11/+21. 54
8 00 |+0. 02|—0. 02, +3. 24|| 38 00 |+0. 10/—0. 071+ 14. 34]] 68 00 — 0. 11/421. 62
8 30 1+0. 02/—0. 02} +3. 44|| 38 30 |+0. 10/—0. 07] 14. 50|| 68 30 —0. 11|-- 21. 69
9 00 10. 02|— 0. 02| +3. 64|| 39 00 |+0. 10/—0. 08| +14. 66ļ| 69 00 —0:31]--21 77
9 30 |+0.03|—0.02 +3. 84|| 39 30 |+0. 10/—0. 08 +14. 81|| 69 30 —0. 11|+21. 84
10 00 |+0. 03 —0. 02, +4. 04|| 40 00 |+0. 10|—0. 08/+ 14. 97ļ| 70 00 —Q. 111+21 91
10 30 |+0. 03|—0. 02} +4. 24|| 40 30 |+0. 10/—0. 08 +15. 13|| 70 30 —0. 11 +21. 98
11 00 |+0.03|—0. 02} +4. 44|| 41 00 |+0. 10/—0. 08| +15. 28ļ| 71 00 —0. 11|+22. 05
11 30 |+0. 03.—0. 02| +4. 64]] 41 30 |0. 10 0—0. 08 +15. 43|| 71 30 0.11/+22 T1
12 00 |+0. 03|—0. 02} +4. 84|| 42 00 |+0. 11/—0. 08|+15. 591] 72 00 —0. 11|+22. 18
12 30 |+0. 03 —0. 03, +5. 04|| 42 30 |+0. 11—0. 08/+ 15. 74ļļ 72 30 —0. 11| 43-22. 24
13 00 [--0. 04.—0. 03. +5. 23]] 43 00 |+0. 111—0. 08 +15. 89l] 73 00 —0. 12 122 $0
13 30 |+0. 04 —0. 03. +5. 43|| 43 30 |+0. 111—0. 08 +16. ol 73 30 —0. 12 +22. 36
14 00 |+0. 04|—0. 03| +5. 63ll 44 00 |+0. 11/—0. 08 +16. 18l| 74 00 —0. 12 +22. 41
IU LIA AE 44 30 |+0. 11|—0. 08 +16. 33|| 74 30 —0. 12/-- 22. 47
+0. 04/—0. 03| +6. O2ļ| 45 00 |4-0. 11|—0. 08 +16. 47|| 75 00 — 0. 12/+22. 52
15 30 1+0. 04.—0. 03. +6. 22] 45 30 |+0. 111—0. 09|-- 16. 62]| 75 30 EE un
16 00 |+0.04|—0. 03| +6. 41|| 46 00 |-+0. 111—0. 091416. 76ll 76 00 — 0. 12/422. 63
16 30 |+0. 04|— 0. 03| +6. 61|| 46 30 |--0. 11/—0. 09/-- 16. 90]| 76 30 — 0. 12| 2-22. 67
17 00 |--0. 05|— 0. 04 +6. 80]] 47 00 |--0. 12 —0. 09/+17. ol 77 00 —0. 12|-- 22. 72
17 30 |+0. 05|—0. 04| +7. 00| 47 30 |--0. 12] —0. 09 3-17. 18|| 77 30 ET
18 00 [2-0. 05.—0. 04| +7. 19|| 48 00 |+0. 12—0. 09 +17 311] 78 00 bus
18 30 |+0. 05.—0. 04| +7. 38|| 48 30 |+0. 12|—0. 09 +17 All 78 30 —0. 12| +22. 85
19 00 |+0. 05|— 0. 04| +7. 58l] 49 00 |+0. 12—0. 09 +17. 58ll 79 00 — 0. 12 +22. 89
19 30 (50. 0510.04 47 T7 49 30 |+0. 12|—0. 09 +17. 72] 79 30 — 0. 12 +22. 93
+0. 05|—0. 04/ +7. 96|| 50 00 |+0. 12] — 0. 09 +17. 85|| 80 00 =
20 30 |--0. 06|—0. 04 +8. 15|| 50 30 1-0 12 o oo 017098 Colo e HE
21 00 |+0.06—0. 04| +8. 34|| 51 00 |+0. 12|—0. 09/+18. 111] 81 00 — 0. 12 -- 23. 03
21 30 |+-0. 06 —0. 04| +8. 53|| 51 30 |+0. 12 —0. 09/+18 aal 81 30 —0. 12 +23. 06
A Fens O +8. 72] 52 00 |+0. 12 —0. 09/ +18, 36ll 82 00 — 0. 12 +23. 09
+0. 06|—0. 05} +8. 91|| 52 30 |+0. 13|—0. 10 +18. 4 =
23 00 |0. 06|—0. 05} +9. 10l| 53 00 1-40. 13/—0. 10 He ól 55 Do B mp
23 30 |+0. 06/—0. 05] +9. 28|| 53 30 |+0. 13, —0. 10 +18. 73ll 83 30 —0. 12|--23. 17
24 00 |--0. 06|—0. 05| +9. 47|| 54 00 |--0. 13 —0. 10|-- 18. 85l] 84 00 —0. 12/+23. 19
7 a |--0. 07|—0. 05! +9. 65ļ|| 54 30 |0. 13|—0. 10 +18. 97|| 84 30 —0. 12 +23. 21
+0. 07|—0. 05) +9. 84|| 55 00 |0. 13/—0. 100 +19 Eo -3:
25 30 |+0. 07|— 0. 05-10. 02]| 55 30 |+0. 13|—0 1027 al 7 ue SUM es
26 00 |-+0. 07 —0. 05|-- 10. 21|| 56 00 |+0. 13|—0. 10/+19. 3211 86 00 — 0. 12 +23. 26
26 30 |--0. 07 —0. 05|+ 10. 39|| 56 30 |+0. 13|—0. 10 +19. 43ll 86 30 — 0. 12 +23. 28
22:09 [FOTO E O 051 #10. 67 57 00 |+0. 13 —0. 10|-- 19. Sëll 87 00 — 0. 12|4- 23. 29
+0. 07 —0.06/+ 10. 75|| 57 30 |+0. 13 —0. 10719 6
28 00 |--0. 07|— 0. 06 +10. 93|| 58 00 |--0. 13.—0 folate 2 A 00 Tanabe ey
28 30 |+0. 08|—0. 06 2- 11. 111] 58 30 |--0. 14 —0. 10 +19. aal 88 30 —0. 12|4-23. 31
29 00 t9 08 —0 90-11 29 59 00 +0. 14|— 0. 10 +19. 98ll 89 00 —0. 12 +23. 32
= +0. 14 —0. 10|--2 EL :
30 00 |+0. 08|— 0. 06|-- 11: 64 60. 001 Lota o er d Pola 28588

1237

TABLE 5

Meridional Parts

Lat 02
0 0. 0 59.6| 119.2) 178.9) 238.6 298.4) 358.2 418. 2
: : . 4. k i 478. h
: L 0 60. 6 20. 2 79. 9 39.6| 299.4 59. 2 19. 2 79. S 085. E 1
å A 0 61.6 212 80. 9 40. 6| 300. 3 60. 2 20. 2 80. 3 40.6] 2
a eU) 62. 6 2259 81. 8 41. 6 01. 3 6192 2172 81. 3 41.0] 3
: Ë ` 63. 6 2312 82. 8 42. 6 02. 3 62. 2 2212 82. 3 42.6] 4
: 64.60 124.2| 183.8 243.6 303.3 363.2 423.2 483. 3 4

> 6.0 65. 6 2512 84. 8 44, 5 04. 3 64. 2 2412 84. 3 di 3 3
TO 66. 6 26. 2 85. 8 45.5 05. 3 65. 2 25. 2 85. 4 45.6] 7

8 7.9 6775 2 86.8 46. 5 06. 3 66. 2 26. 2 86. 4 46.6] 8
> S < 5 28. 2 87.8 47.5 07.3 67. 2 2772 87. 4 47. o 9

k A 129.2) 188.8 248. bh 308.3 368.2 428. 2 488. 4 4

11 ONO 70.5 30. 1 89. 8 49.5 09. 3 69. 2 29, 2 89. 4 tae d i
12 11.9 715 31. 1 90. 8 50. 5 10. 3 70. 2 30. 2 90. 4 50. 7| 12
13 12. 9 42-5 32.11 91. 8 5178 1178 Till, X) 3112 91. 4 tādi 1s,74 KOR
3 13.9 73.5 33. 1 92. 8 52:55 1228 0, 2 32. 2 92. 4 52. 7| 14

14. 9 74. 5| - 184. 1| 193.8 253.5 313. 3. "373.2 © 483. 2| (403. 4| 558. 7| 1

16 15.9 15:15 3551 94. 8 54. 5 14. 3 74.2 34. 2 94. 4 54. 7 16
irf 16. 9 76.5 36. 1 95. 8 99.10 15953 UZ 35. 2 95. 4 559 17
18 17.9 T1. 5 Su 96. 8 56. 5 16. 3 76. 2 36. 2 96. 4 56. 7| 18
= 18. 9 78. 5 38. 1 97.8 57.5 1 8) Mis 22 372 97. 4 57. 7| 19
19. 9 79.5| 189.1) 198.8| 258.5 318.3 378.2] 438.2| 408. 4| 558.7| 20

21 20. 9 80. 5 40.1| 199.8 59. 5 19. 3 79. 2 89. 2) 499.4 59. 7| 21
22 2179 SIN 4119920057 60. 5 20. 3 80. 2 40.2| 500.4 60. 7| 22
28 22. 8 82.4 42.1 oS 61.5 21.3 81. 2 4172 01. 4 61. 7|] 23
= 23. 8 83. 4 48. 1 02. 7 62. 5 2259 82. 2 4272 02. 4 62. 7| 24
5 24. 8 84 4 059844: 1920322109 263. 5) 823. 31 383. 2 4494 21995032 41563. 81125
26 25.8 85.4 45. 1 04. 7 64. 5 24. 8 84. 2 44. 2 04. 4 64. 8| 26
24 26. 8 86. 4 46. 1 05. 7 65. 5 25. 3 8572 45. 2 05. 4 65. 8| 27
28 27. 8 87.4 47. 0 06. 7 66. 5 26. 3 86. 2 46. 2 06. 4 66. 8] 28
29 28.8 88. 4 48. 0 onia 67-5 DS ey Zi 47.3 07. 4 67. 8] 29
30 29. 8 89.4| 149. 0| 208.7, 268.5 328.3 388.2) 448. 3| 508. A 568. 8| 30
31 30. 8 90. 4 50. 0 09. 7 69. 4 29. 3 89. 2 49. 3 09. 4 69. 8| 31
32 31:8 91. 4 51-0 10. 7 70. 4 30. 3 90. 2 50. 3 10. 5 70. 8| 32
33 32. 8 92. 4 52. 0 14577 TITA Sle 91.2 5178 11.5 71. 8| 33
34 33. 8 93. 4 58. 0 127 72. 4 32. 3 92. 2 52.8 1225 72. 8| 34
35 34. 8 UA 490198915 7273, T3333 393. 21409) 3 613.5 1573. 81135
36 35. 8 95.4 55.0 14337 74. 4 3418 94. 2 54. 3 14. 5 74. 8| 36
37 36. 8 96. 4 56. 0 Ils 7 75. 4 35. 3 95. 2 55. 3 JH. d; 75. 8| 37
38 SY f 97. 4 57.0 16.7 76. 4 36. 3 96. 2 56. 3 16. 5 76. 8| 38
39 38. 7 98. 3 58. 0 172077 ila: 3703 97. 2 57.3 17.5 77. 9| 39
40 39. 7 99.3| 159.0| 218.7. 278. A 338.3| 398.2| 458.3 518.5) 578.9| 40
41 40.7, 100.3 60. 0 19. 7 79.4 39. 3} 399.2 59. 3 19.5 79. 9| 41
42 41.7 0173 61.0 207 80. 4 40. 3} 400. 2 60. 3 20. 5 80. 9| 42
43 AWA. Tí 02. 3 62. 0 21. 6 81. 4 41.3 01. 2 61. 3 2] 81. 9| 43
44 43. 7 03. 3 63. 0 22. 6 82. 4 42. 3 02. 2 62. 3 2285 82. 9| 44
45 44°7| 104. 3) 163 9| -293. 6| 283. 4| "343.2 408. 2| “463. 3| 5623. 5| 583. 9] 45
46 4597 05. 3 64. 9 24. 6 84. 4 44. 2 04. 2 64. 3 24. 5 84. 9| 46
47 46. 7 06. 3 65. 9 25. 6 85. 4 45. 2 05. 2 65. 3 25. 5 85. 9] 47
48 An. o 0/285 66. 9 26. 6 86.4 46. 2 06. 2 66. 3 2615 86. 9] 48
49 48. 7 08. 3 67. 9 D ERO 87.4 47. 2 07. 2 0743 27.0 87. 9| 49
50 49. 7 109.3| 168.9| 228. 6| 288.4| 348.2| 408.2) 468.3) 528.5) 588. 9] 50
51 50. 7 10. 3 69. 9 29. 6 89.4 49. 2 09. 2 69. 3 29. 5 90. 0] 51
52 Gils 7 1153 70. 9 30. 6 90. 4 50. 2 10. 2 70. 3 30. 5 91. 0| 52
53 52.6 1273 71.9 3156 91. 4 552 10115724 71.3 31.6 92. 0] 53
54 53. 6 1312 1220 32. 6 92. 4 52.2 12. 2 7092. 3 32. 6 93. 0] 54
55 5456 114.9| 173.9 233.6 | | 293.4) "353. 2] 413.2| 473. 3] 533.6| 594.0 55
56 55. 6 152 74. 9 34. 6 94. 4 54. 2 14, 2 743 34. 6 95. 0] 56
57 56. 6 16. 2 75. 9 35. 6 95. 4 55. 2 T 22 10,9 35. 6 96. 0] 57
58 57. 6 157222 76.9 36. 6 96. 4 56. 2 16. 2 moms 36. 6 97. 0] 58
59 58. 6 1812 77.9 3156 97. 4 DR Tm. 2) Ms 8) 37. 6 98. 0| 59
60 59.6 119.2 178.9 238.6 298. 4| 358.2) 418.2| 478.3 538. 6| 599. 0] 60
Lat 0° ju 29 og 49 D 6? GES 8° 9° Lat

1238

TABLE 5
Meridional Parts |
— — M — —— a —— ——— n
Lat. 113 123 1:32 142 159 16° 1:79. 189 4
0 o 659. 7| 720.51 781.5 842.9| 904. A 966. 3) 1028. 5| 1091. 0
1 20 60. 7 21:5 82. 6 43. 9 05. 5 67.3 29. 5 92. 1
2 .0 61. 7 22:5 83. 6 44. 9 06. 5 68.4 30. 6 93. 1
3 a 6211 23: 5 84. 6 45. 9 07. 5 69. 4 31. 6 94. 2
4 hl 63. 7 24. 5 85. 6 47. 0 08. 6 70. 4 325m 95.2
5 11 664.7! 725.6| 786.6| 848.0| 909.6| 971.5, 1033. 7| 1096. 3
6 t 65. 7 26. 6 87.7 49.0 10.6 205 34. 7 97. 3
7 "E 66. 7 27. 6 88. 7 50. 0 11.16 7315 35. 8 98. 3
8 Hi 67. 8 28. 6 89. 7 51.1 12:37 74. 6 36.8| 1099. 4
9 i 68. 8 29. 6 90. 7 5231 13. 17 75. 6 37. 9, 1100. 4
10 .1 669.8) 730.6, 791.7! 853.1! 914. 7| 976. 7, 1038. 9) 1101. 5
11 SEI 70. 8 al 92. 8 54.11 15. 8 "ls 11 39. 9 02.5
l2 SEH 71.8 SPATT 93. 8 55. 1 16. 8 78.7 41.0 03. 6
13 SEN 72. 8 SI 94. 8 56. 2 17.8 79. 8 42.0 04.6
14 2 73. 8 34. 7 95. 8 02 18.8 80.8 2328 05. 7
15 .2| 674.8| 735.7, 796.8 858.2| 919.9| 981.8 1044. 1| 1106. 7
16 2 75. 9 36. 7 97. 9 59. 3 20. 9 82. 9 45. 1 07.8
17 32 76. 9 37.8 98. 9 60. 3 21.9 83. 9 46. 2 08. 8
18 32 77. 9 38. 8| 799.9 61. 3 23.10 84. 9 47.2 09. 9
19 2 78. 9 39.8| 800. 9 62. 3 24.0 86. 0 48. 3 10. 9
20 2 679.9 740.8 802.0| 863.4| 925.0) 987.0| 1049.3, 1111. 9
21 L9) 80. 9 41.8 03. 0 64. 4 26. 1 88. 0 50.8 1390)
22 32 81. 9 42.8 04. 0 65. 4 2M 89. 1 514 14. 0
23 32 82. 9 43. 9 05. 0 66. 4 28. 1 90. 1 524 LOS
24 13 84. 0 44, 9 06. 0 67. 5 29. 2 91. 1 53. 5 TONI
25 .3 685.0| 745.9 807. 1| 868.5| 930.2 992. 2| 1054. 5| 1117.2
26 53) 86. 0 46. 9 08. 1 69. 5 12 93. 2 55. 6 18. 2
27 13 87. 0 47. 9 09. 1 70. 5 BOA m 94. 3 56. 6 19. 3
28 L8 88. 0 48. 9 10. 1 71. 6 333 95.3 57.6 20. 3
29 13 89. 0 50. 0 ko 72.6 34. 3 96. 3 58. 7 2114
30 .31 690.0) 751.0| 812. 2| 873.6} 935. 3| 997. 4| 1059. 7| 1122. 4
31 ao 91. 1 52. 0 183.597 74. 6 36. 4 98. 4 60. 8 PELIS
32 E 92. 1 53. 0 1412 75. 7 37.4| 999.4 61.8 24. 5
33 E 93. 1 54. 0 11532 76. 7 38. 4| 1000. 5 62. 8 25. 6
34 Á 94. 1 5511 16. 3 77.4 39. 5 01.5 63. 9 26. 6
85 .4| 695.1| 756.1) 817.3| 878.7, 940.5| 1002. 5| 1064. 9| 1127. 7
36 „4 96. 1 57.1 18. 3 79.8 41.5 03. 6 66. 0 28. 7
37 .4 97. 1 58. 1 19. 3 80. 8 42. 6 04. 6 67. 0 29. 8
38 .4 98. 2 59. 1 20. 3 81.8 43. 6 05. 7 68. 1 30. 8
39 .4| 699.2 60. 1 21.4 82. 9 44. 6 06. 7 69. 1 31. 9
40 .4| 700.2} 761.2| 822. 4| -883.9/ 945. 7| 1007. 7| 1070. 1| 1132. 9
41 nA 01. 2 0259 23. 4 84. 9 46. 7 08. 8 1172 34. 0
42 "nd 02. 2 63. 2 24.4 85.9 AT 09. 8 722 35. 0
43 . 5 03. 2 64. 2 2515 87.0 48. 7 10. 8 VB e 36. 1
44 25 04. 2 6512 2615 88. 0 49. 8 11. 9 74.3 Bf 1!
45 .9| 705. 3| 766. 3| 827. 5| 889.0. 950. 8} 1012. 9| 1075. 4| 1138. 2
46 5 06. 3 67. 3 28. 5 90. 0 51. 8 14.0 76. 4 39. 2
47 bd 07. 3 68. 3 2085 9i a 52. 9 15.0 11.4 40. 3
48 NO 08. 3 69. 3 30. 6 92. 1 53. 9 16.0 78.5 41.8
49 85 09. 3 70. 3 31. 6 93. 1 54. 9 1731 79. 5 42. 4
50 .9| 710.3 771.4 832. 6| 894.2) 956.0! 1018. 1| 1080. 6 1143. 4
51 T ila 1214 33. 6 95. 2 57.0 19. 2 81.6 44.5
52 76 192. 4 dE 34. 7 96. 2 58. 0 2089 82.7 45.5
53 20 13.4 74. 4 DU 97. 2 59. 1 2182 83. 7 46. 6
54 .6 14.4 75. 4 36. 7 98. 3 60. 1 2229 84.8 47. 6
55 D 715.4| 776.4| 837.7 899.3] 961.1! 1023. 3| 1085. 8| 1148. 7
56 .6 16. 4 7735 88. 8} 900. 3 62. 2 24.3 86. 8 49. 7
57 „6 1774 78. 5 39. 8 01. 4 63. 2 25.4 87.9 50. 8
58 „6 18.5 79.5 40. 8 02. 4 64. 2 26. 4 88.9 51.8
59 „6 _19. 5 80. 5 41.8 03. 4 65. 3 PAS 90. 0 52.9
60 Vi 720. 5} 781.5| 842.9 904.4| 966.3| 1028. 5| 1091. 0| 1153. 9
Lat Tile 122 39 1:48 15° 16° e 18°

1239

SA US”

TABLE 5

Meridional Parts

ft eet Tato] | Shee || 2299 || teas || 2250 || 1269 || 197* ||-3985 || 229% | tual.
O | 1217. 2} 1280. 9 1345. 0) 1409. 5| 1474. 6 1540. 2| 1606. 3| 1672. 9| 1740. 2| 1808. 1| 0
1 18.2| 81.9 46.0| 10.6 75.7 413 07.4| 741| 41.4 09.3] 1
2 19.3) 83.0] 47.1) 11.7) 76.8 424 085 75.2 42.5 10.4] 2
3 20.4 841 482 128 77.9 43.4 09.6 76.3| 43.6 11.6] 3
4 21.4|' 85.1| 49.3 13.9 78.9 445 107 77.4 447 127| 4
5 | 1222. 5| 1286. 2 1350.3 1414. 9| 1480. 0| 1545. 6| 1611. 8| 1678. 5| 1745. 9| 1813. 8| 5
6 23.5 87.22 514 160 81.1) 46.7 129 79.6) 47.0 150| 6
7 24.0 88.3| 525 17.1| 82.2| 47.8 140 808 481) 161| 7
8 25.0 89.4 53.5 182 83.3 48.9 151 8L9| 493 17.3] 8
9 26.7, 90.4 546 193 844| 50.0 162 83.0 504 18.4] 9
10 | 1227.8| 1291. 5| 1355. 7| 1420. 3| 1485. 5| 1551. 1 1617. 3| 1684. 1| 1751. 5| 1819. 5| 10
11 28.8 oo 568 2L4 866 522 184 852 5206 20.7 11
12 20.9 93.6 57.8 22.5 87.7| 53.83. 19.6 86.4 53.8| 21.8] 12
13 30.9 94.7} 58.9 23.0 88.8 544 20.7 87.5 549| 23.0| 13
14 32.0 958 600 | 247| 89.8 55.5 2L8| 88.6 560| 241|14
15 | 1233. I| 1296. 8| 1361. I| 1425.8 1490. 9 1556. 6| 1622. 9 1689. 7| 1757. 2| 1825. 2| 15
16 34.1 97.9 621 26.8 ou 57.7 240| 90.8 583 26. 4] 16
17 35. 2 1299.0 63.2 27.9 093.1 58.8 251| 91.9 594 1827. 5| 17
18 36.2 1300.0 64.3 | 29.0 942 59.9 26.2 93.1 oa 28 7] 18
19 37.3 ou 654 301| 953 610 273| 942 617| 29.8|19
20 | 1238. 4| 1302. 2 1366. 4 1431. 2) 1496. 4 1562. 1| 1628. 4| 1695. 3| 1762. 8| 1830. 9| 20
21 39.4 03.2 67.5 32.2 97.5 03.2 29.5| 96.4 63.9 32.1|21
22 40.5| 04.3 68.6 33.3 98.0 643 30.6 97.5 oi 33.2| 22
23 41.5| 05.4 69.7. 34.4 1499.7, 65.4) 31.8| 98.7| 66.2 34.4| 23
24 42. 6| 06.4 70.7, 35.5 1500.8 66.5 32.9 1699. 8| 67.3 35.5| 24
25 | 1243.7| 1307. 5| 1371. 8| 1436. 6| 1501.8 1567. 6 1634. 0 1700. 9 1768. 5 1836. 6| 25
26 44.7 08.6 72.9 37.7 02.9 on 35.1) 02.0 69.6 37.8] 26
27 45.8 09.6 740 38.7 04.0 69.8 36.2 03.1) 70.7 38. 9| 27
28 46.8 10.7 75.0 39.8 05.1) 709 37.3 043 71.8| 40. 1) 28
29 47.9 118 76.1) 40.9 062 720 38.4 054 73.0| 41.2| 29
30 | 1249.0 1812. 9 1377. 2| 1442. 0| 1507. 3| 1573. 1| 1639. 5| 1706. 5| 1774. 1| 1842. 4| 30
31 50.01 13.9 78.3 43.11 08.4 742 40.6) 07.6 75.2 43. 5) 31
32 51.1| 15.01 79.3| 44.2 09.5 75.3 41.8 088 76.4) 44.6) 32
33 52.1| 16.11 80.4 45.3) 10.0 76.4 42.9 09.9 77.5) 45.8] 33
34 53.2 "17.1 81.5| 46.3| 117 77.0 440 11.0) 78.6 46.9] 34
35 | 1254.3 1318. 2 1382. 6 1447. 4| 1512. 8| 1578. 7| 1645. 1| 1712. 1| 1779. 8| 1848. 1| 35
36 55.31 19.3 83.7| 48.5| 13.9 79.8 462 13.2 80.9| 49.2) 36
37 56. 4| 20.3| aa 49.6, 15.0 809 47.3) 144 Á820| 50.4 37
38 57.5 214 85.8 50.7 16.1 820 484| 15.5) 83.2| 51.5|38
39 58.5| 225 86.9 51.8 17.1 83.1) 49.5| 16.6 gä 52 7| 39
40 | 1259.6 1323. 5 1388. 0| 1452. 8| 1518. 2| 1584. 2 1650. 7| 1717. 7| 1785. 4| 1853. 8| 40
41 60.6 24.6 89.0 53.9 19.3 85.3 51.8 18.9 86.6 54.9) 41
42 61. 7| 25.7| ' 90.11 55.0) 20.4 86.4 52.9 20.0 87.7) 56. 1) 42
43 62.8 26.8 91.2 56.11 21.5 87.5 54.0) 21.1 88.8 57.2 43
44 63.8 27.8 923 57.2) 226 88.6 55.1) 222 90.0) 58.4] 44
1264. 9 1328. 9 1393. 3 1458. 3 1523. 7| 1589. 7| 1656. 2 1723. 4 EA
46 66.0 30.0 94.4| 59.4 24.8 90.8 57.3 | 24.5 92.2) 60. 7] 46
47 67.0 310 955 60.5 259 91.9 58.5 25.6 93.4) 61 8] 47
48 68 11 32.11 96.6 61.5 27.0 93.0 59.6 26.7 oa 63.0| 48
49 69. 11 33,21 97.7] 62.6| 281 ol 60.7) 27.9 95.6 ao =
1270. 2 1334. 2 1398. 7| 1463. 7| 1529. 2| 1595. 2| 1661. 8| 1729. 0| 1796. 8| 1865.
31 71.3| 35.3 1399.8| 64.8) 30.8 96.3 62.9 30.1) 97.9] 66.4) 51
52 72. 3| 36.4 1400. 9| 65.9 31.4 97.4 64.0 31.2 1799.1 67. 5] 52
53 73,41 37.5 020| 67.0 325 98.5 65.1) 32.4 1800.2 _ 68. 7] 53
54 74.5 38.5 03.1 68.11 33.6 1599.6 66.3 33.5 eee =
1275. 5 1339. 6| 1404. 1| 1469. 1| 1534. 7| 1600. 7| 1667. 4 1734. 6| 1802. 5
56 eel wa 052 70.2 35.8 omg 685 357) 03.6 72.1 56
57 77.7) «417 06.3 71.3 36.9 02.9 696 36.9 047 73.3) 5
58 78 7 428 074 724 380) 04.1| 70.7 380 059 74. 4) 58
59 79.81 Ga 08.5) 73.5 39.1 05.2 718 39.11 07.0) 75.6|59
60 | 1280. 9| 1345. 0| 1409. 5| 1474. 6| 1540. 2| 1606. 3| 1672. 9 1740. 2 1808. 1 1876. 7| 60

1240

TABLE 5

Meridional Parts

38°

2453. 9
55. 2
56. 5
DM
59. 0

D0IDOADN=O `

conos He GO O `

„0
7. 2
.3
„5
Mí
.8
20
. 2
.3
. 5
26
His!
.0
al
.3
SCH
30
.8
LY
yal
29
.4
„6
.8
39
E
6. 3
.4
-6
8
9
ball
.8
„4
36
8

OQ» Q3 C 00 Gil NL Da Al 00 OOO lA B9 CO DOG 00 OT b9 OI -T A CO OO O JUS O TR D CO DO a OO O 02 C O0 t B2

29
ul
.3
5
.6
.8
5.0
et
.9
b)
.6
. 8
20
32
.8
. ð
pd
8
20
12
.4
.5
Ta
4. 9
SH

Qo ln Q5 2 El -1 C1 4» OS! e Qo e| cO - TOt O2 bal e O E NA cO TON O 00 O» 4| 05 e cO OA IND C 00 NG VDO en 4 99 e EE -3 EE ba IND CB

Ei ui — :O N OU Q3? — ONT OU Q5 — ONT OT WH cO NJU Q2 e ONO Q2 5 A B2 C 00 O21 kä e OB CO Alen Q2 i cO - 31 O1 62 BN OO! en i. IND CD 00
|

DADO S AEN OWI DEPNONI AWE ON GU O2 C 00 Ol DO 00 Ol DO WO VU GO e cO - 101 02 O - 1011 GO A cO - 1011 Eu — CO - 101] 62 A cO - 16x
e

Q2 00 DH bo! cO -1 O1 ba SO! MODO ODO RENO N C' A 00 Ol NO - T O1! O HA 00 ODO -1 O01 Q9] OO DOH DO O - En 92 kal OUR hä O! 00 EE |. O
Di f cO OH! e Ta NOA BO O!IN ON OT! C Q2 O 00 GI Q2 e O AMARO De Al CO -14- B2 OI - 101 02 O 001 OV A cO OI ARNON OO En EA

ON PEK cO O Q2 — 00 2» WO O0 Ot Q9 CO - 191 b9 O N NO -J AINO N LO O a E CO | O» dH EA CO Ola rf 00 O) Gul ta 00 O Q9 kal 00 GO VO A cO | OS 4 i OD
Niki UNO DUO NO Gt Q3! C5 Na ARO GUN CO GO» Q3! C5 T ux i cO | O3» Q9 C5 T | e 00 VUGD T BO GU N O N 4 100 O1 92 C -Il RH Om O

Won Pres

1241

TABLE 5

Meridional Parts

0 | 2607. 7| 2686. 3| 2766. 1| 2847. 2| 2929. 6| 3013. 5| 3098. 8| 3185. 7| 3274. 2| 3364.51 0
1 09.0 2057. 6) 1567. 5) n248. 6) n231. 0| =,14.9 310052! 2:87. 11 2275. 7. 66701141
2 10. 3) 4489 01 2568. 8| 2249. 9| 32 4| 5:16. 3. 01.7) 88.6 77.2 B
3 ike 61490. OF 370. WE padi. 3) 2433. El na17. ant Gl 1390. Ll 8375: AERO IAS
4 EK D 0291. GLave 21. 51 1352. 2| 2235. 2) or 19, 1) 1204. | w= 91, 5|. «x RO. 2! 6470: 61,4
5 | 2614. 2| 2692. 9 2772. 8| 2854. 0| 2936. 6| 3020. 5| 3106. 0| 3193. 0| 3281. 7| 3372. 11 5
6 ID. Deanna. 2) 1e 74. 20 055.41 0238. 0| 5621. 0! 2207, din. 94. Bl 83. 21 2473. 61/56
7 16. 8} 7595. 6| 675. 5| 4.56. 8| 1539. 3| +23. 3) 08.8) 95. 9] "84. 7) v2 75. 1 -7
8 15 0 0406. 0976. 9) 6158. 1) 6440. 7) 0224. 8| 410. 3 5397. 4 EE 19876; El 28
9 19 41 1808. 2) 0078. 2 1:59. 5| 1542. 11 126.91) n5 11- 7]. 3198. 8) 3:387. 6) 78 21 49
10 | 2620. 7| 2699. 5| 2779. 5| 2860. 9 2943. 5| 3027. 6| 3113. 2 3200. 3| 3289. 1| 3379. 7| 10
11 2210 2700. 9] | 80. 9] -62. 2| 44.9) 29.0 14.6 .01.8 90.6 81.2) 11
12 233800 E al 8646. al A590. 4! 2416. Ol) 1503» o 4292, 41 2«32- 8|! 12
13 24 0 gads A83: 6 «065-0. 1247; 4]. 9831. 8) 2117.51 0404. 2^ 93.6 vc84. 5]: 13
14 26.01 (504 8) 584. 9| 2666. 3) 240. 1l 5733. 2| «518. 9. 0506. 21 9x95. 1) 2285. 8] 14
15 | 2627. 3| 2706. 2 2786. 3| 2867. 7| 2950. 5 3034. 7| 3120. 4| 3207. 7! 3296. 6| 3387. 4| 15
16 sor 5 909. 1. 9651 8) 2«30. li 221. 81 6609. d. 3698. DT 1255- DIT 16
17 20.9 08.8| 389.0 70.4| 53.2 37.5 23.2| 10.6) 3299.6| on Aus
18 MATI Sl 2S 71. 8| 54. 6 19353. OF 2c24. 71 112. 113801. 1) 3291 LS
19 OSI 2091 o: ll ue 135 | (02. Gl 2203: DI LO
20 | 2633. 8| 2712. 8| 2793. 0| 2874. 5| 2957. 4| 3041. 7| 3127. 6| 3215. 0| 3304. 1| 3395. 0| 20
21 S5 d weld. 1] 194. 4| 2575. 0) 158.8 2 1229.01 216. 5| 1-05. 6) 0996. 5|. 21
22 SAKI AROE 7l E +60. 2 add. 6| 1230. 5| «917 9. 207 1) ee 98A] 22
23 TEIG SU AGO7. 1), 2278: 6) 3261.6] 8846, 0) val. 9i 2x19. 4| 208 Q. 3399. OF 23
24 39.0| 18. 1| 98.4| 80.0 63.0 47.4| 33.4 20.9| 10.1|3401.1| 24
25 | 2640. 3| 2719. 4 2799. 8| 2881. 4| 2964. 4| 3048. 8| 3134. 8| 3222. 4| 3311. 6| 3402. 7| 25
26 41.6| 20.7| 2801.11 828 65.8 50.3| .36.2 23.8 13.1 04.2) 26
27 49 ON 8022. 1| 4102. 5| 1684. 1j 4067. 2) 1051. 71 0637. 7| 0025. 3| 1014. 6| 2605. 74 27
28 EE 9593. 412103. S| 46585. 5) 1668. G) 053. 1 1039. I] 0626. 8) «016. Mr 07. 9] 28
29 45.6| ..24. 7| |05.2| 86.9 70.0] 54.5 40.60 | 283 17.0 08.8| 29
30 | 2646.9| 2726. 1| 2806. 5| 2888. 2| 2971. 4| 3055. 9| 3142. 0| 3229. 7| 3319. 1| 3410. 3| 30
31 009 ET AN 207. 00 0189: El 2972. 8) 8657.4) 143. 5| e03L.2 0620. Ed 31
32 49. 8| 28 7| -09. 9| —.91. 0| 74.2 58.8 44.9 32.7] 22. H -- 13. 4| 32
33 50. 8| +30. 11 210.6) 1192. 4| «75, 6) $060. 2| 6046. 4| 0-34. 2| 2523. 6| 114.9] 83
34 59 TEES ABIS 09193. 7077. Ol SRL. 6) 1027, 8 6025. 6) 2625. 2] onl6. 5|. 94
35 | 2653.4| 2732. 7 2813. 3. 2895. 1| 2978. 4| 3063. 1| 3149. 3| 3237. 1| 3326. 7| 3418. 0| 35
36 BA E Iu eid Gi 4:90. 5. 4470. 8) «64. 5| 2050. 7| 2038. 6] 2528. 2) v119. 5| 36
37 sss 16. 011607. 0! 2181; 2) 2:65. OF 0652. 2) «040. Ll 929. 7) »121- 1] 97
38 BU. 4 uoa 7 221v 3| 92809. 3) 1:82. Gl 1/67, 3. «053. 0| no41. Gl 1:31. 2) 0:22. 6] 38
39 58. 7| 38.1 18.7. 2900.6| 84.0 68.8 55.1| 43.0| 32.7| 24.2) 39
40 | 2660. 0| 2739. 4| 2820. 0| 2902. 0| 2985. 4| 3070. 2| 3156. 5| 3244. 5| 3334. 2 3425. 7| 40
41 CITUR 2 OT 212503. AV A690. Sl 8171.61 2158, 0] 4:46, OV 0135. 71 824. 2] 41
42. 69. 6| 4211 227) 04.8| 1488. 21 73,01 159.4 - 47.5] 37.2] 128.8] 42
43 63. 9| $343. 4) 24 11 06.1 1-89: 6. . 74.5| 60.9] - 49. 0| | 38. 7) 0030. 9|. 43
44 gar c Sor 5S E07 Si ged1. ©) 1075. 9) 6 62.3) 4:50. 4| 1240. 21 2291. 9|. 44
45 | 2666. 6| 2746. 1| 2826. 8| 2908. 9| 2992. 4| 3077. 3| 3163. 8| 3251. 9| 3341. 8| 3433. 4| 45
46 GIGA os oO 3.059] 1078. 71 E665. 3) 1499.4] [743.31 geod. 0| 40
47 69. 2| 48.7, 29.5| 11.7 95.2| 80.2) 66.7) 549) 448 30.5| 47
48 Z0 BI RESO! 1i E30. 91 118 0] 696.6] 2481. 61 2068. 2b 2056. 4| 646. 3| (538. 0 2
49 ik esi. 4) 9439 2) er 14. 4) 2x98. 01 0083. OF 1069. 6) r<57. 9| 05447, 8 E E
50 | 2673.1| 2752. 7| 2833. 6| 2915. 8 2999. A 3084. 5| 3171. 1| 3259. 3| 3349. 3
51 CA RES 1-255 Ob 5-17. 21 3000, St 1/85. 9| 10072. 9) 0:60. 8| 0:50. 8| 1:42. 7 5l
52 25:8 9955, 4| 1936. 3| 2118.6) 9102. 2) $187. 3) et Dr 5162 41 1:44. 2 E
53 27309 28. 911227. 7.1519. 9| 0:03. 6| 0:88. 8| 7275. 5| 7703. 8| 5:53. 9) 45. 8 53
54 Paal mess il kkk 2790. 2) 2276. 9| 2165. 3| 7759. 4) 1147 3] *
55 | 2679. 7 2759. 4 2840. 4 2922. 7| 3006. 4| 3091. 6, 3178. 4| 3266. 8| 3356. 9 3448. 9| 55
56 Fð Ma Mar tl 2107.81 1493. 1] 0179. | 163. 3) 0193. 4 |450. 4 ep
57 39 49562. 11 943. 11 25.5 0109. 2) 1194. 5| 181 3| 2169. 7| £159. 9| 1,52. 0 57
58 sos 4) E44 53406. Ol 4810. 6 1495. 9 8182. 2
84 2 72.7 63.01 55.1] 59
59 GO) 864 8| 9045. 8| 128. 2| 0212 1| 4197, 4 7 | e
60 | 2686.3 2766. 1| 2847. 2 2929. 6 3013. 5| 3098. 8| 3185. 7| 3274. 2) 3364. 5 3456. 6
Eat | «40% 41? 42° 43° 44° 45° 46° 47° 48° 49° | Let.

1242

TABLE 5
Meridional Parts
Lat. 50° 512 522 53° 549 552 56° 57 582 592 Lat.
0 3456. 6| 3550. 7| 3646. 8| 3745. 2| 3845. 8| 3948. 9| 4054. 6| 4163. 1| 4274. 5| 4389. 2] 0
1 58.2 52.3 48. 5 46. 8 ATSO 50. 6 56. 4 64. 9 76. 4 91.1] 1
2 59. 7 53. 9 50. 1 48.5 49. 2 5214 58. 2 66. 7 78. 3 93.0] 2
3 61. 3 55. 5 Sal. vf 50. 1 50. 9 54. 1 59. 9 68. 6 80. 2 95.0] 3
4 62. 8 57.0 Dans 5178 52. 6 55. 8 612 70. 4 822] 96.9] 4
5 3464. 4| 3558. 6| 3654. 9| 3753. 4| 3854. 3| 3957. 6| 4063. 5| 4172. 2| 4284. 0) 4398. 9] 5
6 65. 9 60. 2 56. 6 554 56.0 59. 3 65. 3 741 85. 8| 4400. 8} 6
if 67. 5 61. 8 58. 2 56. 8 57. 7 61. 1 67. 1 75. 9 87.7 02. 8] 7
8 69. 1 63. 4 59. 8 58. 4 59. 4 62. 8 68. 9 77.8 89. 6 04.71 8
9 70. 6 65. 0 61. 4 60. 1 61. 1 64. 6 70. 7 79. 6 91.5 06. o 9
10 3472. 2| 3566. 6| 3663. 1| 3761. 8| 3862. 8 3966. 3| 4072. 5| 4181. 4| 4293. 4| 4408. 6| 10
11 om 68. 2 64. 7 63. 4 64. 5 68. 1 74. 3 83. 3 95. 3 10. 5| 11
12 OS 69. 8 66. 3 65. 1 66. 2 69. 8 7631 85.1 97. 2 1235192
13 76. 8 lo 8; 67.9 66. 8 67.9 7156 77.8 87. 0, 4299. 1 14. 4| 13
14 78. 4 72.9 69. 6 68. 4 69. 6 URS 79. 6 88. 8| 4301. 0 16. 4| 14
15 3480. 0| 3574. 5| 3671. 2| 3770. 1| 3871. 3| 3975. 1| 4081. 4| 4190. 7, 4302. 9| 4418. 3| 15
16 81. 5 7651 72. 8 71718 73.0 76. 8 83.2 92.5 04. 8 20. 3| 16
im 83.1 vns nf 7415 73. 4 TAT 78. 6 85. 0 94. 3 06. 7 222167.
18 84. 6 79. 3 76. 1 75. 1 76. 4 80. 3 86. 8 96. 2 08. 6 24. 2] 18
19 86. 2 80. 9 i, Tt 76. 8 78.2 82. 1 88. 6 98. 0 10. 5 26. 2] 19
20 3487. 8| 3582. 5| 3679. 4| 3778. 4| 3879. 9| 3983. 8| 4090. 4| 4199. 9| 4312. 4| 4428. 11 20
21 89. 3 84. 1 81. 0 80. 1 81. 6 85. 6 92. 2| 4201. 7 14. 8 30. 1| 21
22 90. 9 85.7 82. 6 81.8 83. 3 87.3 94.0 03. 6 16. 2 32. 0| 22
23 92. 4 87.3 84. 3 83. 4 85.0 89. 1 95. 8 05. 4 18.1 34. 0] 23
24 94. 0 88. 9 85. 9 85.1 86. 7 90. 8 97.6 07. 3 20. 0 35. 9| 24
25 3495. 6| 3590. 5| 3687. 5| 3786. 8| 3888. 4| 3992. 6| 4099. 4| 4209. 1| 4321. 9| 4437. 9| 25
26 97. 1 92. 1 89. 2 88. 5 90. 1 94. 4| 4101. 2 11. 0 23.8 39. 9| 26
27 3498. 7 93. 7 90. 8 90. 1 91. 9 96. 1 03. 0 12. 9 203 41. 8| 27
28 3500. 3 95. 3 92. 4 91. 8 93. 6 97. 9 04. 9 1457 24126 43. 8] 28
29 01.8 96. 9 94. 1 9315 95. 3| 3999. 6 06. 7 16. 6 29. 5 45. 8] 29
30 3503. 4| 3598. 5| 3695. 7| 3795. 2| 3897. 0| 4001. 4| 4108. 5| 4218. 4| 4331. 4| 4447. 7| 30
al 05. 0| 3600. 1 97. 3 96. 8| 3898. 7 03. 2 10. 3 20. 3 OS 49. 7| 31
82 06. 5 01. 7| 3699. 0| 3798. 5| 3900. 5 04. 9 1231 22 35 5171852
33 08. 1 03. 3| 3700. 6| 3800. 2 02. 2 06. 7 1320 24. 0 ey 9. 53. 6] 33
x 09. 7 04. 9 02. 3 01. 9 03. 9 08. 4 11547 25.9 39. 1 55. 6] 34
D 3511. 3| 3606. 5| 3703. 9| 3803. 6| 3905. 6| 4010. 2| 4117. 5| 4227. 7| 4341. 0| 4457. 6| 3
36 12. 8 08. 1 05. 6 05. 2 07.3 1230 19. 3 29. 6 42. 9 59. 6 d
37 14.4 09. 7 07. 2 06. 9 09. 1 18}, o PAE il, 2: 44. 8 61. 5| 37
38 16.0 1138 08. 8 08. 6 10. 8 15.5 23.0 3943 46. 7 63. 5] 38
39 We d 12. 9 105 10.3 1285 irt S 24. 8 DOS 48. 7 65. 5| 39
40 3519. 1| 3614. 6| 3712. 1| 3812. 0| 3914. 2| 4019. 0! 4126. 6| 4237. 0| 4350. 6| 4467. 5| 40
41 20. 7 16. 2 13. 8 Sr eg 16. 0 20. 8 28. 4 38. 9 52. 5 69. 4] 41
42 223 17.8 15. 4 1593 UT ET 22. 6 30. 2 40. 8 54.4 71.4] 42
43 23. 8 19. 4 Van 17. 0 19. 4 24. 4 32. 0 42. 6 56. 3 73. 4| 43
44 2514 200 18. 7 18. 7 215 DONI 33.9 44. 5 58.3 75. 4| 44
45 3527. 0| 3622. 6| 3720. 4| 3820. 4| 3922. 9| 4027. 9| 4135. 7| 4246. 4| 4360. 2| 4477. 3| 45
49 28. 6 2412 22. 0 PPA, “il 24. 6 29. 7 31.5 48. 2 62. 1 79. 3| 46
Í 205 2518 DON 23.8 20989 Bille dj 39. 3 50. 1 64. 0 81. 3| 47
4 2197 27.4 2509 25. 5 28. 1 33702 4181 52. 0 66. 0 83. 3| 48
9 ODE 29. 0 27.0 2142 29. 8 35. 0 43. 0 53. 9 67. 9 85. 3] 49
2 3534. 9 3630. 7| 3728. 6) 3828. 8 3931. 5| 4036. 8| 4144. 8| 4255. 7| 4369. 8 4487. 3| 50
= 3019 3213 30. 3 30. 5 3312 38. 6 46. 6 57. 6 al 89. 8| 51
= 25 33. 9 31. 9 3212 35. 0 40. 3 48. 4 59. 5 o 91. 2] 52
E „6 QOO 33. 6 33. 9 36. 7 42. 1 50. 3 61. 4 75. 6 93. 2] 53
41. 2 Sl 35.2 35. 6| 38.5 43.9 5211 63. 2 77.5 95. 2] 54
2: E 3638. 7| 3736. 9| 3837. 3| 3940. 2 4045. 7| 4153. 9| 4265. 1 4379. 5| 4497. 2] 55
2 k 40. 4 38. 5 39. 0 41. 9 47. 5 55.8 67. 0 81. 4| 4499. 2] 56
= 42. 0 40. 2 40. 7 AT n 49. 2 5746 68. 9 83. 4| 4501. 2] 57
n NAE 43. 6 41. 8 4214 45. 4 51. 0 59. 4 70. 8 85. 3 03. 2| 58
2 "I 4542 4385 44. 1 Atri] 52.8 (1 72. 6 87.2 05. 2] 59
3550. 7| 3646. 8| 3745. 2| 3845. 8 3948. 9| 4054. 6| 4163. 1 4274. 5| 4389. 2 4507. 2 60
Lat. o o go o RAO o o o
50 51 52 53 54 55 56 57 589 59° Lat.

1243

TABLE 5
Meridional Parts
Lat 602 612 622 632 642 65° 66° 67° 68° 69° Lat.
0 4507. 2| 4628. 8 4754. 4| 4884. 2 5018. 5| 5157. 7, 5302. 2| 5452. 5| 5609. 2 5772. 81 0
1 09. 2 30. 9 56. 5 86. 4 20. 7 60. 0 04. 7 Do 11. 9 75.61 1
2 RA 33. 0 58. 7 88. 6 DM 62. 4 07. 1 D 14. 5 78. A 2
3 192 35. 0 60. 8 90. 8 2939 64. 8 09. 6 60. 2 itp 81-21] 73
4 1552 Syd 62. 9 93. 0 27. 6 671 121 62. 8 19. 9 84.01 4
5 4517. 2| 4639. 1| 4765. 0| 4895. 2 5029. 9| 5169. 5| 5314. 5| 5465. 4| 5622. 6| 5786. 8l 5
6 19. 2 41.2 67: 2 97. 4 3422 71. 9 17.0 67. 9 2512 89. o 6
Z 212 43: 3 69. 3| 4899. 6 34. 5 74. 8 19. 4 70. 5 27.9 92. 44 7
8 2352 45. 3 71. 5| 4901. 8 36. 7 76. 6 21. 9 731 30. 6 95.2] 8
9 25. 2 47.4 le 04.0 39.0 79. 0 24. 4 75. 6 33. 3| 5798.0] 9
10 4527. 2| 4649. 5| 4775. 7| 4906. 2 5041. 3| 5181. 4| 5326. 9| 5478. 2| 5636. 0| 5800. 8| 10
11 29. 2 51.6 77. 9 08. 4 43.6 83. 8 29. 3 80. 8 38. 7 03. 6| 11
12 3152 53. 6 80. 0 ST 45. 9 86.1 Sal A7 83. 4 41. 3 06. 4| 12
13 332 55: 7 82. 1 12. 9 48. 2 88.5 34. 3 85.9 44. 0 09. 2| 13
14 35, 2 57. 8 84. 3 151 50. 5 90. 9 36. 8 88. 5 46. 7 12. 0| 14
15 4537. 2| 4659. 9| 4786. 4| 4917. 3| 5052. 8| 5193. 3| 5339. 2| 5491. 1| 5649. 4 5814. 9| 15
16 5978 61. 9 88. 6 19.5 5571 95. URAIN 93. 7 5281 ibs A) 6
17 41.3 64. 0 90. 7 217 57. 4| 5198. 1 44. 2 96. 3 54. 8 20. 5| 17
18 43.3 66. 1 92. 9 24.0 59. 7| 5200. 5 46. 7| 5498. 9 575 23. 3| 18
19 45. 3 68. 2 95. 0 26. 2 62. 0 02. 9 49. 2| 5501. 4 60. 2 26. 1| 19
20 4547. 3| 4670. 2| 4797. 2| 4928. 4| 5064. 3| 5205. 2) 5351. 7| 5504. 0| 5662. 9| 5829. 0| 20
21 49. 3 72-3| 4799-3 30. 6 66. 6 07. 6 54. 1 06. 6 65. 6 31. 8| 21
22 5194 74. 4| 4801. 5 32. 9 68. 9 10. 0 56. 6 09. 2 68. 3 34. 6] 22
23 53. 4 76. 5 03. 6 Sond T 12. 4 59. 1 11. 8 qa 3 375123
24 55. 4 78. 6 05. 8 DES 73. 5 14. 8 61. 6 14. 4 TEE 40. 3| 24
25 4557. 4| 4680. 7| 4807. 9| 4939. 6| 5075. 9| 5217. 2| 5364. 1| 5517. 0| 5676. 5| 5843. 2] 25
26 59. 4 82.8 10. 1 41. 8 7852 19. 6 66. 6 19. 6 79. 2 46. 0| 26
27 61. 5 84. 8 1253 44.0 80. 5 22. 0 69. 1 2p. 81. 9 48. 8] 27
28 63. 5 86.9 14. 4 46. 3 82.8 ER) 71.6 24. 8 84. 6 51. 7| 28
29 05:5 89. 0 16. 6| 48.5 85. 1 26. 8 TATI 27. 4 87. 4 54. 5| 29
30 4567. 5| 4691. 1| 4818. 7| 4950. 7| 5087. 4| 5229. 3| 5376. 6| 5530. 0| 5690. 1| 5857. 4| 30
31 69. 6 93. 2 20. 9 53. 0 89.8 els 7 79.1 32. 7 92. 8 60. 3| 31
32 71. 6 95. 3 Do 55: 2 92. 1 34. 1 81. 6 DONO 95. 5 63. 1| 32
33 73. 6 97.4 25. 2 57.4 94.4 36. 5 84. 1 37. 9| 5698. 3 66. 0| 33
34 75. 7| 4699. 5 2174 59. 7 96. 7 38. 9 86. 7 40. 5| 5701. 0 68. 8| 34
35 4577. 7| A701. 6| 4829. 6| 4961. 9| 5099. 1| 5241. 3| 5389. 2| 5543. 1| 5703. 7| 5871. 7| 35
36 79. 7 03. 7 315 64. 2| 5101. 4 Ai, T 91. 7 Ae, 7 06. 5 74. 6| 36
37 81.8 05. 8 33. 9 66. 4 03357 46. 2 94. 2 48. 4 09. 2 tt VU
38 83. 8 07. 9 2021 68. 7 06. 0 48. 6 96. 7 51. 0 12. 0 80. 3| 38
39 85.8 10. 0 38. 3 70. 9 08. 4 51. 0| 5399. 2 53. 6 14. 7 83. 2] 39
40 4587. 9| 4712. 1| 4840. 4| 4973. 2 5110. 7| 5253. 4| 5401. 8| 5556. 2| 5717. 5| 5886. 0| 40
41 89. 9 1472 42. 6 IDA 130 55: 8 04. 3 58. 9 20. 2 88. 9| 41
42 91. 9 1613 44, 8 Ta 15. 4 58. 3 06. 8 61.5 22. 9 91. 8] 42
43 94.0 18. 4 47.0 79. 9 67207 60. 7 09. 3 64. 1 D 94. 7| 43
44 96. 0 20. 5 49. 1 82. 2 20. 1 63. 1 11. 9 66. 8 28. 5| 5897. 6| 44
45 4598. 1| 4722. 6| 4851. 3. 4984. 4| 5122. 4| 5265. 6| 5414. 4| 5569. 4| 5731. 2 5900. 4 45
46 4600. 1 24. 7 53.5 86. 7 DANT. 68. 0 16. 9 7/22. il 34. 0 03. 3] 46
47 02. 2 26. 8 55. 7 89. 0 2771 70. 4 19. 5 y v 36. 7 06. 2 ae
48 04. 2 29. 0 57.9 91. 2 29. 4 72. 9 22.0 Tð 39. 5 09. 1 5
49 06. 3 oT 60. 0 93. 5 31. 8 OO 2475 80. 0 42. 3 as S Ki
$ ` 2| 4862. 2| 4995. 8| 5134. 1| 5277. 7| 5427. 1| 5582. 6| 5745. 0| 5914.
A P RS E SC 4998. 0 36. 5 80. 2 29. 6 85. 3 47. 8 17. 8 EE
52 1254 37. 4 66. 6| 5000. 3 38. 8 82. 6 oo 87. 9 50. 6 20. 7 ES
53 14. 4 39.5 68. 8 02.6 4172 85. 1 94 7 90. 6 DON 23. 6 B
54 16. 5 4197 gts 04. 8 43. 5 87. 5 Bil, 2 93. 2 56.1 o =
55 | 4618. 6| 4743. 8| 4873. 2| 5007. 1| 5145. 9| 5290. 0| 5439. 8| 5595. 9| 5758. 9 !
56 20. 6 45. 9 15. 4 09. 4 48. 2 92. 4 42. 3| 5598. 5 61. 7 32. 3| 56
5) 2207 48. 0 77.6 1717-6 50. 6 94. 9 44. 9. 5601. 2 64. 4 aM. 6j of
58 DIR 50.1 79. 8 13. 9 53. 0 97.3 47.4 03. 9 67. 2 38. 2
59 26. 8 5213 82. 0 16. 2 55. 3| 5299. 8 50. 0 06. 5 70. 0 41. 1 Go
60 4698. 8| 4754. 4| 4884. 2| 5018. 5| 5157. 7| 5302. 2| 5452. 5| 5609. 2 5772. 8 5944. 0
Lat. 60° 61° 62° 63° 64° 65° 66° 67° 68° | 69° Lat.
| | | | : dl

1244

TABLE 5

Meridional Parts

Lat.

cnn mens S

NOU U WIWN NE e| C C C cO cO: cO 00 00 WOO! 00 OO Y A A A --1 Y AY AI) Y Y OO O O0! O0 O0 cO CO Ol cO O OH lA NNHWWIhAAMDAIIMWDOS

a DDO 00 C — ONO O -I Gti Q2 O NORD OO NG DO O 010 B2] OO NO GOOD O OO - 10» GU 0 NH O Oc 00-1-1

RJ O29 En &l-1 03:0 U -1 05 O O» tài OO 00 | GO -1 PON $5 C -105 OI NA RI | — 00 Gt b3 CO | OO 4» I 00 GUI DO O Na kalen E CODI O» I I OAT

WN Gao DI DO O RO GR OD WI ON Co al OA cO G2 00| G2 - T t2 NIN NO A Ol A O) ON ND - 102 OO WOR cO OU O O 1031004 OOH

QOO DNA OS NTO DN 4| GOOD EE! O» 00 OD B2 H1 O» £O S MO O31 00 O WG OT OO | i Q3 DNA JO 99 OO N Ot O0 Al Ot OO i Ha 00| COO BOO CO R20» O V
Ka GO DO 00Í -1 DOP 4| O2 9 HH C cO «O 00 00 DW! AA O» O! O OQ» D O O! O C» k 1l - 100 O0 cO cO! DOD D! Q2 4 CO O» O) NIO ODO! CO O1 -100

OO Ot 0002|x« ^ Ov NW O ON O al NI O IH O JE Hi] 00 VU BO O Ol Q3 — 00 GU] O O GTG | 00 O» PND C OO NO - 101 Q2 291 CO cO - 10» SP

O0 C to4 CO: 00| OM OTRO! G2 O1 Ral -1 CO VW GO 2 GT cO DO O3 cO Q2 DO H« | O0 NO OO DO A gal cO H» CO GO O0! Y Y IN UN] = NS IN O6! Q2 00 Ha CO Qu

1245

TABLE 5
Meridional Parts

Lat. 80° 81° 82° 83° 84° 85° 86° 87° 88° 89° Lat.
0 8352. 2 8716. 0| 9122. 4| 9582. 7/10113. 7/10741. 4111509. 3112498. 8|13893. 1116276. 2] 0
1 58. 0 22. 4 29. 6 90. 9} 123. 3) 752.9) 523.6) 518, 0 921.9 334.0] 1
2 63. 8 28. 8 36. 8| 9599. 1] 132.9) 764.4) 538.0) 537.2 950.9 392.8] 2
3 69. 5 35. 3 44. 0| 9607. A 142.5) 776.0) 552.5) 556. 613980. 2 452. 6] 3
4 75. 3 41.7 51. 2 15. 6| 152.2 787.6) 567.1) 576. 1114009. 2 513.4] 4
5 8381. 1| 8748. 1| 9158. 5 9623. 910161. 9/10799. 2111581. 7112595. 7|14039. 5116575. 4] 5
6 86. 9 54. 6 65. 7 32. 3| 171.6) 810.9) 596.4) 615.4) 069.5) 638.5] 6
7 92. 8 61. 1 73. 0 40.6, 18173 2822. 6) 61151 = 635. 21099. Si 702.71 77
8 8398. 6 67. 5 80. 3 48.9| 191.1| 834.4) 625.9| 655.2 130.3] 768.2] 8
9 8404. 4 74. 0 87. 6 57.3| 200.9| 846. 2| 640. 7| 675.2 161.2 835.0] 9

10 8410. 3| 8780. 5| 9195. 0| 9665. 7|10210. 7|10858. 1111655. 7112695. 414192. 3116903. O] 10

11 16. 1 87. 1| 9202. 3 14. 112 220: 6] 870. 0) | 670; 7 715.7] 2234169725 11

12 22. 0| 8793. 6 09. 7 82.6| 230. 4| 881.9| 685.7| 736. 1| 255. 4/17043. 4| 12

13 27. 9| 8800. 1 1740 91.0) 240. 3| 893.9| 700.8| 756.6) 287.4 115. 8| 13

14 33. 8 06. 7 24. 4, 9699. 5| 250.3 905.9 716.0} 777.3) 319. 7| 189. 7] 14

15 8439. 7| 8813. 2) 9231. 8| 9708. 0/10260. 2110917. 9/11731. 3|12798. 114352. 217265. 3] 15

16 45.6 19. 8 39. 3 16. 5) 270.2 930.0) 746.6) 819.0) 385.2 342.5] 16
17 61.5 26. 4 46. 7 25. 0} 280.3 942.2 762.0) 840.0; 418.4 421.5] 17
18 57.4 33. 0 54. 2 33. 6| 290.3, 954.3 777.5| 861. 2| 451.9, 502. 4] 18
19 63. 4 39. 6 61.6 42.2 300. 4 966.6} 793.0) 882.5} 485.8| 585.3| 19

20 8469. 3 8846. 3| 9269. 1| 9750. 8|10310. 5|10978. 8|11808. 6 12903. 914520. 0|17670. 2] 20

21 75. 3 52.9 76. 6 59. 4| 320. 7|10991. 2) 824.3) 925.4) 554.6) 757. 2] 21

22 81.3 59. 6 84. 1 68. 0| 330. 8|11003. 5| 840.0) 947. 1| 589. 5} 846. 5] 22

23 87. 2 66. 2 91.7 76. 7| 341.0) 015.9) 855.8 969.0) 624. 7/17938. 2| 23

24 93. 2 72. 9| 9299. 2 85. A 351.3 028.4 871.7112990.9 660. 418032. 4| 24

25 8499. 2| 8879. 6| 9306. 8 9794. 1110361. 5111040. 811887. 7113013. 1114696. 4|18129. 2] 25

26 8505. 2 86. 3 14. 4| 9802. 8] 371.8} 053.4 903.7| 035.3| 732.7 228. 9] 26

27 11.3 93.0 22.0 11. 6] 382. 1| 066. 0| 919. 8| 057. 7| 769.5 331. 5| 27

28 17.3 8899. 8 29.6 20. A 392.5 078.6 936.0) 080.3 806.7 437.3] 28

29 23. 3| 8906. 5 37. 2 29. 22 402.9 091.3) 952.3 103. 0| 844.3) 546.4] 29

30 8529. 4 8913. 3 9344. 9| 9838. 0/10413. 3111104. 0111968. 613125. 8 14882. 2118659. 2| 30

31 35. 4 20.0 52. 6 46. 8| 423.7| 116. 8111985. 0) 148.8 920. 7| 775. 7 31

32 41.5 26. 8 60. 2 55. 7| 434. 2| 129. 612001. 5| 172. 0| 959. 5118896. 3] 32

33 47. 6 33. 6 67. 9 64.6| 444.7, 142.4| 018.1 195. 3/14998. 819021. 4| 33

34 53. 7 40. 4 75.7 73. 5| 455.3| 155.3| 034.8| 218 8/15038. o 151.1| 34

35 8559. 8| 8947. 2 9383. A 9882. 4110465. 911168. 3|12051. 5|18242. 4115078. 8|19285. 9| 35

36 65.9 54. 1 91. 2| 9891. 4| 476.5| 181.3| 068.3| 266.2) 119.5) 426.3] 36

37 72.0 60. o 9398. o 9900. 4| 487. 1| 194. A 085.2 290.2 160.6) 572. 6] 37

38 78. 2 67. 8| 9406. 7 09. 4| 497.8 207.5| 102.2 314.3 202.3) 7295.4] 38

39 84. 3 74.7 14.5 18. 4 508. 5| 220.6| 119. 3| 338.6] 244. 5119885. 3] 39

40 8590. 5| 8981. 6| 9422. 3| 9927. 5110519. 2111233. 9|12136. 4|13363. 1115287. 2/20053. 1| 40

41 8596. 7 88.5 30. 2 36.6| 530.0| 247.1| 153.7| 387.7 330.4) 229. 4] 41

42 8602. 8| 8995. 4 38. 0 45.71 540.8 260.4) 171.0) 412.5] 374.2 415.3] 42

43 09. 0} 9002. 3 45. 9 54.8| 551.7| 273.8 188.4| 437.6| 418.6| 611.8] 43

44 15. 2 09. 3 53. 8 63.9 562.5 287.2 205.9) 462.7} 463. 5|20820. 2] 44

4 621. 5| 9016. 2 9461. 7| 9973. 1110573. 4111300. 7/12223. 513488. 1115509. 1 21042. 0| 45

48 : 2137 23. 2 69. 7 80 371584. 4) S314) 2) 19419 21 51387) 555./2MM-279..2| 46

47 33. 9 30. 2 77. 6| 9991. 5| 595. A 327.8, 259. 0| 539. 4| 602.0) 534.0] 47

48 40. 2 37. 2 85. 6110000. 8| 606. A 341.4| 276.8] 565.4 649. 4/21809. 2] 48

49 46. 4 44 2 9493. 6| 010.0. 617.4 355.1) 294. 8| 591.5) 697. 5/22108 3| 49
0 652. 7| 9051. 3| 9501. 610019. 3110628. 5111368. 8,112312. 9,113617. 9,157406. 3 22435. 9| 50

51 i 29; 0 58. 3 09.6 028.7| 039.6 382.6 331.0| 644.5) 795. 722798.1 51

52 65. 3 65. 4 17. 6| 038.0; 650.8 396.4| 349.3 71.2 845.9 23203. 1| 52

53 TAS) 72. 4 25. 7. 047.4| 662.0} 410.3| 367. 6| 698.2 896. 923662. 1 53

54 bile 79.5 33.8| 056.8 673.2 424.3 386.0| 725. 415948. 6/24192 0| 54

4. 2| 9086. 6| 9541. 910066. 2|10684. 5|11438. 3|12404. 6 13752. 8|16001. 1124818. 8| 55

56 n 6 9093 7 50.01 075. 6| 695.8 452.4 423.2 780.4) 054. 425585 9| 56

57 8696. 9| 9100. 9 58. 11 085. U 707.1) 466.5) 442.0 808.2) 108.5 26574. 9| 57

58 8703. 3 08. 0 66.31 094.6| 718.5| 480.7, 460. 8| 836.3| 163.5 27968. 9| 58

59 09. 6 15. 2 74.5 104.1| 729.9 494.9 479.8 864.6 219.4 30351. 9| 59

60 8716. 0| 9122. 4 9582. 7110113. 710741. 411509. 3112498. 8,113893. 1116276. 2; — 60

pq FF sd ast | 86° | 7” [88% | 89" | Lot

E S qq

1246

VOIDOR|ADNDNAO H

Nautical
miles

59.

59.

59.

60.

Statute
miles

68.

68.

68.

68.
69.

69.

703
704

Degree of latitude

Feet

362 753

362

363 412
461
514
566
622

363 675

363 970
364 029
091
154
216
364 281
344
409
472
537
364 603

Meters

110 567

110 938
956
975
994

111 013

111 033
052
072
091
111

111 131

TABLE 6
Length of a Degree of Latitude and Longitude

Nautical

Degree

Statute
miles

of longitude

Feet

280 171
276 040
271 827
267 530
263 150
258 691

Meters

a, Y

1247

TABLE 6
Length of a Degree of Latitude and Longitude

Degree of latitude Degree of longitude

Nautical Statute Feet Meters Nautical Statute Feet Meters

111 131

ern pg | PNODS
SONSRAD IDO

1248

TABLE 7

Distance of an Object by Two Bearings

Difference Difference between the course and first bearing
between
the course
and second 390

bearing i

CPI EB IE BEEÍPEJE N.N OD)
TN
—

A AS IS IS TS IS II IS IIS IO EE E

IT AO SO SS IS SS IO nn os]

SS SS SS SS SS SDS SS SS SS SS a id)

Ss
So

D
ile
1
1.
IL
lie
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0. €
0. :
0. €
0. :
0.
Om
0. :
0. <
H
0. <
0.
0. :
0. 3:
O...
0. <
0.
0.
0.
0. :
0. :
0. <
Oe
0. í
0. :
0. :
0. €
0. :
Jr:
0. í
UE
0. :
0.
0.
0. Z
0.

SS SS TS SS SES TS IT IT S0 PSP IA IS

Do oo po oo ooo ooo nos DD D D eee deg Lg
ur
O)
"SS SAS oo osm on S EE EE E EE E E E SS EE E EE E E E SS ii EN
Ww) Wwe on
NN

SS IS SS IS SS TS IAS AS ii
SS SS IS IS IS A II IAS ITA TS rr NN

ooooooooooolocoooooooocooooooooooocooooococococ|occoclhoecsccbosoeocooecerscr-
eene SS IS IS IS IO O TS IS AS o E

SSSSSSSSSSS SS ii il id ir ii Kand a TECH

SS TS TITS IS TS SS IIS IIS 555555
c Ct
R

s a id aa
e

oocooco

€ MM M |

1249

TABLE 7
Distance of an Object by Two Bearings

Difference
between
the course
and second;
bearing

Difference between the course and first bearing

34° 36° 38° 40° 42° 44° 46°

o

3. 2. 24

9» 1. 93] 3. 39| 2. 43

2. 31| 1. 72] 2. 83| 2. 10| 3. 55| 2. 63

F 1. 55] 2. 43| 1. 86) 2. 96| 2.2713 70| 2. 84

Kd 1. 43] 2. 13] 1. 68| 2. 54| 2. 01) 3.09 2 3. 85. 3. 04

il. 1. 32] 1. 90] 1. 54] 2. 23) 1. 81] 2. 66 2 5922282 4. 00| 3. 24

1.49| 1. 24| 1. 72. 1. 42] 1. 99] 1. 65| 2. 33| 1 A dt 2 3.34) 27 72174214] 3045
1 1.171 1.57) 1.33) 1.80) 1. 53] 2.08| 1 2. 43] 2 2. 87| 2. 44] 3. 46] 2.93
T 1. 10] 1. 45! 1.25) 1. 64 1. 42] 1.88| 1 A AR A Dy 57
1. 15051 1534) 1181 151 1. 341 L 724 1.96 1 2. 25| 1. 98) 2. 61} 2. 30
i 1. 01] 1.25 1. 13| 1. 40] 1. 26| 1. 58| 1 il zoļ dl 2. 03| 1. 83| 2. 33| 2. 09
jÁ 0. 96] 1.18 1. 07] 1.31! 1. 20] 1. 47) 1 1.65 1 1.85 1. 69] 2. 10| 1. 92
1. MAR EE La CAE 3744 1953 d MISS AO ih, WS
0. 0. 891 1. 05) 0. 99} 1.16 1. 09| 1.29 1 AS 1. 58| 1. 49] 1.77 1. 66
0. 0. 861 1.00. 0. 95} 1. 10| 1. 05| 1. 21) 1 Lal 1 1. 48| 1. 41] 1. 64] 1. 56
0. 0. 84] 0.95 0. 92) 1.05 1. O1f 1.15! 1 1.26 1 1. 39] 1. 34] 1. 53] 1. 47
0. 0. 811 0.91! 0. 891 1.00 0. 97] 1.09! 1 1. 20] 1 Tema A O
0. 0. 79] 0.88 0. 86] 0. 96| 0.94] 1.04 1 M ee dh i, DA) 19221159056 1, 63
0. 0. 771 0.85 0. 831 0.92 0. 911 1. 00) 0 1. 09) 1 RT A
0. 0. 75] 0.82 0. 811 0. 89| 0. 88] 0. 96 0 1. 04| 1 TRE 1, Set 2l
0. 0. 73] 0. 79| 0. 79] 0. 86} 0. 85] 0. 93, 0 1.00 0 1. 08| 1. 07] 1. 17| 1.16
0. 71| 0. 71] 0. 77| 0. 77| 0. 83| 0. 83| 0. 89} 0 0. 96) 0 Th OA) 04 Ty, 1
0. 0. 69] 0. 75| 0. 75] 0. 80) 0. 80| 0. 86 0 0. 93) 0 1. 00| 1. OO} 1. 08] 1. 07
0. 0. 671 0. 73! 0. 73] 0. 78] 0. 78] 0. 84| 0 0. 90! 0. 0. 97| 0. 971 1. 04| 1. 04
0. 0. 66] 0.71! 0. 71] 0.76 0. 76] 0. 82| 0 0.87 0 0. 93| 0. 93] 1. 00} 1. 00
0. 0. 64] 0. 69! 0. 69] 0. 74| 0. 74] 0. 79 0 0.85 0 0. 91| 0. 90] 0. 97 0. 97
0. 0. 63] 0. 68! 0. 67] 0. 73| 0. 72] 0. 78) 0 0.83 0 0. 88| 0. 88) 0. 94 0. 93
0. 0. 62] 0. 67| 0. 66] 0. 71| 0. 70] 0. 76, 0 0.811 0 0. 86| 0. 851 0. 91 0. 90
0. 0. 601 0. 65! 0. 64] 0.70 0. 69] 0. 74| 0 0.79 0 0. 84| 0. 83] 0. 89| 0. 88
0. 0. 59] 0. 64 0. 63] 0. 68| 0. 67] 0. 73| 0 0.771 0 0. 82| 0. 80] 0.87! 0.85
0. 0. 58| 0. 63] 0. 61] 0. 67 0. 65] 0. 72| 0 0.76 0 0. 80| 0. 78} 0.85 0.82
0. 0. 57| 0. 63| 0. 60] 0. 66) 0. 64] 0. 70) O 0. 74| 0 0. 79| 0. 76] 0. 83| 0.80
0. 0. 55| 0. 62| 0. 59} 0. 66| 0. 62] 0. 69| 0 0.73 0 0. 77| 0. 74| 0. 81| 0. 77
0. 0. 54] 0.61! 0. 57] 0. 65| O. 61] 0. 68] 0 0.721 0 0. 76| 0. 71| 0. 80} 0. 75
0. 0. 53| 0. 61| 0. 56] 0. 64) 0. 59] 0. 68| 0 0. 71) 0 0. 75! 0. 694 0. 79| 0. 73
0. 57| 0. 52] 0. 60) 0. 55} 0. 63| 0. 58] 0. 67| 0 0. 70) 0 0. 74| 0. 68] 0. 78| 0. 71
0. 0. 511 0.60! 0. 54] 0. 63) 0. 57] 0. 66| 0 0. 70) 0 0. 73| 0. 66] 0. 77| 0. 69
0. 0. 50] 0.59! 0. 52] 0. 63 0. 55] 0. 66| 0 0.69 0 0. 72| 0. 64] 0. 76| 0. 67
0. 0. 49] 0.59 0. 511 0.62 0. 54] 0. 65| 0 0. 68| 0 0. 72| 0. 62) 0. 75| 0.65
0. 0. 471 0.59! 0. 50] 0. 62| 0. 53] 0. 65) 0 0.68 0 0. 71! 0. 60] 0. 74 0. 63
0. 0. 46] 0.59| 0. 49] 0. 62| 0. 51] 0. 65) 0 0. 68| 0 0. 71| 0. 58] 0. 74 0. 61
Q. 0. 45| 0. 59 0. 48] 0. 62 0. 50] 0. 64 0 0. 67| 0 0.70 0. 57| 0. 73| 0. 59
0. 0. 44] 0.59 0. 46] 0.62 0. 49] 0. 64| 0 0.67 0 0. 70| 0. 55] 0. 73| 0. 57
0. 0. 43] 0. 0. 0 0 0 0 0 0 0 0. 0. 72| 0. 55
0. 0. 0. 0. 0 0 0. 64] 0 0 0 0 0. 0. 72| 0. 54
0. 0. 0. 0. 0 0 0.64 0 0 0 0 0. O72) O52
0. 0. 0. 0. 411 0 0 0 0 0 0 0 0. 0.72 0. 50
0. 0. 0. 0. 0 0 0 0 0 0 0 0. 47] 0.72 0.48 _
0. 0. 37] 0. 0. 0.63 0 0 0 0 0 0 0. 0. 72| 0. 46
0. 0. 0. 0. 381 0. 63) 0 0 0 0 0 0 0. 43] 0. 72) 0. 45
0. 0. 35} 0. 0. 36] 0 0 0 0 0 0 0 0. 41] 0. 73] 0. 43
0. 0. 0. 0. 351 0 0 0.67 0 0 0 0 0. 0. 73| 0. 41
0. 0. 0.63 0.341 0 0 0 0 0 0 0. 72, 0. 38] 0. 74) 0. 39
0. 0. 0. 0. 32] 0 0 0 0 0 0 0 0. 36] 0. 74| 0. 37
0. 0. 0. 0.311 0 0 0 0 0 0 0 0. 34] 0. 75) 0.3
0. 0. 0. 67) 0. 0 0 0.70 0 0 0 0 0. 0. 76) 0. :
0. 0. 0. 0. 0 0 0 0 0. 73] 0 0 0. 30] 0. 77| 0. :
0. 0. 0. 0. 0 0 0. 73| 0 0 0 0 0. 0. 78| 0. 2
0. 0. 0. 0. 0.73 0 0 0 0 0 0. 77| 0. 26} 0. 79| 0.

TABLE 7

Difference between the course and first bearing

Distance of an Object by Two Bearings

Difference
between

1250

DO H10 seh len e Cl E + mn HR OS mame — (tO Q1 0 TO em CO p- + 0016 C3 O |E- T CO MN 7010 C0 D
DOH om Āā O00 |F- toa HN (MANA GOD ADO 00 ORD [In S O (010 16 10 10 TH HH HOD 009 CO 00
> fl géi ei ei da O m SR AAA SSA SAN SSI
e i!
OS Ek 00 OC eo MMO «c» MAO — i O31 CO E- (MO FAO OV 190 |A HO C: O>|00 E E E ¡Io E >= [> 00
Ooo H Oi Sm GO OM HHIMANNA r | et C OO OC Cc C 0 S» C: 00 00 |00 00 00 00 00 |00 00 00 00 00 00
Rees esse Ciara ooo cjos co ESE
SSS SS SSR SS SAT T SSS O SS TT TO SM O ODA STS |GI CO E- 1G Cl C2
16 060 DO ON N C E mom N O |O 9: 6: 6: 00/00 ORR (O S O O19 10 10 10 H HH HOD OD 09 09
o BØRN ARNAR al ii ooo ooo C Ce des ee 66660 i occ
00
10 00 100 00 - 00 (00M — C^ ODA KO QV EA K 00 16 C C 00 KO 16 c0 O CO E O/O 19 106 19 19 19 19 10 OOO
DIO MON HINO 6G: 00 r- (Dio «t Ee 69 |Q Q1 A HAHA O O O O ja 6: CO C: |00 00 00 00 00 |00 00 00 00 00 |00 00 00 00 00 00
MN AA Ee cirvi m ooo co o SEARS ooo coosoo
Lo — À—H————————————————————————————————————————————————————————OÓÀMM € E we" — á— Je
KO m IN CO OO 169 CO ml DIO cO | O0 m «f OOD |O0 CD 00 «f CO [ODM DINO TOO Hr 00 CO | «t 0 OO NOD TAS
MOP | CQ 00 NOR dS EH Q1 QY | — OQ QC CO la a 00 00 00 |00 Pe r- OO OO 1919 1910 HHH HD 09 09 00 CN
o Sils a id Ad iii e O A E SS SS SSA SSA SSI
10 BD SON SI FOI- OOO AiO HID NADIINOWO HH OO 00 r- |O 19.10 «f «t JOD C9 co 09 C0 ON H RSS
Ge dod ta DA 409 0 — ŠO O ŠO C o 0o: C G> 00 00 |00 00 00 co oO |00 00 00 OO OO |00 00 GO OO 00 o0
SS RRA vi ec bel wc wl wl wl AS A SSA SS Sei)
——————MÀÓÓÓ——ÓÓ—MM—
C» 169 C9 KO C» De C9 129 |C m 74 CN 169 O O GS ON DININ OO ON C» Pt OO mor Bb [Od O 00 10 09 | 00 cO E O)
Mio nA pu OQ D o: 00 r- OM - (c9 c9 C1 R ŠO OO a 00 00 00 DP | i DDD O19 1919 19 1D HH SHH O9 09 09 09 CN
cost ee] oce eure Ier n etes EE rer te car ec) Ue Teen e d. Oe OO OR CI O Ve Ze ie Zon e IE) EUER
EM 4c Ee lëd Cl Cl El M ed pl O OO Oo O EE O OO O O O E oD Oo 0 oo ooo oo oo E E
Ko DO I E E ODIDAANMDIDAODOINADOMO|WDIMANDIORONDHINNAAD AAA N NA GC +H
€Ó 00 co |0 0m GOD 010 à [co AN | CO 0 G O |o: 6: 6: 6» 6: |00 00 00 00 00 |00 00 00 00 00 |00 00 OO OO GO |00 OO 00 00 00 00
HO có Ci el cd Ni dr A E e e e e AAA SSA SS Seco
A S E E
T 74 OO 10 |O C» N OO O MO OOO HOO OD NOAA HO |E- HAD OOM C» HN C» E 10 M | OO H AN jO 0010 C9 — 00
C «Od O O 00 r- (15 - «c» NANO |O O 9: 6: DOD 00 o0 00 PS e OO O (O 19 19 19 19 JO SH SH SH rt ISP OD 09 OD 00 QU]
EN SNAR elle el vi RS ASAS SAA SSA Sc Seco
1 TOOOSO10O0O FO JW O FO MO MO «Xo co CO r- 15 |co 0 00 «o iio - cO Cl elen Ei Ei Clees E OS DONAS
10 E- N 00 (10 mM DO 00 (010 HH MN OI m ŠO OG o: 0/0 c: 00 00 00 |00 00 00 O 00 [00 O 00 00 DP |P D b- E E [00 00 00 O 00 00
HS MAAN vi cl Iecl vd el cl elle el cl el HHH e ele e e e ele ee e ele ee e le e ee lee ee e GE
bag EE EE FF NE Sera
NANO FOO m CO |^ € OO mo HO ONIDDIND DN ODN CÓ OO HON O E- 10 CQ ele 10 MN 4 |O? E- 100 C C2 O
OO CX 00 1£2 € | A O» 00 r- cO [i2 Hom C | — + O O 0 en 6: 00 00 |00 00 PD [ROO cO O | cO 1919 102 10 (ti ti ti RB rt (00 09 00 CO C9 N
> pe NN vi el HH rr ASA SAS SA SST SSA Scielo
10 1-4 OOM 00 00 | - «t 0010 MIMI RO HO HO (o 6o |O rF- 15 Q1 OO Ro - co NO A 00/00 Pb ii Eh [00 00 C: O A
OO er OO r$ RN Q1, ŠO (OG 6: 6 6: 6:00 00 00 00 00|00 00 00 Pe Pe |> H= Ð Po IÐ tt b |> = E 00 00 00
sdiededa CIE rr rr iocosoaocaooso oooca(oeococooj(oaoooca ooooco
—————— TF oe
MNSANO [O HN «109 [00 C1 DO Ol OD OD «o (Mor m Glen E ANO |00 DN O PO TNAO (00 «D «tf CY C [00 TONO
ONS «Cd O O DN (OMON C3 MO OG ele C: 00 00 00 DDD PD (O co cO O 10 [19 19 19 AM 1D | HH HH HOD OD 69 C9 C0 CH
2, ele ei Cl el eil wl cl vc rd le ec el vi elle ri wl e ele ei e e ele e e e ele ei ee elei Ge e ele ee ele ee EC E
H GÉIE F- C be |00 c0 C 00 el Ee co — (o | E CO CO E | A C C 00 ST m OO OP O19 1919 + HHT WOO OMR IDO
| RIO SR FOOD HHOAN S ŠēS ŠSSO0A 06 00 00 G6 Fe |F- Ec Ec Ec Po [po Po Ee Po Pe [E Fe ES ES E E
HIS ei Cl Cl Cl el el BdBÓddHBAdddloocoooooooooococooococcoooooooooocococoo
ER
Rc
5308
Set OA - «500 | c - ooo = 2
Sas CX «à cO 00 |O CX «t «o 00 ON HDI ON OO ON TOO ON - «o 00 O a + CX +H WO
es ASS 50 60 0b 66 88388 88588 88188 RRĀRA BS cO 69 GO SS dS S BS 8
aq m gel mje e e a AHA
c

1251

TABLE 7

Distance of an Object by Two Bearings

| |
L- (D | C3 co C3 «o i DOI -H [09 09 HOW HOND IAL C300 - | 16 C3 OMON
10 D/O 19 H 00 15 OOP Dio «06 AO ODS 00 G0 PP NÓ 01010 1 H H RON
eS iG HS ee Cl Cl | Ho ei ei e ei le ei e e ele ei ele e e
5 O r-|c C4 M oo A soļo O OO DM OTRO OO OMA OO ODO NO
10 (O |010 A 0010 [M9 NO D O | DIO MOMO NAN NAH N O 0 0G 50 008000 e
19 lei GO po NN Gi El | rr am am EC
FT seg A NES I FT SSO OI TOO TO TO ONIOOTO AO TO SA OT TS SG SSC
10 (O Od] SH e. 0010 | C 00 r- OND PO N NN N O 6 000 00 00 DD (O co O10 19 |1 H HOD OD
a iG c6 [eo c6 Cl Cd Cd ci el HH HH oo le e ei ei ei le ei e e ele ee e Ce
= HN RDA ei Es DIANA o TO IESO qo c Eë zb Gäeren oor E O
| 10 O Od] SH HH 0019 9 | enen 00 E- [01010 HN [eo Cu CL Ca AA ŠO 0 0 005 000000

72°
5
4
3
3
3
2
2
2.
2.
2.
1
il
1
1
1
1
1
1
1
1
1
1
0
0.
0
0
0
0
0
0
0.
0
0
0
0.
0.
0
0
0
0

mM «f 00 SHS [Pe 10 C0 O |00 p- O19 HOD C NO O OG O 00 [00 D be O (O cO 19 1910 (ti i HOD OD OD

68°

N
N
19 -|
= CO OD O O m |0 00 AE 10 [165 cO 00 7-4 HID 09 CA 7 [0010 NDE (110 MO C |P O O19 HI HM C0 09 c9 an
| 1
[=]

Difference between the course and first bearing

6°
5
4
3
3
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0. 9:
0
0
0
0.
0.
0.
0.
0
0.
0
0
0
0
0
0
0
0
0
0.

6
6
9
8
1
6
7
4
5
8
5
3
2
3
5
8
2
7
2
7
3
9

6
3
0
8
5
3

C3 C OQ» b- Oo i «f c9 c9 CL |C ANA m e + =

eh [NM NA ee oo oo oo oo

642
8
2
2
6
1
3
0
1
5
1
0
0
1
3
6
0
4
$
5
1
7
4
1
8
6
4
2
0
8
7
6
5
4

622

Difference
between
the course
and second
bearing
72
74
76
78
80
82
84
86
88

tO OOD O19
LD LD ti «ti OD OD

MO 10 | e onm A e MO ht Lei ORO NIDO en billen HON D vil eo e DO Po vn E IA AE ID EE OI Let ON —
OOO HOR ANO ODIS FMA A OSA GO r- O O 191010 HH GO 00 |Os € 00 | Oo PN GO ROB (D OVIN H H
iG 4 c9 c8 | Ci o ooo ooo ooo o KEES
e
CAM Gäile AR 40 Glen enen OS O [Cu io OF OS | GE HH ANN o] O lt MAR 00 EH E- CO C COA sbb C300 HA
r- 00 — «5 |C1 &: co -P Y | C o0 r- F- DO HAN [e O NAA OO HNO Os HO r.c o OE E O1 [oco co
iG ix o8 N OU Ed Ed IGI Cl vc m el | pel pl cl Hm ARAR le pel pl pel pel m BIH pri éi eo Cl Je CN e i pl les el pel pc ir
ROTO OND 001010 OO 1 OO 00 OO oo TO IN € O» 16 DO OO FOOT C HOM «P eC) e C SP QOO» C9 E Or
ORO «f O |t- - C O 00 NO - 05 Q1 | — GO 6» G5 [00 r- D O (O 1915 HHH DO | «8 O»16 C1 C OO maļ C 6» 00 F- O tO io io H +H
x vs 66 ANNAN A lei ri ra oo oococcoco (oo ocooccoļo TOO N NNN ooo ooo oo)
o e :
e Sei CO Gë 4| E së ole OO C KB Oo: P010 GR ta S HA ROA AR ODIN IN tOO si IO ei e E Cl E
r- SS SS ĒOR A o] — 1D Oo f e 0010 [09 = O e: 00 D «e 1616 «8109 c9 N C3 G3 5
10 B P O CO |CL ANNAN rr iG M c8 c9 08 Cl CL [GL Cd El ri m pl el
C [eo SA ao 00 00 SO TOMO IIA NO DO Co C» X [i toic OC OT or O Šo [E 0 KO CO 160 CO
BÍDOYANMANOOGON 00 000 00 r- r- O «o 1019 ++ xf co ai O DN 0 RI mu Šo DO 00 r- COMM ss
iG din cocococlcocccocas vs ei lech el Rr ARAR ASS
Re) RH OWN — c: 00 co i SERAN] RAS DD ARNO
N ANNA IN =DOOO 19 O O NODO AANNANA
iG e Ir 1G H + a ld Se] Heel A | |
————— Aa o aaron il AAA ln nos Bum o Mr m n m lili Å
tz [ DAD «f CO [i E OOD NO od OD] = IO 1D OD Cd r4 z SOTO TA
RE F- p- CO cO cÓ ho 16 + HN oO ANDO dE BCEE
iG H Seele 15 H 09 ec C rr le E EE Elle E E E EC E
HO 20 C 0015 c0 | O3 00 tO iS + nono 00 cO 1919 O C00 HT 00165
wN Gi NA td Or O19 OD Oro MANA

TABLE 7

Difference between the course and first bearing

ON rr ri

Sk 01000
oocooco

Distance of an Object by Two Bearings

Do co C c3

N CO» 10 r OH

cocco

lb E Ons

+ [NM N O O

78°

between
the course
and second

bearing

8
E
5
E
A

1252

1253

TABLE 7
Distance of an Object by Two Bearings

Difference
between Difference between the course and first bearing.
ver touris
and secon
bearing. 110°

120
122
124
126
128
130
132
134
136
138
140
142:
144
146
148
150
152
154
156
158
160

4. 69
3. 83
3. 22
2. 76
2. 40
2. 10
1. 86
1. 66
1. 49
1. 34
1. 21|-
is
0. 99
0. 89
0. 81
0. 73
0. 66
0. 59
0. 53
0. 47

HHHH H H| EEE NN o go po de pr

DD 05 02 HO O» -100| Oe WON O Hf OOF

Y C» FA GO O6» en -100| SPER Ē 00 t3 —
O A Eo boobs I

ppp pen e| pea E t Ese D] NIN ISO C9 1 O9 hs Cx

Fab pst I CI ipt st s; OI ca CD Se
Be ee EE EE RR D C9 Com! ot
EE ERU II IN Coe ps

A S EEE do

a do SR
SS ii o e
A ii Leg SE) Em

H H H H pl m bo O bo DO o P
Sopop mmmH H| ns
VS OUO» TOO OG NO R «O O
zÄ bäi E GHG DA zl Dä D ODC vs, Cu Ca

pa
to

4°

R
o
w
O
o

PRIN NNN OR
BOW +DOJRPON
ChB HW 00 w ON
ð er SEA ESSEN
atm nl SAO
rss 95 IES
HHEHNNNN O

A and —D

BÐ Bat IAS
SSS REN

PSPSPPSS|RRRHRNNN
zim iz |P ASTES

00
o

1. 14

1254

TABLE 8
Distance of the Horizon

i i Height Nautical Statute
ees JF ies sale ies gu NO EARS feet miles nis
1 ini 1, 6 120 123 14. 4 940 35. 1 40. 4

2 1.6 1.9 125 12. 8 14,4 960 35.4 40. 8

3 2.0 213 130 13.0 15.0 980 35. 8 41.2

4 218 2.6 135 1318 15:3 1, 000 36. 2 41.6

5 2.6 2.9 140 139 15.6 1, 100 34.9 43. 7

6 2.8 312 145 13. 8 15.9 1, 200 39. 6 45. 6

7 3.0 at Je 150 14. 0 10. 1 1, 300 41.2 47.5

8 332 Si qi 160 14.5 1627 1, 400 42.8 49. 3

9 3. 4 4. 0 170 14. 9 17292 1, 500 44, 3 51.0
10 3.6 4.2 180 153 Myr 1, 600 45. 8 52. T.
11 3.8 4.4 190 15.8 18. 2 1, 700 47.2 54. 8
12 4.0 4. 6 200 16. 2 18. 6 1, 800 48. 5 55.9
13 ÆT 4,7 210 16. 6 19. 1 1, 900 49. 9 57. 4
14 El Ss 4.9 220 17.0 19.5 2, 000 51.,2 58. 9
15 4.4 3 d 230 17.8 20. 0 2, 100 02.4. 60. 4
16 4. 6 5.3 240 WS 7 20. 4 2, 200 58.4 61. 8
17 4,7 5.4 250 18. 1 20. 8 2, 300 54. 9 63. 2
18 4.9 5. 6 260 18. 4 2152 2, 400 56. 0 64. 5
19 5. 0 et, 2 270 18. 8 21.6 2, 500 57. 2 65. 8
20 omi 5.9 280 19. 1 22. 0 2, 600 58. 3 67. 2
21 5.2 6.0 290 19. 5 22. 4. 2, 700 59. 4 68. 4
22 5.4 6. 2 300 19. 8 22.8 2, 800 60. 5 69. 7
28 DO 6.3 310 20. 1 2032 2, 900 61. 6 70. 9
24 5.6 6.5 320 20. 5 23. 6 3, 000 6247 72.1
25 & vl 6.6 330 20. 8 23. 9 3, 100 63. 7 78.8
26 5.8 6. 7 340 2198] 24. 3 3, 200 64. 7 74.5
27 5. 9 6.8 350 2171 24. 6 3, 300 65. 7 45. Y
28 6. 1 7. 0 360 2107 2510 3, 400 66. 7 76. 8
29 032 751 370 22. 0 2089 3, 500 67.17 77.9
30 6. 3 782 380 22.8 25 3, 600 68. 6 79. 9
31 6. 4 (29 390 2295 26. 0 3, 700 69. 6 80. 1
32 6.5 (ao 400 22. 9 26. 3 3, 800 70. 5 81. 2
33 6. 6 7. 6 410 232 26. 7 3, 900 14 82. 2
34 6. 7 TET 420 23. 4 27.0 4, 000 72. 4 83. 3
35 6.8 7.8 430 Dist Tf DOES 4, 100 MUS 84. 8
36 6. 9 7.9 440 24. 0 27. 6 4, 200 74.1 85. 4
Bt 7. 0 8. 0 450 24. 3 27. 9 4, 300 75.0 86. 4
38 esch 8. 1 460 24.5 28. 2 4, 400 75. 9 87. 4
39 GA Sao 470 24. 8 28. 6 4, 500 76. 7 88. 3
4078 LUZ 8.3 480 2528]. 28. 9 4, 600 dd 6 89. 3
41 T 8 8.4 490 2538 20:2 4, 700 78.4 90. 3
42 7.4 8.5 500 2556 29. 4 4, 800 79. 3 91. 2
43 D 8.6 520 26. 1 30. 0 4, 900 80. 1 92. 2
44 7.6 8. 7 540 26. 6 30. 6 5, 000 80. 9 93. 1
E: TEL 8. 8 560 27.4 Oum 6, 000 88. 6 102. 0
46 TEB 8.9 580 27. 6 SR 7,000 95. 7 110. 2
47 T8 9. 0 600 28. 0 9289 8, 000 102. 3 117. 8
48 jt. Qi 9. 1 620 28. 5 32. 8 9, 000 108. 5 124. 9
49 8.0 9. 2 640 28. 9 33. 8 10, 000 114. 4 131. 7
E 0H 8. 1 93. 660 29. 4 33. 8 15, 000 140. 1 161. 3
55 8.5 9.8 680 29. 8 3413 20, 000 161. 8 186. 3
60 8. 9 10. 2 700 30. 3 34. 8 25, 000 180. 9 208. 2
65 9. 2 10. 6 720 30. 7 JDS 30, 000 198. 1 228. 1
70 9.6 1180 740 535 il Sys fa 35, 000 214. 0 246. 4
75 9. 9 SA 760 315 3X9 8) 40, 000 228. 8 263. 4
80 10. 2 11. 8 780 31. 9 36. 8 45, 000 212847 279. 4
85 1075 1122. 1] 800 32.4 37.3 50, 000 255. 8 294. 5
90 10. 9 192. 55 820 32.8 Sil. TI 60, 000 280. 2 322. 6
95 i.» 12. 8 840 9332 38. 2 70, 000 302. 7 348. 4
100 TITA 1382 860 33. 5 38. 6 80, 000 323. 6 942.15
105 iil, 7 DON 880 33. 9 39. 1 90, 000 343. 2 395. 1
110 12. 0 1358 900 34. 3 39.5 100, 000 361. 8 416. 5
115 | 12.3 1471 920 34. 7 39. 9 200, 000 511. 6 589. 0

1255

TABLE 9

Distance by Vertical Angle

Difference in feet between height of object and height of eye of observer

a
e

60 90 180

S
=
hy
Ze

Miles i i Miles i i ile i i Mil
5 0 45 89 1 72 1 89 26 99 "63

2.5
2.
2.
2.
1.
1.
il.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.

op osorno poopoo HH n| NN Ņ

Sleeeeeleeeeeleeeeeleeeeeleeeeelrararar tal w w o g go
AS ASS poppoo PPOP a HHH w |y g g go go

cloooooocooooocoooooooooooooococ-ccreccmppop p
oococoopooooooooooooooooooooooooococoer-omme9ogEE

O|oOoooomoooooooooooooooooooooooomtoemrntermnr EN N NO og PERO

OOo ÀÍOooooooooooooooooooooooooooooornmntoenmmemr a AIR oor
OoOooo(ooooooooooooooooooooopoooooooomrmtmrnnrtrmrrocrmtmtoopg BAS

colcooooooooooooooooooooooooooooooooo-looeoermmwpRIPRO IPS
E SS TIT IS A EE

ii id ii il SAA A uoo oM

1256

TABLE 9

Distance by Vertical Angle

Difference in feet between height of object and height of eye of observer

Angle = Angle
200 250 300 350 400 600 800 1,000 1,200 1,400 1,600 1,800
2 A Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles Miles | Miles | Miles | Miles a :
0 10 8. ag 9.9511. 44/12. 83 14. 15118. 87/22. 96/26. 61/29. 95/33. 04/35. 93,38. 65] - 0 10
0 11 7. 89| 9. 44/10, 88112. 2413. 51118. 17/22. 20/25. 81/29. 12/32. 1835. 05/37. 76| 0 11
0 12 7 47| 8. 96110. 36 11. 69/12. 9517. 50/21. 47/25. 05/28. 32/31. 36/34. 21/36. 90] 0 12
0 13 7.08 8. 52 9. 88111. 17112. 41/16. 87/20. 78/24. 31127. 55/30. 56/33. 3936. 06] 0 13
0 14 6.72 8.11 9. 43110. 6911. 90/16. 26/20. 1223. 60/26. 80/29. 79/32. 61/35. 24 0 14
0 15 6.39 7. 74| 9. 02/10. 25/11. 4115. 69/19. 48/22. 91/26. 08/29. 03/31. 81,34. 444 0 15
0 20 5.11 6. 25| 7. 35| 8. 41. 9. 43113. 26116. 72/19. 91/22. 88/25. 67/28. 31/30. 83] O 20
0 25 4. 23| 5. 20| 6. 15| 7.07! 7. 9811. 39114. 53117. 47/20. 23/22. 85,25. 35|27. 73] 0 25
0 30 3. 59| 4. 44| 5. 27| 6. 08| 6.87! 9. 9212. 78/15. 48/18. 04/20. 48/22. 82/25. 08] O 30
0 35 3. 11| 3. 86| 4. 60| 5. 32. 6.02 8 77/11. 37/13. 84116. 22118. 49/20. 69/22. 81] 0 35
0 40 2. 75| 3. 42| 4. 07| 4. 72| 5. 36| 7. 88110. 21112. 49/14. 69/16. 81/18. 87/20. 86| O 40
0 45 2. 45| 3. 06| 3. 65| 4. 23| 4.81! 7. 06| 9. 25/11. 35/13. 39/15. 37/17. 30/19. 17] 0 45
0 50 2. 22| 2. 76| 3. 30| 3. 84. 4. 36] 6. 43| 8. 44/10. 40/12. 30/14. 14/15. 95/17. 71| 0 50
0 55 2. 03| 2. 52| 3. 02| 3. 51| 3. 99| 5. 90| 7. 77| 9. 58111. 35,13. 09/14. 78/16. 44 0 55
1 00 1. 86| 2. 32| 2. 77| 3. 23| 3. 67| 5.44 7. 18| 8. 87/10. 53|12. 15/13. 75|15. 31 1 00
1 10 1. 601 2. 00! 2.39| 2. 78 3. 17| 4. 71| 6. 23] 7. 72) 9. 19/10. 63/12. 05/13. 45] 1 10
1 20 1. 40. 1.75 2. 10| 2. 44| 2. 79| 4. 15] 5. 50| 6. 82| 8.14 9. 43/10. 71/11. 971 1 20
1 30 1. 25| 1.56| 1. 87| 2. 18| 2.48! 3. 71| 4. 91| 6.11! 7. 29| 8. 46 9. 62110. 77] 1 30
1 40 1.12 1. 41| 1. 68| 1.96! 2. 25| 3. 35| 4. 45| 5.52 6. 60) 7. 66| 8. 73| 9. 78] 1 40
1 50 1. 03| 1.28 1. 53| 1. 79| 2. 04. 3. 04| 4. 05| 5.05| 6.02, 7. 01| 7. 98| 8.95] 1 50
2 00 0. 95| 1. 17| 1. 41| 1. 64| 1. 89. 2.80 3. 72| 4 64| 5. 55| 6.44 7. 35| 8 25| 2 00
2515 0. 81| 1. 04. 1. 25] 1. 46] 1. 66| 2. 49| 3. 32| 4 14| 4. 95| 5. 77| 6. 50, 7.36) 2 15
2 30 0. 75| 0. 94| 1. 13| 1. 32| 1. 50. 2. 25| 2. 99| 3. 73] 4. 47| 5. 20| 5. 93. 6.661 2 30
2 45 0. 68| 0. 86| 1. 03| 1. 19| 1. 37| 2. 05| 2. 72| 3. 40, 4. 07| 4.74 5. 41 6. 07] 2 45
2 00 0. 63] 0. 78| 0. 94. 1. 10| 1. 25. 1. 88) 2.50 3.12 3. 74| 4. 35| 4. 97, 5.58] 3 00
0. 56. 0. 71| 0. 85| 0.99 1.12 1. 69| 2. 35| 2. 81| 3. 37| 3.92 4. 48| 5.03] 3 20
3 40 0. 51| 0. 64| 0. 77| 0. 90| 1. 02| 1. 54| 2. 04. 2. 56| 3. 06| 3.57) 4. 08| 4. 58| 3 40
4 00 0. 47] 0.59 0. 70| 0. 82) 0. 94. 1. 41| 1. 88) 2.35 2. 81| 3. 27| 3.74 4. 21| 4 00
4 20 0. 43 0. 54| 0. 65| 0. 76| 0. 87| 1. 30) 1. 73| 2. 17| 2. 59| 3. 02| 3. 46, 3.88] 4 20
4 40 | 0. 40] 0. 50| 0. 60) 0. 70| 0. 81, 1.21 1.61) 2.01) 2. 41 2 81) 3.21 3.61] 4 40
5 00 0. 38] 0.47 0. 57| 0. 66) 0. 75| 1. 13] 1. 50| 1. 88) 2 25| 2. 62| 3. 00| 3.37] 5 00
5 20 0. 35) 0. 44 0. 53] 0. 61, 0. 71| 1. 05) 1. 41] 1. 76] 2. 11 2. 46) 2.81) 3.16] 5 20
5 40 0. 33| 0. 42 0. 50) 0. 58) 0. 66) 0. 99) 1.32 1.65 1. 98| 2. 32| 2.65 2. 97| 5 40
6 00 0. 31] 0.39 0. 47| 0. 55] 0.62 0. 94| 1. 25| 1. 56| 1. 88|. 2. 19| 2. 50| 2. 81 6 00
f E 20 0. 29| 0.37 0.45 0.52 0.59| 0.89| 1.19 1. 48] 1.78 2.07| 2. 37, 2.66| 6 20
40 0. 28| 0.35 0. 42| 0. 49| 0. 56| 0. 85| 1. 13, 1. 41| 1. 69 1. 97| 2. 25| 2 6
7 00 0. 26| 0. 33) 0. 40) 0. 47| 0. 53) 0. 80| 1. 07| 1.34 1. 61| 1. 87 2.14 2 R 7 5
7 20 0. 26| 0. 32| 0. 38| 0. 44| 0. 51| 0. 76| 1. 02! 1. 28| 1.53 1.78 2 041 2 30] 7 20
7 40 0. 24| 0. 31] 0. 37| 0. 43| 0. 49| 0. 73) 0. 97| 1. 22| 1. 47| 1.711 1. 95 2 19] 7 40
E of ` ee 0. 29| 0. 35} 0. 41) 0.46 0. 70| 0. 94. 1.17] 1. 41| 1.64 1.87 2.10] 8 00
. 22 0. 28) 0.34 0. 39. 0. 45| 0. 67| 0. 90} 1. 12| 1. 35] 1 1
8 40 0. 22| 0. 27| 0. 32| 0. 38] 0. 43| 0. 64| 0.86 1.08! 1. 30 mee la 7 a S AD
9 00 0. 21| 0. 26| 0. 31| 0. 36| 0. 41| 0.62 0. 83| 1. 04| 1. 24| 1. 46| 1. 66,1. 871 9 00
9 30 0. 20| 0. 24) 0.29 0. 35] 0. 39| 0. 59| 0. 78 0.98 1.18 1.37! 1.571 1.77) 9 30
i) Ss | 0. 19) 0.24 0. 28) 0. 33| 0.37| 0. 56| 0. 75| 0.93| 1.12 1. 30| 1. 49| 1. 68] 10°00
0. 17| 0.22 0. 26] 0.31! 0. 35| 0. 53) 0. 71 0. 89! 1.06! 1
i 00 0. 17| 0.21 0. 25. 0. 30| 0. 34| 0. 51| 0. 67| 0. 85 e? 1 15 UE i € n 00
n " 0. 16} 0. 20| 0. 24| 0. 28| 0. 32| 0. 48 0. 65| 0.81! 0. 97-1. 13! 1. 29] 1. 46] 11 30
12 0 0. 16| 0.19 0. 23| 0.27| 0. 31| 0.47 0. 61| 0.77 0.92 1. 08-1. 24 1. 391 12 00
x 7 i Tr 0. 19. 0. 23| 0. 26| 0. 30) 0. 44) 0. 59) 0. 74| 0.89 1. 04| 1. 19| 1.33] 12 30
: 1 0.18 0. 22| 0. 25| 0. 28| 0. 42| 0. 57| 0. 71| 0. 85| O. 99
e 3 0. 14| 0. 18| 0. 20| 0. 24| 0. 27| 0. 41| 0. 55| 0. 68| 0. 82| 0. 96 ios i 53 13 30
u 0 0. 13 0. 16| 0. 20 0. 23| 0. 26| 0. 40| 0. 53| 0. 66| 0. 79| 0.92 1.05 1.19] 14 00
E 30 0. 13| 0. 16) 0. 19| 0.22 0. 25| 0. 38| 0. 50| 0. 63| 0. 76| 0. 88] 1.02 1. 15) 14 30
e E 0. 12| 0. 15) 0.19 0. 22| 0.24 0.37| 0.49| 0. 61| 0. 73| 0. 85| 0. 98] 1. 10] 15 00
0. 11} 0. 14| 0. 17| 0. 20) 0. 22) 0.34 0. 45| 0.57 0. 69
M of 0. 10) 0. 14| 0. 16| 0. 19| 0.21 0.32 0.42 0. 53| 0. 65 D 7 d ue W 00
15000 0. 13| 0.16) 0.17| 0. 20| 0. 30| 0.40 0.50 0.61 0.70 0.81 0. 911 18 00
10 0. 13| 0.14 0.17| 0.18 0. 28| 0. 38| 0. 48] 0. 57| 0. 67) 0. 76| 0. 851 19 00
0 0.12 0. 13| 0. 16| 0. 18| 0.27 0. 36| 0.45 0.54 0.63 0.72 0. 811 20 00
|

1257

TABLE 9
Distance by Vertical Angle

Difference in feet between height of object and height of eye of observer

3,000

WORD VSIV A O OO GT O

NOV DI TVG ODO LUT KP DO OO TO O Cr
DO NO N C Qo O DOT -1 00 V DO OOP O5 02 02

CIOS
DH WOOO

00 — Q3 OQ» cO | t9 O» RON OD -1 O1 Cr OO! -J cO bào cO cO

Qo P. i» ll OUST OO» NI} 00 000 t

BOD N OOOH t2 WIP OO» -100! O | O5 di» O:| -I1 CO GGU NO VW GO a cO Hi O 00 RT -1 60 p» | OY CO Ot JI OO DO A DOD O PO OO NI
GO --I OO «O | — bà b2 Q3 H» | C' O» NO CD Í b O2 NODOMS En OO! QC V GO O21 00 GO O» Hx ! i O2 RANN H CO C» ep legen as a — 00 CI OO -1 -10»
DA WORN Q2 HE OG OQ»! - 100 cO CD NA C1 -1 cO CD NA O» 00 OI O2 O tO O2 AIN -31 O ODO HAIR CO O» ANA AO NEAR Ot CO A CO | 00 -1 -1 O C?
IEEE! IEEE EMO ES euet c
Y Qo cO O DIV Hi» C OQ» NO O AH NA | Ot NIO A WIP DWH Glen CO Q2 O» | O» r9 00 O VT O O 00 DO cO | G2 00 RIO rl O Gt O1 MA IN O YO GV Ot En

e ka bal ba Fa ka Hä
Em m Pe TN BO BO BO | DDD DY) C9 99 92 EE pa f He | He OT OT OT | DD OOO S Eo i| IDO

F SS ASAS O9 9 CO 95 P Pp e| OUT OT SSI | Co E: Bo Go €
Qo «O C to 02 Or enen Aler NACÍ A Qo GU -1 60 I O co t0 OO iS ODOWVRO to oo En A

FEE EE EO DODO ES BO BO BO EO | NIN go Go cd | co co G3 Hes ges rie ee Ov t| DIS OO (D DES CS LS CRUS qe ps UE C ES
ge ON OO DOD V | VO cO e to S | OC -100 O rol PRO ORO MU t O O R JU O cO He GO El IN 00 OUO 001 WHE ele 00-31-10»

QC Q rm tà o»! i PPE ao O» -100 cO O O t5 Q2 4» Ot O» -100 cO Al t2 DO Ala Y A O 100 PO Octo een bal N — 00 NI 00 Q2» b2 GTO b2 CO cO ON
E m IN O al CO OO: DN Q6 cO to O ID CT O» -11 DOE B2 OTTO DO GU O0 DO AHN Ha 00 00 cO 100 CO e It ON OO OR ROI Or O2 NHH

.8
20
.4
JI
no
.8
.2
oY
10. 8
9: 9
971
8. 2
7. 4
027
6. 2
5. 6
orl
4.7
4.3
4.0
3. 7
3.5
3. 3
3. 1
3. 0
2.8
2.7
2.6
2. 4
2.3
2. 2
2. 2
arl
2.0
139
1.8
197
1. 6
1.5
1. 5
1. 4
1. 4
1. 3
1. 3
1. 2
1.1
IKEA
1.0
1.0
0. 9

o o IAS ESAS SI o AO DSS Ce ESE
PPP PP PP PRP PPP RPNNINN NNN) NN o O a P pa | a or Oro OOOO C

PPP PRP PRP d N NIN DL N D9 w OO GO GO GO 92 P PP | VS DNT

WW 4» GO NO 00 «o Ol 9 to 0o Glen OO O LG S O» -3 0| i GOOD GO JV 00
PR RN) DN NN NIN ND WW) Oo O 02 HP HP PR BB on] Or OO OS BIND PO O ¢
FDD D BO BO BO BO BO O w (O 92 O9 O HP HH HR HR Ot St Or OT ER S NI] - 100 O cO €
EE EO EO BO BO D EO D DĪ O2 w w (O POLO C9 pa P | f HR OC OL OT OO» D> NIN 00 90 co OF

P2 BO EO PO BO | 2 BO BO BO WWW WWW) a OT OT LOT | NIN} 00 co co t

es A ESIS9 E99 T9 RSS GO POROS
WN Q2 i Ot O - 1-100 Q0| cO O HN 021 i O» -3100 col O D 02 Jr O

1258

TABLE 9

Distance by Vertical Angle

Difference in feet between height of object and height of eye of observer

4,600 | 4,800 | 5,000 | 5,200 | 5,400 | 5,600 | 5,800

8 8

.8
.8
.8
DS
29
.0
„6
Lf
La
.8
.8|
22
Gerd
«5
„5
Lal
.2
18
n7
29
.4
.5
39
„5
„4
I1
1
2
4
8
2
7
2
8
5
2
9
6
4
1
9
ti
6
3
1
9
7
6
4
3
1
0
9
8
Y
5
4
2
1
0

RIN Q2 CO O3! Q0 DO ola TO HG O1 00 O la O» 00 RIO D O OU A 00 O OO NO NINO - TOO G2 | 00 O O 010 O 02 02 TO O O1 Ot C1
BO d > AA | O DY OU cO f» | D NO DO

N 02 4 O» 00| «D (OO b2 O2 RIO TO ED Ot - T OD BO SI O» 00 rS ENR OO qe OI Or Q2 ODO OO QD n TOO Hf» Hx | i NOOO 00 bà cO O GI Q2 to DO DO DO
Ge TO! NWRAINOON d. | IO NA O3! 00 na ziel ONNW]ONOON! DONO] O» O10 C O»^ Q9 OG OO Ke DG TER OY OI co © 00 00 00
D D D D D D D D H D 5 D D sz P D h b H 5 D D D D h 5 D N

Q2]01O» 00 OG t2 02 RON cO DOD O1 = H4 O» 001 ka Gu GO WOODOO NTV DODOS T O» O1 -T| 4 0100 OA lO) NT TOOL -T O GU Or ER e
PONTO! us, GTO ON RAW IOWRWOIWRONTUOLOKRO'INABOWIWNWNOTUWPRORDOIWDORKFOINALAHIOOCOOCSO
Conseil, O»-1000|l— r201-10 | t3 000 C GTO GTO NA NJ OO O GS cO Q2 DO VOID 0200 OD | OO to NR WIA i cO O! OS O1 OT O1 Ot
ER Sog SUN SOON OU NSO Ra a Sl LO? m Oto» T

DO MO HRH0|D-100 nl AC DR JO Nal Ote A Al OO GU NI TNW GVO OO ALTIRO NAAA NOOO OA O DO
TOO NE TOO El Vë GO ka El en Hi -1l C 020» OA lo wao E HU! O 00 OO al O V a OO NT NT O NNDO OO OO OO GT OTUVO
WOH WHIDDEN KEIDMWON VU 00 a TO | NO NA! ONO VU OQ) r2 t2 GTO -T t2 O — N 10 O» NVO OD TOS - O2 t2 | O O ODO
O NES ¡ROJAS TES CASE EAS AECE TOTO T3 00 TO GV GTO ON AIN — -1 O1 O»| O O» O cO GV GT PP Cn

pi pi i i | pi pi pi pi
NN NN N G2 Ļo Ļo 69] 69 09 G2 I g OT OT] IO S NNN OON e En S3 EO?

RA bech ke | ji bech bet Fei
II a ie i E E D H MI] NNP O OOH EES ET

HA kt pl kat bat kat pl kal Fi
A TEE AAA EE ke Ni 00 1 DS E DH SUS O0] O O 1 C

10.
9,
8.
8.
7.
7.
6.
6.
6.
5.
5.
5.
5.
4,
4,
4,
4,
4,
3.
3.
3.
3.
3.
3.
3.
2.
2.
2.
2.
2.
2,
2.
2.

ATI DD G2 (2 oo| 99.09 Q2 PO i | f i i P on] Cr EN ED elen NII 90 Go| o O €
DO DO RO PO gol 99 G2 PO G2 CO | G2 i i iR RI CN D OO m NI] 106 00 =

= | kt
NN 08/99 09 BO G2 CO i i i RR OO PA Y 00 00 S/O

DD D 09 GO 92 O A OT OL OT | DD NINN! 00 O D CO €
bO ho D O 09} 09 02 A OT OT D | Oo NNN 00/00 SO £O D C
D D G2 Q2 O O C2 jf i He | | HR RR OT OT OV DT OO S| N N N oojo £O SO © }
bo 92 02 Q2 2| a PR TOT OI OT? DOP NI] 23-100 90 9o SO SO o

ho 92 DO 92 G2 | G2 COR a d [f HR OT OT OT) OID DH | NN N90 ADO

TABLE 9

Distance by Vertical Angle

Difference in feet between height of object and height of eye of observer

1259

Angle
Angle
6,800 7,000 | 7,500 8,000 | 8,500 | 9,000 | 9,500 | 10,000 | 10,500 | 11,000 11,500 | 12,000 Á
a dl Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Mi i eU
` s 84. 3| 85. 7| 89. 0| 92. 3| 95. 5| 98. 51101. 5/104. 4/107. 3/110. 1 112.8 115. 4 0 10
it 83. 3) 84. 6| 88. 0| 91. 3| 94. 4| 97. 5/100. 5/103. 41106. 2/109. 0/111. 71114. 4 0 11
0 12 82. 2 83. 6| 87. 0| 90.2 93.4 96. 5| 99. 4102. 4/105. 21108. 0/110. 7/113. 3 0 12
0 13 81. 2| 82. 6) 86. 0| 89. 2 92.4 95.4 98. 4101. 3/104. 2/106. 91109. 61112. 3 0 13
5 i5 = 2 81. 6| 85. 0| 88. 2 91. 4) 94. 4| 97. 41100. 31103. 11105. 9/108. 6/111. 2 0 14

le 80. 7| 84. 0| 87. 2| 90. 4| 93. 4| 96. 4| 99. 31102. 11104. 9/107. 6/110.
0 20 74. 6| 76. 0| 79. 3| 82. 5| 85. 6| 88. 6| 91. 5| 94. 4| 97. 2/100. 0/102. 6/105. 3 20
0 25 70. 3| 71. 6| 74. 9| 78. 0| 81. 1| 84. 1| 87. 0| 89. 8| 92.6! 95. 3| 98. 0/100. 6 0 25
0 30 66. 3| 67. 6, 70. 8| 73. 9| 76. 9| 79. 9| 82. 7| 85. 5| 88. 2| 90.9! 93. 5 96.1 0 30
o 2 62. 6| 63. 9| 67. 0| 70. 0| 73. 0| 75. 9| 78. 7| 81. 5| 84. 2 86. 8 89.4. 91.9 0 35
59. 2| 60. 4| 63. 5| 66. 5| 69. 4| 72. 2 75. 0| 77. 7| 80. 3| 82. 9| 85. 5
0 45 56. 0| 57. 2] 60. 2| 63. 1| 66. 0| 68. 7| 71. 5| 74. 1| 76. 7, 79.3 81.8 7 ; 0 R
0 50 53. 1| 54. 3| 57. 2| 60. 0| 62. 8| 65. 5| 68. 2; 70. 8) 73. 3| 75. 8 78. 3| 80. 7 0 50
0 55 50. Ai 51. D 54. 4| 57. 2) 59. 9| 62. 5| 65. 1| 67. 7| 70. 2 72. 6) 75. 0| 77. 4 0 55
i "o 47. 9| 49.0| 51. 8| 54. 5| 57. 1| 59. 7| 62. 3| 64. 7| 67. 2| 69. 6| 72. O| 74. 3 1 00
T 43. 5| 44. 6| 47. 2| 49. 7| 52. 2) 54. 7| 57. 1| 59. 5| 61. 8| 64. 1| 66. 3| 68. 6 TAL

1 20 39. 7| 40. 7, 43. 2| 45. 6| 48. 0| 50. 3| 52. 6| 54. 8| 57. 0| 59. 2| 61. 4| 63. 5 1 20
1 30 36. 5| 37. 4| 39. 7| 42. 0| 44. 2| 46. 4| 48. 6| 50. 8 52. 9| 55. 0| 57.0! 59. 0 1 30
1 40 33. 7| 34.6] 36: 7|-38. 9| 41.043: 1| 45. 11147. 2| 49.21 51. 2| 53. 1| 55. 1 1 40
1 50 31. 2| 32. 0| 34. 1| 36. 1| 38. 1| 40. 1| 42. 1| 44. 0| 45. 9| 47. 8| 49. 7| 51. 5 1 50
2 00 29. 1| 29. 9 31. 8| 33. 7| 35. 6) 37. 5| 39. 3| 41. 2| 43. 0| 44. 8| 46. 6| 48. 3 2 00
2 15 26. 3| 27. 0| 28. 8] 30. 6, 32. 3. 34. 1| 35.8 37. 5| 39. 2 40. 9| 42. 5| 44. 2 2-15
2 30 24. 0| 24. 7| 26. 3| 28. 0| 29. 6| 31. 2| 32. 8| 34. 4| 35. 9| 37. 5| 39. 1] 40. 6 2 30
2 45 2230152297102492 82537 1827:32 928: 78 30929 E 31497! 33.2219 34:16/9002 1183735 2 45
3 00 20. 4| 21. 0| 22. 4| 23. 8| 25. 2, 26. 6) 28. 0 29. 4| 30. 8 32. 1| 33. 5| 34. 8 3 00
3 20 18. 5| 19.01 20. 3| 21. 6| 22.:9| 24. 2) 25. 5/26. 7| 28. 0. 29. 3) 30. 5|. 31.8 3 20
3 40 16.91.17 4.1857|.19..8.21.0|.22- 2|. 28: 4.24. 5|.-25.«7|.26..9|. 28..0,-29..2 3 40
4 00 15. 6| 16. 0| 17. 1| 18'2| 19.3| 20. 4.21. 5] 22. 6| 28. 7| 24. 8| 25.9| 27. 0 4 00
4 20 14. 4| 14. 8| 15. 9| 16. 9| 17. 9| 19. 0| 20. 0| 21.0| 22. 0| 23. O| 24.0) 25. 0 4 20
4 40 13. 4| 13. 8 14. 8| 15. 8| 16. 7| 17. 7| 18. 0. 19. 6| 20. 5| 21. 5| 22. 4) 23. 4 4 40
5 00 12. 0| 12) 9) 13981714. 7| 15. 6) 16: 5| 17. 4) 18. 3| 19. 2) 20. 1) 21. 0/-21. 9 5 00
5 20 11. 8| 12. 1| 13. 0} 13. 9| 14. 7| 15.5| 16. 4) 17. 2 18. 1| 18. 9| 19. 8. 20. 6 5 20
5 40 Tí 0184091293] 713. AUS TONTAS 7 85:5 ee 17:31] 9 17:19] 118. 6/419:4 5 40
6 00 10. 5| 10. 8| 11. 6. 12. 3| 13. 1] 13. 9. 14. 6, 15. 4| 16. 1| 16. 9| 17. 6) 18.4 6 00
6 20 1090/51023/9120/ 5311171512344 13: 2 713:9| 014 6| 11533/$16::0 $107 7 $1755 6 20
6 40 99553928 107471 1. IOLE E EE kee 11:5. 9121626 6 40
7 00 9.0 9.3 10.0| 10. 6| 11.3| 11. 9 12. 0| 13. 2) 13. 9| 14. 5| 15. 2) 15. 8 7 00
7 20 8.61 8.9 9.5| 10. 1] 10. 8] 11. 4 12. 0| 12. 6. 13. 3| 13. 9| 14. 5. 15. 1 7 20
7 40 8 3) 8/51 19: 9. 71 10: 3) 10: 9) 11.5 12: 1| 12. 7|: 18. 3| 13. 9/114. 5 7 40
8 00 rx cede OS 5999/51074 "11570 F1K 01232012777] [003 81539 8 00
8 20 YEG 78 AA ANT AO HOA 1147012212. 8 Nlēja 8 20
8 40 ZS E745 S70 «169911 oO 6) 1039 11077) 11:322 8118 12. S E3258 8 40
9 00 70) TESTI 8:31 12981817 9: 3|. 9:8) 103 108/1114. 3| 11. 8 4123 9 00
9 30 627/9689) AS 7383s. sis. s S929 1098 LOS d er H 7 9 30
10 00 635657 0 747798 4) 88103 Sadie O 2 1077 ELT 10 00
10 30 ero e RA AAA IA 188 | 980. 91710. 1810. 6| 10 30
11 00 5971 ISO f6*3 dr Kr ve 6 | 1830 Sid 1 818009 9:9 9. 7, 10.1] 11 00
11 30 535/5586 151630/0 634/0018 097. ol) 3786 [85:0] | 835/00 8:18. 9.3 9.71 11 30
12 00 P2509 584 83585 GEO IG AO: OATES iK ES AS TO S. 9 9.2 12 00
12 30 OA OIE O IAE TAO | TEE EI 8.5) 8.9 12 30
13 00 uus RON I5ES LE R 610564 Ho Hv | 739) SES. 21318. 5 13 00
13 30 286/9485 915512 5451535 (62 1 695 01678 "427587. 980821 | 19130
14 00 2555/48611 1459 2 5.385.625: 911 (69290: 6, | 649 7.127. 6 227591 14100
14 30 Ag A Ae Sis 7 | Šēle ACTION ame 6 14 30
15 00 2059105465 1126/98 4:19/5095.2 (0x5 RONS NOST 6.4 6.7 7.0| 7.8| 15 00
16 00 390 7 1410/9 453/08 464 FO (005: 21. 0) 4: 7. 6.01 6.3| 6.6| 6.9] 16 00
17 00 B E E 4:3 804306 TA Ss Fon 1080 5-4 5.6 5.9 6.2 6.5] 17 00
18 00 oU AS 1398 4. 112124 5 LESS H: Ill | 5. a 5.60 5.8 GU 18 00
19 00 55013318 033860 M: AS GM CES 520898549 88555 385771 9 19 00
SA E, DE le 33107338 e E 9 Aa An 5.075. 2 $0524] 20100

1260

TABLE 10
Direction and Speed of True Wind in Units of Ship's Speed

Apparent Difference between the heading and apparent wind direction Apparent

wind speed 0° 10° 20° 30° 40° wind speed
0. 0 180 1. 1. 00 | 180 1 1 1. 00 0. 0
0.1 180 0. 0. 90 | 178 0 0. 0. 93 0. 1
0. 2 180 0. 0.80 | 175 0 0. 0. 86 0. 2
0.3 180 | 0. 62715172400 0. 0. 79 0.3
0. 4 180 0. 0.61 | 168 | 0 0. 0. 74 0. 4
0. 5 180 0. 0. 51 | 162 0 0. 0. 70 0. 5
0. 6 180 0. 0. 42 | 155 0. 0. 0. 66 0. 6
0. 7 180 0. 0. 38 | 145 0 0. 0. 65 0. 7
0.8 180 0. 0. 25 | 132 0 0. 0. 64 0. 8
0. 9 180 0. 0.19 | 117 0 0. 0. 66 0. 9
1.0 calm 0. 0.17 | 100 0 0. 0. 68 1.0
kO 0 0. 0. 21 85 0 0. 0. 72 d
1.72 0 0. 0. 28 73 0 0. 0. 78 1. 2
[23 0 0. 0. 36 64 0 0. 0. 84 t.3
1.4 0 0. 0. 45 57 0 0. 0. 90 1.4
1.5 0 0. 0. 54 51 0 0. 0. 98 1.5
1.6 0 0. 0. 64 47 0 0. 1.05 1.6
1.7 0 0. 0. 74 44 0 0. 1. 18 1
1.8 0 0. 0. 83 42 0 1. 1. 22 1.8
1.9 0 0. 0. 93 40 1 1. 1. 30 1. 9
2. 0 0 de 1. 03 38 1 1 1. 89 2.0
2.5 0 1. 1852 32 1 il; 1. 85 2.5
3.0 0 2. 2. 02 29 2 2; 2. 32 3.0
3. 5 0 2. 2. 52 28 2 2. 2. 81 3. 5
4.0 0 3. 3. 02 26 3 3. 3. 30 4.0
4. 5 0 3. 3. 52 25 3 3. 3. 79 4.5
5. 0 0 4. 4. 02 25 4. 4. 4. 28 5. 0
6. 0 0 5. 5. 02 24 5 5. 5. 27 6.0
7.0 On $6. 6.02 | 23 | 6 6. 6. 27 7.0
8.0 0 ds 7. 02 23 dl Ë 7. 26 8. 0
9. 0 0 8. 8. 02 22 8 8. 8. 26 9.0
10.0 0 9. 9. 02 22 9 9. 9. 26 10. 0

-1
©
O
00
©
o

ooooooopoo

Oo ooo Oo om og oj|o OO A A PWN OO O OO RO NAO

SO CONT? E CO N ba baut E E be Fabi atb Fa EE OOD OS EE Et

SS A NN a OO OOS ore
SEA a a ERI E ER EL e ER E p E EL Oooo

PORNO SS EE
DO DO ODODOGOomomOoj OO TO Club, VD OO O CD oa Eé bäi O

+

es RIO LSL IS SS sea E O (le ba cm (T a

DONDU A HH n H R H| ©

00
00
«e
a
+
-

1261

ER TABLE 10
Direction and Speed of True Wind in Units of Ship's Speed

Difference between the heading and apparent wind direction

A y
pparent Apparent

wind speed 90° 100° 110° 120° 130° wind speed

0. 0 180 | 1.00 |180| 1.00] 180 | 1.00] 180] 1.00 | 180 | 1.00

0. 1 174 || 1.00 | 174 4.02 1 175.1. 1.04 |. 175 | 1.05 | 176 ||. 1.07 01
0. 2 lóga 1 02 1169 | 271705 | 170) 1.08 | 171 | 1.11. | 172 EES SE: 0. 2
0. 3 163 | 1.04] 164] 109|166| 1.14] 167 | 1.18] 169 1.21 0.3
0. 4 158 | 1.08 | 160| 1.14] 162| 1.20] 164] 1.25] 166 | 1.29 0. 4
0.5 EN l 4519 1168—1526: | 1613 101792. | 164 73558. 0. 5
0. 6 149 | 1.17] 152| 1.25] 155 1.83|158| 1.40] 162| 1.46 0. 6
0. 7 145 122|148 1.32] 152] 1.40 | 156] 1.48 | 160) 1.55 0. 7
0. 8 141 | 1.28| 145| 1.38| 149 1.48] 154] 1.56 |158| 1.63 0. 8
0. 9 138 | 1.85 | 143 | 1.46] 147 1.56] 152| 1.65( 156| 1.72 0.9
1.0 135 | 1.411140] 1.53] 145| 1.64] 150| 1.73 |155| 1.81 1.0
131 132 | 1.49| 138 | 1.61] 143 1.72]|148| 1.82] 154 | 1.90 1.1
12 | 130| 1.56|136| 1.69[141| 1.81 | 147 1.91] 153| 2.00 TÐ
153 128 | 1.64 | 134 | 1.77 | 140 | 1.89| 146 200] 152 | 2.09 138
1.4 126 | 1.72 | 132 | 1.86 | 138| 1.98 | 145| 2.09 |151| 2.18 1. 4
1.5 124 | 1.80|130| 1.94|137| 207]|i43| 218| 150 2.28 1.5
1.6 122.9 «sor (C29) 812.103) 1864) 12.16, | 142 At 2027 [1149 002187 1.6
ke 120 p 107 11908152012) 1851) 1225 | 141 1 2636 [5148 (552046 1.7
1.8 119 | 206] 127 | 221 | 134| 2.34] 141 | 2.46 | 147 | 2.56 1.8
1.9 118 | 215] 125 | 230| 133 | 2.43 P 1.9
2.0 117 | 2.24) 124 | 2.39] 132| 252] 139 | 265 | 146 275 2.0
2. 5 112 | 269 | 120| 285| 128 | 2.99| 136 | 3.12| 144 | 3.23 2. 5
3.0 TOS) gh Sal EE E | 1265 78.47 |4184 3761! [$142 (03972 3.0
3. 5 106 | 3.64 Í 115 | 3.80| 124 | 3.96 | 132 | 409| 140 | 4.21 3.5
4.0 104 | 4.12] 113 | 4.29 | 122| 4.44] 131 | 4.58] 139 4 71 4.0
4.5 103 | 4.61 | 112| 478| 121 | 493 | 130 | 5.07 | 138 | 5.20 4.5
5. 0 101 | 5.10 (111 | 5.27 | 120 | 5.42|129| 5.57 |138| 5.69 5.0
6. 0 99 | 6.08 | 109 | 6.25 | 118 | 6.41] 128| 6.56 | 137 | 6.69 6. 0
7. 0 98 | 7.07 | 108 | 7.24| 117| 7.40] 127 | 7.55| 136 | 7.68 7.0
8. 0 97 | 8.06 | 107 | 8.23 | 116 | 8.39 | 126 | 8.54 | 135 | 8.68 8.0
9. 0 96| 9.06| 106 | 9.23| 116 | 9.39 | 125 | 9.54| 135 | 9.67 9. 0
10. 0 96 | 10.01 | 106 | 10.22 | 115 | 10.39 | 125 | 10.54 | 134 | 10.67 | 10.0

140° 150° 160° 170° 180°

0. 0 180 | 1.00] 180} 1.00] 180] 1.00 | 180 | 1.00] 180 | 1.00 0.0
0.1 177 | 1.08|177| 109 | 178] 1.09] 179 | 1.10] 180 | 1.10 0.1
0. 2 1742 m el wal 18 | 1225) 1:895 [178 JK 01.20 [80 | 1220 0. 2
0. 3 ma ios 173 527 175] 1.290] 178 |1 00:30 |(180 |. 1:80 0.3
0. 4 1691. 133 | 172 | 1.36 | 1741 128] 177 (1:40 |.180 | 1.40 0. 4
0.5 167| 1.42 |170| 1.45] 173 | 1.48]| 177| 1.50 | 180 | 1.50 0.5
0. 6 165| Lš1|169| 1.55|178| 1.58 | 176 | 160 |180| 1.60 0. 6
0. 7 ic Ls 564 | 727]! 1568)| 176 | (2 69 [1180 |, 1:70 0. 7
0. 8 Ww | 6018167. ra larvas raise] 176 8 de 79: |0180 | 1480 0. 8
0. 9 k LØ 1.84 [171 | 1.87.) 175 | 1789. | 1807. 71/90 0.9
1.0 160 L88 [|165| 1.93 | 170 1.97] 175| 1.99 | 180 | 2.00 1.0
iyi 159 1.97| 164| 203 | 170 | 2.07 175| 2.09 | 180 | 2.10 Ce
1082 158 207 | 164| 213 | 169 | 217 | 175 | 2.19 | 180 2 20 EZ
ji 1574 2-16 | 163 | 222 | 169 | 2.27 | 174 || 2.29 |:180 | 2:30 ES
154 157 226|162| 232 | 168 | 236 | 174 2.39 | 180 2.40 1,4
1.5 156| 2.36| 162 | 2. 42] 168 | 246] 174 | 249 Í 180| 2.50 1.5
1.6 1551 245| 161 | 252 | 168 | 256 | 174 | 2.59 | 180 | 2.60 1.6
i. 155 | 255 ler | 2.61 | 167 2.66.) 174 | 2 69 [180.270 L7
1.8 15441 2 G5 M3 161-]- 2: 710]. 167] 25761 174 | 2.79 [11804 0 2.80 1.8
1.9 154 | 274 | 160 | 281 | 167 2.86] 173 | 2.89 | 180 | 2.90 1.9
2. 0 1531284 | 160 | 291 | 167 2.96 | 173 | 2.99 | 180 | 3.00 2.0
2. 5 151 | 333l 158 | 3.40] 166| 3.46 | 173 | 3.49 | 180 | 3.50 2.5
3.0 150| 3.82 | 157| 3.90| 165 | 3.95| 172 | 3.99 | 180 | 4.00 3.0
3.5 149 | 4311157 | 4.39] 164 | 445| 172| 449]| 180 | 4 50 3.5
4.0 i48 | 481 | 156 | 489 | 164 4.95] 172 | 4.99] 180 | 5.00 4.0
4.5 147! 5311155 | 5.39 | 164 5.45] 172, 5.49 | 180 | 5.50 4.5
5. 0 146 | 5.80 |155| 5.89] 163 | 5.95] 172 | 5.99 | 180 | 6.00 5. 0
6. 0 145 | 6.80 Í 154 | 6.88 | 163 | 6.95] 171 | 6.99 | 180 | 7.00 6. 0
7. 0 | 7 7428, | 1620 007-95 1711, (3 99 | 180: 8400 7.0
8. 0 144| 8 79 | 153 | 8 88] 162] 895] 171 | 899] 180) 9.00 8. 0
9. 0 144| 9.79 | 153 | 9.88 | 162 | 995] 171 | 9.99 | 180 | 10. 00 9. 0
10.0 143 | 10.78 | 153 | 10. 88 10.95 | 171 | 10.98 | 180 | 11. 00 0.0

TABLE 11

Correction of Barometer Reading for Height Above Sea Level

1262 |
:

All barometers. All values positive.

Height

Outside temperature in degrees Fahrenheit

in feet

= 10°

20°

60°

70°

Inches
0

Fa
3
os
Ze
co

Inches

Inches

Inches

Height

in feet

IO
o

Sesssissessissessissessissess
ooopo0o0|locooopoooopooooocooso

OoOooOooo|(oooo|pooooopoooo»poooo

Ooooo||ooooooooooooooooooo
o

ooo0o0o0|eosocoosoosoooooo|oeoso
=

SSess|sesesisesesisssssisssse
©

TABLE 12

A A a ii DPDDPS

EI id ia DP PDPPS

Correction of Barometer Reading for Gravity

Mercurial barometers only.

SS AAA Aid id bd
o

PSSS 99986599655
o

AAA ii D PRPP rd

bm E

Latitude Correction Latitude Correction Latitude Correction Latitude Correction
9 Inches 9 Inches 9 Inches 9 N
0 — 0. 08 25 —0. 05 50 +0. 01 75 10.07
5 — 0. 08 30 — 0. 04 55 +0. 03 80 +0. 07
10 — 0. 08 35 — 0. 03 60 +0. 04 85 +0. 08
15 — 0. 07 40 — 0. 02 65 +0. 05 90 +0. 08
20 — 0. 06 45 0. 00 70 +0. 06

TABLE 13

Correction of Barometer Reading for Temperature
Mercurial barometers only.

Height of barometer in inches

1263

PSU. Temp:
21. 5 28. 0 28. 5 29. 0 29. 5 30.0 30. 5 31. 0
E Inches Inches Inches Inches Inches Inches Inches Inches K
— 20 +0. 12 | +0.12 | +0. 13 0. 13 | +0.13 | +0. 13 | +0. 14 | +0. 14 —20
18 0. 12 0. 12 0. 12 0:12 0. 18 0. 13 0. 13 0. 13 18
16 0. 11 0. 11 0. 12 0. 12 0. 12 0. 12 0. 12 0. 13 16
14 0. 11 0. 11 0. 11 0. 11 0. 11 0. 12 0. 12 0. 12 14
12 0. 10 0. 10 0. 11 0. 11 0. 11 0. 11 0. 11 0. 11 12
— 10 +0. 10 | +0.10 | +0.10 | +0.10 | +0.10 | +0.11 | +0.11 | +0. 11 — 10
8 0. 09 0. 09 0. 10 0. 10 0. 10 0. 10 0. 10 0. 10 8
6 0. 09 0. 09 0. 09 0. 09 0. 09 0. 09 0. 10 0. 10 6
4 0. 08 0. 08 0. 08 0. 09 0. 09 0. 09 0. 09 0. 09 4
—2 0. 08 0. 08 0. 08 0. 08 0. 08 0. 08 0.09 | 0. 09 —2
0 +0.07 | +0.07 | +0.07 | +0.08 | +0.08 | +0.08 | +0.08 | +0. 08 0
+2 0. 07 0. 07 0. 07 0. 07 0. 07 0. 07 0. 07 0. 08 +2
4 0. 06 0. 06 0. 06 0. 07 0. 07 0. 07 0. 07 0. 07 4
6 0. 06 0. 06 0. 06 0. 06 0. 06 0. 06 0. 06 0. 06 6
8 0. 05 0. 05 0. 05 0. 05 0. 06 0. 06 0. 06 0. 06 8
+10 +0.05 | +0.05 | +0.05 | +0.05 | +0.05 | +0.05 | +0.05 | +0. 05 +10
12 O. 04 0. 04 0. 04 0. 04 0. 04 0. 05 0. 05 0. 05 12
14 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 14
16 0. 03 0. 03 0. 03 0. 03 0. 03 0. 03 0. 03 0. 04 16
18 0. 03 0. 03 0. 03 0. 03 0. 03 0. 03 0. 03 0. 03 18
20 +0. 02 | +0. 02 | +0. 02 | +0. 02 | +0.02 | +002 | +0.02 | +0.02| +20
[ES 0..02 0. 02 0. 02 0. 02 0. 02 0. 02 0. 02 0. 02 22
24 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 24
26 +0. 01 | +0.01 | +0.01 | +0.01 | +0.01 | +0. 01 +0.01 | +0. 01 26
28 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 28
30 0.00 0.00 | 0.00 | 0.00 | 0.00 | 0.00. 0.00 | 0.00 | +30
MES: —0.01 | —0.01 | —0.01 | —0.01 | —0.01 | —0.01 | —0.01 | —0.01 32
34 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 0. 02 34
36 0. 02 0. 02 0. 02 0. 02 0. 02 0. 02 0. 02 0. 02 36
38 0. 02 0. 02 0. 02 0. 02 0. 03 0. 03 0. 03 0. 03 38
40 =0.03 | —0.03 | —0. 03 | —0. 03 | —0. 03 | —0. 03 | —0. 03 | —0. 03 | +40
842 0. 03 0. 03 0. 03 0. 04 0. 04 0. 04 0. 04 0. 04 42
44 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 0. 04 44
46 0. 04 0. 04 0. 04 0. 05 0. 05 0. 05 0. 05 0. 05 46
48 0. 05 0. 05 0. 05 0. 05 0. 05 0. 05 0. 05 0. 05 À
= 0.05 | —0.05 | —0.06 | —0.06 | —0.06 | —0. 06 | —0.06 | —0. 06
hee 0. 06 0. 06 0. 06 0. 06 0. 06 0. 06 0. 06 0. 07 52
54 0. 06 0. 06 0. 07 0. 07 0. 07 0. 07 0. 07 0. 07 54
56 0. 07 0. 07 0. 07 0. 07 0. 07 0. 07 0. 08 0. 08 56
58 0. 07 0. 07 0. 08 0. 08 03082 E 0. 08 0. 08 0. 08 EA
—0.08 | —0.08 | —0.08 | —0.08 | —0. 08 —0.09 | —0. 09 | —0. 09
Ee 0. 08 0. 08 0. 09 0. 09 0. 09 0. 09 0. 09 0. 09 Zi
64 0. 09 0. 09 0. 09 0. 09 0. 09 0. 10 0. 10 0. 10 ër
66 0. 09 0. 09 0. 10 0. 10 0. 10 0. 10 0. 10 0. 10 á
68 0. 10 0. 10 0. 10 0. 10 0. 11 0. 11 0. 11 o m
zu Zorio -0 MI OST | SO SON mo U)
es ote 0. 11 0. 11 0. 11 0. 12 0. 12 0. 12 0. 12 Ur
74 0. 11 0. 11 0. 12 0. 12 0. 12 0. 12 0. 13 0. 18 de
76 0. 12 0. 12 0, 12 0. 12 0. 13 0. 13 0. 13 0. 13 th
78 0. 12 0. 12 0. 13 0. 13 0. 13 0.13 | 0. 14 0. 14
+80 =, 1 | 0 8 | S0 | 0,58 OA (| SX | = 4 E
82 0. 13 0. 14 0. 14 0. 14 E V oe "EY. F
0. 14 0. 14 0. 15 R h Å .
A 0. 15 0. 15 0. 15 0. 15 0. 16 0. 16 GE 2
88 0. 15 0. 15 0. 15 0. 16 0. 16 0. 16 0. 16 0. P
90 — 0.15 | —0.16 | — 0. 16 | —0. 16 SEE o 4-8
T 0. 16 0. 16 0. 16 0. 17 0. 17 0. 17 a Nee i
; j . 18 E |
94 0. 16 0. 17 0. 17 0. 17 0. 17 0 ot
. 18 0. 19 0. 19
96 0. 17 0. 17 0. 17 0. 18 0. 18 0 OMS <a 98
k 0. 18 0. 18 0. 18 0. 18 0. 19 bal IK Å
100 bate 0. 18 0. 18 0. 19 0. 19 0. 19 0. 20 0. 20 100

F
Millibars Millimeters Millibars Inches Millimeters Millibars Inches Millimeters

1020 30. 765.
1021
1022
1023
1024

1025
1026
1027
1028
1029

1030
1031
1032
1033
1034

1035
1036
1037
1038
1039

1040
1041
1042
1043
1044

1045
1046
1047
1048
1049

1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064

1065
1066
1067
1068
1069

1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080

720.

675.

1264
TABLE 14
Conversion Table for Millibars, Inches of Mercury, and Millimeters of Mercury
4
^
|
E
:
d
3
4

ener oe S Q0 — c2 2» 06 Bð w o DÉI = | 000 HH 0 | Wr 00 OO HW 00 | 0 00 HW DOH WHI 00 Q2» DÉI ka 020» 00 Kc

TABLE 15
Conversion Tables for Thermometer Scales

F=Fahrenheit, C=Celsius (centigrade), K= Kelvin

1265

F C K F C K C
—20 |—28.9 | 244.3 | +40 | +4.4 | 277.6 10 de Cen
19 |§ 28.3) 944.8 || 141. (15.0 278.2 ES de «0 |8 22.2
18 1127.51 245.4 | [42 || 5.6|| 278.7 „4 2 rā 8 ei.2
171827. 2/1 245.07] 143 | 1] 6: 11] 279.3 .6 de eS BER
16 | 26.7 | 246.5 | 44| 6.7 | 279.8 .8 Ð 25-8 419.2
—15 |—26.1 | 247.0 | +45 | +7. 2 | 280.4 20 2 "m" EE
14 | 25.6| 247.6| 46| 7.8| 280.9 12 42 (R 8 7,2
ET AI 47 |1| 8.31] 291.5 4 Ja 29 | 6, 2
12 | 24.4 | 248.7 | 48| 8&9 | 282.0 4 Ð tr M
E EE |9.4]] 282.6 xd 42 SEN MC
—10 |28. 3 | 249.8 | +50 |+10.0 | 283.2 Ü qo 38 CHE
9| 22.8 250.4 || 51| 10.6 | 283.7 6. 8 B SE DN
801222)! 230008 1522 111.11 284.3 „6 2 50 112
TES: 7 281.5 11 1534 11.71) 284.8 „4 Ð O i02
6.492121 252.0 |. 541. 12.2'| 285.4 Ð E .5 9.2
=5 |—20. 6 | 252. 6 | +55 |+12. 8 | 285.9 0 Ð mi 2572
4 |420.0 | 253.2 | 56| 13.3 | 286.5 9 .8 2 E 7.2
S 19.4 | 253.7 | 57] 13.9|| 287.0 |) 8 .6 2 9 6.2
AV 18.0 | 254.3 1 58) P 4 Ð a7 5.2
21.118.941 254 8] 59] 15, 0i| 288.2 6 La 12 .5 4.2
0 —17.8 | 255.4 | +60 |+15. 6 | 288.7 | —5 de m TUNI E
bra |9172 | 255.9 |. 61] 16.4 | 289.8 || 54 .8 2 al D
2|.16.7|256.5 | 62| 16.7|289.8 || 3 .6 Ð MO 112
318 16.1 | 257.0 |. 62. 17.2||1290.41 [| 72 „4 42 v Ea
u A F2 2 .5| +08
v o | 258 2 |. +65 1+18,3 ¡29.5 |. 0 -0 ES .8| +18
6 | 14.4 | 258.7| 66 | 18.9 | 292.0 | +1 18 Ð Í 2.8
7T 813.9 | 259.8]. 674] 1914/6292. 6: ||. 12 .6 bo .9 3.8
8 9123. | 259: 8 |8| 68301 20700 6203.24 |, 53 „4 Ð eu 4. 8
9. 12.8 2604| 69| 20.6 | 293.7 || 4 2 | Pado? .5 5.8
+10 —12.2 | 260.9 | +70 |+21.1 | 294.3 | +5 -0 Ð .3 | +6.8
E KEE 26185 |01 719 217112045 |) J6 .8 m Mi 7.8
12 18 31.101262: 0 ee 720k 224212295. 4 7 .6 IÐ .9 8.8
13 | 10.6|262.6| 73| 228|295.9| 8 4 2 M 9. 8
14 | 10.0} 2632 || 74| 23.3|296.5|| 9 32 2 E
+15 —9.4 | 263.7 | +75 |+23. 9 | 297.0 0 "S .8 | +11.8
16| 8.9|264.3 | 76| 244 297.6 .8 2 500 32.8
17| 8&3|264.8]| 77| 25.0 | 298.2 .6 E 29 |4 43.8
18| 7.8| 265.4 | 78| 25.6 | 298.7 E 2 A 14.8
19| 72 2659]| 79| 26.1| 299.3 EZ 2 256 8 5.8
+20 | —6.7 | 266.5 | +80 |+26. 7 | 299.8 0 2 .8 | +16.8
21 | .61|267.0| 81 | 27.2 | 300.4 .8 2 ag JK us
22 | 5.6|26.6| 82 27.8 | 300.9 || 1 .6 | 290.2 CH 18.8
23 B5. 0326852. || OLSEN [28491] 1301.5 E 2 a” 9 d9.8
24 | 4.4|268.7 | 84 | 28.9 | 302.0 * 2 25 aus
+25 | —3.9 | 269.3 | +85 +29.4 | 302. 6 0) 293.2 Lp
26| 3.3|269.8| 86| 30.0| 303.2 .8 2 Bad M. 22.
27 | 2.8|270.4 | 87| 30.6 |303.7 .6 E 9| 238
28 | 2.2 | 270.9 | 88.| 31.1 | 304.3 E 2 T| 248
29 |J a1. 700027185 BB 8905 | 3227 | 304. 8 2 Ð „5 5.8
+30 | —1.1 | 272.0 | +90 |+32. 2 | 305. 4 0 KS M SE
81 880.6 1027236 ($391 32/8| (305. 9 .8 | 299.2 1| 278
32 16020127342 |9 920] 3398 || (306. 5 6 Ð SSES
33 | +0.6 | 273.7 | 93] 33.9 | 307.0 A 22 29. 8
34| 1.1 | 274.3] 94 | 34.4 | 307.6 £ Ð 8 |
+35 | +1.7 | 274.8 | +95 |+35.0 | 308. 2 0 = 3 +308
36 | 2.2 275.4 |. 96 | 35.6 | 308.7 .8 Ð SC
37 11:28 1275.9 | ee 36-1 |-309. 3 6 Sð «dl ES
38 | 33|276.5| 98| 36.7 | 309.8 E 2 HE
bo |88 995) 13752 | 5310.4 P 2 V eae
+40 | +4.4 | 277. 6 |+100 |+37. 8 | 310.9 0 2 ` Å
LALO A AAA A ET

1266

TABLE 16
Relative Humidity

Difference between dry-bulb and wet-bulb temperatures

13 2° 3° 4° 5° 6° 794-891) 99 | 109 19-129 1351 145

$ Cr % % p % % % RI E eent e

20

18 14

16 21

14 27

12 32
ESCH 37

8 41 2

6 45 9

4 49 | 16

mo 52 | 22

0 56 | 28 TEE
+2 59 | 33 7

62 | 37| 14
6 64| 42| 20
8 67 | 46| 25 5

1267

TABLE 16
Relative Humidity

Difference between dry-bulb and wet-bulb temperatures Dry-bulb
temp.
F

128 LSS) 19% 201, 218,229 239124392591 2691278

% % % % vq Wal vs x | %

Difference between dry-bulb and wet-bulb temperatures Dry-bulb
tempi

320 1339 MA E 3595/36? 137^ | 98" | 39*

% % N % za Za Wo de Ye

1268

e 5 MM... áh

TABLE 17
Dew Point

Difference between dry-bulb and wet-bulb temperatures

4° 5° 6° (lon Ws Ða ae L

o o o o o o o o

1269

TABLE 17
Dew Point

Difference between dry-bulb and wet-bulb temperatures

temp.
IAS 17818" 199% 20% 1212 129°) 938 1.249 1195919621279 1989 5

+46

48

+50

52

54

56

58

+60

62

64 32 0291. "251" 112015 115 9 0|—13,—52 64
66 36, 33 29| 25| 21| 15 +9 0 —14—59 66
68 39) 36| 33 29 25| 21| 16 49 0—14 —68| 68
+70 +42) +39) +36| +33 +30 +26| +21|+16| +9 0—14 —76 +70
72 451 48 40 37| 34 30) 26) 22 16/+10) +1|—14|—77 72
74 48| 46) 43) 40| 37| 34) 31) 27 22 17 10| +1|—13|—70] 74
76 Si "48 246 "44! 41 -38/035| 031) 27/23/17] 11) 4212] 76
78 53| 51 49) 47 44 AU 38] 35 32 28| 23 18 11) +3] 78
+80 +56| +54 +52 +50) +47| +45) +42/+39| +36 +32|+28 +24 +19|+12| +80
82 59) am 55 Dë 501 48 45) 43 40| 37 33) 29) 25) 20] 82
84 61 59 57 55 53 51] 49| 46| 43 41] 37| 34 30 26] 84
86 64 62 60) 58 560 54 52| 49| 47| 44 AU 38) 35) 31] 86
88 66| Gu 63 61| 59 Am 55) 52 50 48 45) 42 39 36) 88
+90 +69| --67| +65 +63| +62| +60| +58/+55 +53 +51 +48|+46| +43 +40] +90
92 71| 69% 68| op 64| 62 60) 58 56) 54| 52 49 47| 44] 92
94 73| 72 70) 68 67| 65 63| 61) 59| 57| 55| 52| 50 47] 94
96 70 74 73 71 69| 07 66| 64| 62 60 58 56) 58 51] 96
98 PS urs 75h 273 TAE TO 168/*67,65/- 63611 59% 57] 5403 98
+100 +80| +79 +77 +76 +74) +73 +71|+69/+67/+66|+64| + 62|+ 60|+57]/+ 100

Difference between dry-bulb and wet-bulb temperatures Dry-bulb

emp.
298603 631328 3303405 33521300375 3851394041 1427 3

+76 —61 +76
78 —11| —53 78
+80 +4| —10 —45 +80
82 13 +5) —8 —39 82
84 20 14 +6 —6 —33 84
86 27009 E ale A 28 86
88 sv MG at Ona 7287328 ; 88
+90 +36| +33| +28) +24 +18 +10 0|— 18 +90
92 AIP 37" 28410, 830 425 19012 562/14 92
94 Aa 238" 3 ASE 261007201 1013/04/10 94
96 49/9465 9430 395. 5362 32/118 27] 1022 1 15/4611 71-148 96
98 solī 1900 247/79.44/1-740/^$* 37/133 1-28] 23| 17] +9 74—30 98
--34|4-30|2-25|--19|--11| 0 —2H-r100

+100 +55| +58| +50| +47) +45) +41 E

1270

TABLE 18
Speed Table for Measured Mile

IAS

2 3 4

m
s =
b

Knots Knots Knots
30. 000/20. 000/15. 000
29. 752/19. 890/14. 938
29. 508/19. 780/14. 876
29. 268/19. 672/14. 815
29. 032/19. 565/14. 754

28. 800/19. 459/14. 694
28. 571/19. 355/14. 634
28. 346/19. 251/14. 575
(1/28. 125/19. 149/14. 516
27. 907/19. 048/14. 458

27. 692118. 947 14. 400/11.
. 481/18. 848/14. 343
. 27318. 750/14. 286
. 068/18. 653/14. 229
. 866/18. 557/14. 173

. 667/18. 462114. 118
18. 367/14. 062
18. 274/14. 008
18. 182/13. 953
18. 090/13. 900

18. 000/13. 846
17. 910/13. 793
17. 822/13. 740
17. 734/13. 688
17. 647|13. 636

17. 561/13. 585
17. 476/13. 534
17. 391/13. 483
17. 308 13. 433
17. 225|13. 383

17. 143/13. 333
17. 062/13. 284
16. 981|13. 235
16. 901|13. 187
16. 822|13. 139
16. 744|13. 091
16. 667|13.
16. 590/12,
16. 514/12.
16. 438|12.
16. 364/12.
16. 290/12.
16. 216/12.
16. 143/12.
16. 071|12.
16. 000/12.
15. 929|12.
7|15. 859/12.
15. 789/12,
15. 721/12,

15. 652/12.
15. 584/12.
15. 517/12.
15. 451/12,
15. 385/12.

15. 31912.
15. 12.
15. 190/12.
15. 12.
15. 12.
15 12.

©
ETT
d N

DTN TY TY UT A SSA RRA TU TY OU TU UH SSA

ELE EE Pi Og» [a | oO» oO» ocn» E IS SES ESS IES FSIS EE (SU ISIS SUIS

m

90 90 9o Qo PO 90| 90 9o Qo Qo 90| G0 Qo Qo 90 90| 90 Qo OO o o o o | c tO t £O £O OO DOD HO E
1

NANA NULO A MA A N90] 90 90 90 00 00:00 G0 B0 90 90| 00 B0 00 G0 00| 90 90 00 G0 90} P0 00 90 90 90) 90 00 90 90 90

TE TY UG TU TT TT TT TT UU TU TY Or Or HH] OT OT

per We WE Mr a El e WE = ds KE HE

1271

Speed in knots

TABLE 19

Speed, Time, and Distance

Neo HILO SE OS

=
00
= 00636 —Q x 15:600 6 O ANAIS A NA DI SO MAN RA DO IDO AN TOS ODO HN SAN HO
N vie el el el lech ei vi vi vi KAR ci ci có ed |0506 i a tH HH SS nas dc do S NENE
= RO0ODOA |co «16 t6 00 ODO ANN | 4 «6 E- 00 5» ON AA O r- 00 O AAN ODO 6: O HA | P1 co D 00 e GÉIE
m GOS el ec lei vc vi vi vi ESAS ai ai ai Cl |05 nn 06 có Jd e c9 HHH tl ti ti SH | H E 10 25 fd 10 15 19.15 SS d dr
= «5006» 6 |t co «15 c6 |F- 00 O MA «15 c E- |00 6 O — lait 16 c6 r- 00 |o: O 9 0160 | S et 00 6 |O e 6 69 tf AGS
S GO OH HH HH AANA le ci cd Cl Cl ed ei e cd 05 |68 e 05 e c6 |06 sti sti sti ati | ti ti SB SB 5 19 15 19 15 SSS dd
= ORO DOING «15 |t r- 00 6: 6 |f 6 co «19 KO r- 00 6 O || e eo rao ko r- 00 6 O NAMS ko r- 00 6 O RADO
D ei e OO HH HH lei vi vi vi E le ed ci AAA ci o Cl c6 |09 cd cd cd 05 lech 05 od c6 Ht ti sti HH HH Had 1G 15 1515S
E DOR 00 Os | C^ 4 QN eo FO có ep E 00 |O» CO e C3 c0 | HOON 00 |o00 6: O — Glen HQ OR |o0 00 6: O — (N NM tan co HON eh Vi
i OO O ei ei le el el el AIHA GAGA NAA AIA Cl Cl cic cci c e 05 |06 06 e 03 c3 |05 06 66 di BSEC i ti 19 19 19 gas
= 15 «5 F- 00 00 |Os C — Q1 C3 NH co r- |00 00 DO c [C4 C NA [co r- 00 00 O ANA 66 | aa O r- 00 00 Ce r-ooooo _
ið Oo ao ei ei lei wl O SS SS AIA cd |06 ci cd ed 05 |00 cc 06 oaa +H =H =t tas
|
= HID OR OID es e E M|AM T si lee SE E OO ODO ri E Glen To c r- 00 00 6: O ANO co «| i OF 00 NHH
<~ eieiei ei elei ei el el EEEE EEC vc vi ri elle SS AAA AIAN AIAN ei 05 J 05 05 05 05 66 |65 có eo 05 00 sti =ti SÉ <i <i
= PID 1D ORR 00 6:6 OLA 7 Q 66 co | ** 19 16 eet |F- 00 6 6: O |. e C169 c9 | Fio 16 (o ODO | e e 669 GS r-000o0o0
E eieiei ei elei ei e e lech cl cl vc vc lc vc G elei ei ei ei bd |66 66 cd cd Gi cd cd cd F
Ð HID 1D DOOR IIA DOS ANA cc «16 [i5 DIR 00100 CEO tas SO DODOS 60 C9 <H KS
ec eieiei ei elei ei ei e S O el cl vc elle vc el cl vc el el HH |HHHANN|NN ei ed elle ei ei Gi ei ei ci ei NO ed cd cd cd 60
= EE EE EECHER Es N| H H H 19 DOASS
D ei ei ei ei ei lei ei ei ei ei lei ei e HH HH HH HH HH d Gill ei ci ei eieiei ei ei ei AAA có cd
Ë AMA F TEE e ee SIE E 00 00 00 |O: e O OG O | H rf C Q1 GI NN B Pa i16 O DN] 000000 |o — H =H 1019
A RSS a ei ei e a O D HH HH HH HH el sr vil sr ri eieiei Cl Gi ei ANNAN
5 AA C6 C9 CO EH «P iG 16 i OS to E- |E- E- 00 00 00 |O: 6 6 O O |O e 9 e Q [C3 6 60 NOA H 1919 pio O O OÐ BAR
a A lei ei ei ei elei ei ere ele ei a vi ri ri dada bd cl ec ri Cl el
= ue C INNA A OD AH ROL DOO O OONHFOJONNARJAÐOOSJOOAAHAnnan HH taigas
= A ` ` `... . o ice lo elo o rr
= SO DO AAA A ei EA ET GH N C |609 M 09 60 69 | SH SH SH SH SH) SHH 19 19 10 105 S O O (9 S OOD | D r- 1100 0 00 00 00 DOS oo
x elei eieiei ei lei eieiei elei eieiei ele ei e ei ei lee ee ele e ee i ee le ee e e EE
= OOO OO O III IIIA AAA oo|o o o o NN 019 60 69 60 [69 e OD C9 C0 [C9 H H H H | <H H SH XH SH 19 19 19 19 19
vie ei ei ei leie ei ei ele ei eieiei lei ei ei e ele ei ei ie leie ee ele ee e ee ee ee leie ee le ee E SSSSS

1272

TABLE 19
Speed, Time, and Distance

Y
+
o
g
=
E!
Ð
D
Ý
a
n

NOD OD co «ti

0 c «doo

Y YH $10 10

rA YODA

NONON

OD 16 RO m=

165 10 10 a O

NRNENNO

$C ooo

CY co 1 bt O

QC C H co oo

O maior

2N orc

m CO 19 co 00

Ri 00 O

&O r- O» c OQ | xf «o 00 CO —
Y Y $10 10) [16 29 10 O O

N HONO

loo fo fo fe)
=

Q5 c4 c6 xt co
CO? OS CH

$cococ

Mao 00 O | Y co 16 r- 00

eo |19 D O O AN

8.5 | 9.0 | 9.5 | 10.0) 10.5 11.0) 11.5| 12.0] 12.5] 13.0| 13.5 14.0| 14.5 15.0| 15.5| 16.0

NN CY CX C

OMAN

Ø tt Ib | bt- 00 O 00

165 D COD SIN H19 co O

1273

TABLE 19

Speed, Time, and Distance

Speed in knots
Min- Min-
utes utes
16.5 17.0 17.5 18.0| 18.5] 19.0| 19.5 20.0| 20.5| 21.0 21.5| 22.0] 22.5] 23.0| 23.5! 24.0
Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles
1 0.3 0. 3} 0.3 0. 3| 0.3 0.3 0.3 0.3 0.3 0.41 0.41 0. 4| 0. 4| 0.4 0.4 0.4 1
2 0.6 0. 6| 0. 6| 006 0.6| 0.6 0.6| 0.7| 0.7| 0.7| 07 0.708 08 0.8| 0.8 2
3 0. 8! 0. 8| 0.9 0:9] 0. 9| 10 1.01 1. OF 1.0 1: 0| L1 L1 L1 L2 1.2 L2 3
4 (I FS P2 IES S E EC UE Mr e A
5 Ar ASA E 016/4770 20 2-0 5
6 3I996 rs 1198/1: 8199 2*05*2*0/*2:0| 2 1122/2220 282/422 6
7 1*0 2*02*0/ 9*1 9*9 9-99. 3 0.3 94v 92-4 9-5! 9:69»g 0:7] 0-7 E98 7
8 AUR o4 2 25 26127027128 2920303 11035110302 8
9 2h 2 Gl 26) 2 72 82 8-2 9/3. 0-3. 1| 3: Qi 329133134341 353.6 9
10 2.8 2.8 2. 9| 3.0 3,1 32 3.2 3.3 3.4 3.5 3.6| 3.7| 38 3.8 3.9 4.0) 10
11 303.113.273. 33.41 3.5/3.6-3.7/3.8 38 3.9| 40^41 42| 43/44 11
12 3.3 3.4 3.51 3.6] 3.7 3.8 3.9 4.0 41 42 43 44 45/461 4.7| 4.8] 12
13 3.6 3. 7| 3. 8] 3.9] 4.0 4.11 4.2 4.3 4.4 46 47 48| 49 50 51 5.2] 13
14 3.8 4.0| 4.1 4.2| 4.3| 4.4 4.6 4.7| 4.8 49| 5.015.115.2 5.4 5.5| 5.6| 14
15 4.1| 4.2 4.4 4. 5] 46 4.8| 49 5.0 5.1 5.2| 5.4| 5.5| 5.6 5.8 5.9 6.01 15
16 4.4| 4.5| 4. 7| 4.8 4.9] 5.1| 5.2 5.3 5.5, 5.0, 5.7 5.9 6.0, 6.1, 6.3 6 4| 16
17 4.7| 4.8| 5.0| 5.1, 5.2| 5.4| 5.5 5.7 5.8 6.0] 6.1] 6 2] 6. 4) 6.5| 6.7 6.8] 17
18 5.0| 5.1| 5. 2| 5.4 5.6 5.7! 5. 8| 6.0 6.2 6.3 6. 4| 6. 6| 6. 8| 6.9 7.0 7.2] 18
19 5.2. 5. 4| 5. 5| 5. 7| 5. 9| 6.0, 6.2 6.3| 6. 5| 6.6| 6.8 7.0| 7.1| 7.3| 7.4 7. 6 19
20 5.5| 5. 7| 5.8| 6.0| 6.2 6.3 6.5 6.7 6.8| 7.0| 7.2 7.3 7.5 7. | 7.8 8.0| 20
22] 5. 8| 6. 0| 6: 1| 6. 3| 6. 5| 6.6. 6.8 7.01 7.2| 7. 4| 7.5| 7. | 4.9, 8.0 8.2 & 4| 21
22 6.0 6. 2| 6. 4! 6. 6| 6.08 7.0 7.2| 7.3| 7.5 7.7 7.9 8 1] 8 2) 8&4| 8 6| 8.8] 22
23 GS) 6.5) 6 72] 8,9] 7. 17. 8| 757.779 8/0! 82) 8 4/8, 6,8 8| 9. OF 9.2] © 23
24 6.6|6.8| 7. O| 7.2| 7.4| 7.6 7.8 8.0] 8.2 84|8.6 8.8| 9.0 9.2 9.4| 9.6 24
25 6.9 7. 1| 7. 3| 7. 5| 7. 7| 7. 9|.8.11 8. 3| 8. 5| 8. 8| 9. 0| 9. 2} 9. 4) 9.6; 9. 810.0] 25
26 7.2 7.4 7.6 7.8 8.0 8. 2| 8.4 8.7 8. 9| 9.1| 9.3| 9.5| 9. 810. 0/10. 2/10. 4| 26
27 74 7.6 7.9 8. 1| 8 3| 8&6 8.8 9. 0| 9. 2| 9. 4| 9. 7| 9. 9/10. 1/10. 410. 6/10. 8| 27
28 7.7 7. 9| 8.2, 8. 4| 8.6| 8.9 9.1| 9. 3 9. 6| 9. 8/10. 010. 3110. 5110. 7|11. 0/11. 2| 28
29 8.0 82 8.5| 8.7! 8. 9| 9. 2| 9.4 9.7| 9. 910. 2/10. 410. 6/10. 9/11. 1/11. 411. 6| 29
30 8.2 8. 5| 8.8 9.0 9.2 9.5| 9. 8110. 0/10. 210. 510. 8|11. 011. 2/11. 511. 8/12. OF 30
31 8 5| 8.8 9. 0| 9. 3| 9. 6, 9. 8110. 110. 310. 6/110. 811. 1111. 411. 6/111. 9/12. 1112. 44 31
32 8.8 9. 11 9.3 9.6 9. 9110. 110. 4110. 7/10. 911. 2/11. 5/11. 7112. 012. 3112. 5,12. 8| 32
33 9. 1| 9. 4| 9. 6. 9. 9110. 210. 4/10. 7111. 011. 3111. 6/11. 812. 112. 412. 612. 913.2] 83
34 9. 4| 9.6! 9. 9110. 2/10. 5110. 8/11. 0111. 3/11. 6/11. 9/12. 2112. 5112. 8/13. 0/13. 313. 6] 34
35 9. 6. 9. 9/10. 210. 5110. 8/11. 1111. 4111. 7112. 012. 2112. 512. 8/13. 1113. 4/13. 7/14 0] 35
36
36 9. 9/10. 2110. 5110. 8111. 1111. 4111. 712. 012. 3/12. 6112. 9/13. 213. 513. 814. 114. 4
37 110. 2110. 5/10. S11. 1111. 4111. 7112. 0112. 312. 6/13. 0/13. 3/13. 613. 914 214. 5/14. 8] 37
38 110, 4/10. 8 11. 1/11. 4/11. 7/12. 012 412. 7/13. 0113. 313. 6/13. 9/14. 214. 614. 9/15. 2] 38
39 110. 7/11. 0111. 4/11. 7/12. 012. 4/12. 7/13. 013. 3113. 614. 0114. 3/14. 615. 0/15. 315.6] 39
40 (11. 0/11. 3/11. 712 012 312 713. 0113. 313. 7/14. 0/14. 314. 7/15. 0/15. 315. 716. 0 2
] 4
41.411. 3/11. 612 012. 312 613. 0113. 3/13. 7114. 014. 4/14. 7 15. 0/15. 4115. 7 16. 1116.
49 [11 611 912 212. 6113. 013. 3/13. 614. 014. 4114. 7/15. 0/15. 4/15. 8/16. 1116. 416. 8 a
43 hu 8112. 212 512 913. 3/13. 614. 014. 314. 715. 0|15. 4115. 8/16. 1/16. 5/16. 817. 2 :
44 112. 1112 5112 813. 213. 6113. 9/14. 314. 7115. 0115. 4115. 8|16. 1116. 516. 917. 217. 6| 44
45 12. 412. 813. 1/13. 513. 914. 214. 615. 0/15. 415 8/16. 1/16. 5/16 9117 DIT. ATEO 5
2, 613. 0113. 4 13. 814. 2/14. 615. 015. 3/15. 7/16. 1/16. 516. 9|17. 2117. 6/18.
i 12 913 813. 714. 114 514.915. 315. 716 116. 416. 817. 2/17. 618.018 418.8 d
48 13, 2113. 6/14. 0/14. 4/14. 8115. 2115. 6/16. 0/16. 4116. 8117. 2/17. 618. 0/18. 4118. 8/19. € e
49 13. 5/13. 9/14. 3 14. 7115. 1115. 5115. 916. 316. 7/17. 2117. 6/18. 0118. 4118. 8/19. 2/19. 8 3
50 13. 8/14. 214. 6/15. 0/15. 4115. 8.16. 216. 717. 117 5/17. 9118 3 18. 8119 2119. UT E
5 70114 414. 915. 315. 716. 2116. 617. 017. 417. 8118. 3118. 7119. 1119. 620. M
52 14. 8/14. 715. 2115. 616. 0116. 5116. 917. 3117. 818. 218. 6 19. 119. 5|19. 9/20. 4/20. 8 2
53 14. 6115. 0115. 515. 9 16. 3 16. 817. 2117. 718. 1/18. 6119. O 19. 419. 920. 320. 8121. ^ a
54 14. 8115. 3/15. 8/16. 2116. 617. 1117. 6 18. 0/18. 4/18. 9 19. 4119. 820. 2/20. 7121. 212. 0 šā
55 15. 1|15. 6/16. 0/16. 5|17. 0/17. 417. 918. 3/18. 819 219. 720.220. Mo. do bb 5
4115. 9116. 3116. 817. 317. 7118. 218. 7/19. 1|1y. 6/20. 120. 521. ; :
7 13.716. 216. 617. 1117. 818.018 519 019. 520 020. 420. 921. 421.822 322 5 2
58 116.016. 4/16. 9117. 417. 918. 4/18. 1 S | l "3219222227252
` 7117. 217. 718. 2118. 7119. 2119. 7/20. 2/20. 6 21. 1/21. 6/22. 1/22. . 123.
60 16. 216. A 5118 0118. 5119. 0.19. 5120. 020. 521. 0121. 522. 0/22. 5|23. 0/23. 5/24. 0 60

1274

TABLE 19

Speed, Time, and Distance

Speed in knots

Min- Min-

utes utes
25.0 26.5 27.5| 28.0| 28.5| 29.0| 29.5| 30.0
Miles! Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Mi
1 0.41 0. 4| 0.4 0. 4| 0.4 0. 4| 0. 5] 0.5 0. 5| 0. 5| 0. 5| 0. 5| 0. 5| 0. 5| 0. 5| 0. 1
2 0.8 0.81 0.8 0.9 0.9| 0.9 0.9| 0.9! 1.0| 1. 0] 1.0| 1.0| 1.0 1.0) 1. 0| 1. 2
3 112 122) 1535017 30 123 AL dd A EA ie 5125135 Olle Gis 3
4 1.641 7177” 12 7 17 Sh 198. Srl Sie 1398 92012 02-02 112162 4
5 201 251]; Qe 11 202025 2492. 21.232 38 2: A 24428 GR 2558 2: 5152261522612: 5
6 E ANO 25260 21712. RS O ESO ESO O lie se aie a: 6
7 2 9/- 2, Ole 3014350153. 1153. 2/1 832 8» diras ohh Se Ak Se Ale da Ol) 92 08830829783: 7
8 3.31 3.31 3. 4) 325) 3.5| 3.6 3. 7) 3. 7} 8. 8.3.9, 3. 9] 4. 0| 4-1, 4 1] 4 2). 4 8
9 3.7.3.8 3.8, 3.9| 4.0] 4.0, 4.1 42) 4.3] 4. 4| 4. 4| 4. 5| 4. 6| 4. 6| 4. 7| 4. 9
10 4. 1| 4.2| 4.2) 4.31 4. 4| 4. 5| 4. 0, 4. 7| 4. 8 4- 8| 4 9| 5: 0|. 5- 1|. 5. 2) 5. 2]. 5. 10
11 415409474 81490520. 520) Se di bs 2/15: 3/1 53 41 9: 95 2-0] 92 4] 92 Siva: 11
12 4. 91-5. 01 5: 1| 5. 2). 5. 8|. 5. 4|. 5. 5| 5. 6|. 5. 71 5. 8|. 5. 9} 6: O} 6: 1) 6- 2| 6: 3) 6; 12
13 5:3115: 45. 505. 0 5: Cleo: Sik G. O O T8 0721603100 41s 6. 5/1 On Oly 677 909 87560 13
14 5s Tbe S| 6s O 62 I. 6 2/56: 316. 4). 6,51 60 616 SiG. 98 7809772 Li an eae E 14
15 A Gos Gy O 68869 78087911174 219 ea Atala Ole AS EAS a BS 15
16 645/062 11 678/10, 91173 UE 722 ce al We Ol ve OD 77701850853 MESAS SAS 16
17 6.9| 7. 1) 7.2| 7. 4) 7.5| 7.6| 7. 8. 7.9| 8.1| 8. 2) 8. 4] 8 5| 8 6) 8. 8} 8 9) 9. 17
18 7.4| 7.5| 7.6| 7. 8) 8.0 8.1, 82 8. 4| 8.6 8. 7| 8. 8] 9.0 9. 2) 9. 3| 9. 4| 9. 18
19 7.8| 7.9 8.1, 8. 2| 8. 4) 8. 6, 8. 7| 8. 9| 9. 0] 9. 2| 9. 8| 9. 5| 9. 7| 9. 8/10. 0/10. 19
20 8.2 8.8 8.5 8. 7| 8. 8| 9. 0| 9. 2| 9. 3| 9. 5| 9. 7| 9. 8/10. 0/10. 2/10. 3/10. 5/10. 20
21 8.60 8. 8| 8. 9| 9. 1| 9.3| 9. 4| 9. 6| 9. 8/10. 0110. 2/10. 3/10. 5/10. 7/10. 8/11. 0/11. 21
22 9.0. 9. 2| 9. 4 9. 5| 9. 7| 9. 9/10. 1/10. 3/10. 4110. 6/10. 8/11. 0|11. 211. 4/11. 6/11. 22
23 9.4 9. 6| 9. 8/10. 0/10. 2/10. 4/10. 5/10. 7/10. 911. 1/11. 3/11. 5/11. 7/11. 9/12. 1/12. 23
24 9. 810. 0/10. 2/10. 4110. 6/10. 8 11. 0/11. 2/11. 4111. 6/11. 8/12. 0/12. 2112. 4/12. 6/12. 24
25 . 2110. 4/10. 6/10. 8/11. 0/11. 211. 5 11. 7/11. 9/12. 1/12. 3/12. 5112. 7/12. 9/13. 1/13. 25 u
26 . 6,10. 8/11. 0/11. 3/11. 5/11. 7111. 9/12. 1/12. 4/12. 6/12. 8/13. 0/13. 2113. 4113. 6 26
27 . 0111. 2/11. 5111. 7/11. 9/12. 2/12. 4/12. 6/12. 8/13. 0/13. 3113. . 7114. 0/14. 2 27
28 . 4/11; 7/11. 9/12. 1/12. 4112, 6/12. 8/13. 1113. 3/13. 5113. 8 . 2114. 5/14. 7 28
29 |. 8/12. 1/12. 3112. 6/12. 8/13. 0/13. 3/13. 5/13. 8|14. 0/14. 3 s MLD 0522 29
30 . 2112. 5/12. 8/13. 0/13. 2/13. 5/13. 8/14. 0/14. 2/14. 5/14. 8 ; 215. 51578 30
31 . 7112. 9/13. 2/13. 413. 7/14. 014. 2/14. 514. 7/15. 0/15. 2 . 8|16. 0/16. 3 31
32 . 1113. 3/13. 6/13. 9/14, 1/14. 414. 7114. 9/15. 2115. 5115. 7 . 3116. . 8 32
33 . 5113. 8/14. 0114. 3114. 6/14. 8/15. 1115. 4/15. 7116. 0116. 2 . 8 73 33
34 . 9/14. 2/14. 414. 7/15. 0/15. 3115. 6/15. 9116. 2/16. 4/16. 7 ES .8 34
35 . 3/14. 6/14. 9/15. 2/15. 5/15. 8/16. 0/16. 3116. 6/16. 9/17. 2 .8 .4 35
36 . 7115. 0 15. 315. 6/15. 9/16. 2/16. 5 16. 8/17. 1117. A 17. 7 .8 .9 36
37 . 1115. 4/15. 7/16. 0/16. 3/16. 6/17. 017. 3117. 6117. 9/18. 2 . 8 .4 37
38 . 9/15. 8/16. 2/16. 5/16. 8/17. 117. 417. 7/18. 0118. 4118. 7 . 3 . 0 38
39 . 9116. 2116. 6116. 9117. 2/17. 6/17. 9/18. 2/18. 5/18. 8119. 2 . 8 . 5 39
40 . 3/16. 7/17. 0117. 317. 7/18. 0/18. 3118. 7/19. 0119. 3119. 7 L9 .0 40
41 NA .8 . 1118. 4/18. 8/19. 1/19. 5/19. 8/20. 2/20. 5/20. 8/21. SN 41
42 . 2117. 5/17. 818. 218. 6/18. 9/19. 2/19. 6/20. 0/20. 3/20. 6/21. . 4121. 7/22. 0 42
43 . 6117. 918. 318. 6/19. 0/19. 4/19. 7/20. 1/20. 4/20. 8/21. 1121. 5/21. 9/22. 2/22. 6 43
44 . 0/18. 3/18. 7/19. 1/19. 419, 8/20. 2/20. 5/20. 9/21. 3/21. 6/22. 0/22. 4/22. 7/23. 1|: 44
2 „4 „8 . 1119. 5/19. 920. 2/20. 6 . 0: . 4121. 8122.22: . 9/23. 2123. 6 45
. 8/19. 2/19. 6/19. 9/20. 3/20. 7/21. 1/21. 5/21. 8/22, 2/22. 6/23. 0/23. 4/23. 8/24. 2 46
47 . 219. 6/20. 0/20. 4/20. 8/21. 2/21. 5/21. 9/22. 3122. 7123. 1123. 5123. 9|: - 3124, 7 47
48 . 6/20. 0/20. 420. 8/21. 2/21. 622. 0/22. 4122. 8/23. 2/23. 6/24. 0/24. . 8/25. 2 48
49 . 0/20. 4/20. 8/21. 2/21. 6/22. 0/22. 5/22. 9/23. 3/23. 7/24. 1124. 5 24. 39/257 49
50 . 4/20. 821. 221. 7/22. 1/22, 5/22, 9/23. 323. 8 24. 224. 6/25. 0125. 4/25. 8/26. 2 50
51 . 8/21. 2/21. 7/22, 1/22. 5 23. 0/23. 4/23. 8 24. 2/24. 6 25. 1125. 5 25. oz 4/26. 82 51
02 . 2/21. 7/22. 1/22. 523. 0/23. 4/23. 8 24. 3/24. 7/25. 1125. 6126. 0126. A . 9127. 8 52
53 . 6/22. 122. 5/23. 0/23. 4|23. 8/24. 3124. 7/25. 2125. 6 26. 1 . 5126. 9/27. 4127. 8 53
54 . 0122. 5 Ur . 4/23, 8/24, 3/24. 825. 2/25. 6/26. 1126. 6/27. 0127. 4127. 9128, 4 54
= = = = E 3 . 8/25. 2/25. 7/26. 1126. 6 27. 0|27. 5/28. 0128. 4 28. 9 55
: f 85 - 3/24, . 225. 7/26. 1/26. 627. 1|27. 5128. 0/28. 5 28. 9/29. 4 56
2 x No ME. zi Pe one .1 . 6/27. 1|27. 6/28. 0/28. 5/29. 0|29. 4/29. 9 57
J ; 4. 2124, . 1125, 6/26. . 6/27. 1127. 6/28. 0/28. 5/29. 0/29. 5130. 0130. 4 58
Go . 1124. 6 . 1125, 6: ZI . 6 27. 0127. 5/28. 0/28. 5/29. 0/29. 5/30. 0130. 5131. 0 59
. 5/25. 0/25. 5/26. 0/26. 5/27. 0/27. 5/28. 0/28. 5 29. 0 . 5130. 0.30. 5/31. 0/31. 5 60

1275

TABLE 19

Speed, Time, and Distance

Speed in knots
Min-

- Min-
utes
32.5| 33.0) 33.5 34.0| 34.5 35.0 35.5| 36.0 36.5] 37.0| 37.5| 38.0 38.5] 39.0! 39.5| 40.0 ye
Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles | Miles
1 0. 5| 0.6, 0.6 0.6 0. 6} 0.6 0.6, 0.6, 06 0.6 0.6 06 06 0.6) 0.71 0.7] - 1
2 USAS LA 25122 192/1921 052 1x29 2 N LS VISS ESI i 31 9 2
3 IIA 71 OI Medes 8 UC 8 NVS IIS 130 tO) 190240102: 0 E230 3
4 22 2220189-2/12-31 1259/3223] 244| 2: 41 2:34 2::0| 2) bl) 255| 2316) 28672. 6) 2.7 4
5 AU 2872-812. 81823082 (9.340 3:0 320r 34173: 1352 3721 33243. 313. 3 5
6 3.21 3.31 3.4 3. 4) 3. 4) 3. 5| 3.6| 3.6| 3. 6) 3.7| 3.8] 3.8) 3.8 3.9, 4.01 4.0 6
7 tr AO RASO AULA E ee 464. 6 a 7
8 A4. 3| 4. 4164. 5| (4. 5|14.. 0| 4.71 4.57) 4.81 419 42:9) 5.0 51 5.1 5.21 5. 3) 5.3 8
9 | 4.9) 5.0155. 0} 5. 1145. 2) 5.2 5.3] 5. 4) 5. 5) 5:6| 5.6| 5. 7| 5.8| 5. 8) 5.9| 6.0 9
10 5:4 5. 515. 61 15. 715.85. 8| 529) 6. O} 621106216. 2) 653) 624] 65516: 6/6. 7 10
11 6.0) 6.046. 1) 6. 26.8 6. 4- 625| 6. 6 627 6:'8] 6. 9/ 7.0; 7.11 722| 7. 277.3 iil
12 65 66/76. 7] 16. 860. 9 7: 0| 7281 7:2] TESTA 7:5 - 796) 72 7| 78; 7.9) 8.0 12
13 IZ) ie Rr sI sss E35 46 87 13
14 7. 6| 7.7 7.8 7.9 8.0| 8. 2| 8. 3| 8. 4) 8. 5| 8.6 8.8 8.9 9.0] 9. 1| 9.2) 9.3 14
15 8. 1| 8.2 8.4 8. 5| 8 6| 8.8 8.9 9.0 9. 1] 9.2 9.4 9. 5| 9.6 9. 8| 9. 9110. 0 15
16 8.7, 8. 8| 8.9 9. 1| 9.2 9.3 9. 5| 9.6| 9. 7| 9. 9/10. 0/10. 1/10. 3/10. 4/10. 5/10. 7 16
Le 9.21 9. 4| 9.5 9. 6| 9.8 9. 9.10. 1/10. 2/10. 3/10. 5/10. 6/10. 810. 9/11. 0/11. 211. 3 17
18 9. 8| 9. 9.10. 0/10. 2/10. 4110. 5110. 6110. 811. 0/11. 1/11. 2/11. 4111. 6/11. 7111. 8/12. O 18
19 110. 3/10. 4110. 6/10. 8/10. 911. 1/11. 2/11. 4 11. 611. 7/11. 912. 0/12. 2/12. 4112. 512. 7 19
20 110. 8/11. 0/11. 211. 3/11. 511. 7111. 8/12. 0/12. 212. 312. 512. 7/12. 813. 013. 2113. 3 20
21 | 11. 4/11. 6111. 7111. 9112. 1112. 212. 412. 6112. 813. 0/13. 1/13. 3/18. 5 13. 6 13. 814. 0 2l
22 411. 9112. 1112. 312. 5112. 6/12. 8/13. 0/13. 2113. 4/13. 6/13. 8/13. 9/14. 1114. 314. 514. 7 22
23 112. 5112. 6112. 8/13. 0/13. 2/13. 4113. 6/13. 814. 0/14. 2/14. 414. 6/14. 8/15. 0/15. 1/15. 3 23
24 113. 0113. 2113. 4113. 6/13. 814. 0/14. 2/14. 4114. 6/14. 8/15. 0/15. 2/15. 415. 6115. 816. 0) 24
25 113.513. 814. 0114. 2114. 4/14. 6114. 8/15. 0115. 2115. 415. 6115. 8/16. 016. 2/16. 5/16. 7 25
26 114. 1114 314. 5114. 7/15. 015. 2/15. 4115. 6/15. 8/16. 0/16. 2116. 5116. 7116. 917. 117. 3 26
27 (14. 6114 815. 1115. 3/15. 515. 8/16. 0/16. 2/16. 4116. 6/16. 9117. 1117. 3117. 617. 818. 0 27
28 115. 2115. 4115. 6115. 916. 1/16. 3116. 6116. 8117. 0117. 3117. 5117. 7118. 018. 2/18. 4/18. 7 28
29 415. 7/16. 0116. 2116. 4116. 7/16. 9/17. 2117. 4/17. 6/17. 9/18. 1118. 4118. 618. 819. 1/19. 3 29
30 [16 2116. 5/16. 8117. 0/17. 2/17. 5,17. 818. 0/18. 2/18. 5118. 8/19. 0/19. 2/19. 5/19. 8/20. 0 30
31 116. 817. 0/17. 3117. 6117. 8118. 1118. 318. 6/18. 9/19. 1/19. 419. 6 19. 9/20. 2/20. 4/20. 7 31
32 117. 3117. 6117. 9/18. 1118. 4118. 7118. 9 19. 219. 5119. 720. 0 20. 3/20. 5/20. 8/21. 1/21. 3 32
33 117. 918. 218. 4118. 7/19. 0/19. 2/19. 5119. 8/20. 1/20. 420. 620. 9/21. 221. 4/21. 722. 0 33
34 |18. 418. 7/19. 0119. 3/19. 6/19. 8/20. 1120. 4/20. 7/21. 0/21. 221. 5/21. 822. 1122. 4/22. 7 34
35 119. 0119. 2119. 5119. 8/20. 1/20. 420. 7/21. 0/21. 3/21. 6/21. 9/22. 2/22. 522. 8/23. 0/23. 3 35
36 119. 5119. 820. 120. 420. 7/21. 0/21. 321. 621. 922. 222. 522. 8/23. 1/23. 4/23. 7/24. 0 36
37 120. 020. 4/20. 7/21. 0/21. 3/21. 6/21. 922. 222. 522. 823. 123. 423. 7/24. 0/24. 4/24. 1 37
38 120. 620. 9/21. 221. 5/21. 8/22. 222. 522. 8/23. 1/23. 4/23. 824. 1/24. 4/24. 7/25. 0/25. 3 38
39 121. 1/21. 421. 822. 1/22. 422. 823. 1/23. 4/23. 7/24. 0/24. 4/24. 7/25. 0/25. 4/25. 7,26. 0 39
40 121. 7122. 0/22. 3/22. 7/23. 0/23. 3/23. 7/24. 0/24. 324. 7/25. 0/25. 3/25. 7/26. 0/26. 3/26. 7 40
41 29. 222. 622. 9/23. 223. 6/23. 924. 324. 6/24. 9/25. 3/25. 6/26. 0/26. 326. 6/27. 0/27. 3 41
42 ba 823. 1123. 423. 8/24. 2/24. 524. 825. 2/25. 6/25. 9/26. 2/26. 6/27. 0/27. 3/27. 6/28. 0 42
43 23. 323. 624. 024. 4/24. 7/25. 1125. 4/25. 826. 2/26. 5/26. 9/27. 2/27. 6/28. 0/28. 3/28. 7 43
44 123. 824. 2/24. 6/24. 9/25. 3/25. 7/26. 0/26. 4/26. 8/27. 1/27. 5/27. 9/28. 2/28. 6/29. 0/29. 3 44
45 24. 4194. 8/25. 1125. 5125. 9/26. 2/26. 6/27. 0/27. 4/27. 8/28. 1/28. 5/28. 9/29. 2/29. 6/30. 0) n:
46 79125. 3/25. 7/26. 1126. 4/26. 8 27. 227. 628. 028. 428. 829. 1/29. 529. 9/30. 3,30. 7
47 25 5125. moe 2126 627 027 4127. 8128. 2/28. 6/29. 029. 429. 8130. 230. 6/30. 9/31. 3 47
48 |26. 026 4/26. 827. 227. 6/28. 0/28. 4 28. 8/29. 2/29. 630. 030. 4/30. 8,31. 231. 632.0] 48
49 |26. 5/27. 0127. 4/27. 828. 228. 6/29. 0/29. 4/29. 8/30. 2/30. 6/31. 0/31. 4/31. 8/32. 3/32. 7] 49
50 27. 1127. 527. 9/28. 328. 829. 2/29. 6/30. 0130. 430. 831. 2131. 7182 15% 23% 9/88. 8 =
1 76/28. 0/28. 5 28. 9/29. 329. 830. 2/30. 6/31. 031. 431. 9/32. 332. 7|38. 2/33. 6/34.
52 24 9128. aer 029. 5129: 9130. 3130. 831. 2/31. 6132. 1/32. 532. 933. 4|33. 8134. 2/34. 7 52
53 los 7/29. 2/29. 630. 0,30. 530. 931. 4/31. 832. 2/32. 7/33. 1/33. 634. 0/34. 434. 9/35. 3 5
54 |29. 229. 730. 2/30. 631. 031. 532. 032. 4/32. 833. 3,33. 834. 2 34. 6/35. 1/35. 6/36. 0 4
55 29. 830. 2/30. 731. 231. 0/32. 132. 533. 033. 5133. 9451 134. 8/35. 355 836. 295.7 ad
56 ; 0.8 1. 331. 7/32. 232. 7/33. 1133. 634. 1134. 535. 0/35. 5135. 9/36. 6 i
57 A SL 15r 8 32. 332. 8/33. 2/33. 734. 2/34. 7/35. 235. 636. 1 36. 6/37. 0/37. 5/38. 0 x
58 131. 431. 9132. 432. 933. 433. 834. 334. 835. 335. 8/36. 2/36. 7/37. 2/37. 7/38. 238. 7
59 132. 0/32 4132. 933. 433. 9134. 434. 9/35. 4/35. 9/86. 4/36. 937. 437. 9/38. 4/38. 8/39. 3 59
60 32. 533, 0133. 534. 0134. 5/35. 035. 536. 0,36. 5,37. 0/37. 538. 0/38. 5/39. 0/39. 5/40. 0 60

1276

——————————————————————Á
TABLE 20

Conversion Table for Nautical and Statute Miles

1 nautical mile=6,076.11548 . . . feet 1statute mile- 5,280 feet
Nautical miles to statute miles Statute miles to nautical miles
kar Statute miles a Statute miles || Statute miles e Statute miles Pay
1 15151 51 58. 690 1 0. 869 51 44. 318
2 2. 302 52 59. 841 2 1. 738 52 45. 187
3 3. 452 53 60. 991 3 2. 607 53 46. 056
4 4. 603 54 62. 142 4 3. 476 54 46. 925
5 5. 754 55 63. 293 5 4. 345 55 47. 794
6 6. 905 56 64. 444 6 5. 214 56 48. 663
f 8. 055 D7 65. 594 7 6. 088 57 49. 532
8 9. 206 58 66. 745 8 6. 952 58 50. 401
9 10. 857 59 67. 896 9 7.821 59 51. 270
10 11. 508 60 69. 047 10 8. 690 60 52. 139
idi 12. 659 61 70. 198 11 9. 559 61 53. 008
12 13. 809 62 71. 348 12 10. 428 62 53. 877
13 14. 960 63 72. 499 13 11. 297 63 54. 746
14 IO BRI 64 73. 650 14 12. 166 64 55. 614
15 17. 262 65 74. 801 15 13. 035 65 56. 483
16 18. 412 66 75. 951 16 13. 904 66 57: 3532
da 19. 563 67 77. 102 17 14. 773 67 58. 221
18 20. 714 68 78. 253 18 15. 642 68 59. 090
19 21. 865 69 79. 404 19 ak deu pl 69 59. 959
20 23. 016 70 80. 555 20 17. 380 70 60. 828
21 24. 166 71 81. 705 21 18. 249 qui 61. 697
22 25317 72 82. 856 22 19. 117 72 62. 566
23 26. 468 78 84. 007 23 19. 986 73 63. 435
24 27. 619 74 85. 158 24 20. 855 74 64. 304
25 28. 769 75 86. 308 25 21. 724 75 65. 173
26 29. 920 76 87. 459 26 22. 593 76 66. 042
2 31. 071 Jf 88. 610 27 23. 462 Til 66. 911
28 32. 222 78 89. 761 28 24. 331 78 67. 780
29 33. 373 79 90. 912 29 25. 200 79 68. 649
30 34. 523 80 92. 062 30 26. 069 80 69. 518
31 35. 674 81 93. 213 31 26. 938 81 70. 387
32 36. 825 82 94. 364 32 27. 807 82 71. 256
33 37. 976 83 95. 515 33 28. 676 83 72. 125
34 39. 127 84 96. 665 34 29. 545 84 72. 994
35 40. 277 85 97. 816 35 30. 414 85 73. 863
36 41. 428 86 98. 967 36 31. 283 86 (4. 732
37 42. 579 87 100. 118 37 32, 152 87 75. 601
38 43. 730 88 101. 269 38 33. 021 88 76. 470
39 44. 880 89 102. 419 39 33. 890 89 77. 339
40 46. 031 90 103. 570 40 34. 759 90 78. 208
41 47. 182 91 104. 721 41 35. 628 91 79. 077
42 48. 333 92 105. 872 42 36. 497 92 79. 946
43 49, 484 93 107. 022 43 37. 366 93 80. 815
44 50. 634 94 108. 173 44 38. 235 94 81. 684
45 51. 785 95 109. 324 45 39. 104 95 82. 553
46 52. 936 96 110. 475 46 39. 973 96 83. 422
47 54. 087 97 111. 626 47 40. 842 97 84. 291
48 55. 237 98 112. 776 48 41. 711 98 85. 160
49 56. 388 99 113. 927 49 42. 580 99 86. 029
50 57. 539 100 115. 078 50 43. 449 100 86. 898
aa T TS EA

kkā ds m T

1277

TABLE 21
Conversion Table for Meters, Feet, and Fathoms
Me- 5
iie Feet Fath Meters Feet Fath Feet | Meters || Feet | Meters Tath; Meters Tath Meters
il 3. 28) 0. 55 61 | 200. 13| 33. 36 1 0.30! 61| 18. 59 1 1. 88|| 61 | 111. 56
2 6. bp 1.09 62 | 203. 41| 33. 90] 2 0. 61 62| 18. 90]| 2 3. 66||) 62 | 113. 39
9 9. 84| 1. 64|| 63 | 206. 69) 34. 45|| 3 0. 91 63| 19. 20|| 3 5.849 65011521
4 193125 2-19 64 | 209. 97| 35. 00] 4 1. 22| 64) 19. 51 4 (TS IICA 11704
5 16. A0 2.73 65 215.25 35. SAW D 1.52| 65| 19.81 5 9. 14| 65 | 118. 87
6 | 19.69 3.28| 66 | 216. 54| 36.09] 6 | 1.83| 66| 20.12] 6 | 10.97| 66 | 120. 70
Á 22. 97) 3. 83 67 | 219. 82) 36. 64|| 7 2:131 2671620342] 997 r280 8074181227253
8 20225|- 4. 37||- 68 | 223. 10| 37. 18|| 8 2.44| 68] 20. 73| 8 | 14.63| 68 | 124.36
9 29. 53| 4.92|| 69 | 226. 38| 37.73] 9 2. 74| 69| 21.03] 9 | 16. 46|| 69 | 126. 19
10 32. 81| 5.47| 70 | 229. 66| 38. 28|| 10 3.05| 70} 21. 34ļ|| 10 | 18. 291| 70 | 128. 02
11 36.09, 6.01 71 | 232. 94| 38. 821 11 9199] 9021. 64190 2012 97122129284
12 39.87, 6.56|| 72 | 236. 22| 39. 37|| 12 90072021505 IN[2 21895720015 167
13 49305 (lel 73 | 239: 50} 39. 92|| 13 90073102225 15 ES ANS 33.50
14 45. 93| 7.66|| 74 | 242. 78| 40. 46|| 14 4. 27|| 74) 22. 561 14 | 25.:6011 74 || 1385. 33
15 49. 21| 8.20| 75 | 246. 06} 41. 0111 15 495251 9651922: SONS 2-443) $452 86187016
16 52.49 8.75| 76 | 249. 34| 41. 56|| 16 4. 88, 76, 23.16] 16 | 29. 26| 76 | 138. 99
17 asi 19890 $8 00:11252. 62/1 49 L0| T7 DLS) ef 23. 40 led 31309 1140282
18 59. 065 9.84| 78 | 255.91) 42. 65|| 18 5.49| 78} 23. 77|| 18 | 32.92| 78 | 142. 65
19 62. 34; 10. 39| 79 | 259. 19| 43. 20|| 19 5. 79|| 79| 24. 08|| 19 | 34.751 79 | 144. 48
20 65. 62} 10. 94| 80 | 262. 47| 43. 74|| 20 6.10, 80 24.38| 20 | 36. 58| 80 | 146. 30
21 68. 90| 11. 48| 81 | 265. 75| 44. 29|| 21 6. 40|| 81| 24. 69|| 21 | 38. 40| 81 | 148. 13
22 72. 18| 12. 03| 82 | 269. 03| 44. 84|| 22 6371 82| 24. 99|| 22 | 40. 28| 82 | 149. 96
23 45.46, 12. 58|| 83 | 272. 81| 45. 38|| 23 7.01 83] 25. 30|| 23 | 42. 06|| 83 | 151. 79
24 78. 74| 13. 12| 84 | 275. 59) 45. 93|| 24 7. 32|| 84! 25. 60|| 24 | 43.89| 84 | 153. 62
25 82. 02| 13. 67| 85 | 278. 87, 46. 48|| 25 7.62| 85, 25.91| 25 | 45. 72 85 | 155. 45
26 85. 30| 14. 22 86 | 282. 15| 47. 08|| 26 7392/086 26 201261 55 8860157428
26 88. 58| 14. 76| 87 | 285. 48| 47. 57|| 27 85 23)| 87) 26; 521 27 |) 491385 287511 2159701
28 91. 86) 15. 31 88 | 288. 71| 48. 12|| 28 8. 53|| 88| 26. 82|| 28 | 51. 21 88 | 160. 93
29 95. 14| 15. 86|| 89 | 291.99! 48. 67|| 29 8.84 | 89] 27. 18|| 29 | 58. 04|| 89 | 162. 76
30 98. 43| 16. 40| 90 | 295. 28) 49. 21|| 30 9.14 | 90| 27. 48ļ|| 30 | 54. 86, 90 | 164. 59
31 | 101. 71| 16. 95| 91 | 298. 56; 49. 76|| 31 9. 45| 91| 27.74] 31 | 56. 69 91 | 166. 42
32 | 104. 99) 17. 50|| 92 | 301. 84) 50. 31|| 32 9. 75|| 92) 28. 04|| 32 | 58.52|| 92 | 168. 25
33 | 108. 27| 18. 04| 93 | 305. 12| 50. 85|| 33 | 10. 06|| 93| 28. 35]| 33 | 60. 35); 93 | 170. 08
34 | 111. 55| 18. 59|| 94 | 308. 40| 51. 40ļ| 34 | 10. 36|| 94| 28. 65|| 34 | 62. 18| 94 | 171. 91
35 | 114. 83] 19. 14| 95 | 311. 68 51. 95|| 35 | 10. 67|| 95) 28. 96|| 35 | 64.01| 95 | 173. 74
36 | 118. 11, 19. 69 96 | 314. 96| 52. 491] 36 | 10. 97|| 96| 29. 26]| 36 | 65. 84| 96 | 175. 56
37 | 121. 39] 20. 23| 97 | 318. 24| 53.04] 37 | 11.28|| 97, 29.'57|| 37 | 67.67| 97 | 177. 39
38 | 124. 67| 20. 78| 98 | 321.52! 53. 59|| 38 | 11.58| 98| 29. 87|| 38 | 69. 49| 98 | 179. 22
39 |127. 95; 21. 33 99 | 324. 80| 54. 13|| 39 | 11.89| 99| 30. 18]] 39 | 71.32| 99 | 181. 05
40 | 131. 23| 21. 87|| 100 | 328. 08| 54. 68ļ| 40 | 12. 19| 100| 30. 48|| 40 | 73. 15|| 100 | 182. 88
41 | 134. 51| 22. 42| 101 | 331. 36| 55. 23]|| 41 | 12. Sou 101! 30. 78|| 41 | 74. 98| 101 | 184. 71
42 | 137. 80| 22. 97|| 102 | 334. 65| 55. 77|| 42 | 12. 80/| 102 31. 09|| 42 | 76. 81| 102 | 186. 54
43 | 141. 08] 23.51|| 103 | 337. 93| 56. 32]| 43 | 13. 11| 103] 31. 39/| 43 | 78. 64| 103 | 188. 37
44 | 144. 36| 24. 06| 104 | 341. 21| 56. 87|| 44 | 13. 41|| 104 31. 70|| 44 | 80. 47| 104 | 190. 20
45 | 147. 64| 24. 61|| 105 | 344. 49 57. 411] 45 | 13. 72!) 105| 32. 00|| 45 | 82. 30|| 105 | 192. 02
46 | 150.92 25.15| 106 | 347. 77| 57. 96|| 46 | 14.02! 106| 32. 31|| 46 | 84. 12| 106 | 193. 85
47 | 154. 20! 25. 70| 107 | 351. 05| 58. 51|| 47 | 14. 33, 107| 32. 61|| 47 | 85. 95|| 107 | 195. 68
48 | 157. 48 26.25| 108 | 354. 33] 59. 06|| 48 | 14. 63| 108| 32. 92] 48 | 87. 78| 108 197. 51
49 | 160. 76. 26. 79|| 109 | 357. 61| 59. 60|| 49 | 14. 94 109| 33. 22|| 49 | 89. 61| 109 199. 34
50 | 164. 04| 27. 34|| 110 | 360. 89) 60. 15|| 50 | 15. 24|| 110| 33. 53]| 50 | 91. 44| 110 | 201. 17
51 | 167. 32| 27. 89|| 111 | 364. 17| 60. 70|| 51 | 15. 54| 111| 33. 83|| 51 | 93. 27| 111 203. 00
52 | 170. 60. 28. 43| 112 | 367. 45| 61. 24|| 52 | 15. 85| 112| 34. 14|| 52 | 95. 10 112 | 204. 83
53 | 173.88. 28. 98| 113 | 370. 73| 61. 79|| 53 | 16. 15| 113| 34. 44|| 53 | 96. 93 113 | 206: 65
54 | 177. 17| 29. 53| 114 | 374. 02| 62. 34|| 54 | 16. 46| 114| 34. 75|| 54 | 98. 76 114 | 208. 48
55 | 180. 45| 30. 07|| 115 | 377. 30| 62. 88|| 55 | 16. 76| 115 35. 05|| 55 |100. 58|; 115 SE R
à 63. 43|| 56 | 17. 07|! 116| 35. 36ļ| 56 |102. 41|| 116 S
a T3 o ķi T e HEN SS ES 98ll 57 | 17. 37|| 117| 35. 66|| 57 |104. 24| 117 | 213. 97
58 | 190. 29| 31. 71/| 118 | 387. 14| 64. 52]| 58 | 17. 68|| 118| 35. 97 58 |106. 07|| 118 | 215. 80
59 | 193. 57| 32.26| 119 | 390. 42 65. 07|| 59 | 17. 98| 119| 36. 27|| 59 |107. 90|| 119 | 217. 63
60 | 196. 85| 32. 81|| 120 | 393. 70| 65. 62]| 60 | 18. 29|| 120| 36. Sail 60 |109. 73|| 120 | 219. 46
ÉL NN

Dis-
tance

asino Br eh qn

19 IO MONO

TABLE 22
Dip of the Sea Short of the Horizon
Height of eye above the sea, in feet

15

10

1278

Q» 109 SH SH ON | SH XH OD 00 N:D Om
"sed ot | CN OO e$ 06 [o6 r- r£ SS

BO «P OC Od —- ia 4

O «t C 02 16 |E- HH A [DONADO +
~ SOT OG rZ cO c RS xi

M Cd nA

C5 C1 C1 O0» CO c9 O15 Q1 |o Or 019
BRL hd Hed od od oS AA AN

SEN a

Sooooo

ORODO| NM tas

oooor-

i ri pl ri el

A A lech vc vc ech schlech ei ei ei lA mama AS S N Njo doS

> 19 SH C» 00 [Hi F= CO I= | V 090010 (00 07 10 D O |m 00 09 O <H HADNA — O 0 Or =R O DDD DO DO
B| NrndoS(n oi Std Sods «cisci SØGA o6 o6 r- r- r- N Ø «o ko [xo «o co «co

ao dl pu eed ANNAN FARR rd rat | + A A A rr

CO tt OO H|RR-ND OO OO |o r- OS CA c6 | O 1 OO N 19 OD + Or HHONN O M) iio 10101010
3 | HR GSS Hi oido ei OS /GHSAN os E BAS GO tn oo doo woo:

sētā «ti C 00 C3 CX | CL C + + | + + |P A A A A

M NO RAD (ODO CIOOJO rt O D |0 O 9 D (O NO rt O HON AO 00 00 = b- cO CN AA St Sst ra
S| Sedas Sad GA Gados HSN cai (tiesai ai SSS o6 00 o6 o6 N O «8 «B «B «B Co] RARA RAR)

A CO CO CH CIA HH HH | 4 A

CQ c n p- 00 [00 (o e «B Q1 i OO r- 00 |O KD NOP (O DONO RIO fi CN rA NANO Reik
$ | 00g doo|eoiadcd,éri$--4wmoa--cooooc NNNNN eO «O «o «o «o 1D 191915215

SOON MANNA lei ra ri li + + + |

00 O D «o CI |i 1 GNR rt |O» co O PD O r- aR mio: mn 00 OO &O 105 SH OD © O 10 19 19 CO CO CY) OD CO
S| ~ SHSANHlSOH HON RRA |o oo or SSSSS iG 1G 1G 10 1) iG 19 19 1 1d

OWDIWIHMINAN | rel rei A A A A

v

19 00 € 10 16 |00 1 DO e cO (MA el E CIMCON 0» | c eo ON Ok r- co ic cooo co O) ooo 0
a| ¿ORADOR |6 a SS GO SOON ØS iG 10 10 10 15 19.16 <H H t H Hd t «ti

Hd HONINA e ri ri A A A rei H

rad

AE 00 16 00 | i i OP |FONKNA KHOR 10 [09 e OS E- O > oor HH SH OD Co OD 6D CD CD CO
S8 | < ed roc Goa MO eio 0000|r- r- r£ e SS et vi ue ve <H i i st oH +H H «ti t oi sti u

00 00 00 00 00
Nada

A rel A ri ri

m

A NNNNA
NANNN

SMS
O ooo
red

1279

TABLE 22
Dip of the Sea Short of the Horizon

Height of eye above the sea, in feet

tance
Miles d Miles
0.1 1311. 2 1339. 5 |367. 8 | 396.1 | 424. 4 | 452.6 | 480.9 | 509.2 | 537.5 | 565.8 | oi
0.2 [155.6 |169. 8 (184.0 | 198. 1 | 212. 2 | 226. 4 | 240.5 | 254.7 | 268.8 | 283.0 | 0.2
0.3 4103.8 |113. 3 |122. 7 | 132.1 | 141. 6 | 151.0 | 160.4 | 169.9 | 179.3 | 188.7 | 0.3
04 [78.0 | 85.0 | 92.1 | 992 | 106.2 | 113.3 | 120.4 | 127.5 | 1345 | 141.6) 0.4
0.5 l624|68.1|73.8| 794 | 85.1 | 90.7 | 96.4 | 102.0 | 107.7 | 113.4] 05
06 |521]|568|6L5| 6463| 7LO| 75.7 | 80.4| 851) 89.8| 945] 0.6
iz 1944.74 asis 15290811 56.9 | 609 | 64.91 69.01: 73.0 |. 77.11 81.1 1207
08 [|392]|428]|463]| 49.8 | 534 | 56.9| 60.4| 640 | 67. 5| 711] 08
O 9 134 94 381 4121 144 4 | 4755 | 50.7 | 538.81 56.91 60:11 63.21 0.9
UE (31. 54 344 | 8702 | 40.0 | 42781 (46.7) 48'5|.51.3| 5421 570] LO
1235172873. 31131 33.91 136. 6 le 390 (41 '6 2 57 ES ES POSENT
CH ka la 483579 3509] 1382 „6 9 13 el 12
MA By 2617 PS SH SLO I 33.2 ||35 4 .5 vu .9 31" ike:
14 |228|248|268| 289| 309| 329 4D 0 .0 20. |. 094
15513: 41 93131 25. 11] 270 | 28,9 11308 SC ^6 „5 GK
156—1:20.1:1:21.9.1-23.61|. 25.4 |. 27. 2.| 1 29.0 vm 5 IÐ Do ELA
1-7 1-19. 0-4) 207 $ 22-31| 240 |. 25:71 1 27:3 0 a FS No Burg
18 li80/196|21.2| 228] 243] 25.9 8 KO 6 CS Las
ro | i1v945138!719011!| 26 | 231 | | 246 A 6 um E [39
> 041 16.41 17/81 19.2]| 20:6 || 22:0 | 123:5 .9 3 t ch 2210
oU i5 71710 E | 21*X|1224 .8 «i 15 zs not
pr) 1 1643-1176 = 18-9-1—20-2-]-F21:5 SS -] ES 61 22
311557 16,91 sra | 19.4 |20: 6 .9 e f3 A AS
9.496) 14. 0 15.11 163) 175]| 187|/199 .0 2 P4 .6| 24
2 57|13.5|1461157| 169] 180| 19.1 i A .5 71 2.5
26 |13.0|1411|15.2| 163] 17.4| 185 6 7 .8 .8| 26
2221 19 as 174.7: aes | 15/8. 17.0 .9 .0 .0 Hl
SEK pr a eg ele E e a TN 11773 wë x5 „4 PM eov
ao $1.07) 19*94 13. 9^! 14 0*1 715: 8| 16.8 .8 8 n TAÐ
32:081 oc 13.561 124) 15.411163 bee RO 2 gd ESTO
Sisi io. 2:|. "a | 190 [1159 VB T 6 bli
aso lito 191628 18:37" 1406 | 115.5 „4 2 ui pes
ese s ites 0-127511 14527 +15. 1 9 .8 n 5. [24353
BIG T0. 6. 44114 3 12-2!| c3 | 13594] | 14 7 „6 4 2 keg
20591 10. 311121120 | 128 | 136 | | 144 .2 Ü 8 P
A O 1019 1 Tr 71115274 | 13378 |] 14.1 .9 -6 „4 3: EXEAT
Say SI | 1370 || 13.8 5 B ik .8 3.7
3.8 95010151 £1.31) 120) 12/7/|| 13.5 2 0 2 .5 3.8
3.9 at ei La TT IS] 12.5 11 132 .0 "7 „4 āsi 3. 9
4.0 6 OLIO 9| 11.6 | 12-3 || 13.0 ex eT ki .8
4.1 APOT NOTO 71) lied | baat || 126% 3.4 T ES 35 41
4,2 @ ote gis M0. BPLSLIJ2 | «1148 |] 12:05 3.2 3.9 .5 „2 4.2
4,3 0 ete OF7 era Si) eitao| i157 |} 12:8 Z0 „6 a .9 43
4,4 eons Ot 110. 21) 1048 | 10 5 11.124 8 Sr) 20 7 d
4.5 Sí N 010:7 Fl 9 6 2 ES, ; ;
4.6 847116 9/3 K 10. 0 | 010.5. | biol .8 SÉ RO) 6 2 4.6
4.7 soba | tind 6 $9 8 M DIES
4.8 Se Olden, 711. 610-2} 1098 „4 „0 16 Ð rin:
4. 9 sug 050480. 5 | $101 | 1027 oR $9 4 T) 395 Io
5.0 gr 8) 9, | 0, 4 10:0» 10.6 x E 3 aS £2
5.5 7.91 85| 9.0 9.5 | 10.0 5 0 .5 SEI p T
6. 0 Ze 8! 2.08. 6 9. 1 9. 6 KO 5 .0 .5 bm
6. 5 zumo 719108. 4 8.8 9.2 7 bI .5 So P
7.0 7 un 7i 810958. 2 8.6 9. 0 „4 8 2 6 DI
7.5 gät 75.6 8.0 8.4 8.8 2 5 .9 E Ls
8.0 A rere op re eO 8.3 8. 6 0 CS "7 T £e
8.5 7/9107: 5) 07 9 8. 2 8.5 9 2 n i P Le
GOS 37:900 755. pints 8. 1 8.5 8 zi pot 7 dee?
9.5 74240 71 5 hay. | Bis! 8. 4 7 0 B Ge pim
10. 0 TION 7154] 7.8 8.1 8.4 1 7 0 2 .5 } !

1280

o
H
5
+
g
H
o
a
H
o
E
5
<
H
o
Ka
g
<
+
o
o
E
H
o
O
o
E
=|
Be
=
<

Altitude

Temperature—degrees Fahrenheit

Altitude

Altitude

ahrenheit

Temperature—degrees F

Altitude

1281

TABLE 24

Altitude Correction for Atmospheric Pressure

Pressure in inches or millibars—Subtract correction from sextant or rectified altitude

2 SSI 3 -Ə9900 [mosso |009
E HO HAN | HO AFRO | MO E HOANNM |HONAS|HS
= OO ODO | ON | Nm RH |oosn on | 00 00 O s o D D O ODO |OAHHN | AN RHN | oros |00 000
+ + aE J
o | 3 Cocooy|oOocoolooooo|lcooocoloocos ajg ODWRO|HMNATO | DILO | HHA | HHOOO
e E EE EE EE se ēēliēēsd se SISS S/H) an | Leäeieieicei ossos Ssss
pue en Rd des as F + +
o
"a
B
© E NN NNN | A HAHAHA DOD O D D O O O O O O = $ Ne WOW H INN HOQ | ONON | HNNAN | AH OOO
S = SSS SO eos EFE E EE E EE EE = Sls "HHBdHBdHB|BAÓOSdolcoooo|looocoo|coooooó
= | | | E bla > + Ë =
5
e
Es
N z IDHHHH IMMAN AAA AA AMA MOD |oooool s | ola AHNA | MO 0000 |RoOIMdH | MONAT | HAHOOO
S o 10
s 8 SODA SO OS LSL I O S S SS SSC | 2 8 An | dos LEE E EE Lee e ee Lee ee e
Set | | | SET 6 t E + +
o
n
8
=H S DOG O |1019 rt ti | MOAAN | A HAHAHA |Aooool g ma ANHAHHAHO |GOOO MO | C109 mmm | MANNA DODOS
. zz o A te eat iu. A | ee A IRE O o S ae = eege USUS EC Al eer ef itur. d lt mae "uu How uy INE err T
S 8 cocccoloocococolooocoolooocolooocco|z S | SS SS (SS SS SS oo
= | | | | | E GN Eh T ch F ss
S
eo
us}
o a eor |MOOWIN | doma [NANA | ]F0000| 7 | oO] 8 SODMO|RROOMW | H#HYNNA |ANA HH | HOOOO
S 8 BASSSSISSSSSI/SSSSSO!/SSSSSISSSSO] | S S| =“=HOSO | SSDOS | SSB |SSSSS | SSSSS
es | | | | | g Zi + + + + +
=
=
oo E ATHAHOD|DARRO |1010 «coco | NNNNA N| OOo Ë als ODO O | (C109 10 tt coco» Og N | AHAOOOO
S = Hr rr E Lë Ee ee LEE e LEE ec Lee ee 2 S E NO OO So ss |0 0 8 8 Nes ēdē
"dl a | | | | | E + ch Há + Sr
o
P
o R «HK NH |DODOOD | O 019 rt | NARRAN | HAHOOO 4 "ig CS | HMMM | NNN mm |nan j ooon
= Ed HH | HAOOO | oo ooo | oo ooo |SSSS 8 S alle oo co) SA A (SSA (SS
E | | | | | 2 $| + is $ F
H
A
N SS rKOwmdtd | NHOGO INNAN | NNNMNNN | HAOOO «ts NAAAA | AANAR | M N ODO ODO | 0 O O 0 O
bz] e
= 8 Hm | AA l l oo ooo | SSS SSSss Ed = MoOoOoooOoeoccoceileooossisgcdscoloogegco
a = | | | | | =| + F + T
nooooļoo Soceoli moocoe oo
3 EI-IELT SEI ESTE E ` HOANM | ooawuo|weo
3 coooo|omn-mumu-.najwaowuoo|t-oooon|coooo E ocoocoo|lonae5munu|nawooo|roooo|ooooo
< =p m E ES +

1282

Latitude

De HOD SH 19
Dd 00 r- das

TUE Ai AAA Or TS" P

CO 19 > sh
ch zb OCH CH

C c3 «tf C cd
10 Y OD ODN

OD m ooo
N N A o

wN OO cd

DOM co NO

© OO 10 C2 mM
MARIO CO cO

0. 0 |90. 0 136. 9 |53. 2

«O O 00 t r-

«o 00 C CY C»
© cO Ett

OD 10 Iy OO

O 0300 00 |r- =D cO cO
mm

> CO |00 O rt I~

hb r- be ty
OO 00 00 00 00

E
©
E
=
+
E
en
n
a
o
H
3
S
o
H
E
g
g
=
+
g
E
zi
o
$
A

OP 1909 C» [i O HON

75.5 |14. 5 |60. 0 |30. 0 |41. 5 48. 6

0. 0

Meridian Angle and Altitude of a Body on the Prime Vertical Circle

90. 0 0.0 170. 5 |19. 5 148. 2 |41. 8 | 0.0 [90.0 [41.5 |48. 6 153. 2 |36. 9

90. 0

Latitude

n italics indicate nearest approach to prime vertical

Numbers

1283

TABLE 25
Meridian Angle and Altitude of a Body on the Prime Vertical Circle

Declination (same name as latitude)

Latitude Latitude

E
+

o

RR
rasas

ONPRNRDA OU OGOR DO OA RIO DN OO Glen STOP O TRP bäi Ce OO O OD ODO O RTG OG OO 9o ` Æ WKORWS

Kn D|D Y Y Oo CO
V | te
SI

OO ND GOD ’?
Se OR UD VO O
NO» BICONKS
OQ OH Q1 00 2 YO
DAN oļu
WHR =
99 YODO an ono
Ce R

SOPA EE Ed EK IEA NO DONA SO EE E
c o0) -1oO omo tomo?

Ka
Ze

QUE Va DA DO
EE or oo
anve HO

NWWWW PRR O
SS DON PE NO OO Ot P| Oo

NONI NP WDD OO W|O

00 œo Nane -10O NEO 00 OO bod co CIM ?9 Ot WIDNAWSD

DD 0 S G2 G2 O] Gr Or Or Or d» | BB CO DO

ij

DO DOOM O OO WD) WO DW] BOOTH DH DARDO O HOT ee A NOA O Se N ee] SIR -2 09 ACE RNS

COrabä AOE Na GO O A Ni GOOD ln OCI HPA RT OTO Eu CO Gallen kä 00| TOO GO ANY O| O NH Of OO moo
ONP?0D0O0d|0A PANE WANODN| HOOWNOR NODO] DA sl VO sl En EA V E ba E SDD RO OO On O

OAHNaIIA| NAL NOA D 00 O | WONTON RNOWI DO V NN] DOME WI PNODDOIONANHI NOON ANY = Of R ODO BO

B» 00 TOO DO GTO Ra NO A NODOS O A NANO Aa IO DO 09 00 VO 00 OO RIP Ot cO -100 O D = OF | = $9190 O
92000 to02| O Oo NN O LAND Oo 00 O sl len O02 00 | O en enen selen oo elen el CR en Glen, ep ei ls E ED et Noa Ola D ete 9$ oo
O H 00100 NR Na o:00] tod4|O:00 OO toc 00 — 4» -1O Hx Oo tO IN AIN cO Or 9| O LIDO 0200 i 02 01 t2 0 00 jo Olk Q O | OUS O

. 0
. 4
. 6
5
.8
32
„0
zu
.6
.4
.4
AS)
„4
. 9
TL
Em
.5
"9
41
.2
PA
el
ms)
B
.3
. 0
26
bo
.6
21
. ð
MO)
s
Ba
=0
.4
gk
20
.8
AO
bel
5 di
23
.5
.8
„0
„2
„4
.6
.8
29
.3
. 6
. 9
„2
.5
.2
29
.4
uo
.5

PHM DD nn | 90 90 90 90 90} 90 PO (O so t0 | o so ¢

N N N N N pol 90 90 90 90 O © cO cO cO cO | © €

Numbers in italics indicate nearest approach to prime vertical

1284

TABLE 25
Meridian Angle and Altitude of a Body on the Prime Vertical Circle

Declination (same name as latitude)

Latitude 128 13% 142

Latitude

Alt

0 90.0 | 0.0 190. 0 | 0.0 |90.0 | 0.0 190. 0 | 0.0 [90.0 | 0.0 190. 0 | 0.0 0
1 85.3 | 4.8 185.7 | 4.4186.0| 4 1 |86.3 | 3.9 l86.5 | 3.6 186.7 | 8.4 1
2 80.6 | 9.7 181.3 | 8.9 |81.9 | 8.3 l82.5 | 7.7 183.0 | 7.3 183.4 | 6.9 2
3 75.7 14.6 |76. 9 113.5 |77. 9 |12.5 l8. 7 |11. 7 179. 5 |10. 9 |80. 1 10.3 3
4 70.8 |19. 6 |72..4 18.1 |73. 7 116.8 |74. 9 [15.6 |75. 9 |14. 7 [76.8 |18. 8 4
5 65.7 24. 8 (67.7 22.8 (69.5 |21. 1 (70.9 19.7 (72.2 118.4 173. 4 17.8 5
6 60. 4 |90. 2 |62. 9 |27. 7 |65. 1 |25. 6 |66. 9 23.8 |68. 5 |22. 3 169. 9 |20. 9 6
7 54. 7 |85. 9 |57. 9 |32. 8 |60. 5 |30. 2 |62. 7 |28. 1 |64. 6 |26. 2 |66. 3 |24.6 7
8 48.6 |42. 0 |52. 5 |38. 2 los. 7 |95. 1 los. 4 (32. 5 |60. 7 |30. 3 |62. 6 |28. 4 8
9 41.8 |48. 8 |46. 7 |44. 1 160. 6 |40. 3 los. 8 |87. 2 |66. 5 |34. 6 |58. 8 |32. 3 9
10 88.9 56.6 |40. 2 50.5 |45. 0 45.9 18. 8 42.1 162.1 |99. 0 |54. 8 36. 4 10
11 23.9 |66. 6 |32. 7 |58. 0 |88. 8 |52. 1 |43. 5 |47. 5 |47. 8 48. 8 150. 5 |40. 7 11
12 0.0 190.0 123. 0 |67. 6 |81. 5 |69. 3 |87. 5 |58. 4 |42. 2 49.0 146. O 45.3 12
13 23.0 |67.6 | 0.0 190. 0 |22. 2 |68. 4 180. 5 eo. 4 |86. 4 |54. 7 ls. o |50.3 13
14 31. 5 |59. 3 |22. 2 |68. 4 [0.0 190.0 127. 5 |69. 2 |29. 6 |61. 4 |85. 4 |55. 8 14
15 37. 5 |53. 4 |30. 5 |60. 4 |21. 5 69. 2 | 0.0 190. 0 |20. 9 |69. 9 |28. 8 (62. 3 15
16 42.2 |49. 0 |36. 4 |54. 7 |29. 6 |61. 4 [20.9 169. 9 | 0.0 190.0 120. 3 |70. 5 16
17 46. 0 |45. 3 |41. 0 |50. 3 |35. 4 55. 8 128. 8 (62. 3 120. 3 (70. 5 10. 0 190. 0 17
18 49. 1 |42. 3 |44. 7 |46. 7 |39. 9 |51. 5 |34. 4 |56. 9 |28. 1 |63. 1 119.8 |71. 1 18
19 51. 9 39.7 |47. 9 43. 7 |43. 6 |48. 0 138. 9 |52. 7 |33. 6 |57. 8 |27. 4 163. 9 19
20 54.3 37.4 |50. 6 41.1 |46. 8 45. 0 |42. 6 |49. 2 138.0 |53. 7 132.9 |58.7 20
21 56. 4 |35. 5 |53. 0 |38. 9 |49. 5 |42. 4 |45. 7 |46. 2 141. 7 |50. 3 |37.2 |54.7 21
22 58. 3 |33. 7 |55. 2 |36. 9 151. 9 |40. 2 |48. 5 |43. 7 144. 8 |47. 4 |40.8 |51.3 22
23 60. 0 |32. 1 |57. 1 |35. 1 |54.0 |38. 3 150. 9 |41.5 |47. 5 |44. 9 143.9 |48 4 23
24 61. 5 |30. 7 |58. 8 |33. 6 155. 9 |36. 5 |53. 0 |39. 5 |49. 9 142 7 |46. 6 46.0 24
25 62. 9 |29. 5 |60. 3 |82. 2 |57. 7 34. 9 |549 37. 8 (521 40.7 149.0 43.8 25
26 64. 2 |28. 3 |61. 7 |30. 9 |59. 3 |33. 5 |56. 7 |36. 2 154.0 |390 151. 2 41. 8 26
27 65. 3 |27. 3 |63. 1 |29. 7 |60. 7 |32. 2 |58. 3 |34. 8 155. 8 |37. 4 153. 1 |40. 1 27
28 66. 4 |26. 3 |64. 3 |28. 6 |62. 0 |31. 0 159. 7 133. 5 |57. 4 136. 0 154. 9 138. 5 28
as 67. 5 |25. 4 |65. 4 |27. 6 |63. 3 |29.9 |61. 1 132. 3 158. 8 134. 6 [56.5 37.1 29
0 68. 4 |24. 6 |66. 4 |26. 7 |64. 4 (28. 9 162. 3 31. 2 160.2 33.5 158.0 135.8 30
31 69. 3 |23. 8 |67. 4 |25. 9 |65. 5 |28. 0 |63. 5 |30. 2 |61. 5 132. 4 l59. 4 134 6 31
32 70. 1 |23. 1 |68. 3 |25. 1 66. 5 127. 2 164. 6 (29. 2 l62. 7 31. 3 |607 335 32
33 70. 9 |22. 4 |69. 2 |24. 4 l67. 4 26. 4 |65. 6 |28. 4 163. 8 |30. 4 |619 [32 5 33
Y 71.6 21.8 |70. 0 |23. 7 |68. 3 25. 6 |66. 6 (27. 6 |648 |295 163. 0 [31 5 34
5 72.3 21.3 |70. 7 |28. 1 |69. 1 24. 9 [67. 5 26. 8 165. 8 28. 7 164.1
36 78. 0 |20. 7 |71. 5 |22. 5 169. 9 24. 3 |68. 4 |26. 1 166. 8 (28 0 EE dà
37 73.6 |20. 2 [72.2 21.9 |70. 7 |23. 7 |69. 2 25. 5 l67. 6 27. 3 66. 1 |29 1 37
38 74. 2 |19. 7 |72. 8 |21. 4 |71. 4 23.1 |69.9 24. 9 168. 5 |26. 6 |67.0 |28 4 38
2 CU EM 73.4 |20. 9 |72. 1 |22. 6 |70. 7 |24. 3 l69. 3 (26. 0 |67. 8 27. 7 39

5.3 |18. 9 |74. 0 |20. 5 |72. 7 22.1 |71. 4 23. 7 |70. 0 195 4
41 75. 8 |18. 5 |74. 6 |20. 1 |73. 3 |21. 6 |72.0 123. 2 170. 7 24. 8 Goba 265 Se
42 76.3 18.1 [75.1 19.6 173. 9 21.2 |72. 7 |22. 8 |71. 4 (24 3 |70.2 125 9 42
43 76. 8 |17. 7 |75. 7 19.3 |74. 5 |20. 8 |73. 3 |22. 3 |72. 1 23. 8 |70.9 (25 4 43
- alte 76. 2 |18. 9 |75. 0 |20. 4 |v3.9 21.9 |72. 7 (23. 4 171. 5 24 9 44
5 17.1 |76. 7 18.5 |75. 6 (20.0 174.5 21.5 173.3 122
46 78.2 16.8 |77. 1 |18. 2 |76. 1 (19. 7 |75. 0 21 1 173. 9 22 $ oe one 46
47 78. 6 |16. 5 |77. 6 |17. 9 |76. 6 19.3 |75. 5 |20. 7 |74. 5 |22. 1 173. 4 (23 6 47
48 79. 0 |16. 2 |78. 0 |17. 6 |77. 0 |19. 0 |76. 0 |20. 4 175. 0 21.8 |74.0 |23 2 48
49 79. 4 |16. 0 |78. 4 |17. 3 |77. 5 |18. 7 |76. 5 |20. 1 |75. 6 21.4 l74. 6 22 8 49
50 79. 7 |15. 7 |78. 8 |17. 1 |77. 9 |18. 4 |77.0 |19. 7 |76. 1 21. 1 |75 1 22 2 50
52 80. 4 15.3 |79. 6 |16. 6 |78. 8 |17. 9 |77. 9 |19. 2 |77. 1 20.5 |76.2 21 8 52
54 81. 1 |14. 9 |80. 3 |16. 1 |79. 6 |17. 4 |78. 8 |18. 7 |78.0 19.9 |77. 2 21 2 54
56 81.7 |14. 5 [81.0 15.7 |80. 3 [17.0 |79.6 |18. 2 |78. 8 19.4 |78. 1 20 7 56
58 82. 4 14.2 |81. 7 |15. 4 [81.0 16.6 |80.4 17.8 |79.7 19.0 179.0 20.2 | 358
60 83. 0 |13. 9 |82. 3 |15. 1 |81. 7 |16. 2 |81. 1 17.4 80.5 18. 6 170.8 |19 7 60
65 84. 3 13.3 |83. 8 |14. 4 |83. 3 |15. 5 |82. 8 |16. 6 |82. 3 |17.7 |818 |188| 65
70 85. 6 |12. 8 |85. 2 13.8 |84. 8 |14. 9 |84. 4 |16. 0 |84.0 17.1 |836 18 1 70
75 86. 7 |12. 4 |86. 5 |13. 5 |86. 2 |14. 5 |85.9 |15. 5 |85. 6 |16. 6 185. 3 |176 75
80 87. 9 12. 2 87. 7 13.2 |87. 5 |14. 2 |87. 3 |15. 2 |87. 1 16.3 |86 9 17.3 80

88. 9 |12. 0 |88. 8 |13. 1 |88. 8 |14. 1 |88.7 |15. 1 |88.6 |16 1 [88 5 117 1 85

Numbers in italics indicate nearest approach to prime vertical

Latitude

TABLE 25
Meridian Angle and Altitude of a Body on the Prime Vertical Circle

Declination (same name as latitude)

1285

Latitude

ES
S
=

87.

OO NO Sīka DO D o

OO NO T DDD o

DR O | ®W O O O O 2 0o O (O O

Ze

Co Co

BD] Co DW NG t6| ONO] Co OD | WH DOO

ha
90} 9)
SES

RTS
SSS

SS SS Co SS
k Els O» Code N| ONDA Y 00 O yA Y O to Y O

~ DD Gr DH o C6 Gel WB W hú a ER a

Ze NAN

GO O =
poco =

us
i
pa

HO Pw Na

Hx | Go Q9 Go] N
NOUWON PORN ©
NOW OTH elen O

Q2 WWW DNA] PRR E ln En OT OT A AY ©
NOOR IR OY N90 CO| ho 92 OLS GH) ON OG NI NW CD
AWOWA/ AMAR Oil RARO LANDA En o

PA Q3 RT cO «O| i» cO OY — 00| NOD DS O VT NI] PE cO RIO OC O» NT O D] ODO 00 O| PW DO DO DN O] k H| Or GH |+ 00 29 C] O Oo Sr W O
RO INIA A On lA NOA O RO TU O IR | NV O 00 DO O] DO NIO D O DO CO O BÍ VIR PW r|o[- O OR QO Y Y OW) O Y O Co WHO

euronun 02 02 Q2 Q2 DO] DO Sowane Ne VT El DD O RTG 00| — w DO Ut bäi OG Ojo — 4| TO 72 — Eë bal 00 0o | O) Y Ca OD
GO CUNT 00 00 01 C O OU DO] DO 02 O CO] H w On RT 00] 00 O CO NI OY WO DOB] DO Or 4| 05 00 UND Of Co + D HD TO OD Æ|] O KO e W | Æ W |W hO

NWP PN OO 00 RI VT bO| O cO D K NIO CO DOD O2| DO - 1| Q2 cO H» - 140 OORNNI t2 O N Ot OFS © DOD OO O RO WW Co Ð OS O1 Co

R Q3 -102 D WOR ONO OR CO i» cO | DU A (CO RIO O O RIO N AN) co OO NOD O O OFW BD NNW

= w OG QC O Q2 I «O| 0 00 Q2 O Cl A TREO -1 0» GTO | cO DO HA 00 | -100 — 00 OD O O ko ©

Numbers in italics indicate nearest approach to prime vertical

«o DIA DOA O4 O OA O2 01-100 ED cO «Oo co OO N VN OO toto N OO DO OTUV DOS X DO & DAD Q CA e - SR TS 9»
RH O DO CDs A O ANA LUN ONDE PRPON O] WONWRNWKHROD DO] O O BIR C HOT Co WH WHA] DH WAG) Co Y ka O5 C

1286

TABLE 26
Latitude and Longitude Factors

f, the change of latitude for a unit change in longitude i
F, the change of longitude for a unit change in latitude b
Latitude 4
|
1
4
J
1
0.00 FILĒŠ 0: 001 | A Kú 00 Á E= 0800" ES 0:00:99 1
0.02 | 57.29 | 0.02 | 57.32 | 0.02 | 57.43 | 0.02 | 57.61 | 0.02 | 57.85
0.03 | 28. 64 | 0.03 | 28.65 | 0.03 | 28. 71 | 0.03 | 28.79 | 0.03 | 28. 92 1
0.05 | 19.08 | 0.05 | 19.09 | 0.05 | 19.13 | 0.05 | 19.19 | 0.05 | 19.27 i
0.07 | 14.30 | 0.07 | 14 31 | 0.07 | 1434 | 0.07 | 14.38] 0.07 | 14.44
0.09 | 11.43 | 0.09 | 11.44 | 0. 09 | 11. 46 | 0.09 | 11.49 | 0.09 | 11.54 |
0.11 9.51 |0 ir |” 9/52 1-0. 10°). 19:54 | 20730] 79. 5711 0.10 | 9 B1 |
0.12| si4lo12| 8151012) 816] 012] 8.19] 0.12| 8.22 |!
om 7190 E014. A2 tech 00014. 57 150 OF Ta as
016 6311016 | 632 10.161 16.33 | 0.16 | 26.35 |) 0.161.888 |
0.18 ^ 567] 0.18 | E | 0181 ^5. 20.13 0.17 1.578
021| 4.701 021 | £4 7110.21] 4:72) 002 14731 0.21 | 275 k
025| 401|025 401[|[025| 402] 025| 403] 025|.405 4
0.29| 3.49|029| 3.49| 0.29 | 3.50] 0.28| 3.51] 0.28 | 3.52 |
032| 308lo.32 | 3.081032! 3.08] 032| 3.10] 032| 3.11 |
0.36 ^ 2.75] 036 | 2.75| 0.36 | 2.751 0.36 | 2.76.) 0.36 | 277 |
0.40. 2.48|0.40| 2.48| 0.40 | 248] 0.40| 2.49| 0.40 | 2.50
0.45.| 2.25 [-0-44-»2«95:|-0. 441-12. 25 | 0044 It Q 4210 212 97
0.49| 205|049| 205|0.49| 205| 0.49 | 206| 0.48| 207
0.53 | 1.88] 0.53] 1.88] 0.53 | 1.88 | 0.53| 1.89 |. 0.53 || 1:90
0.58 | 1.73 | 0.58 | 1.73| 0.57 | 1.74] 0.571 1.741 0.57| 175
062| 1.60] 0.62! 160|0.62] 160| 0.62| 1.61}. 0.62 |- 162
067| 1.48] 0.67 | 148|0.67 | 149] 0.67 | 1.49] 0.67 150
0.73 | 138|073| 138|0.72| 1.38] 0.72 | 1.38] 0.72 | 1.39
0.78 | 128|0.78| 128|0.78| 1.28] 078) 1.29] 0.78 | 1.29
0.84| 1.19] 0.84| 1190841 1191 0.83| 1.20] 0.831 12
0.90) 1.11]0.90| 1.111090] 1.11] 0.90] 1.12] 0.89 Da
097| 104|097| 104[096| 1.04] 096| 1.04] 0.96 |. 105
1.04 697|104| 097| 103 097| 103| 0.97 | 1.03 | 0.98
Lu. 0.90] 1.11 | 6090| 111. 090] 1.11] 0.90] r10| 0.91
1.19 |" 0.84] 1.19 | 084.1 1,19 | 10-84 | LS 80 E
128| 0.78] 1.28 | 0.78] 128 | 0.781 1.271 0.79 Lar 0:79
1.38 1 0573 | 1.38) 80973 (+1. 37- | 0. 72: | ^ 1-379) BO. 7348 T 36 5 0073
148| 0.67] 148 | 0.67 | 148| 0.68] 147 | 0.68l 147 | 0.68
ie 0.62] 1.60| 0.63] 1.60 | 063] 159| 063] 158| 0.63
G58| 1.73 | 058| E73 | 0.581 10721 0. 58]. 1. 79
Lag 053|188| 0.53|188 | 0.53) 187 | 0.53 ree di
205| 0.49|205| 0.49] 205| 049] 204| 0.49| 203| 0.49
2.25 | 045|2.24 | 0.45| 2.24 | 0451 223] 0.45| 2.92 - 0.45
E Du 2.47 | 0.40|2.47| 040] 246| 0.40| 2.45) 0.41
.36| 2.75 | 0861274 | 03601 273 037 2
308| 0.32] 3.08 | 0.331 3.07 | 0.33] 306| 0.33 X 05 des
3. 49 | 0. 29 Í 3. 49 | 0.29|3.48| 0.29] 3.47 | 0291 345| 029
4.01 | 0.25| 401 | 0.251400] 0.25] 3.99 | 0.25| 3.97 | 025
4.70 | 0.21] 4.70 | 021469 0.21] 468|-0.21|] 466| 021
5. 67 0.18 | 5.67 | 0.18] 5.66| 0.18) 5.64| 0.18] 5.62! 0.18
6. 31 0.16] 6.31 | 0161630] 0.16] 6.28| 0.16] 625| 0.16
0.14 | 7.31. |" 0:14 [7:30 1410. vel. 22072] Posa O Mí
8. 14 0.12:| 8: Jā | 0:12 [$8.12 0/ 12.1 8301 b 1021 OG
Eg on 9.51 - 0.10] 9. 49414, 0. 11 | a mn
Ip -09 Jil. 42 | 0.09 |11.40 | 0.09 | 11.37 | 0.09
14. 30 0. 07 14. 29 0. 07 14. 27 0. 07 14.22 | 0.07 W SE
i Í 9. i i 18. 98 | 0.05 | 18.
28. 64 0. 03 |28. 62 | 0.03 |28.57| 0.03 | 28. 48 | 0.03 25 20 obs
.29 | 0.02 157.26 | 0. 02 [57.15 | 0.02] 56.98 | 0.021 56.73 | 0.02
0.00 | '—* |» ao | AO ooo PEE ee DNO

29

Correction to latitude=f X error in longitude

R
o

6° 8°

Correction to longitude=F X error in latitude

1287

TABLE 26

Latitude and Longitude Factors
f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
Jk,
1:
is
IL
d
IL
d
1:
uF
2.
2.
2.
2.
3.
3.
3.
4.
5.
6.
i
8.
9

DIOS ad a a ša SS CUPIDE
AA SRA dcc sā
noe culnae colon dalla B eta. ae S
SNAPP ebe EE EE SS IO

PEELE SSL RPP SSS SP|SSSPSSSSSSS ER
PEEL E E Ei E El SSS EE EE E EE E EE El SPSS Pe Eee SAA Ww BOO o Ot

OODoOoooOoooooocoooooooooooooooomnomnmnoemnobo mmt t VO 9 e ge oo 0 O +
OODODOoooooooooooooooooooooomncednrmomnmonmn|m rtt |o 9 E
PEPE SSE SISS SLES SPS SPSS|SSPSS|SSSSS ER

Correction to latitude=f X error in longitude Correction to longitude=F X error in latitude

1288

TABLE 26

Latitude and Longitude Factors
f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

0.
0.
0. 0:
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0. d
0.
0.
03:
1.
H
1.
IL
1.
il,
18
il
il,
2.
2x
2.
2.
8.
3.
4,
5. :
5. 9:
6.
Ze
8. §

DS NN HH HH IS IS IO IT IS
A A a IS IT O IS IIS IIS

NS a E bi SS SO SO SS SS SS SS

in il E o SAA ASS SES Te SN

54

SSSSSSISSSSSISSSSS|SSSSS/SSSSS PERE E EE gaļu DS!

A SS EE HH mlo EE EE EE EE
CEET EE A AD ANDI

SSSSSS SSSSSSSSSS|SSSSS|ISSSSS ET a R ER

ss

Correction to latitude=f X error in longitude Correction to longitude=F X error in latitude

1289

TABLE 26

Latitude and Longitude Factors
f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

o
o
i=)

SQ LIOSgueBugtmtr|!mErmÁBmÍÁ!oÍÁ|mcÍtoOoOo»ooooÍÀ|coooceocoocooojoooooooooooooooc

E IS II EE ee e ee e ee III
DESEO bar rt IS SEO eene ele enee lee ee ele es

0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
I
1%
1
1.
1.
lr
IL
de
2.
2.
2.
3.
3.
4.
4,
5.
6.
d
8.
g.

A dos ii a A id EE E DS SSL EE EE
1

A N=

SS SS ST IS HHHH Hlm Hmm nto o no N eoleo m OL [100 os
ococooooooooooooooooooooool-oerm-ir- HH H p| nn no gole e e oo 190 50 +
SSSSSS|SSSSS|SSSSS|SSSSS|SSSSFI EE Bo] p:
essseslessoslesssslSSSSSs|SSSSoF RIN | YO O SI
ASS SS ISS SS SS HHHH H| AS ASE ETS SI

Correction to latitude=f X error in longitude Correction to longitude=F X error in latitude

1290

TABLE 26

Latitude and Longitude Factors
f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

o
o
©

0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
ilc
ils
JA
ils
il.
A
ile
I
2.
2.
2.
3.
3.
4,
4,
5.
6.
7:
8.

SS a DODOS ee e ele IS AS IS O 9999
PRESS IS nr IS IIS O O IS O IIS

SS IS SS ISS SRE Pee ele II SS ESTO

AAA TS SS IS a a TO ETE IES IST
TAO IT SIS IIS o H H H H| py pons) TES ES go go = g g
SSSSSS/SOSSSISSSSS/SSSSS|IS SH PSS H H H H| c IST ISE eo i en e o polso S Eé
SO AS ISS EE S1 ESTOS

Correction to latitude=f x error in longitude

Correction to longitude— F X error in latitude

—-———

1291

TABLE 26

Latitude and Longitude Factors
f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

A rr DP ODA PD D DPS rd rd ri rd D DODPSDPS

9oggummPspmpmmmLmEmÁEmÁEmEÓÁmÁtrmOoooooO^oooooooooooooooooooooooooooooo

O9 go|guesSPU$EmLEPTÁmÁHEPÓÁPOOOOOOÀOooooooooooooooooooooooooooooo
OLEOguep$p9prtmLtmmELÍEEmmPEPOOCOooooooooooooooooooooooooooooooooo

= 00 NI] Or oT IW

0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1:
I
1:
ils
is
its
L
ilt
2.
2.
3.
3.
4.
4.
5.
6.
73
9.

n o PP PRPP DPS EH Lag AS Lb a Ore NI PO $

aaa d s aaa FRPP RP SSA d Soda ASE

A o PP DO DP a a SAA a AA ON wos

ii SO D SP DP PPP rl Ka ode ml o EE ke El V 7
PPP SPP DP PSP D PO D ri o a ESAS WWW a A o AS:

Correction to latitude=f X error in longitude | Correction to longitude=F X error in latitude

1292

TABLE 26
Latitude and Longitude Factors

f, the change of latitude for a unit change in longitude
F, the change of longitude for a unit change in latitude

Latitude

A Azimuth

SERENA 60° 62° 64° 66° 68° s
ES | |
f F f F if F f F F

0 0. 00 = 0. 00 = 0. 00 = 0. 00 == 0. 00 = 180
1 0.01 |114. 58 | 0.01 |122. 03 | 0.01 |130. 69 | 0.01 |140. 85 | 0.01 [152.93 | 179
2 0. 02 | 57.27 | 0.02 | 61.00 | 0.02 | 65.32 | 0.01 | 70.40 | 0.01 | 76.44 | 178
3 0. 03 | 38. 16 | 0.02 | 40.64 | 0.02 | 43.53 | 0.02 | 46.91 | 0.02 | 50.94 | 177
4 0. 03 | 28. 60 | 0.03 | 30. 46 | 0.03 | 32.62 | 0.03 | 35.16 | 0.03 | 38.18 | 176
5 0. 04 | 22.86 | 0.04 | 24.35 | 0.04 | 26.07 | 0.04 | 28.10 | 0.03 | 30.51 175
6 0. 05 | 19.03 | 0.05 | 20.27 | 0.05 | 21.70 | 0.04 | 23.39 | 0.04 | 25.40 | 174
7 0.06 | 16.29 | 0.06 | 17.35 | 0.05 | 18.58 | 0.05 | 20.02 | 0.05 | 21.74 173
8 0. 07 | 14.23 | 0.07 | 15.16 | 0.06 | 16.23 | 0.06 | 17.49 | 0.05 | 18.99 | 172
9 0. 08 | 12.63 | 0.07 | 13.45 | 0.07 | 14.40 | 0.06 | 15.52 | 0.06 | 16.85 | 171
10 0.09 | 11.34|0.08 | 12.08 | 0.08 | 12.94 | 0.07 | 13.94] 0.07| 15.14 | 170
12 0.11 | 9.41 | 0.10 | 10.02 | 0.09 | 10.73 | 0.09 | 11.57 | 0.08 | 12.56 | 168
14 0-12 | 8,02 | 05120 8:541 0.11 p 9.15 oldi 9:86:11 0-09 11071 166
16 0.14 | 6.97 1/0.134 7.434 0. ī3 7.96 1 05125 855701 E 0411 9. 31 164
18 0.16 | 6.15] 0.15 | 6.56 | 0. 14 |, 7.02 |, 0.13.) 7.5771! 0512 | | 8:22 |^ 162
20 0.18 |. 5,49 | 01171 | 5:85 0.16 k 6:27 1; 01150 62275411 0014 7 2683 ET
22 0.20 | 4.95 110.19 | 5:27.| 0.18 | 5.65 |. Osi6.| 6.0914 0015 | 6561 158
24 0,22 | 4.49 | 0.21:| 4-78: 0.20 + 5.124. 10-18.| 552.1) 0:17 | | 6:00 ll 156
26 0:24 | 4510 | 0.235) 4.37.1 0.21 | 4. 68.£ 03200] 75.0444 1 0:18 |! S470 154
28 0:27 |. 376.100.251 4.0141 0.23 | 4.29 |: 0:22 462 150.90 | | 5202 D 152
30 0.29 | 3:46 [0.2731 3691 0.25 | 3.951 0,23% 4.269) Mee 7162 WTA
32 0.31 | 32011029) 3410 427 b 3.651: 10:959 (3103/18 0222. |) 4492 148
34 0.34 | 2296 103328 34161] 0.30 K 3.38 |4 (032701 3265511 0425 |) 220040 AE
36 0:36 | 2°75 110.245 2293.4 0 32 3.14 bh (10:30 3538400 0127 tsch
38 0.39 | 2.56 | 0.87. 2.73 | 0.34 |+ 2.92 |. 103320 3315.41 0:29 | | 3,42 142
40 0.42 | 2,38 [1007397 2954 [| 037 E 2772 i 033411 2203470031 113213 140
42 0.45 | 2:22 105427) 2537.| 0.39 | 2.53 IP 10:837 1| 2573/14 0934 || 2:06 Betas
44 0.48 | 2.07 | :0.45;| 2.211 0.42 | 2.36 |, (0.39 | 2.554? 0.36 || 9278 D 136
46 0.52 | 1.93 | 0.49 | 2506] 0.45 | 2.20 |. (0:42: 2.8701) 0:39 || 2558 le 124
48 0.56 | 1:80 | 0:52 | 119241 0,49 |. 2 05 |: 00.45: 222141 0:49 || 2-40. [9 139
50 0.60 | 1.68 [10.56 || 1979 0.52] LAI 0.48: 206,11 0/45 | 2704 130
52 0.64 | 1.56]0.60| 1.66|]0.56| 1.78] 0.52 | 1.92| 0.48 | 2.09 128
54 0.69 | 1.45 [05651] 1:55.) 0.60 | 1.66 |i 08564) 1:79:11 0552] | $294. 126
56 0.74 || 4-35 [/0.70.| 14445 0.65 lr 1.84 h (066041 1466:01 8556 || $250 DIS
88: | 0/80 |, 1.25 [10175;]- 1:334] 0.70 | 1.43 fy 1036511 added) 0560 || mice 122

60 0,87 |^ his | 10. 81 19258101702 ei 070 1.42 | 0.65 1. 54 12057
62 0:94 |. 1,06 | 0788 14181] 0.82 b 1.21 || age Hlasmi 10970 NM BAS 118
64 1.03 | 0.97 | 10.96.) 1,04: 0.90 |, 1,11 | (0-834 (132011) 0877 1. 30 116
66 1.12| 089| 105 | 095[|0.98 | 1.021 0.91 1.09 | 0.84 1319 114
68 |124| 0.81] 1.16 | 0.86] 1.09 0.92 | 1.01 | 0.99 | 0.93 | 1.08 112
70 19378 ORT AE S| OL IS SO ee TME 089 1.08 | 097.1 tae
72 1484 || 0:65 | 16440) 04690:| 35 0 0. 74 || 17254 0.80 tals || 053% metas
74 1:74 | 0:57 | 1.644 (02611 E 534p 0,65 E m20 0x20: 1 gaol 0.77 | 106
76 2:01 | 0:50 [11:882] 052531] M 76 p 0. 57 Ms 061 1.50 | 0.67 104
78 | 2.35 | 0.42|2.21| 0.45] 2.06] 0.48] 1.91 | 0.52] 176| 0.57 102
80 2.84 | 0.35 12.66 | 0.38|2.49 | 0.401 2.31 0. 43 < 2:12 | 0.47 | 100
81 8.16 | 0.32 | 2.96. | 0.34|2.77 | 0.36] 2.57 | 0.39 |) 2-37 | 0.42 99
82 8.56 | 0.28| 3.34 | 0.30 |3.12| 0.32] 289] 0.35] 2.67 | 0.38 98
83 4.07 | 0.25|3.82 | 0.26|3.57| 0.287 3.31. 0.30] 305! 033 97
84 |476| 0.211 4.47 0.22| 4. 17 | 0.24 | 3.87 | 0.26] 356! 0.28 96
85 872 || 0007 k oe Ol 0.20 | 4.65| 0.22] 428 0.23 95
86 7.15 | 0.14 | 6.71 | iii 5-36 | 0.19 94
87 9:54 | 0.10] 8.965 Ostet 8.36 | 012 | ured) ora 1 2015] lOO 93
88 14.32 | 0.07 [13.44 | 0.07 112. 55 | 0.08 | 11.65 | 0.09 | 10.73 | oo 92
89 128. 65 | 0.03 [26.90 | 0.04 125. 11 | 0.04 | 23.30 | 0.04 | 21. 46 0. 05 91
90 i 0. 00 — 0. 00 — 0. 00 — 0. 00 E. 0. 00 90

609 62° 64° 66° 68° EN

Correction to latitude=f X error in longitude

Correction to longitude=F X error in latitude

U I l dú.

1293

TABLE 27

Amplitudes

Declination

Latitude

| Rent ema
[^]
ye)
= Ononņo 19) O19 C 10 S19 S19 © 19 OVA © 29 O19 O19 ©
= A A A AAA ds ds AE a ea a e nr a els ls 974] cesa
5 C C16 cuo C CX T c Gi © N H co 00 O m AN MN H 19 cO b- 00 O) OQ 2000 tH 19 10 O O b= I~ 00 00 O) O OO an bei 165 Q CO O b>
S| CNC OD C OD CO OD <H txt ti si 1D 10 O 1D LO UD UD 10 10 10 O cO cO «o co © co «o cO cO «o co coco NS ll [>= I~ be E Fr [>
© SANTO | DAN RO At o <H COOC N Get enk d IDO MO | MODAL | BANOO 0 N NO MODO OR Oo O r-
Que, S i RT S a C pe, a tes | as ed po odd ii e tees uuum ICO bh lee... [| sc wt €] ar a e
e O EC cO co cO OS > P bt r rt 00 00 O (or Ker or kar CH SOTA ANN MOD <H eh fi 19 1) 16 O O hh I~ OOOO Sonne OO Hid O E
ae AAA oc ri rr mr mm n mr A A ANNNAN ANA
19 19 CO tb Co rA =H 19 O no Atom © 0 O Gs O O rd eh E mH COONS ti «O O CN 19 00 No Co OOP Oo n Or mo NANNAN
Oe E oa ee SS o a lo e Mer al, ye pe ap te) ei er [9 ei ak ei val ee GOO O A [Pe a ss x] 7e mie € CAC wo] oo: e ox. 05
19 19 101010 CO Ø O O OH r= ii 0 CO 0 O) C» OO oo ooo mr Cl CH OD CO CÓ CO SH SH 101010 OONO o0 O» CO» C5 H NO =H 12
rr m rr mr mmm oa! mr Mr (IC NANA
c Cramo no OC N H 1 b- ON IW MO | R-RONIR | OMR as O HO O; N NOAH 00 10 O + o0 co OTS ~ + 000
Oe GENEE er E **14'9 :'e*e e br e "oe e ee RK IBO $9... bh e 9 9 e lx | "e a aw e e
Dei 19 19 101010 1910 CO O O eC O r= hh D 00 00 00 00 00 O O OO ooo mm HANNA ANH «ti keete “O p- r- 00 C: DO HQ
Lan rd rd r pl rr rd A ved vost! en St v A rd r rd ra rr e rel re ANNNN
10 1D ORO NO «^ ceo D Omid lt ON 10 rt O c C0 19 00 OO Oo RO m0 00 c Toc COOC OD D ODO rn «o c9 OH
o. aaa ae ae es te e en e H -€»-—» € ee e Jr Tee oe eg Te eh ee e R Ar ee e Ee AA
ka +H ai <H ei 10) 19 10 19 1010 19 CO cO cO co b> b> > ti ~ 00 00 00 O ooo oo C CO c-r rd ene Ke Kee Cd C OD cO n «ti 1 10 CO O bh > 00 00 DO
ee esses Sess gi rr ri rd ri =P vn vr Sal m Cl
© O m m D H Or 00 C: c N +H co OCH CX ca p- O C N +H co o0 S MIDA 19 b C3 co ROI | O=VYIO -00 NR SOA 00 TA
o. a V i dd A AAN Bee E eer e CODA e Ta ou. uale
+ «ti «ti «ti «ti ei <H H ti ao 19 101010 O O «O cO cO co D b= t- b= t- MAD | Go ooo EE cu ANAND C0 CY) SH ac 1) O O nao e)
rr Les mr rat rr mi mc mr rr a!
10 19 CO O D O E Ecken OR AON mo» OO CH m C HO 00 ON Noro 6919 EC OCH CX -^ co oo c OD 19 0C c TH D rt O N OO N le
o- a a i m oz het ACA BV a ee Ta BSC CROSS bh Te "eu .
co co cO co co co <H «ti «fi «ti «tt <H H HNA 19 10 1010 O O cO cO cO co Ri 00 00 00 00 00 C: DDDDO c CO unu HNNAN C9 =+ +H 12 ac
mi rr oe HAHAHAH rr hamn]
© cocoraeo 1910 CO P= 00 DONN 12 ooo rn Ntiogb oo | DN OO HHMH D QOON HO OO M 19 00 Smoon 10010
o» A O | pe WN AE ISSN g db e V v e e 2]. s RIA A OK OS O
co co MANN OD C co OD OD C «ti «ti «ti «ti t ti <H ac ao 1919190190190 | cO cO cO cO cO h> h> IM I> IÐ > 00 00 00 00 GC O Dd) O ies ANNO OD
mr rr i om on onc
10 1910 OE OC oo o—a co Hid or DON Hig «O lO ONN YIÐ DO Nm st 1 ow 00 O CN 09 19 r O n DO O 0 m H RO kee)
o. VANA AAN AAA bra sla bori ee dari e BS rs ass IO ARA RS RAS | | Tu. n Meer || (e a n
N NN ANNAN CX CX Co co eo NM CO co CO OD OD «ti «ti «ti tH <H ti ti «ti «ti 1G 10 10 10 10 165 CO O cO co O O O rtr b> b= p- t- 00 00 00 00 O) C? SUE
o OO HHN M +H Paca «ero cc AN OD +A 10 (O D 00 O) On Ho E DÉI ED OH CX Mia (Dl ooa mo RO mI ECO On
KM a R TÐ ð ltr cod BO E BV A VE Te ee Ca Ah ie e e e e
N AAA CL CY ANNAN C C C CX OD OD OD ANN OD OD OY) CO CO ttt tH tH =H H tg ae AD 19 UD 12 LD 10 OD OOO (O O = ho > => 00 00 00 O
10 NIDO sde etc Kb Kei OD «n - aod Or 00 00 C» O QNN+ OO 00 o0 DONA "accro Ono Ho o0 c Qtr
o. FE RR A AO (AA a i-e o e al t.v úl Les e * ia s e | h O
= e e rr So ANNAN NANNN NA A AQ OD NAAA € MN NA CO «ti «ti «ti «ti <H ti ti «ti «ti LD 10 10 UD 10 IDO OHO
© S00- C1 CY CY CY C» OD C0 ch ao Ø O O tv k= r-o0009»0» oOHHNM + H aac co Ort 00 CO» DONA OD Hid dcr Oo rcs
H o
=
10
KM o
©
©
o. o
©

1294

TABLE 27
Amplitudes

Declination

Latitude

gen | 6%5 | 7%0 | 725 | 8%0 | 8°5 | 9%0 | 995 | 1020 | 1095 | 1120 | 1195 | 12°0
60|65/|7.0 755 8&0/|85]|9.0|9.5 |10.0 |10.5 [11.0 |11.5 |12. 0
6.1|66|71|76|8.1|8.6|9.1|9.6 10.2 |10.7 |11. 2 |11. 7 |12.2
6.2 | 6.7/7.2] 7.8| 8.3188) 9.3] 9.8 10.4 (10.9 |11. 4 (11.9 |12.4
6.4/6.9! 7.5| 8.0] 8.5 | 9.0] 9.6 |10.1 10.6 (11.2 |11. 7 (12.2 |12. 8
6.6| 7.21 7.7| 83188] 9.4] 9.9 10.5 11.0 11.6 (12.2 (12.7 (13.3
69/7.5/81]8 7] 9.2] 9.8 110.4 [11.0 |11.6 12.1 12. 7 (13.3 113. 9
7.1|7.7| 8.3] 89 | 9.4 (10.0 10.6 11.2 |11. 8 |12. 4 (13.0 13.6 14.2
7.2|7.8| $5|9.1| 9.7 (10.3 10.9 11.5 (12.1 (12. 7 |13.3 (13. 9 |14.
7.4|8.0|8.7|9.3|9.9 10.5 11.1 (11.8 |12. 4 (13.0 |13. 6 (14.3 |14.
7.618.3|8.9|9.5 102 [10.8 11.5 (12.1 (12. 7 |13. 4 14. 0 |14. 7 |15.
781850032 15948 1105 | E143 (181124 11301 (1848 14 e
8.1|8.8 9.4 [10.1 (10.8 (11.5 (12.1 (12.8 (13.5 |142 (14.9
849.51 129,58 110.5 111.9 11191126 118431140 14471504
8.7 | 9.4 (10.1 (10.8 (11.6 12.3 113.0 13.7 14.5 |15.2 (15. 9
9.0 | 9.7 10.5 (11.2 (12.0 12. 8 |13. 5 |14.3 15.0 |15. 8 |16. 6
9.4 |10. 1 10.9 [11.7 |12. 5 13.3 14. 1 |14.9 15.7 16.5 17.3
9.6 |10. 4 |11. 2 |12. 0 12. 8 |13. 6 114.4 15.2 16.0 |16.8 17. 7
9.8 |10. 6 11.4 |12.2 13.1 |13. 9 |14. 7 15. 6 |16. 4 |17. 2 (18, 1
10. 0 10.8 11.7 12.5 |13. 4 (14.2 |15. 1 15. 9 16. 8 |17. 6 18.5
10.2 11.1 12.0 [12.8 (13.7 |14. 6 |15. 4 16. 3 |17. 2 |18. 1 18.9
10.5 11.4 12.3 |13. 2 114.0 114.9 |15. 8 16. 7 |17. 6 |18. 5 19. 4 |20. 3 |21.3 | 55
10.8 11.7 12.6 13.5 |14. 4 115.3 |16. 2 17. 2 118.1 (19.0 |20 0 209 |21. 8 | 56
11.1 12.0 |12. 9 13.9 |14. 8 |15. 7 |16. 7 117.6 |18. 6 |19. 6 |20. 5 |21.5 22.4 | 57
11. 4 12.3 13.3 |14. 3 |15. 2 |16. 2 |17. 2 18. 1 119.1 |20. 1 |21. 1 (22 1 |23. 1 | 58
11.7 (12.7 13. 7 14. 7 15. 7 |16. 7 117.7 18. 7 |19. 7 20.7 21 7 |22.8 23.8 | 59
12. 1 |18. 1 |14. 1 115. 1 [16.2 |17. 2 (18.2 (19.3 (20. 3 |21. 4 |22. 4 |23. 5 124. 6 | 60
12.5 |13. 5 |14. 6 15. 6 16. 7 [17.8 18.8 (19.9 |21.0 22.1 (23.2 |24.3 (25 4 | 61
12.9 |14. 0 [15.0 16. 1 |17. 2 |18. 4 19. 5 (20.6 21.7 22. 8 |24. 0 |25 1 26.3 | 62
13.3 |14. 4 |15. 6 |16. 7 |17. 9 |19. 0 |20. 2 21.3 (22 5 23.7 24.9 26.0 27.3] 63
13.8 15.0 [16.2 17.3 |18. 5 19. 7 (20.9 22.1 (23.3 |24. 6 25. 8 27.1 |283| 64
65.0 ]14.3 [15.5 [16.8 |18. 0 |19. 2 |20. 5 |21. 7 |23. 0 |24. 3 (25.5 26.8 28.1 29.5] 65.0
65.5 |14. 6 15.8 |17. 1 |18. 3 |19. 6 |20. 9 |22. 2 |23.5 24.8 26.1 27.4 28.7 30 1|655
66.0 114. 9 |16. 2 |17. 4 18.7 |20. 0 |21. 3 |22. 6 |23.9 |25. 3 (26. 6 (28, 0 129. 4 30 7 | 66.0
66.5 [15.2 |16. 5 [17.8 |19. 1 |20. 4 |21. 8 23. 1 124. 5 25.8 (27.2 28.6 30.0 31. 4 | 66 5
67.0 [15.5 16.8 |18. 2 |19. 5 |20. 9 |22. 2 |23. 6 |25. 0 26.4 127. 8 |29. 2 30.7 32 1|67 0
67.5 115. 9 17.2 18.6 |19. 9 |21. 3 |22. 7 |24. 1 |25. 5 |27. 0 |28. 4 29.9 131. 4 |32.9 | 67.5
68. 0 |16. 2 |17. 6 |19. 0 |20. 4 (21.8 |23. 2 |24. 7 |26. 1 127. 6 |29. 1 |30.6 |32 2 |337| 68. 0
68. 5 |16. 6 |18. 0 |19. 4 |20. 9 |22. 3 |23. 8 |25. 3 |26. 8 |28. 3 (29.8 31.4 133. 0 34.6 | 68 5
69.0 [17.0 18.4 |19. 9 21.4 |22. 9 |24. 4 |25. 9 |27. 4 |29. 0 130.6 32.2 338 355 | 69 0
69.5 117. 4 |18. 9 |20. 4 21.9 |23. 4 |25. 0 |26. 5 |28. 1 29.7 31.4 330 34736 4 | 69.5
70.0 [17.8 |19. 3 |20. 9 |22. 4 |24. 0 |25. 6 |27. 2 |28.9 |30.5 32.2 |33. 9 135
70.5 |18. 2 19.8 |21. 4 |23. 0 |24. 6 |26. 3 (27. 9 (29. 6 (31.3 33 1 34 9 B X 2015
71.0 ]18.7 20.3 |22. 0 |23. 6 25.3 [27.0 |28. 7 |30. 5 |32. 2 34.0 35.9 37. 8 39.7 | 71.0
71.5 [19.2 20.9 22.6 24.3 26.0 27.8 |29. 5 |31. 3 33.2 35.1 |37-0 38. 9 40.9 | 71.5
72.0 |19.8 |21.5 23.2 25.0 |26. 8 |28. 6 |30. 4 |32. 3 34. 2 36.1 38.1 140.2 (42 3 | 72:0
72.5 |20.3 22.1 |23. 9 |25. 7 |27. 6 |29. 4 31.3 |33.3 135.3
78.0 |20. 9 |22. 8 |24. 6 |26. 5 |28. 4 |30. 4 32.3 |34 4 36 4 K E 30 SE 13:0
73.5 [21.6 23.5 |25. 4 27.4 |29. 3 31.4 (33.4 (35.5 37.7 |39. 9 42.2 44 6 l47 1| 73.5
74.0 22. 3 [24.2 |26. 2 28.3 30.3 |32. 4 |34. 6 |36. 8 [39.0 |41. 4 43. 8 146.3 |490| 74.0
45 [23.0 25.1 27.1 29.3 31.4 |33.6 |35. 8 [38.1 [10.5 43.0 45.6 48.2 51. 11745
75. 0 [23.8 [25.9 |28. 1 30.3 |32. 5 [34.8 |37. 2 39.6 42.1 44.8 4
75.5 [24.7 26.9 29.1 31.4 33.8 36.2 (38. 7 41.2 143. 9 (46 7 ae SC saki SCH
16.0 |25. 6 (27. 9 30.2 [32.7 (35.1 |37. 7 (40.3 (43.0 (45. 9 48.9 52.1 |55 5 59.3 | 76.0
76.5 26. 6 29.0 [31.5 (34.0 [36.6 (39.3 (42.1 45.0 |48. 1 51.3 (54.8 58 7 [63.0 | 76 5
C [27.7 ¡30.2 |32. 8 [35.5 38. 2 [41.1 |44. 1 47.2 (50.5 |54. 1 58.0 162.4 67. 6 77.0

1295
TABLE 27
Amplitudes

Declination
Latitude

Latitude

12°0 | 1225 | 1320 | 1325 | 1420 | 1425 | 1520 | 1525 | 1620 | 16°5 | 17°0 | 1725 | 18°0

13.0 |18. 5 |14. 0 114. 5 y 015.5 16. 0 |16. 5117.00
14. 2 |14. 7 22815: 08 16:939 16:288 TES
14.5 15.0 Ë UGS 1 ION d 1! 76 (0
14.9 |15. 5 SOS 16259 151767 1831
15. 5 |: SIA IS E SES
14.5 |15. 1 4 : 4 : + (9 (RB) 1 HORN
14. 8 |15. 4 X : 4 4 : „0 |19. 6 20.2
15.1 |15. 7 i : : : d „4 |20. 0 |20. 7
15. 5 |16. 1 E , q : | „9 |20. 6 |21.2
15. 9 |16. 6 å ` 5 5 LS 21518 2128

16. 4 17.1

ROO*»0| RODDO

H Qo OG» 00 Cu
NOR BRN

www C 00 Ha 000)

RODON| DD AIDA
NOUDRN-= | AFANODO| ONADO
Or Or Ot c» O WN 00 Orc N
Nee eb O m NAW

kä A Nye
Onon

N dH» 00 Q2 cO C 9D Va RD «O S

ooo ooo
~ N 00 Cr Ca

KS POR S| 0000050 NO O20! NO000 | DARIO
> OBRAS | WHOLRNO

WON MO o o
Kik Echt Za OO nn
FR WoOONN O w oo Rr

NTR AN RR

O o»00 [MS H

OTOJ ORONMNO | HONDO

CC

cO coc oma mo | TRONO ooo
GO NMS R | ONNONW | IND NO

CON N C DD Ee

ĪLES SSS
«o0 o:

1296

TABLE 27
Amplitudes

Declination

Latitude

Latitude

1820 | 1825 | 1990 | 1995 | 2020 | 2075 | 2120 | 21°5 | 2220 | 2225 | 2320 | 2395 | 24°0

o o i
18. 0 |18. 5 |19. 0 [19.5 |20. 0 |20. 5 |21. 0 |21. 5 |22. 0 |22. 5 123. 0 |23. 5 |24. 0 I
18. 3 |18. 8 |19. 3 |19. 8 |20. 3 |20. 8 |21. 3 |21. 8 |22. 4 |22. 9 |23. 4 |23. 9 |24. 4
18. 7 |19. 2 |19. 7 |20. 2 |20. 7 |21. 3 21. 8 |22. 3 |22. 8 |23. 3 |23. 9 |24. 4 |24.9 j
19. 2 |19. 7 |20. 3 |20. 8 |21. 3 121. 9 |22. 4 123. 0 |23. 5 24. 0 |24. 6 |25. 1 |25. 6 ]
19. 9 |20. 5 |21. 1 |21. 6 |22. 2 |22. 7 |23. 3 |23. 9 |24. 4 |25. 0 |25. 5 |26. 1 |26. 7 |
20.9 (21.5 |22. 1 |22. 7 |23. 3 |23. 9 |24. 4 |25. 0 |25. 6 |26. 2 |26. 8 |27. 4 28.0
21. 4 |22. 0 |22. 6 |23. 2 (23. 8 |24. 4 |25. 0 |25. 6 |26. 2 |26. 8 |27. 4 28. 0 (28. 7 Å
21. 9 |22. 5 (23. 1 23. 7 |24. 4 |25. 0 |25. 6 |26. 2 |26. 9 (27. 5 |28. 1 |28. 7 |29. 4 |
22. 5 |23. 1 |23. 7 |24. 4 |25. 0 |25. 7 |26. 3 26. 9 |27. 6 |28. 2 |28. 9 (29. 5 |30. 2 !
23. 1 |23. 7 |24. 4 |25. 1 |25. 7 |26. 4 |27. 1 27. 7 |28. 4 |29. 1 |29. 7 |30. 4 |31. 1 y
23. 8 |24. 5 |25. 2 |25. 8 |26. 5 |27.2 127. 9 |28. 6 (29. 3 |30. 0 |30. 7 |31. 4
24. 2 |24. 9 |25. 6 |26. 3 |26. 9 |27. 6 |28. 3 |29. 1 |29. 8 130. 5 31.2 131. 9
24. 6 |25. 3 |26. 0 |26. 7 |27. 4 |28. 1 |28. 8 29. 5 (30.3 |31. 0 (31. 7 |325 h
25. 0 |25. 7 |26. 4 27.2 27.9 |28. 6 |29.3 130. 1 |30.8 131. 6 32.3 133. 0 |
5. 4 |26. 2 |26. 9 |27. 6 |28. 4 |29. 1 |29. 9 |30. 6 |31. 4 |32. 1 132. 9 |33. 7
5. 9 |26. 7 |27. 4 |28. 2 |28. 9 |29. 7 |30. 5 |31. 2 |32. 0 132. 8 133.5 134. 3
6. 4 |27. 2 27.9 (28.7 (29.5 130.3 31. 1 131.8 |32. 6 |33. 4 134. 2 135.0 e
6. 9 |27. 7 |28. 5 |29. 3 |30. 1 130. 9 (31.7 132. 5 |33. 3 |34. 1 35.0 135. 8 |
7.5 |28. 3 |29. 1 129. 9 |30. 7 |31. 6 |32. 4 133.2 |34. 0 |34. 9. 35. 7 136.6 |
8. 1 |28. 9 |29. 8 |30. 6 |31. 4 |32. 3 |33. 1 |34. 0 134.8 |35. 7 |36. 6 |37. 4 |
28. 7 |29. 6 |30. 4 |31. 3 |32. 1 33. 0 133. 9 |34.8 |35. 6 |36. 5 137. 4 138. 3
29. 4 |30. 3 |31. 2 |32. 0 (32. 9 |33. 8 |34. 7 135. 6 36.5 137. 5 138. 4 139. 3
30. 1 [31.0 |31. 9 |32. 8 |33. 7 134.7 135. 6 136.5 137. 5 38. 4 (39. 4 (40 4
30. 9 |31. 8 |32. 8 (33. 7 |34. 6 |35. 6 |36. 5 137. 5 138. 5 139.5 (40.5 41.5
31. 7 |32. 7 |33. 6 |34. 6 |35. 6 |36. 6 |37. 6 |38. 6 |39. 6 |40. 6 |41. 7 (42 7 |
32. 6 |33. 6 |34. 6 |35. 6 |36. 6 |37. 6 138. 7 |39. 7 140. 8 41. 9 42. 9 |44. 0
33.5 |34. 6 |35. 6 |36. 7 |37. 7 |38. 8 |39. 9 41.0 |42. 1 (43.2 |44. 3 45.5
34. 6 |35. 6 |36. 7 |37. 8 |38. 9 |40. 0 |41. 1 |42. 3 (43. 5 l44 6 |45. 8 47. 1
35. 7 |36. 8 |37. 9 |39. 1 |40. 2 41. 4 |42. 6 43. 8 45. 0 46. 2 (47 5 (48 8
36. 9 |38. 0 |39. 2 |40. 4 41.6 |42. 8 44.1 |45. 4 46.7 148. 0 |49. 3 50. 7
„0 [38.2 |39. 4 |40. 6 |41. 9 43.2 |44. 5 |45. 8 147.1 |48. 5 |49.9 |51.4 |52.9 0
„5 138. 9 |40. 1 |41. 4 |42. 7 44.0 |45. 3 |46. 7 |48. 1 149.5 (51. 0 152 5 |54 1 5
.0 139. 6 |40. 9 |42. 2 43.5 |44.9 |46.3 [47.7 49.1 [50.6 152 1 153. 7 55.3 20
.5 140. 4 (41.7 143. O |44. 4 |45. 8 |47. 2 |48. 7 (50.2 (51.7 153, 3 155. 0 |56 7 5
.0 141. 2 42.5 43.9 45.3 46.8 |48. 2 |49. 8 [51.3 |52. 9 [54.6 56. 3 |58 1 |60. 0
62.5 142. O 43.4 44.8 |46. 3 [47.8 |49. 3 |50.9 |52. 5 |54. 2 [56.0 157.8 59. 7 l61. 7 | 62.5
63. 0 142. 9 44.3 |45. 8 |47. 3 (48.9 (50.5 |52. 1 153.8 155.6 |57. 5 |59.4 61.4 63.6 | 63 O
63.5 [43.8 |45. 3 [46,9 |48. 4 |50. 0 [51.7 |53. 4 |55. 2 |57. 1 509.1 61. 1 163.4 l65 7 | 63 5
64.0 144. 8 |46. 4 |48. 0 |49. 6 |51. 3 [53.0 |54. 8 |56. 7 |58. 7 (60.8 l63.0 l65'5 log 1 | 64.0
64.5 [45.9 |47. 5 |49. 1 |50. 8 |52. 6 |54. 4 |56. 3 |58. 4 |60.5 |62. 7 |65.2 167.9 170.9 | 64 5
65.0 [47.0 |48. 7 |50. 4 |52. 2 |54. 0 |56. 0 |58. 0 |60. 1 |62. 4 |64. 9 |67. 6 70.7 |74. 2 | 65.0
65. 5 |48. 2 |49. 9 |51.7 |53. 6 |55. 6 |57. 6 |59. 8 |62. 1 |64. 6 67. 3 |70. 4 74.1 78 8 | 65.5
66. 0 149. 4 |51. 3 |53. 2 |55. 2 |57. 2 |59. 4 |61. 8 |64. 3 |67. 1 [70.2 |73. 9 78. 6 |90.0 | 66.0
66. 5 150. 8 |52. 7 |54. 7 |56. 8 |59. 1 |61. 4 |64.0 |66. 8 |70. 0 |73. 7 178.5 |90.0 66. 5
67.0 |52. 3 |54. 3 |56. 4 |58. 7 |61. 1 |63. 7 |66.5 |69. 7 |73. 5 |78. 4 |90 0 67.0
67.5 153. 9 |56. 0 |58. 3 |60. 7 |63. 3 |66. 2 |69.5 73.3 |78. 2 190.0 7.
68.0 155. 6 |57. 9 |60. 4 |63. 0 |65. 9 |69. 2 |73. 1 |78. 1 |90.0 a
68.5 157. 5 160.0 |62. 7 |65. 6 |68. 9 |72. 9 177.9 190. 0 68. 5
69.0 159. 6 |62. 3 |65. 3 [68.7 |72. 6 177. 7 |90. 0 69. 0
69.5 61.9 |65. 0 |68. 4 |72. 4 |77. 6 (90.0 69. 5
70.0 |64.6 |68. 1 |72.2 |77. 4 |90.0 70.0
70.5 67.8 |71.9 177.2 |90. 0 70. 5
71.0 [71.7 |77.1 190.0 71.0
71.5 176.9 |90. 0 71.5
72.0 190. 0 72.0
eS

1297

O 190190 | 190219 O29 | S1940190 | 190019019 | onono

Latitude
o

OOLMOLN|ORTYLÓO | ONTDNO | onm | aonn | onm | 1818 S OÓ lS |I-00A0 | OO HANN | Nedod | 1910 So SD
HANN | 69060000900 | HH HHH | 10101910109 | 19191919190 | SOO OO | «6 co «6 co «o | «o «o co «0 cO. | rr p.p E ANNDAN NNNNA
a OA NANA | 1915910 OC | RRoDOo|onmma | ro 000 | NrtOo me | ea
E camo AO OO ro 0/992: ee VIESOS, WA e eier PRA |
N oasscos|oscoco|oco0ooconA | HH HH | HH NNN | D
= onann|mooo|rronol|nnan|ocnor|non5o|noati
Ciri AA ts er ARES | l e s END
g e S990019900900 | D O O OH | HH HH | HH HH | HANA | cda
N
5 E SAND | HIND co «o | r- r- 00000 | GO 9 600 | eo co x15 O | r- 000 HM | r- 00600 lebt
DV bo due EROR AL «sed EE WU rm x c dog pu CD ed nuo (te fad NETS Med ag ener CIS ai e r . D D D
H N Seese O D O O D O D O OC OH | NH HH | HH HEH aa aaa A NAN INN Ga | HHO
o
3 a SANMOD | rip 1 0 O | OP WOOD | DOMA | exeo co ti | OKRRAADIAMNODW!] DNIOOM | oo
H SS LE «x | e fe e e ke F ee ll eise e 0 el » e e e "e IFA
T kl asosco|aococoa|aoscooco| HH | HH | AN | ANAARN | NGM | 1000
>
E es Q n0 0909 | rt «ioc do |«r-oo009|oooonu|coaoacdose |ooro|om5mdoc[19woo0oo« | OO | rt S
Gh adgang uem EP ao MO o tz V D SD bs ek E ato cO ed IO Mie, ra N oul Bl See a “ov ef Na of AAA a a NE RR Sg e
= = co ooo UE oo ooo Do O OO | D O HH | HH HH | Arm | AQAARAR | NONNA | OOOH HIS | OO
g
S e: SAND | HH1919 OS | ODL OW | G oO OO m | ANAND | To c co r- | ODO [exco 15 | OOANMO | Dr «o o0 | eo
DENVER ea AE CVM". meret. “ee e e e|... -.5 MEZONI ( AEREOS ee D
= [S Ë = S99090 (999009090 | O O O O O | D O HH Annn ai DS SS | NANANNN ES Aoc ISR os
E Q
= =
Bes 3 2 SAN | «t HINA | OOO | Goo OO | Ox 000 | HO | ROARS |OHANH | io co r- 9 O | e «500 Q1 | r- co c6 co 1
E et et et m (ss O o Ee SOS ler v BS e'€-e] E wo 9--1.o-».2 9]. e A O o oem C
R 3 = m SSS (99090990 199999 | O O HH | AA] LRN I NNNANN | ANNAN | Sod os ed ti iL
Oo =
n A
5 3 E DOH cO SH | HH1910 | ODL DWH | MAMMO | AAN | mana RH | OMS==00 | AOOARA | taisno eo Ran A
EA AO AO IS AA ASA A EN, ES AAA O AAA PP PA | A
i m ooo oo 190990909 | DO O O O O | D O O OH | AAA | HH HH EH | AAA NINNIN cacao Eb ddd | 06 0d Hi iid
=
= ^ O nO c9 | 19191919 cO | OD OM 00 | GO OO | Me CX | AM P SF | O co r-r-r- | 00 H | íINMHFH iS r-000 0o | eis r- OG
E O O O O Mute. Oe S. NUTS IM Esiste me]. el a etie e. "e. IEA A E ere ee e T . ". "e
S e S99990 (9909099 | 9999090 | D O O OH [ss [As | HH HH | HAMA I NANNANN | NNN | Oooo si
<
4 5 OH 0909 | qt ioi | COOH DH | ONOONADO |OOHAHHAR |ANOMFH190 | OIR |RD ORAR | 919 ODO | GG OO cx eoi
LENT QE LE ou suci T» neu wel euil I s sep amy [mt mney eo EE, Le umm ome ae ree orc 6 *.x 43
o = ooo oo | oo ooo | D O O O O | D O ODO rr aa HH HH NNNANN INNA | Nod eese
g
o
E o OH 0000 | ti 10 O | co c! r- r-00 | 00000 | OO HAR | ANN H SH | 1910 O OM | F-00000 6 | GO NC | co iiS r- | 00009 ON
Ear a A O PCIE EMG T ee ee AA O o OA SR ar DAA se! sel Me “el e.» sre Ae ms we |) "ae e a s
9 xi oo on oo D D O D D O | D O D O O D O ODO O O ODO OH | HH | M HH PH HEH | HH | NNNN | NNNNN | NANOA
H
3 5 SHAN | HHI9100 | OOO | AONADOO | COHHANAIAMMHH [iioc OM | I=-0000 | DOOM | No |nomo ri
V A a SR EN A l IA NA hom TAN KI IES AA AO BS ACI IER AAA PEA WEEN NM"
e ooo oo 190900090 | D O O O O ODO ODO H | HHHHH [At] HARA HM] ANNAN | NNN | NNN oS os
oona | oonan | ODO HA | amada SH |1010 O OBM |RD-OOO | ROCHA | an sti ras | ON IDO
oadasosļ|oodadcs SSSSSI/SSS | Hi | ri rr | ri || ANNA | NN | Ns
o
3 omomo | momon | O19 OVS | 19 019019 | ON OWS
EN CAE E Ee RAN A ee AN Me ve a a CV rauer «is twee oh eo eo ée la et Zenner e e mp 8 up
= OQNAH+HOO leesch nono | ODA rt | SHOOK | I=-00030 | DO HA | Nedod H H | 1010 O or
3 HSH SH HH | 101910 1919 | 191919191 | COOOO |odododo:do|ododododgo!|rrmrrrrrmbrr|rrrmrrrp

e correction to the observed amplitude in the direction away from the elevated
d the elevated pole.

ly half the correction towar

anet, or a star, apply th

For the moon app

For the sun, a pl

pole.

1298

TABLE 29

Altitude Factor
a, the change of altitude in one minute from meridian transit;

used for entering table 30

9°

Ro

TÉR

6°

5°

4°

So

29

Declination same name as latitude, upper transit: add correction to observed altitude

ne

28
3s
s

1299

b

TABLE 29
Altitude Factor
a, the change of altitude in one minute from meridian transit:

used for entering table 30

QO cO 219 SH OD HO 000 O
OD € OD C0 C9 [C9 C9 CL CL CL | CR CI AN A CI

QC» b O19 HIN — O O 00 [Eo (O cO 105 «H
OD OD CO C C (C9 C9 C9 CL CH

CQ Ord aij O 0
HOD OD CÓ CO |09 C0 CD CON

HO O = OO (S 19 1910 H

C9 O OH C» i HO 10 CN

Declination contrary name to latitude, upper transit: add correction to observed altitude

o
a
=
È
2
=
a
ð
o
>
=
o
a
Q
o
o
2
g
E
z
o
o
E
t
tel
o
=
ð
E
n
A
a
Le
B
CH
Ý
a
=
F
d
"a
Ei
5
=
=
a
=
o
2
o
g
c
A
El
ke
-
ë
g
o
=
=
a
A
E
o
w
A

DM Hb-t| O bt Nļ O» b- O +H R 01010 «B [MA A HO
ANNAANINANANINANAR

Be S cO S 10 [19 29 SH SH A OOD A

o

Lati-
tude

Lati-
tude

T

nono oa

«o 00 C mas

E „iet emite

10 00 cA x 00

00 a OH

PI

NANA CY

HOO

Orr O19

ANNAN

TABLE 29

0 10 EEN

Altitude Factor
altitude in one minute from meridian transit;

used for entering table 30

NANANN

OO cO 165 xh CO

NN CY CL CH

Do «oco CQ

a, the change of
Declination same name as latitude, upper transit: add correction to observed altitude

1300
Lati-
tude

16 |26. 5

17 |21. 1 |26. 2

18 117. 5 |20. 9 |26. 0

19 | ies) 17320: 71257

15

Declination same name as latitude, upper transit: add correction to observed altitude

tude

Lati-

1301

its

TABLE 29

Altitude Factor

D
E
e
RE
+
g
3
—
=
E
o
E
šo
m”
+ e
až
a
53
a
Æ
M
R
o
as
og
a
E
Be
23
=
"d
+
©
o
Gd
g
3
a
o
o
oj
+
Ð

Declination contrary name to latitude, upper transit: add correction to observed altitude

"tt ti ti H H (00 C0 C9 00 09

EI

1302

TABLE 29
Altitude Factor
ltitude in one minute from meridian transit;

used for entering table 30

a, the change of a

36°

NA A A Nm H

HOD AN © c» 00

> [00 Py cO 19 10

LO be O ri

b= Ó 1919 |<

O» CY b- CY 00

Declination same name as latitude, upper transit: add correction to observed altitude

1 14.0 |16. 7 |20. 6
9310299 3810312092

9 [7302/19].

9
4 |21.5

7 |21
O 7.
4 |14
7 |12
4 |10

17
14
12

9

32
33 [10
34

30
3l

Declination same name as latitude, upper transit: add correction to observed altitude

1303

,

TABLE 29
Altitude Factor
a, the change of altitude in one minute from meridian transit:
used for entering table 30

Lati-
tude

o
"a
=
2
=
Ee]
=
ci
"d
o
>
E)
E
an
Q
o
Q
+
E
=
=
o
o
-
E)
e
5
©
=
a
u
g
E
Ki
5
ke
&
a
=
o
ro
5
=
=
ge
a
=
o
5
E
c
a
R
«a
ke
=
E
E
e
=
=
a
5
©
o
a

oo 00 O»

Declination same name as latitude, lower transit: subtract correction from observed altitude

Lati-

tude

1304

TABLE 29

Altitude Factor We Å
ltitude in one minute from meridian transit;

used for entering table 30

a, the change of a

Declination same name as latitude, upper transit: add correction to observed altitude

R Pus NA. s

Declination same name as latitude, upper transit: add correction to observed altitude

=
o

S itd aaa h ci bi bb ol cl lad ci ci ci ci ci cd 05 có od k cd ed SO ek 15 15 H od 05 S;

ē 00 00 00D à |O OG O O rc [m n C c 60 [co «t «tio OO RO DOH (1 09 ODO MIOJO FH INOWINHMOO O m H o

S Hriri nn [Bciciciciciciciciei|cicici ci ci ci ci ci cd 06 |05 05 05 ed 03 [o3 ed Midi 5 o rod oi i od Hoi (Sid H H 09 09 Es

r=
o DP GO: O DOH re OI NA 60 09 H |f 1 CO OM |00 D DO O 00 10 CO 00 |O GI XH (O D |00 D NO 10 jH HO H 19 O ë
SANA >b bba aia ci [oi ci ci ci ed | ed ed ci 05 cd od có cd có 08 | e in kai NO 6 ad H H 09.09 cd E
=
3 DADO [HAAN AOD 09 rt st 10 («o CO O O |0 O HO 09 10 CO D O [an 00 e HO HORRÍO 0019 OOO S
SNS SO SS SISSI [ci E GE Gl Gd ol cd cá 05 05 fod c3 05 c8 sti ti tt stas ia S oS iur AI 00 515 ad Hod od có AÝ E
GA ri
ļ
% |. SODOA ANNA NN B iod qr 0000 6 elen C0 ALA 60 GL | DONADJOJONDOMJNO HINHOON eS
MINS AAA AIA A ai jaiai [ci ci ei ci có 05 ed có có có [os oS i tt i] HH aS IES e$ | WN «P iG i sod a SN
| um ri
Bal Cm m e ex (CN 09 co st H i6 co O L> Elo DO e (09 XH 1D co 00> rH 09 10 00 | HOON | HAV 00 D O lan CO (O |t 09 co H 00 E
H| eicicicicileicicicici ci ci i ci ei ci ei cd od có jos cd 06 cd o |06 WH sti Hifi adas S| OS ei ai hs GOS |0 D c£ iG «i | eo co NN +
= =i
|. ANNAN SP HD 19 (O OO OD O UN 00 10:9 t- OO O ONE O OO 1019000 cooo(o1w o 2
HL eicicicicicicicicici ci ci i ci ci |có có od od 66 |66 ed OS oS Hl tl ti ti ad ion XH GO Sidid fl ll e SNA MB
y" v v =
Qi |. AN NN HH 29 19 CO 0 ODO | N 09 H 19 00 O e M | 19 00 O 09 HO MOD [00 eo HID 1D HOD O | DANO A =
HI eicicicici cicicici ei ci ei ei ci e65 |66 05 06 od Rida Narnia sird (Gidad si Ss cd Cl) +
pl zl r= ir
o |. PO x HIN NDO OM WO HOC sio co DOR TO | NA co Q3 |E- 00 E mono others Oe o 0o o ric o,
HANNA AIA AA AAA ci od cd od lod ed c3 ed có dad (SD dod Gcr 1G - o o06r-| iG ooi ec cd oio H
y [rt rr ==! 1
SL |. c9 sio co [0 r- r- 00 6 |O e e 01 09 |f o E- 00 O | MODO NO O x OS 10 NN S OS AH CO wo o ro O10 o r-|co 00 OHAN] o.
"zl eiciciciciicicicicici |08 od 6G cd 05 |06 od od od | ti sti sti iš SS S ro ooo rr NASON cO ioa sti Sx eo [eo eB cd e e ON H
vu or |r = v ov |
|
_ ao qo E- |E- 00 O €: O | e NO XH 10 («0 00 ON | 00 H e ei E m 19 B o e vele COI 1919 00 HO C4 00 10 NADAR | o
NN lia zi as oe ice MW E MET ET eA. ul s s Ner s < a le
T

1305

DH

+
Hd
n
a
a
-
+
a
E
ð
Eh
o
g
=
ES
He
La OO
—

e 858
N 3.2 w
E g
FE.
kel 000
mvEee
r3 iE
E EH.
202
ST
ED
53
a
—
o
o
0
a
Ei
Eel
eo
o
Ho]
+
S

Declination contrary name to latitude, upper transit: add correction to observed altitude
Declination same name as latitude, lower transit: subtract correction from observed altitude

ANNAN

SAN OD +H nod r-00c»

612

60?

DOS

58?

57°

612 62° 63°

60°

WCANDOlOHON

09 09 «fi sh 1G 16 O D C3
|

TABLE 29
Altitude Factor

used for entering table 30
56°

55°

SH 19 10 O h>

54°

IN 00 H>
1) 10 Ø r- o6

the change of altitude in one minute from meridian transit;

a,
53?

O RR

Declination same name as latitude, upper transit: add correction to observed altitude

52°

28
a
Ee

1306

ame as latitude, upper transit: add correction to observed altitude

Declination same n

Lati-
tude

1307

TABLE 29
Altitude Factor
a, the change of altitude in one minute from meridian transit:

2

used for entering table 30

Oooo

2

O O oO cO co co

from observed altitude

o
Oo
=
5
=
d
a
o
>
E
o
n
2
o
Silio > p. b. b. b |b- OO (o O O OO O | „
S Bl Hih noo) | | ||ooooccococo eloesossoesoecococ ala
JS |Ø SMS
> 5
E —| 8
| -
Slo NANA (NAAA HHDOO(0000O0 000000 DDD o(ooooSoOSļ< |Ë
z Br EECH 1-1 ooocso veco sojas ==. es Seal z
E | Ns
E F ES
2 SI ANUN ANA AA AAA nm boer eeler ee eeler zs 0000 t. r- a | oooo0|9, |F
ato oleo lO SS AAA E AN t, dro jū gt etl ENCES. Tti EG Seon ESSE PISCIS S, c qe cec LUI
s 19 rr mr rij | ri rr rej =O SOS SOS sj) „es O HES
- D E = LARA
E E
É|o | MMMANINAAAA AHHH AAA HO Sono ooo o ii |Ë
Exo 7 LL A o AA A A | IPC EOS pag V s SQ FE ISA B IEEE EE Ez
= 1 PM MM M NM M A A | oo on oo oo oo oj ooo E Oļi 5
KE SE
E o OOD C0 CO C0 [e CN CY CL NIANA AN AM |o oO O O O CO GO 00 00 00 f+ |P t> I IÐ b- [I> br O (O (O ES E
Æ| 2S3| < a NET OM EET S LITT OEC HN UE NERO E NAMEN Dowcke | dy OMA PATA, ASAS TS E E oo so eee EN
S 10 pol el fl i oc C0 Tel toe pel c c ren heen pl zl he ee hae pl an he ri ban een rd ra (ej eo |O ©: oe |e C G'S: I =
o =
E dz
El o el «H 00 CO C0 (09 C0 C0 C0 ANAN N AN NAN JAN + — HH eo O OOOO 00 00 00 00 00 [f+ Py b- Pr [E bb OO S5 a
bultu gg N ONE EDD TOT VĒ, S PC ASE VAR VĒ eem. Dr (tt Ss ed ARA peer)
= 19 nt el et AA lA A A A A lA A A A A kan A A A A A A A A A A ri A A ri ASAS D O O O (miel) 1G <
o
E | | at LS
Slo HH HH HIM C0 c9 c0 co (00 c CN CY CL [C CL CY AN e. |. + + m m |I OOOO GO 00 00 00 00 |00 00 r= b= f= [Pe I~ bb O O EE
su S E e os | io as BOSA K! ASU NOP SKS : ENERO Xo ED SE A A NE
$ 10 — A A A A get A A A UA AA A A A A A A A A A ri A A A ri ri E OO D O O |0 Er © E E e'e'o' e'o K:
s
Ð
£ A 10 109 ch H SHH HHO 009.1000 C0 000 009 C0 N ANA AN C N JN AN AH — + j + e OD OO GO 00 00 00 00 |00 00 OO P k= |> D he I~ O Ga a
BA i dE QU i ROOMS IL] Reeg deg E AC) IRC RR EC «ur K O O EE ala) ad ES [s]
CNES e pel pel pl pl Ir pc pi pl pl Iech PP: e pl pl pl lei ei Sooo aloo 00 0/00 00 en e19 E
z Ë
= o 100 1D 1D 1 CD | SH OSH ch SH SHIH C0 060 009 C0 (00 C0 C3 C3 QA A NN HAHAHAH DO Q» O) 00 00 GO [00 00 00 QC P [E E E E bt EIE
(x demo EDI Uter he) om cee oe EAM Deal 1929 29 Als eise a ALIM MM Es ues o te lle eus sous e |
10 oooooooooóoolooooo|s!R8
O? C) C) 00 00 |00 00 00 00 GO [E Db DDD E
Lo d On rn MERLO ORE NAAA AA TREO RR RO AA CIAT Y VOR ATO ONE CCS ERU NES
19 0 r- 00 |o EE H legt ee) 53
Zonen o ta Sta CE
2

1308

3
ū
g
g
R

H
g

s

"d

“E
o

=
E
o

de
© o
SA
55
e 5
e 2
EO
e
o
rð
E
>
s
=
kd
o
o
en
=
g
X
O

t, meridian angle

3m 00: äm 20: | 3" 40: An 00* | 4m 20: | 4m 408

2m 40»

2m 20»

ooooo

oooco

O OoOo

Lm r r r ri

Om 20° | Om 40° | 1^ 00: | 1” 20» | 1” 40s | 2” 00°

N MN Yao co
NAAA ANN

1309

TABLE 30

Change of Altitude in Given Time from Meridian Transit

E
=
3

E

Kai

E
o
H

4

2720'

215'

2910”

2905'

1°55’ | 2900'

1°50’

1°45’

1°40’

1935"

1°30’

1915” | 1920” | 19257

ps al a a a R O Ee I IAS wee ae Eme d ES. E QUEE e SOTO PORO SO AAA

Do
A cual TO geil FY AO So C. AP Oe es Vis
TASA AS roc ciis San AAA SS HHS or o

TABLE 30

t, meridian angle

Change of Altitude in Given Time from Meridian Transit

table
29)
+

a

1310

"m E <H
e > Oo
(ji BD a taa X oy gv VAI K AC A one) moi . . JATE A PELA E A E AA ce s Pe Ta
E GG dddlciciciec ln iN SS S| I EST S4: 1:66
= AH NANO Ki 9o MINN
5 NODAD |Os Q1 12 00 A [C3 66 E à z CARADHAANDOONIDHO
MA Pee ee M Kat wn DV TIC) V A IR Ce Ne O qu ok Vp 2 PCS. ACA ) D . >
e | eieiei el elle Cl elei rd O ES eg le lui (SO
m HA NANO + Es HANN
E NODRAN [00 A YO | 6: 63 00 00 |E- E E O Á 5 10 E EE Glen en HONDO
A a Se ege, Ce PL S A 3a | Le ën A — Dn ée EAS 6 OO > . .
:|-ddd-dd|ciciciciiéd-rr|odGco S| P| ERAS SES
3 Sa o CH = Es | Cl CH
E Co «5 00 4 -h OMNIA to TOMO a HA 3 n i56 0 -G-Kqpara-uuoo
IX lie eae 1 eee a la Li ys de ale . o =P AR A dier E PRO RE S. aja,
E | = SOSOSHAIANN AA ld or si ep ocio a) F | ES TS aoho S
Eo m lei CEA Mos | Sa = HANNA
> Sou O ANDA - Ee |o O r- FON bei H A S| w6On5oOmnonmonooooo
"CIIM e O ee se RT, ` *"» qv [jS] A. |]. | x» LV ge we lei 45.2 Lef . .
O ES ST SR SRA oe A] S| ES SS SS
å FRRANANA Su E HANN
5
5 MIA 00 OM [iG 00 O c6 16 | cO — E- Q |E- MOHD Ā 5 166 HD TO HD NDA
SA EEN av A O ANO eler, ee IA < 5 | U ee COS we u$ ua H D D
Ss Is eieiei ell lei e d Gilet ei ed wi lte Gd E =| P| ETS TS EENEG
å N len Gi EA CH CH + en et aN
2 S
5 CO r- OG [roO HONDO « [00 OO - 00 g= = 15 6 «f G5 co 00 | E- ADN 0
i a oj O OO S IS — PL e bf S in a * e Ze .l.u a ut a wm . : D D
E eieiei el elle E ST --dG|o O E SS
à ARANA 5 E ò HANN
=
E NOR 6: |-8 «5 00 O co [iG 00 DARRO aa el eek ME - G6 0600 I-|9 «c O FO NAVN
"UM LETTO Ws IRA Sele. ee Zoe ale ents e at Ze EE MIN ØK, IS CH. uL. d ee Be heb 9; cs 4 e. P e. + D D +
EA TS sabi ps dS Gi wëlt O u ERR - - or cid
> ARARNNAANIAR ES E Lin GG
=
= A TOO (MIO O je ODO O 00 mis |0 O E z HOOK OO TO MIO OO
GB a TEM K BV C A ARO RR AN AC e Ë e O . O A NA ES NO e a le ee AA + D M D
R eieiei ei vi ec vd el el Gill eg oi ei ed lët od ed po m S S| 2 | ~ SSAA elle ei ed tid cir: nas
å ARAH e Cl Cl EE + © CNN
=
5 ATONO|JA HOMO OO N SIF AAAANINAAN 3 5 HF 0 105 C15 |060 — Q1 (60 1019
Self ee N BELL V C id Xr] ler M d II ON J IU ` . AA AAA Heger lt, M — e. ei ROO O Tier iere ee D D D "
SAS TS RS RSS Lal pi o ei el SHS ES SS GS ti
= AH AH CG CC CO eo 15 TONO
3 = C4 «tO 00 6 | MAO O todos) E = HO ADO F-15660 OP (15 +
A Oo Ge a A a PI e Lea Aer an A —-. .... l Ip 0 o $... o.
SI: EAS ll el sl sl el lët e el leg ugi teg ei SER GS Bl S|) RTS SS leien og Es
N E zc Lei ri el rd CA IA GC CA CO Se e rr Cl Cl
ra
= AAORDAAHODISCMAORIINNODO|HHONR 0M SIS FOAN OOTAN NANO
Go qm a cum a Lo AS AR EE e ELE S A MS oen A ln MET ROPA r
Q È cesēs jE ES EE DS a O O SS sa eG co
E
= E N MAR 00 | C C1 MME |co ODO [HOOP co |O r- co O D0 | 3 Š HR BHONPINANON|OMOM TE
Sl lu aaa ls am ala a E ean alm NM Fi) | oo ok eles es ss] ce ee es
Q & occae ir (S C ioc i EE > A y OGNI Uo eS C HS OS
= C
R 2 CX MIA cO 00 | O» N HO | e CY 0000 |O» 10 O (O (D C 00 + Cu E Q Go be O HR e Lei p rd sl DÉI |0 10 +
SC eieiei ei ei lei iii PS A O eg e ei SMS E |. R=
S T M A A rA [A Cd C Cd C3 Cà + ls Sm SB Sana

OD Hid cO b- 00

0.
0.
0.
0.
0.
0.
0.
0.
0.
iE
21
3.
4.
5.
6.
Te
8.
9.
0.
1
2:
3.
4,
5.
6.
7f.
a
(table
29)
0
0
0
0
0
0
0
0
0
1
2

1311

TABLE 30
Change of Altitude in Given Time from Meridian Transit

zm
Ki
g
a
g
E:
a
E
o
H
5

7°00’

28™ 00»

6°55’

27m 408

6°50’

27m 20*

6°45’

27m 008

6°40’

26m 40s

6°35’

26m 20»

6230"

26” 00»

t, meridian angle

6%25'

25” 40*

6°20’

25™ 20:

6°15’

257 00:

6°10’

6°05’

19700*|19720*|19740*| 20" 00» | 20" 20: | 20" 40* | 21m 00* | 21m 208 | 21m 40* | 22m Q0» | 29m 20* | 22m 40* | 23m 00: | 23m 20»

5955" | 6°00’

23740* 24m00*|24m20*| 24m 40»

1312

o
«179
E 31 tions
TARL etric Func Dueti S Di
Trigonom 1⁄4 Y 7
Natural sri 60
> D
Diff. cot 1. 00000 0 59
iM . 000 : 00000 q 6
Diff) ese et ee las 00. 6 . 000 5
0 sin |1; 00000) 29 3487. Trio se Gent 0 | 00000 0 | 55
" 0. 00029 29 1718. zi a . 00000 0 L en À RE
7. 75 718. 88 - 00058 2 359. 136 771: guy] 00000 p 905661 0 32
dl 0 Gata, 2 1718. 87 1718 88 Gear = 687. 549 17! 592 0000 a UGU 0 | $1
` 000 29 11718. 92 6. 483 00 68 7 ` 851 00 00 0
Pali 58 29 145. 92/986. 7 45| 30 2. 957, gp ` 00000 0 | ` 000 50 |
000 1 7 1. 88 001 3 57 6 388 00
Zi, 87| 59 9. 43717 5 1.106| 61. ` 00000 0 0000 y 49
00087 5 85 921 0017 29 |49 8 7471 000 1.0
3|. 16 29 550114. 5 4 29 9. 718) 47 : 0 9999| o 48
001 687. 51| ` 0020 29 149 1 197 0000 1 leo |
E 958 81. 8 33| 29 1. 971| ae L 1 99999 o 47
00145 30 572. 7 388 002 2 38 253 0000 0 f 9 6
5 J0. 75 29 1. 107| 61. 262| 59 774| an ` 00001 0 | ` 9999 0 46_
001 29 |49 19 47 747 00 343 1 0431 ` 000 9 p |
6 |. 04 29 29. 1191 47. 7 Pos [aue 921! ae .00001| o 9999 45
. 002 4 2 38 19 00291) 2 31 0371 ` 00 :
EE TEF ELE. TE-EIE
.0 343. ` 044 00 2 . 37 00 |
H HY DIEI CER T á
` 003 2 2 43 8. 889 00 229 : 639] ` 000 8
11 ` 00349 29 264. 4 1 ` 370 0436 29 214, 858 17 35 00001 1 9999 0 40
osos 29 |245. 5541 15 totes 0120252191 145 02 9 0. 99998| „ 39
003 2 241” 0046 30 Lon 0521 ` 000 0. 99
13 |. 07| 59 184 143 5 984 10, 998 o 38
004 229 39] ` 0049 29 |190 047150002 0 1” 99
ESTE 6 860 12. 6 24| 59 0. 932 9. 0 9 ` 99998 0 37
00436) 29 214 1 2341 ` 005 29 |18 1851” 0000 019
E repe. os (2022211 44 553 29 885 g, ei: le 0 | 36
ee a EM E 7| 10. 052 00 171 441) "000 8 351
ARS Bee g |180. 935| IO. Cone O TA 2 1 0.99997 0 | 34
00524) 9 18 85” 0061 29 1156. 2281 ` 0000 0. 999 3
DEE 53 29 888 8 1 465 g, : 97 0 3
00553) 2 171 411 ` 00640 29 1149, 73050003 0 | 999 3
19 |. 2 708 74 69| 29 3. 237| p 1.0 ` 99997 0 | 39
00582) 29 163 2 7941 ` 006 29 1143. 2881" 00003 0 | ` 99
AK erm 30 |156. 260 00 2271 | 00698) 39 137. 507) 5 8l : 00003) 0 50006 E
diosa 9 |149. 468| E: SREL 3 . 99996 ` q 0
00640) 5 14 1 730 00727| 99 132. 547| ` 0000 IIe 3
E Ge 29 |148. 241) 9 tētis ri .321| y 4 6 R Aal
00 1 5. 2891 0075 29 |197 2341 ` 0000 0 0. 999 2
SE reete 29 H37.511 ku |; OR d. .99990 6 28
Ë 971 ` 007 30 |12 51 0004) o . 99
5 0. 00727 29 D K : 00815 29 |118. = Ë Fen 00004 0 99996 : 27
00 1 8 ` 934 00844 114. ; 466 0000 1 9
27 | | 00785 30 |122 778) 4 Sot 00873 99 110. 892 y Š] 00005 / oe 0 Lët:
27 |. 14| $0 8.544 3 0. 00 426 395 0 399993
00814) 2 11 961” 00902 29 1107. 641 ` 00005 0 99995 o 24
28 ` 00844 29 114. 598) 3 6 ` 00931 9 |104 171 3. 0 0 995 y 23
S 4661 ` 009 29 1104. 91 0005) o . 99
50 |6 EE 107. 431 3: 466 E E ral 00005 o | 99994 dE
00 1 ` 064 0 ; . 006 o 9
32 | 00091 SO bts 2. 8890]. 01018 29 as 9083] 2 5810 vm Ó 9 Ri ER
00 1 7983 . 01047. 29 92. SLOT anon 1 [799993 0 | 19
33 . 00989) 29 2230| 2 72 `" 01076 4633 2. 31 0 93 o 8
98. 08| ` 0107 29 |90, 038 0007| 9 999 H
34 8 4947| 2 58 ` 01105 1436 » 9 0 .99993 | 7
E 01018) 29 95. 44501 ` 0110 30 lee 31 00007 0 |” 999 1
Sauka oža 9 |90. 4689) 5 31 alias oo iar 1. 9965] ` 00 99992 9
01076 5 90 2 2 2036 1164) 29 83. 8 6| ` 00008 0 | ` 999 15
avr: 05 29 - 1492) y 0. 0 470. 1. 903 0
01105) 5 88 1” 01193 29 121 8 11 00008 1 999911 p 14
38 |. 01134) 39 85. 9456 2. 09611" y 222 29 9. 9434| 1 817 0 0. 910 13
39 |. 4 2 8495| 1. 9963 POL 1 Ds 1209 0197503 DON d ds 1
0116 29 83. 035 0125 29 78. 12 8 0009 0 9999 1 12
40 10. 01193 29 81. 8532 1279 701 : 1280 29 3900 1. 660 0 09 1 99990 0 11
01222) 5 79 361 1309| 29 74. 72 H ` 00010 0 | ` 999 10
42818 51 29 1327 1 7 0. 0 90 1 593 0 ae
01251 5 78. 7|" 01338 29 |73 13 il 8| ` 00010 1 9989 9 9
43 |. 80| 29 |78 66 1 660 .0 151! 1 461 0 0. 9
01280) 3 76. 39 1| ` 01367 29 |716 1 2 1 99891 o 8
44 0. 01309 7359 1. 590 .0 1533 1. 403 0001 0 .9
^45 lo. 0130 29 74. S 237 01396 29 70. 153 011 0 99989 1 7
1 T o |73. 1458. 1-5 301495 to A ee utt
01338) 2 73. 616) ` 0149 30 68. 7501| y 7 011| 4 99988 o 6
46 ¿01867| 34 EE gs 81| — . 4019 1. 2964) Zon . 99988 `
4 455| 99 67. 4 9| ` 00012 0 | ` 999 5
os 29 |70.1605| 1- 46 p 20: aee 1. 2475] ` q E
: ; 1 9987 o 4
48 25| 29 68. 7574| 1 3481 . 014 66 80 1 2013 0001: 0. 9
014 2 68. 75 3 1513 29 64. 85 1 2 3 987 1 3
49 > 01454 0931 1.296 .0 RE 00013, . 99
) |0. 01454) 4 67. 4 4731 ` 01542 29 |63 SE 1313 99986) o 2
SAR o |66. 1130 1-2 ECT EE 000
01483 3 66. 0111 ` 0157 SH l. 014 9 99986) y 1
De 13) 29 8657 12 S 62. 29| 1. 0771 00 :
01513) 5 64. 574 1600| 29 1.38 jl. 014 4 99985| o 0
52 |. 42 59 6646) 11 0.0 6 98 1 0309 00 .
01542 2 63. 66 1 ` 01629] 29 0. 3058 |: al lee
58 |. 71 Oa 72 1 1161|7 9 60. 59 0047 00 0. ā 4
01571) 2 62. 50 0| 01658 29 |59 26: 1. 15 l IT. ogo
54 501600 8911) 1 077 0 29. 612) 9 0712 1. 000 Di 89
01600) 29 61. 98| ` 01687 29 [53 2 0. if. ls
55 |0. 29 3141 103 900 Dif.| gi
AT Ge Eet ml P
De 01687 29 58. 2698 0. 9 0. 01 iff ian 1’
58 . 01716 29 57. 2987| t i Å
59 0. 01745 Diff co
DU i H Diff sec 1
9o. cos i

ET
-—
A

a

-—

1313

TABLE E Functions “1780
Natural Trigonome Diff. cos DIE. y
Diff. sec T 1: :
Diff) cot 14 "M £s
A | tan ki 0. 99985| , 59
Ei ry | ese bet Lað ee EE Die
ER K 57. 2900 9394 |” 00016) y .99984| y 57
y 0. 01746) 29 56. 3506| 9091 - 00016 y : 99983 0 | 56
Sa 57. 2987 9992 . 01775| 59 55. 4415| ` 8802 $0007 0 | ` 9998 le
o lo. 01745 29 156. 3595 9090 | ` 01804 29 |54 5613 8527 | ` 000 A NGHE: o | 55
0 |0. 01774 29 55. 4505 8800 . 01833 29 53. 7086 8265 1. 00018 o[- 99982 1 | 53
2 01803 29 154. 5705 8526 |" 01862 RABATT 8014 |" 00018 1 - 99981 1 | 52
2 ` 01832 30 53. 7179| 8063 0. 01891| 59 52. 0807| 7775 SEE 1 - 99980 015
: . 01862) 99 52. 8916| 2913 . 01920) 59 51. 3032 7547 <00020 : .99980| 3 "Br
0. 01891} 29 52. 0903 7774 | ` 01949 29 |50 5485 Tepe . 00 i 0 99979 DE
5 Jo. 01920 29 51. 3129 7545 . 01978 29 149. 8157 711 L 00021 o |“ 99979 lee
6 ` 01949 29 |50 5584 7326 | ` 02007 Ëer 6918 00021 1 - 99978 1 | 47
` - 01978 29 149. 8258 S 0. dE 30 48 slan GES 100022 o pur ; as
` 0200 9 1 17 |“ 020 29 |47 7 6 > 4
LER rd Se jj: 4224 6724 . 02095| 59 ae 0853 6364 . 00023) y 0. 99976 5 ia
Rn 02065) 29 47. 7500 6540 |” 02124 29 |46. 4489 6195 F 50024 0 ue 1 | 43
11 . 02094 29 147. 0960 6364 Í ` 02153 29 45. 8294 6033 |” 00024 1 | 9997 iS
dE BHR) gt SIE a ae | A tdi
-02152 2 pe Ty eS 29 |44. 6386) 2 i aries
Aš Kā 240 661| 5580 . 00026) y 99973 | 39
wen 29 |15. 6408 5723 ` 02269 29 43. 5081 3440 {i 00027] | Eod OK
dE EE TECHE
"A5 5196) 5489 0. 02328 FUTT e pe i
022691 39 43. 519 54 0. 02328) 59 42. 4 2 970 |
AE 298 7 05 2357| 29 1. 9158| 5059 . 000 LI a ) SS
2 lo 02327 20 qu 5175 ` 02386 Moe 4932 | "00030 ! 0. 99060] „ | 35
E 0. 02356 29 FE 9277 5050 EE 29 40. 9174 CR 1 pest d SE 33
2 „02385 29 1. 4227 4931 „024 29 40. 4358 470 0 i 8
23 | 02 40 6 14 73 6551 4596 .00032| | - 99967) 1 31
02414 59 40. 9296) 49 0. 02473) 29 39. 9 Es 966, J |31.
28 |. 3 502) 29 5059 4491 . 00033 3 . 99966 30
02443) 59 4482 4702 . 02 29 |99 34
25 |0 02472| 29 uo 500 29 |39. 0568) 1191 SE UR
al. 72) 99 9. 9780) 4595 . 02 29 |29 a 0. a
od abes 1 S 5 89 | ` 02560 29 138. 6177 429 1.00084 , ` 9996 1 | 38
02501) 39 39. 5185) 44 ; 2 38. 6177 035) 1 TOME 8
SEA: 2530) 30 0696) 4389 . 02589) 30 38. 1885 4199 . 00 o 2 2
2E xt 2r 7 91 [02619 686| 4107 .00036 , .99963| o 26
02560) 59 38. 6307| 45 0. 02619} 9 37.7 £ 963] 9
Szt: 48 ola e 0 | : 99963 3
02589| 59 2225004155 [0028 29 ares 37
EE Be 677| 29 9560) 2933 . 000 1 0. 99962 , 24
-— 618 29 137 7818 4105 | ` 09 29 Le 1 å eil !
Lod Pags 7 P 13 4018 02706} 29 36. 5627| 385 1.00038 , . 999 23
02647) 59 RYA ayi 4 à 36. 56: 039) ! 9960] 1 23
32 | 02676 63. 3932 | 02735 SOCIAL ist ` 00 9
a e 3 49 764| 29 8006) 5695 . 00 Se
02705} 59 36. 5768) 38 0. 02 20 Ge oai | 9960; 9
33 |- ĒST 793| 29 4313 3618 . 00 . 9995€ 20
02734. 59 1914 2769 202 29 Gs oi % | 190 5
ed e Kā 2111028221852 tach Pa R 0.99958 | 20
be: 763| 29 5. 8145| 269 20 35. A jā J 957, | 9
zn 2 4 94 3616 02851) 30 34. 7151| 34 1. 000 LI 99 5 1
02792| 59 35. 44 3 $ 1 043| 1 9956) ! i:
36 |. 1 88| 3543 02881 59 3678 3405 . 00 .9
02821) 59 35. 08 3 á 34. 0044) | 99055) ! 17
E 0 95| 3472 910| 59 . 0273) 3338 . 00044 ; 16.
02879) 29 Bi 72 3403 [0- 02 Ba 3 |: 00045) ! 29954 | 16
> ees 31 3803 3 |. 029391 29 EEE ION ` 9995 T
02879| 59 RE 0 eee s Mgr 046 3|.9 SS
E Šā 7 2968| 29 36621 2210 . 0004 0. 999 ilg A
a 908 30 4. 0420) 229 „0 33. 2109210 i'oópi A 0052 | 14
Cl e 8 3 83| 3971 02997| 59 33. 0452 3 1. 00 . 99€
02938| 29 33. 70 3 : 26 a 0048 | 99952 Q 15
E EE 29 os 3090 |” 6 - 99952
EE SEI Zen IS TE
` 0302 29 (227455 3088 |” 9 32. SIRE ng
ole Ee 36 0 3114| 59 1. 8205) 595 . 000. 0. 99 9
—— 054 29 2. 4367| 203 Ü 3 Fa 051| | 90048] 1 `
AA 8 3 37 2975 . 03143| 59 31,52 2 1. 00 . 9€
03112 29 EE 5 72 6 17 | 00052 1 | ` 99947 1| 7
A tenes 362) 2920 209142 859 Geh eh TAIT e
H EE ze | IEC
` 0317 29 2576 2815 ge 30. TT E pee Tis ggal 1 :
49 | . 03170 31 5 3259 29 130. 4116 267 0005 0. o
| 50 |0. 03199} 29 Eh 829 Weër EE dE 4
50 |0. 03 8 96. 2716 . 03288) 29 30. 1446| 5 1. 0005 . 99943 :
03228) 29 30. 69 2 17 Ec epe i 999421 | 4
enaiis 57 4280 2668 . 033 29 29. 882 25 ; 58 "ee 1
JE ICE AS EE IE
53 03316] Ze 29.8990 2576 ; 08878 29 La oul 21 (00000 ! 0.99939.
E 03345 29 |29. 6414| 2576 1 ti E 1220 E Secher = Dit ot.
Se 03374) 59 99. 3881 SE E 2. a Sc 2 ien | SES sin P88
ees 1392 24 i f
57 103432 dd 2 89441 5407 0. 03492 - Diff. cese ||
ds . 03461 29 198. 6537 i Diff.| tan 1
4 0. 03490 Diff. cot |1
$0 Diff. sec 11
919» cos T4

1314

E 31
TABL ic Functions «177°
| Trigonometri
Natura Diff cos Dif. y
Diff sec 17 1’ |
ari Diff. cot i" j
iff. tan 1 60
29 Diff. ese 17 1 99939| , 59
sin |; 1.00061 , 99938| | 58
n 28. 6363 2369 . 00062) , 99937 1 57
0. 03492! 29 .3994| 9990 „00063| 1 99930| 1 56
; A 28. 6537| 9367 03521) 59 28. 1664) 9999 . 00064; 3 99935} 1
JE ESSERI SEHR
ÍM. 28. nu x ep 1 933
2 | . 03548) 29 27.9551| 2553 03609) 99 | .7117 1. 99 1 | 53
4899| 2184 00067 | 9932
Ar le coos 2218 sees 27. 9 1 | 52
6 0. 0 29 |“ 9715 2149 | ` 00068 1 31
4 | -03606| 29 27.5080 9182 MEN PIC Sea 2116 | * 00069] 1 og 1 | 51 |
03635! 29 98 8 6 2 999 1
I BEER DE AE BS E
2 2 „6 ro 1 27
MEA auo ZOBA (103764 N aa kava) Ht oie 99926, || 48
: 1 926
8 | .03723| 29 .6555| 2050 783 26 2 . 00 99 l| 47
2 0. 03 29 |“ ` 2296 1989 | ` 00074 1 925
9 | -03752 59 26.4505! 9018 03812 39 |... 7 1 o 1 | 46
RM 1 : 26. 0307! 1959 .00075| | 99924 i
10 [0. 03781 29 |” ` 9487 1988 | ` 03842 29 |95 8348 1930 | ` 00076 1 45
11 | . 03810) 29 26. 0499) |957 03871) 29 „6418 LOOT ts S 99923 ey + 44
^ 077| 41 922
S dio esa 19201 03000185 73 |1. 00 99 1 | 43
8 25. 4517| 1873 00078) | 921
13 | . 03868) 59 . 6613) 1900 29 Da 99 2 | 42
7 0. 039291 29 2644 1846 00079) 9 19
EX : 25. 0798) 1890 00081| 4 99918| |
15 |0. 03926| 29 .2841 1844 03987| 29 24. 8978| 1793 .00082 | - 40
16 | . 03955) 59 25.0997 1818 04016) 30 . 7185 678 5 99917) y 39
4 17 0083| | 16
17 | . 03984) 29 24.9179) 1792 04046) 99 | .7185 1.0 999 1 | 38
418) 1743 00084 3 15
18 | . 04013 29 7387 1766 75 24.5 a q 999 2 2
9 0. 04075) 29 3675) 1718 00085) 2 13
19 | . 0404 29 24. 5621 1741 04104 29 ` : E 999 1 36
1 : . 1957| 1694 00087) 1 99912
A EN EE et LE SET E Se 1 des
21 | . 04100 29 . 2164| 1693 04162) 59 23, 8593 1648 | - 99955 99911 1 34
22 | . 04129 30 24. 0471 1669 04191) 29 : 45 1. 00089; 99910 1 33
m 24 090) | 9
23 | .04159 29 23. 8802| 1646 20 23. 6945 16 . 00 99909 5 2
8 Ee ee cee 1603 | ` 00091 i|3
24 | . 04188) 29 S a n 29 | -53 "000981 2 | 199907 1| 31
1 -3718| 1581 00093) 3 906
25 10. 04217 29 15533 1601 04279 29 2137 1560 |: 99 1
; 0094| |, 30
AAO E El MG 3. 0577| 1239 | - 00094 eer EE
27 | .04275| 29 . 2352 1558 04337| 29 |23. 1. 00095| 9 99904} 5 8
4 9088 1519 0097 2
28 | . 04304) 59 28. 0794; 1538 04366] 29 |22. 9038 19 .0 1 | ` 99902 1 | 57
29 | . 04333 29 22. 9256 1517 0 4395 „75 1499 „00098 1 99901 1 26
Pest 2 22. 0 29 | '6020 1479 | ` 00099 1 900
30 |0. 04362| 59 .7739| 1498 04424. 39 1 99 2
1 -4541 1460 00100| 2 25
31 | . 04391) 29 .6241| 1477 04454] 59 081 344 |-- 99898| 4
. 04420 a Tk 1 -8 1441 0102 1 7 -
2 mmm 29 | . 4764 1440 s 29 |22 1640 oig 1428 |" 00104] 1 [09890 1 =
34 |.0 29 53-1865 1421 |^ 04541 SCH GE : 2 1 | 99894 1
r : E 1. 8813 1387 00106) 1 93 2l
35 |0. 04507| 59 22. 0444 1403 04570} 29 |2 7426 TORT Geess?
! 1370 | ` 00107 1 20
AA Ede dr i Tt (31 6056 : 99892] ə
E 1352 8 19
37 | .04565| 29 . 7656| 1368 04628) 39 | . 6056 1.00108) 5 99890 3
4 1335 110 18
38 | .04594| 20 . 6288| 1351 04658 21. 47041 |9 . 00 1 | ` 99889 1
E | > 29 3369| 1320 111 17
39 | . 04623 30 3 0 . 33€ 1 . 00 2 9888
21. 4937| 1334 04687| 99 2049 1509 113 È 2 | 16
AMNES 13010 |5«04716/0291 | odas len . 00 1 | 99886) 7
„04682 : e 21. 0747| |987 .00114 | 15
iz comi 3° | asp SA 29 BL oTa] 1287 EE E E
44 | ei? |20. 9608) 1286 0. 04803) 3p po 8188 DUREE 1 | 12
Ad E j k 1 . 00 2 1
FIRES EET al 291 1228 | (0012) 1 | 109879) 2 S
. 04827 : m „00 1
T 291 29 E P EC 2 in RAS 2 90876 ` 2
48 |.04 29 | ` 3499 1196 1040 20. 20 1184 |" 00124 ME ec o
49 | .04914| 22 0. 04949 99 20. 0872| 1170 «00125| 5 7
50 [0. 04943) 39 |20. 2303 1169 | - 04978 29 |19. 7 1156 Soo raei X | bon :
51 | .04972| 29 19. 9952| 1154 05037 i 11 RUP) 870
1 . 29 7408 1130 99 1 4
52 | . 050011 54 .8798| 1149 05066| 29 |. 7 |} 00130) | 99869 2
ZR 080023 7656| 1128 1920205 dee .00131 3 67 3
54 GER Ps 11 Meu Mies 1092 134 ? TE
55 |0. 05088 29 | ` 5412 1103 | 03153 20 | - sal 00 2 | ` 99864 1
Sc é - 29591 1080 136 0
56 | .05117 59 4309 1091 05182 35 2 - 00136) | 99863
T | 20SEC) 54 | 2 3 - 1879) 1068 0137
` 05205 ; 1067 |0 0524 3 Diff. sin 1'€8
59 1.0 29 |19 1073 A Diff ese 1’
60 0. 05234) ^" E pum E
Diff. e | Dif cot |1

1315

TABLE 31
Natural Trigonometric Functions
"CE «176?
0» : : ; Diff. Diff.
3 sin me ese Dim. tan rd cot 1! Ke ga i BE M
l 7| > |o. 99863 60
I MUTET an fie oema! rogo Pero ht > [oo
11.0 29 |19. 1044 | ` 29| "$711 . 00140 . 99860 58
2 | . 052921 59 |18. 8975 |031 |.05299| 39 |. 1033 | ` 2 | "90858, 2 | 57
` 7678 00142 7 |. i
3 | . 053211 29 | .7944 1021 | - 05328| 59 g 1022 | ` 09143 . 99857 56
4 |. 05350 ` 6923 . 05357 ra ES 9 2
5 |0. 05379 * 18. 5914 eg CE 3 rr LODO! [nOD ae : P. 90854 5 54
6 | . 05408 29 | - 4915) ogg |- SON 990 | ` 99852 53
3655 00148 l|. i
7|.05437 59 | -3927| 977 | . 05445) 59 ` 2677, 978 | 00150 99851 52
d : 2
8 | . 05466 29 | -2950| 967 | - 05474 29 | “1708, 969 00151) ! | ` 99849 51
e : 3 || See |
9 | . 05495 . 1983 . 05503] 39 |. 958 2
o Jo. 05524) 29 |18. 1026 od 0.05533 29 |18. 0750| ous |1. 00153| » deor "M pts
11 |.05553| 29 |18. 0079 947 |. 05562 Z KREE Es
12 | 105582. 29 |17. 9142 Geyer 055911050 | 8868/0 939 tte dt ie GIE
PAREIS doti Ms er S oola 001E 5 | 90841] 3 | 46
14 | ` 05640 ` 7298 _- 056491 59 | .7015| ggg |. 7
15 |0. 05669| 5° [17. 6389 Ka o E PT J J
16 |.05698| 29 | : 5490 890 | :95708| 59 | .5205 ` 891 Boote al co h
Aaa | 460000 r | ampa| s 831 00166 2 |:90834| 2 | 42
18 |.05756| 29 | | 3720 872 | - 057661 29 | .3432 g74 00168 2 |. 99833) ! | 41
19 |.05785 E, . 2848 864 |. 09795 59 | .2558 865 |- 69 | 0. 99831 > 40
20 |0. 05814| 3. |17. 1984 GE ag LEE [150016985 998291 2 | 39
21 | . 05844] 39 | :1130 854 | 05854 3° |17. 0837] 858 ‘oo173| 2 | 09827] 2 | 38
22 |.05873 39 |17. 0283 847 | 05883 29 |16. 9990 84035001754 ll
23 |.05902 59 |16.9440| 837 |:05912 29 | .o150] $29 “00176 l| 99824 2 | 36
:05931| 29 | | 8616 05941) 70 Ir 831919 293 |. 0017610 5! | 215
24 | . 05 CH c ES E SE 1. 00178 0.99822 , | 3
25 |0. 05960 16. 7794 3 [> 05970| 29 |16. 7496 aus [1. 00178] 2 |0. 99822 34
EIC SE EIGNET IE
. 6175 : 799 |: ` 99817
28 c0 29 | -Sarri 798 cons 29 | 13075 A
. 06076| $ . 4587 ER e SEO E 13 30
Hi Ha ka a rä HH.
31 | .06134 29 | . 3029] Aë). 30 | : ` 00190 .99810| >
6175 . 1952 762 2 27
32 | .06163 29 | . 2261) 761 |-0 29 ` 00192 .99808 2
6204 . 1190 755 2 26
83 |. 06192158 |. 1500 ^ 761 |: 0 29 |; + 1190 :00194| 2 | 99806/ 2
„06221 16. 0746 _-06233 59 |16. 0435 748 |-— ` 99804 25
-34 | . 062211 5g |16. 0746] 747 DT 15. 9687| 749 |1.00196| 5 |0.99 Kidu IER
36 | 062791 29 | 9260] ` 729 | 06201 sa ESTE a SE den ee
36 | . 0627 29 5 733416 3 ` 8211 . 00200 . 2
. 8527 . 06321 : 728 1 | ` 99799 22
38 | ` 06337 Šā ` 7801 E : 06350 2 - 7483 721 p 2 |: 99797] 2 | 21
. 06366 . 7081 En 2 1) E a 1. 00205 . 99795 20
E 0. 06395 * 15. 6368 Ze 0. 06408 30 PEE m "00207 a Nu 4 T:
Ai 06424155 |0. 8861/4 - 707. |7 29 | < 5340 (00209 2|:99792| 1
` 4961 .06467| 29 | . 695 1 ` 99790 17
43 | 106482 dl |] C SE, See Pe ` 00213 2 | 99788 2 |16
à . 3579 . 29 688 | m5 = 86 15
al ero oscail oo ean eps ci E i
ü : : M 99782
46 |.06569| 55 | . 2222) 669 lr Ee 2
. 06613 665 99780 12
47 |.06598| 28 | .1553| 66% 29 7 ` 00220 2
.06642| 30 |15. 0557] Bro 2 8 11
49 | (066561 29 |15:0231| 993 | 0d671| 29 [12 9808 639 e |010 RR
0-06685| 29 līz 9579 0. 06700| 30 114.9244 gag |I 00228. 5 [0 99776 219
51 |. 06714) 29 | 8932 641 | -06730| 29 7052 842 | * 00228 2 | 99772] 3 :
SE CS ` 06759 Å TS 99770
52 | . 06743) 30 | - 8291] 635 |-06759| 29 | -7954 00230] 5 |. St
| Å 632 ` 99768
54 | 06802 29 | 7020 $29 | : oes17| 29 | loses 632 nv eos
A CSN alen ot ar NE EN EE
56 | .06860| 55 | . 57 614 | "06005 29 | ` 4823 uos A | 5882/65
206905) E 611 ; 99760
BIER LUE de Goat ce 201 | anne A ud AP
59 | . 06947 29 | - 3955] ggg | 06963 30 | 3607 1. 00244 ` 997:
60 |o. 06976 14. 3356 0. 0699: ! a EE eu
3 IH. > sin H
T Diff. Diff. cot pu tan 1 csc 1 SE
939 cos 1 1

TABLE 31

Natural Trigonometric Functions

. 06993 . 00244 . 99756
AE ` ` 07022 ` 00246 ` 99754
` 07034 j ` 07051 : : ` 00248 . 99752
` 07063 ` 1589 ` 07080 ` 00250 ` 99750
` 07092 q 979 | ` 07110 f ` 00252 ` 99748

7 0. 07139 ; 1. 00254 0. 99746
Torte ` 07168 ; ` 00257 ` 99744
` 07179 i . 07197 : ` 00259 ` 99742
` 07208 E : ` 07227| : : ` 00261 ` 99740
` 07237 ; í ` 07256 ` 00263 ` 99738

1 y ; . 07285 3 . 00265 . 99736
dec 4 : 07314 Á A „00267 „99734
„07324 „6 „07344 Å d . 00269 . 99731
. 07353 i ..07373 i „00271 „99729
„07382 „546 „07402 S „00274 „99727

„07411 : . 07431 : . 00276 . 99725
. 07440 i . 07461 . . 00278 . 99723
. 07469 : ( . 07490 : . 00280 . 99721
. 07498 ; . 07519 : . 00282 299/209
. 07527 . . 07548 S „00284 . 99716

S.

„07556 ; 0. 07578 : . 00287 . 99714
. 07585 : , . 07607 : . 00289 . 99712
. 07614 : d . 07636 : . 00291 . 99710
„07643 s C . 07665 6 „00293 . 99708
. 07672 E j . 07695 : ` . 00296 . 99705

. 07701 „98: „07724 : . 00298 . 99703

. 07730 : . 07753 : „00300 „99701
„07759 : . 07782 : . 00302 2909099
. 07788) . . 84 . 07812 3 „00305 „99696
„07817 : . 07841 x . 00307 . 99694

. 07846 d ; . 07870 : . 00309 . 99692
. 07875 . 698 . 07899 : . 00312 . 99689
. 07904 : . 07929 : . 00314 . 99687
. 07933 : ; . 07958 : > . 00316 . 99685
¿07962150 . 0598 . 07987) af : . 00318 . 99683

„07991 . 5142 0. 08017 E . 00321 . 99680
. 08020 . 4690 . 080461 sc : . 00323 . 99678
. 08049 . 4241 . 08075 a . 00326 . 99676
1050785. . 3795) . 08104 : . 00328 . 99673
BV S . 3352 : . 08134 : . 00330 . 99671

. 08136 . 2913 . 08163 ; . 00333 . 99668
. 08165 . 2476 . 08192 : . 00335 . 99666
. 08194) Šī . 2043) | . 08221) af : . 00337 . 99664
. 08223 Si . 1612 . 08251 : 4 . 00340) 5 | . 99661
. 08252) 5 1185 . 08280 : ; „00342 | . 99659

. 08281 2. 0761 . 08309 : . 00345 . 99657
. 08310) Sa |12. 0340 . 08339 ao ; . 00347 . 99654
. 08339) 54 |11. 9921 . 08368) . e E . 00350 . 99652
. 08368) 5, . 9506 . 08397 : . 00352 . 99649
. 08397) 5c . 9093 ( . 08427 z ; . 00354 . 99647
). 08426 .8684| , . 08456| ac : . 00357 . 99644
. 08455 . 8277 . 08485 S F „00359 . 99642
. 08484) 5 HUSO RE . 08514 : . 00362 . 99639
. 08513} : „7471 „08544 : . 00364 . 99637
. 08542) 54 1073 2 - 08573) > A i "|. 00367 . 99635
. 08571 . 6677 . 08602 : . 00369 . 99632
. 08600) . . 6284) ; . 08632 A EN . 00372 . 99630
. 08629. — . 0893 ^ . 08661| < e S „00374 . 99627
. 08658) 5c . 59051 Sor . 08690) $5 e 2 E .00377| 5 | . 99625
. 08687) 5 . 5120 : . 08720 . 00379 . 99622
A . 08749 ;Å . 00382 . 99619

T . d . o
949. cos S F cot i E csc | sin

WWNWN GO DO DO GO DO WNWNW BO DO Q2 DO DO GO DO GO DO DO GO DO BO DO GO DO DO GO D9 D9 DO GO DO DO DO NW DO NN NNNWN DOD DO DO DO DO DO DO DO DO

oT
Ots NO re A (1s E

J
ER

^:

GO
Que

o

PIE V Up Pu Ps a t€ ES Mc UT RU.

TABLE 31

Natural Trigonometric Functions

0. 08716 11. 4737} 200 (0. 08749] 5, |11. 4301) aco |1. 00382] . lo. 99619 60
08745 29 | 4357 380 | 08778 29 | “3919 382 | 00385 3 | “00617 2 | 59
.08774 39 | .3979 378 | 108807 20 | 2800 379 | | 00387 2 | 096141 3 | 58
.08803 3g | .3604 373 |.08837 39 | .3163 354 : 00390] 2 TRUE 3 J

ACA Ce T No Kia a Man MA m ‘ ns 2 -55
^ ` 0p ^ < € . í a - Dr - h €

.08889| 29 | `. 2493| 398 | 08925 30 | “2048 369 |“ 00397 2 | 99604 3 | 54
08918| 29 | :2123| 365 | 08954 29 | 1681) 387 |: 00400] 3 |: 99602 53
.08947 29 | ¿1765 368 | 08983 29 | "ae 365 | 00403 3 | 90509] 3 | 52
.08076 29 | .1404 359 | -09013| 30 | maa 362 | 00405 2 | 99596) 3 |51
10 |0. 09005 11.1045} zen |0. 09042] 5, |11. 0594| oz» |1. 00408 3 |0. 99594| 2 | 50
090341 29 | “0689 356 |” 09071 30 [10237 39: |.00411| 3 | 99501] 5 | 49
09063! 29 |11. 0336) 393 | 091011 39 fio. 9882) 395 | | 00413 .99588| ? | 48
090921 29 |10. 9984) 352 | 09130| 29 | “9529 353 | 00416] 3 | | 99586 47
09121) 29 | .9635| 349 |: 09159 20 | :9178 351 |:00419| 3 | | 99583] 3 | 46

15 |0. 09150 10. 9288. 4- |0.09189| 5,, |10. 8829] ` 444 |1. 00421 0. 99580 5 | 45

09179| 29 | .8943| 345 |.09218| 29 | .8483| 346 [00424 3 | : 99578 44
:09208| 29 | 8600) 343 | 09247 30 Liege 1.325 |s 00427) | S095700 | 43
ee Ugen asu | 09277) 96. | rez! 1,333 | 00429] 12. | 1905721515. | 42
. 09266] 29 | .7921 336 |-09306 29 | :7457 35g |.00432 3|.99570| 3 | 41
20 |0. 09295) 29 [10.7585 334 [009335 39 |10. 7119) 336 |I- 00485) 3 [9.99567 g [40
09324 sTāāiļon 285 | 09385520; |^ S6783|r: 255 | 0488/03 | 199564] '2 | 3
:09353| 29 | ` 6919 332 | 093941 29 | :6450| 333 |: 00440 .99562| 2 | 38
09382 39 | .6589| 329 |:09423| 20 | og 322 |.00443| 3 |.99559| 3 | 37
094111 39 | :6261 328 |.09453 20 | :5789 325 |.00440| 3 Hours LS
i : 1. 00449 0. 9955: :

25 adios 22 ead 26 óli 29 (TE 326 | 004511 2 | 90551 a | ae
:09498| 29 | 5289 322 | “005411 30 | aam 323 | 00454) 3 |.99548| 3 | 33
` 09527) 39 | .4969| 320 |:09570| 20 | .4491| 312 |.00457 3 | . 99545] 3 | 32
09556] 29 | . 4650; 31? |:09600 30 | :4172 318 | 00460) 3 | . 99542] 3 šī

30 |0. 09585 10.4334| 344 |0.09629| 29 |10. 3854) 44 |1 00463 5 [0.99540] 3 |3

09614| 29 | Agen, 31% |” 006581 2% | .3538| 31% | 00465 :99537| 3 | 29
:09642| 28 | :3708| 312 |:o9688| 30 | :3224 314 | 00468] 3 | . 99534] 3 28
096711 22 | ` 3397]. ` *09717| 2 ` 00471 :99531|. 2 | 27
` 09671 ` 339 ` 09717 IPTE PEE ZI S
“097001 29 | :3089 308 |: 09746 20 | 32602 342 | 004741 3 |.99528| 5 | 26

0.09729 22 l10.2782 29" |n-99776| 29 |10.2294| ax |1.00477 ; |0. 99526] 3 | 25
.2477| * : 99523| :

36 | | 09758 NEE KEREN Wee 99523 3 | 24
.09787| Sq | .2174|. 36? |.09834| 50 | .1683| 392 | 00482 3 |.99520 3
09316 29 | 31873 301 | 09864 39 | 1381 39r | 00489 3 | 99517] 3 | 22

39 | 09845 29 | :1573| 300 |:09803 29 | .1080 300 |.00488 3 E AED

40 lo. 0987 7 10. 07 - |1. 00491 . 9€

41 [^ 09903] 29 | Q979| . 296 |” 09052 a is 297 [.00494| 3 |.99508 3 19
- 09903) 99 |. 294 | ` 00081 29 lio 0187 „296 | ` 00497 99506} 2 | 18
` 09961] 29 | :0392, 293 | ` Tooni 30 Io, 98931| 3939 | 00500 3 | - 99503) 3 "
:09990| 29 | -0101| 5221 |:10040| 24 | .96007| 2906 |.00503 3 PD S AE

RE H ` ‘ 5 II D

46 [^ 10048] 29 VEH 2875 |” 100091 30 |”: 02111 2890 " 00509 3 |. mama 3 | 14

L : s ta ME End ro 3 las
10077, 29 |:92389| 2559 |: 10128 30 |.87338| 2856 | 00512, 3 |.99491| 3 | 13
10106 29 | .89547| 2832 |.10158 39 |.84482| ¿gay | 00519 3 | . 99488) 3 | 12
:10135| 20 | 86722) 3899 | 10187| 29 |. 81641 2894 |-00518| 3 | 9t 35 a

| 50 |0. 10164 NEIPR We NIC 7 [07 78317 1.00521| 4 |0.99482| 3

50 |0. 1016 ( OS bee 2808 D. 99479 2| 9

28 al. SS 0246 76009 E . 00524 DW 3

10192 "81119 2793 |j 20 | + 76009] 3799 | 00024 3 |.99479 al?

29 |'7 2010946 ned Keen Ee E E | 2904761013 | $8
Ko 29 | 755701 2762 |: 10305 39 | seat 2776 | 00530 3 |.99473 3 | 7
"10279! 29 | ` 72833| 2746 | : 10334, 29 |: 67680 ar ih E 005335 | 199470). 3 | ð

pees vos Lan 510363 29 kaal 2745 [-oosse| * r99467| 3 | 5

36 |” 10387 29 | 67387) 2716 |”: 10393 30 eene 2720 |.00539 3 |.99464 3 | 4

10366] 29 | 64687 2700 |. 10422 20 |.59490| 2699 | 00542 3 | - 99611 3 | 3
¿103951 29 | 620021 2985 | "10452 30 |. 56791) 2685 | 00545, 3 | 99458) 3 | 2
2100089 | í 559524002070. 19: 10487 29 | 54106 2020 | -00548| 3 q 99455 al)

60 lo: 10453 29 |o. 56677 289% |o. 10510| ^^ |9. 51436 L. 00551 si a

siet ; Dile i ES

4 : Diff. Diff. Diff ! sin Jr? |

959. cos pit. sec l' cot y, | tan V cse us 1/<84

Lome AA AAA REN —

1318

TABLE 31

Natural Trigonometric Functions

0 |0. 10453 „56677 0. 10510 9. 51436 „00551
1 . 54037 . 10540 . 48781 . 00554
2 . 51411 . 10569 . 46141 . 00557
3|. . 48800 . 10599 . 43515 . 00560
4]. . 46203 . 10628 . 40904 . 00563
5
6
7
8

e

0. 10597 . 43620 0. 10657 9. 38307 . 00566
. 41052 . 10687 . 35724 . 00569
. 38497 . 10716 . 33155 . 00573
: . 35957 . 10746 . 30599 . 00576
9 | .10713 . 33430 . 10775 . 28058 . 00579

10 |0. 10742 „80917 „10805 9. 25530 „00582
C os TOUR: . 28417 . 10834 . 23016 . 00585
12 | . 10800 .25931| . . 10863 . 20516 . 00588
13 | . 10829 . 23459 . 10893 . 18028 . 00592
| 14 | . 10858 . 20999 . 10922 . 15554 . 00595

E 0. 10887 . 18553 . 10952 . 13093 . 00598
. 10916 . 16120 . 10981 . 10646 . 00601

. 10945 . 13699 SELO „08211 . 00604

. 10973 . 11292 . 11040 . 05789 . 00608

. 11002 . 08897 ə | - 11070 . 03379 . 00611

0. 11031 . 06515 0. 11099 . 00983 . 00614
. 11060 . 04146 . 11128 . 98598 . 00617
. 11089 . 01788 . 11158 . 96227 . 00621
. 11118 . 99444 5 dili er . 93867 . 00624
. 11147 . 97111 1217 . 91520 . 00627

25 10. 11176 8. 94791 0. 11246 . 89185 . 00630
26 | . 11205 . 92482 . 11276 . 86862 . 00634
27 | . 11234 . 90186 . 11305 . 84551 . 00637
28 | . 11263 . 87901 . 11335 . 82252 . 00640
29 | . 11291 . 85628 . 11364 . 79964 . 00644

30 |0. 11320 8. 83367 . 11394 . 77689 . 00647
31 | . 11349 . 81118 . 11423 . 75425 . 00650
32 | . 11378 . 78880 . 11452 . 13172 . 00654
33 | . 11407 . 76653 . 11482 . 70931 . 00657
34 | . 11436 . 74438 S UTE . 68701 . 00660
35 |0. 11465 8. 72234 . 11541 . 66482 . 00664
. 11494 . 70041 . 11570 . 64275 . 00667
. 11523 . 67859 . 11600 : . 62078 . 00671
. 11552 „65688| < . 11629 . 59893| . . 00674
. 11580 . 63528 9 |_ 11659 . 07718 . 00677

0. 11609 8. 61379 0. 11688 . 55555 . 00681
. 11638 . 59241 "IKS „53402 „00684
„11667 . 94113 . 11747 . 51259 . 00688
22196906 . 54996 o Yuki . 49128 . 00691
. 11725 _. 52889 . 11806 . 47007 . 00695
45 |0. 11754 8. 50793 0. 11836 . 44896 1. 00698
46 | . 11783 . 48707 . 11865 . 42795 . 00701
47 | . 11812 . 46632 . 11895| : . 40705 . 00705
48 | . 11840 . 44566 . 11924 „88625 „00708
49 | . 11869 . 42511 . 11954 „86555 „00712

E 0. 11898 8. 40466 . 11983 . 34496 a 1. 00715
„11927 „88431 : . 12013| : . 32446 . 00719
. 11956 .36405| < . 12042 . 30406 . 00722
. 11985 . 34390 . 12072 .28376| . . 00726
. 12014 . 32384 . 12101 . 26355 . 00730

0. 12043 . 30388 a 0. 12181| 5, |8. 24345) . . 00733

. 12071 . 28402 . 12160 . 22344 o | . 00737

. 12100 . 26425 . 12190 . 20352 . 00740

. 12129 . 24457 . 12219 . 18370 . 00744

. 12158 . 22500 . 12249 . 16398 . 00747

60 lo. 12187 . 20551 0. 12278 8. 14435 . 00751

K e i P
96% XU) | sec A | tan : ese

Va DA Ka EA a ORROR GO bs GO Ve GO WWW Ke GO GO RW PWW ERD w Ke GO GO Ha GO GO GO Ka Q0 GO GO Ka GO GO Q2 GO 4» Q2 020 GO Q2 GO 4» CO. O5 Q2 O2 O2 Ca
Q2 HH» V Ha Q2 RWW Q2» GO 02H» GO Hx Q2 02H» GO Hx» Q2 02H» ww a GO GO GO K GI DO Ka Q2 GO GO 02H» Q2 Q2 Cu Cu K GO GO GO GO GO GO CO GO Q9 Q2 Q2 Q2 GO DO

ON WH a] O 100

13

CO
V>
o

1319

TABLE 31 Ee
A ic Functi
Natural Trigonometric Dif 172?
M MI. : y
Diff A | see [PE] cos Bie
1 : Diff. tan i! cot 1 f
79» Diff ese 17 TENE 60
sin 1/ 0. 99255) 4
y tow cites A taa PM d MEUS E
TA 0. 122781 39 |8 12481 1945 el E DABIS
; 87 8. 20551) 1939 12308 30 | .1 36 194 00758| 4 99244| 4 | 57
METEO a isesi) 1931 |: 12398 29 | ” 08600 1926 00765| 3 | 99940 SES
E11 166 1921 | ` 15367 : 4 |[- 5
2 RB 20 14760 1911 ` 12397 29 S SC dë Get HEP 00233 S 41
E 1 190 426 : 1 00 3 | ` 99230
4 | 12302 28 eer O eese 1900 | ` 00776 24 2152
Aš 8. 10946. 894 456 : 0 4 9226
5 |0. 12331 29 A ers CH Se Bue GH KE 3 ā
6 |: „671 1876 | 12515 29 |7. 6 315 99219
SET ae 05291| 1868 . 12544 -97170 1874 00787, , [0. 4 | 49
Å ‘ 0 2 1 4 | ' 99215 4
HN kien la Ca 1864 |“ 00791 48
7 : . 12574 4 | ` 99211 3
d T2478 29 [8-01565 Td aa 30 ' onoga] 1856 e He E
JB EINE LOO IE EE E E
ti |: 97873 1833 . 12662 30 |. 95 4 (709200 3
atisae | ee izm e 12092 (o | vana 11539 1.00806 , |0. 99197 šis
13 | . 12562 29 94216) 1817 | - za 7. 86064) 1559 00810) 3 .99193 $ | 43
E a 4
14 | 12591 29 = Ee | Beis et KE 9 42
7. 923 1807 |" 15751 30 498 .99189| 3 41
15 |0. 12020 29 [7. 92399 1791 | 12781 39 | : 82428) 1806 00821) 4 | 90186 4
S ` 22 1797 21 : 0
17 | 012678 29 | ` 86792 EE 1221059 | P50622011 -00821| 4 2 `
: 25 90.32 ea 0. 99182) 4 9
17 | .12678 58 87001| 1783 12840) 99 | .78825| 17 1. 00825 3 99178 3|3
18 | . 12706 59 .85218 |775 | 12840 7. 770351 1781 00828 4 |. 175 =
. 12735 MOTO EE db 4 | 00832 R d n
2 |0 12764 2° |7 stūrī. 1788 |” 12899 2s | 3 78480. 1705 | ee IR EIE
. . 1 1 758 | ` 00840 Fog
21 | . 12793) 59 79918 i75] 12958| 36 Moo 1 0 4 63
$ 0. 991 8 4
22 | . 12822) 59 78167 |743 12988 99 |. 699 1749 1.00844 4 99160 4|3
23 | . 12851) 59 76424) 1735 | - 7 7. 68208) 1749 .00848 3 99156 2
. 12880 59 | - 76424 0. 13017) 30 6466 34 51 aL
CT. Do (ibus EAS pā ties 29 ` 64732 1727 tk A MAE oot
. i 005 1718 | - 0859 30
26 | . 12937 20 a EE Kë 30 | - 63 .0 4 144
1 287 1719 0. 99 3 | 29
kär | a1225 pe EE | 261287 tb once EE 4
28 | . 12995) 59 67826) 1696 0 13165 7. 59575 1703 . 00867) 4 991371 4 | 28
29 | . 13024 29 ð 0.1 30 | ` 57872 1696 | ` 00871 4 133 27
— 7. 6613 1689 13195 29 6176 89 75 99 4 | 26
30 |0. 13053 28 64441) 1689 ` 13224 30 |:* af ; 008 3 SEEN E
: 4487) 1681 00878 25
31 | . 13081 29 62759 674 13254 39 |.5 . 4 (709125
| 2806) 1674 2 0. 3 | 24
32 | . 13110) 29 61085 1667 13284 59 | - 52806 1. 00882) 4 99122 y
: 23
33 | . 13139 59 99418 1659 |-13284 VIGLIEZĪN 1667 . 00886) 4 99118
13313 30 65 0 ZE
34 | . 13168) 59 7 57759 0. . 494 1659 | ` 0089 4 | ` 90114
— IO 1652 13343 29 7806 652 94 . 4 21
785 |0. 13197| 29 leede 30 | - 4 1645 | 00894 4 E |
: 6154| 1615 00898 20
36 | . 13226) 28 54462 1637 13402 26 Māt 38 |-: 4 10, 99106 4
| ) 19
1o 020 152402 1051 |: 13432 20 | | 44509 1638 [00902 1|.99102 4 ie
Fs | 13283 29 51194 1623 ea 742841 1631 . 00906 4 ` 99098 4
2 0. 13461 40 240 1624 10 17
39 | . 13312) 59 571 „41 16 „009 4 | ` 99094 3
7. 495 1616 13491| zu 39616 1617 914 16
| 40 |0. 13341| 29 47955 1809 . 13521 29 |: i to 4 | 99091 F
: 37999 1610 00918 4 15
41 | . 18370) 29 o MATES occa 30 |: 99087| 4
! 36389 1803 2 0 14
42 | . 13399 53 44743 | 15095 580 : Stērstu Kr 4
i bte 1588 c on SE 34786 1598 90930, £ | aen 4 T
ua 29 7. 41560 1582 |“ > 1 „0 + 99075 4
ESU 13639 30 31600 1582 0934 11
| 45 |0. 13485 99 o PA a Ay petes ro 4 |-99071 4
e 5 Å 30018) 1576 00938| 4 10
47 | . 13543) 59 36835 1561 ` 13728 Ee E 99063 4
2 Ë 30 6873 63 0946 5 8
0 a 556 | ` 00950 7
331360 7 ]2 E 30 | ` 23754 1550 | ` 00954 4 9051
50 |0. 13629) 59 321711547 13817| Ze 29204 9 4
1543 | ` 00958 4 5
51 | .13658 29 30630 1535 13846| $6 | - 1 po ies 0. 99047 ¿| €
7 30 | ` 2066 1536 0962 4
52 | . 13687) 29 29095) 1529 13876] 3) 5 1. 0 1|.99043 4 3
Å 6
53 | . 13716 28 27566 1522 0 13906 ESO 1531 . 0096 4 99039 4 2
4 Bekas" 0. 13906| 29 17594 |5983 0970 5
hae 7 1 418 30 | 16071 1518 | ` 00975 4 | ` 99031
55 |0. 1377 29 24529 1510 13965 30 53 f 9 4 0
9 s „145 1511 | ` 0097 4 lo. 99027
56 | . 13802) 59 23019 1502 13995) 29 13042 1505 . 00983 d Å
57 | . 13831 59 21517) 1497 | - 4024 11537 1. A DT. che
58 | . 13860| 59 20020 ¡490 0. 14054 90 fz. 1153 Diff.| gin 82
59]. tt 28 7. 18530 : Dif " me Cee 1
60 Jo. 13017) ^ A cot loa
4 Diff sec 1’
972. cos 1’

1320

TABLE 31

Natural Trigonometric Functions

Dä ; ; ; :
8 sin 1 ‘| ese 1 : tan 1 cot 1’ sec Dif. L
0. 13917 7. 18530 0. 14054 7. 11537 1. 00983 60
1 | 213046 D. ` 17046 s ` 14084 Ge ` 10038 ta ` 00987 : 59
2 1113975 29 |:15568 1479 |.14113 35 | 08546 |487 | - 00991 4 | 58
3 | : 14004) 29 | 14006 |466 | - 14143) 50 | .07059| 1480 | - 00995 4 157
4 | 14083 29 | 12630 1296 | 14173 59 | -05579 ¡474 | 00999 dE
5 |0. 14061) 59 |7. 11171| 1454 |0. 14202 39 |7. 04105) 146g |1 01004 4 | 55
JE HE EN. JE
7 | ` 14119 : : ;
8 | ` 14148 šā ` 06828 E 14291 20 |6. 99718 ne ` 01016 $ 52
9 | :14177 29 | | 05302] 1430 | 14321 30 |.98268| ¡495 | - 01020 ART
10 |0. 14205) 59 |7.03962| 1494 |0. 143511 5, |6. 96823) 143g |1. 01024 4 | 50
11 |.14234 ` 02538 ` 14381 ` 95385 ` 01029 4 | 49
12 | ` 14263 5 7.01120. 1419 | . 14410 co ` 93952 Y ` 01033 5 | 48
13 | | 14292| 29 |6. 99708 |407 | .14440| 30 | .92525| 141 | - 01037 3 | 47
14 |: 14320) 28 | : 98301 1407 |. 14470] 30 | - 91104 3416 | -01041 4 | 46
15 |0. 14349 59 |6.96900| 1395 |0. 14499 3, |6. 89688| 1410 |I. 01046 4 | 45
16 |.14378 29 | .95505 1308 |.14529| 30 | .88278| 1404 | - 01050 4 | 44
17 |.14407 20 | .94115| 1584 | 14559) 30 | - 56874 1395 | - 01054 4 | 43
18 | 14436 29 |.92731| 1355 | 14588| 30 | .85475| 7393 | - 01059 5 | 42
19 | 14464 28 | 91352] |373 |. 14618] 30 | .84082| 7393 | - 01063 5 | 41
20 |0. 14493 29 |6. 89979 1367 |0.14648| 2) |6. 82694 1355 |1. 01067 4 | 40
21 | 214522128 Kees 1507: | iaevece |38 18123 IRON 4 | 39
22 |.14551| 29 |.87250| 1302 |.14707| 20 |. 79936 137% | .01076 5 | 388
23 | 14580 29 | :85803| 1391 |: 14737] 30 | 78564 1372 | : 01080 2 Lët
24 | 14608 38 | 34542] 1351 |. 14767) 30 | .77199| 1365 | * 01084 4 |36
25 |0. 14637) 29 |6.83196| |1340 |0.14796| 3, |6.75838| ¡355 |l. 01089 4 135
26 | .14666 29 | 81856] 1325 | í 14826) 30 | . 74483, 1358 |. 01093 5 | 34
27 | .14895 22 |.80521« 1335 |. 14856] 30 | : 73123). 1350 | . 01097 2 | 33
28 |.14723 28 | 70191 1395 |. 14886) 30 |. 71789 1935 | 01102 4 | 32
29 |.14752| 28 |.77866| 1325 |. 14915 29 | 70450 133% | * 01106 WEL
30 |0. 14781] 29 |6. 76547) ¡314 |0.14945| 3ọ |6. 69116) ¡399 |1. O1111 5 | 30
31 |.14810| 28 | .75283| 1305 Le 14975] 30 | ervey) 1524 01115 $ | 29
32 |.14838| 25 | .73924| 1309 |.15005 30 | .66463| 132% |. 01119 1138
33 | .14867| 29 | .72620| 1305 |.15034 28 | 65144) 1319 | * 01124 =| Oe
34 |. 14806) 22 |. zīszījs 1294 | 15064) 80 | .638311 oA 01198 3 | 26
35 |0. 14925) 59 |6. 70027) 1989 |0. 15094 2, |6. 62523) 1304 |1 01133 4 | 25
36 |.14954 22 | .68788 1554 | -15124 30 |.61219 130% |. 01137 5 | 24
37 |.14982| 28 | .67454| |268 |.15158| 30 |.59921| 1298 |” 01142 21%
38 | . 15011 29 | .66176] 127% | 15183) 30 | 58627 1294 | 01146 Ta
39 |.15040| 53 | 64902 1272 |. 15213 30 | :57339| 1288 | * 01151 das
40 |0. 15069 g |6.63633| 1964 |0. 15243) 59 |6. 56055| 57g |1. 01155 20
41 | . 15097 55 | 62360] 1263 |. 15272 30 | .54777 1278 |: 01160 t | 19
42 | . 15126| 55 | 61110 1222 | . 15302| 30 | 53508 127% | 01164 5 | 18
43 |.15155| 29 |.50855 1955 |.15332| 30 | .52284| 1262 | | 01169 4 | 17
44 | . 15184) 23 |.58600 |94; |.15362| 39 |.50970| 1264 |: o1173 : 16
45 |0. 15212] 59 |6. 57361 1940 |0. 15391 30 |6. 49710 155, |T. 01178 15
46 | . 15241 29 | 56121 1239 | . 15421 30 | .48456| 125% | 01182 4 | 14
47 | . 15270) 59 | .54886| 1285 | | 15451 30 | . 47206 e ` 01187 5 |13
| 48 | . 15299] 2g | .53655 7256 |. 15481] 30 | 459061] 1245 |: 01191 4 | 12
49 | .15327 29 |.52429 1320 |. 15511] 39 |. 44720 |341 |. 01196 2132
50 |0. 15356) og [6.51208 |917 |0. 15540 30 |6. 43484 1931 |1. 01200 | 10 |
51 | . 15885 29 |.49991| 1913 |.15570| 30 | . 422581 1231 | : 01205 5| 9
52 | . 15414) 28 |.48779] 1507 |.15600| 39 |.41026| 1227 |. 01209 tl 8
53 | . 15442 59 | .47572 1993 | . 15630| 30 |.30804] 1222 | 01214 915%
| 54 | . 15471) 59 |. 46369] 119 | 15660 $9 | 88587] 1217 |. 01219 S 6
| 55 10. 15500| 20 |6. 45171 1194 |0: 15689| 39 |6. 37374 1999 |I. 01223 EU
56 |.15529 33 | .43977 1194 | - 19719 30 | .36165| 1209 | 01228 + | 4
57 | . 15587) 59 |.42787] |195 | - 15749| 30 |.34961| 1204 | Í 01233 5| 3
| 58 | . 15586| 29 |: 41602 . 15779 337611 1200 | * 01237 SE
Gel 85725 15820 1180 30 1195 5
. 15615 ` 40422 ` 15809 ` 32566 ` 01242 1
28 1177 29 1191
60 lo. 15643 6. 39245 0. 15838 6. 31375 1. 01247 4199
4 EG
989, cos p sec ua cot ae tan pi ese Deise

SESE A ee e TTT E

1321

1
TABLE 3
1 Trigonometric Functions TIT
Natura = T EU
i Diff. sec 1/ A
Diff tan p cot 1” Å
ALL.
ER 1. 01247| , (En 5 5
y 6. 31375 1186 "01251 d 98764 i A
å E JE. 1178 | - 01256 9 | ` 98755 4 | 56
| : 1 17 15898 30 -29007| 1178 . 01261) 4 ` 98751 DP uod
B. A 1163 | - 15898 30 | ` 57829 1174 | * 01265 d'en 55
1 p x UE E TER 30 | ` 56655 1169 1501976 ; 0. 98740 ; a
2|. 35 1 1 E Sei E E
a dam 28 34584 1155 15988| 79 a Sem he RE : : 98737 5
4 | . 15758 29 6.33429! |150 16017! 30 - 23160} 1157 ABE : 98732 JE
5 ries 20 51133) 1146 16047| 30 . 22003| |152 „ 01289) 2 |. 8723 50
6 Ep 2 2d dem lend 30 | ` 20851 1148 io 294 ? 0, 98723 S
St 29 11 1 ds o 1148 | ET mā
81. iris 29 28853 1134 16137 30 t Ie abo ache s pur 5 ü
E E 1120 | - 15167 30 | - 17419 1136 Í ` 01308 5 | 98704 4 E
de 29 25464 ES 16196 30 . 16283 1132 ed s 4 98700 5 45
Ë dus xd or 1117 | - 16226 30 | ` 15151 PS E oT 5 om 5 | 44
i P JE Up | 10280 20 |6. 14023 1124 |” 01329 5 | ^ 08690 4 dā
AM = GE 1109 [$ iex i 12899| 1120 ` 01327 5 | ` 98686 5141
141.16 28 6. 22113 1109 16316 30 À 11779 1115 ` 01332 ae ER ;
1 |: 1108 29 19898) 1100 16346) 30 „10664 1112 5013971807 98676 5 | 40
R dum d em lant Je 16876 29 | ' 09552 e ero 4 o 4 dm
i meo 29 Murs 1095 | 16405 30 [508444 Tii Kee 54 gts 5 37
> E: A m 1090 [^ 16435 30 | - 07340 1100 | ` 01351 A 5136
19 [1.16 29 6. 16607 1090 16465 30 . 06240 1097 "01356 A 98662 ;
20 |0. 16218| 3g 15517| |085 16495| 30 . 05143} 1092 01361 Č 35687 å 8
ABE 13350| 1082 16525) 36 . 040511 1089 101366 5 98648) 5 33
n K de ele 18555 30 |5- 02962 1084 |” 01371 5 | ` 98643 5 |39
- i ki 1070. [0-16585 30 |” 01878 1081 | ` 01376 5 | "08638 5131
24 | . 163 28 6. 11199 1070 16615 30 6. 00797 1077 Bon 5 | 98638 ; i
25 |0. 16361| 29 10129! 1067 16645| 59 5. 997201 1074 .01380| Š SE 3
26 die 29 09062 1062 16674) 30 - 98646) 1070 Lone] ? 98629 JE
Size s 16419 28 08000 1059 16704 30 5. 97576 1066 ` 01395 SIE 98624 ; a
J sar 2 ees 1055 16734) 49 |5. 96510) 1062 . 01400) 5 |. 98614| 5 26
30 |o. 16506] 2 esa 1052 16764| 30 ` 95448 1058 | ` 01405 5 | ` 98609 SIE
30 |0. 16505) g 04834 1047 16794] 30 . 94390) 1055 .01410| Š "E >
31 | . 16533| 29 03787] 1944 16824) 39 .93335| 1052 e es de
5 uem 2o 01702 1036 | -16854| 30 5,922891 hr .01420| 5 .98595| 5 22
ue Hm 1033 [© 16384] 30 .91236| 1045 TA E dm 5 | 21
aoe 5 99633] 1033 16914) 30 ST oo .01430| 3 . 98585] 5 20
HE E > 08603 1030 16944) 39 . 89151] 1037 .01435| 7 0. 98580| „ 19
BE 97577] 1020 16974| 39 .88114| 1034 1.01440 5 ` 98575 5 | 18
5 dum sl i2 VW d See eo TOO adeo 5 |:ossz0| 9 17
ime e 1015 |0- 17033| 30 - 86051] 1027 | - 01445 > | 98565] 5 16
mA 94521] 1015 P 17063 TA E ae etl Boc dad kis SE
SEI 1008 | - 17093| 30 Sri o 5 |0.98556| 5 14
2 | 10840 25 92501| 1008 17123) 30 . 82982) 1016 1, 01466 ; ` 98551 5 | 13
AB ERU 1001 | -17153| 30 5. 81966| |013 RE A "D
t des ms Los |0. 17183 30 |” $9953 1009 | ` 01476 9 | 08541 5111
AE "soo; 908 "ien rone 1006 (iS O24 ER 7 -98536 | 5 10
HE. le SS 17243) 30 . 78938) 1002 .01480| 5 0.98531] 5 9
REI 987 | 12273) 30 S) 999 |e 2 | 98526) 5 8
USE 36524] 987 . 17303| 30 5. 76937| 996 .01490| 5 ` 98521 5| 7
ARE een 5 - 17333) 39 kiss cece .01501| 5 . 98516] 7 6
Au Fig 977 | 173681 30 at gen S | cossis 5
RE 975 | - 17393] 30 Leti e 1 03525 > |0.98506| > 4
52 | í 17138) 25 526001 975 17423) 90 „72974| 389 1.01517| 5 .98501| > 3
53 [ne 33 az 971 17453) 30 5. 71992] 979 .01522 5 . 98496] 7 2
SE Ku ci 17483) 39 71013 976 | ` 01597 9 | ` 98491 5 14
Sa as | son 961 | + 17513) 30 Ub edet d See e |.98486| 5 0
FE HE: 950 | - 17543] 30 69064 ` 970 Eeer sl 1
AME Dona 17573) 30 . 680941 966 1. 01543 DO No
58 | ; 17308 28 ` 76829 Cie 17603 30 5. 67128 Diff sin 180
dg : : "ei E. Tn Diff ese 1'
59 |. 17336] 29 5 70823 xU
60 |0. 17365 I a
Ģ Diff sec
99°. cos

1322

TABLE 31
Natural Trigonometric Functions = 69°
Diff 1
i Diff A cos iff. y
GER Dit | an (PHP cot PHP | see BIR] cos jā
sin :
Y metu.
67128 1: 013481 OASIS E
5. ` 984
o lo. 17365 essai EE EE dea || 01548): p RE E
1 |. 17393 946 | 17693| 30 | ` 65205 957 |: 01553 5 | - 984711 5 | 58
2 | .17422 942 | ` 17723 A ER nc 6 | 08461 5 | 56
1 i : E
4 ` 17479 936 Eo SR 991 i 01569 5 |0. 98455| 5 on
5 |0. 17508 932 [917253 30 |5 61307 947 |' 01574 B | ema |:
; . 1781 . Bum ||. 79 5
6 | . 17537 290 | 117843/:99 | 2604820 (243 nia Poena 5 | 52
8 |.17594 gaiss]: 17003170 | Gees. | Olen E 0. 98430| > |50
abs rad "i 30 |5. 57638 1.01595| g |0. 98 5 | 49
"10 |0. 17651 S ee TE s Saa 101601567 Aa E
. 17680 ( E 80 | ` 55777 . 01606 ple 6 | 47
12 ` 17708 911 | - 17998 30 p 924 |: 01611 5 : 98409 5 | 46
13|.17 909211" 18053 .53927| 9997 | 01616 (ES 45
14 | . 17766 205 |0.18083| 30 |5. 83007 917 |l. 01627, 5 | S8399] 5 | 44
15 |0. 17794 903 |” 181131 29 |". 52090 ATR ena E
Sat 30 914 01633 . 983 5
16 | . 17823 FEIN EE En | SS HIS Tees .01638 2 |. 98389] 5 | 42
d gets 894 | 18173| 30 |.50264 gog |.01638| 5 .98383 Ë | 41
18 | . 17880 894 18203| 30 | 49356 905 |.:91943 e SIR 5 3n
SA EEE sss |0. 18233] 30 |5. 48451) goa "01654 5 |. 98373, 5 | 39
20 |0. 17937 888 F 18263 30 . 47548 900 20b i 5 ` 98368 5 38
22 | | 17995 883 | ` 18823] 30 | 45751] 897 | ! 01665] $ EE
23 | . 18023 879 SN): 18388599 | Vassar o [Orea Fæ D Las
24 |. 18052 BM EU 5.439601 ee cid, KE 5 ark
26 | b 871 |.18414 30 42192 886 | 016871 9| osi 5 | 33
26 |. Yan de . 4219 : 513 32
27 | . 18138 869 | ` 18474| 30 | : 41309) 883 | :01692 6 | : 98336) 5 | 32
29 | ` 18195 863 | 18504 59 | - 404291 877 |. 1703 > |0.98325| 9 |30
R) 359 [0 18534) 30 |5. 39555] 875 [1 ung © |": 98320 5 | 29
2 |0 19262 ESSE ` 185041 30 | 37805) 872 | oral 5 | osaīs] 5 | 28
: : . 18594 - 87 869 |: 6 | ` 98310 27
32 | . 18281 854 18624| 29 | ` 36936 .01720 5 |. 6 | 56
. 36 66 98304
33 | . 18309 852 | :18654| 30 | ^ 36070) $ 017280 |: dee
j : 64 25
34 | . 18338 3 ea 2° lo 794" T oraid 1038206 E
[LEA 84 5. 35206 . 5 24
dā di [iela [aiao Soa Coal e E
36 |. aed . 18745 UN TI T 5 | ` 98283 22 |
37 |.18424 841 |: 30 |” 32631 „01747. 8 | 6
. 18775 Å t 21
39 | 18481 23601 12 138050 | Ol nea EL
"ken sss (Sne 848 E
Ee 830 | :18895| 30 | :20235| 845 | 01769 E e
42 | | 18067 Zae ECCE Sen Kijts Gatis Li
pā 828 |-18955| 30 | 27553] 840 |:o1781| $ d oss OS
44 | . 18624 dd ES T 5. 26715 1.01786| |0. 9 5
le 318 | . 19016) 30 | 25880 aa i aaa OEE
46 | . 186 818 | 19046 . 25048 L01706 pas EE,
zu EEG 815 |” 19076 30 .24218| $5) |. 01803 E 05222 6.111
oak NU 81215 19106 eM BE! 825 01809): Ë x
. ^. ə R 166 : á D 8
52 | | 18852 T ` 19197 26 | 520025 E T cun 6| 7
53 | . 18881 Boti] 19257| 30 | 0592 814 |: 01882 e | 98196, 3| 6
54 | . 18910 TOT cd S Ale 513 īsas] 9 [o 98190 5| 9
55 |0. 18938 795 |0. iur 30 | A eh R ` 01849 A SE 6 E
56 | . 18967 793 |: 30 | * . 01854 . 981 5
. 19347 . 16863 805 6 174 2)
3B SA AE
o 756 |o 19438| 30 |5 14455 99! Í1. 01872 9 lo. 98163 d
Å i Dif,
1 DÉI, Toe DIET | Dis dE ce Dit) sin 1799
100925 cos 1’ 1

1323

TABLE 31

Natural Trigonometric Functions

0 , 144858 1. 01872 0. 98163 60
1 | . 19109 28 13658) 797 |.01877| ? |. 98157 HET
2 | ` 19138| 29 .12862 793 |.01883| 6 |.98152| 2 | 58
3 | .19167 29 ` 12069 ` 01889 ` 98146 57
4 | 19195 Ce ` 11279 nah ` 01895 : ` 98140 E 56
e |: 10259) 28 “Ohana e786 EE Eed Re
| dioana .08921| £83 | "01912 9 | 98124) 5 | 53
à CEA 28 .08139| 752 | "01918 9 | 08118, 9 | 52
A eee 29 ` 07360 ui ` 01924 i ` 98112 S 51

10 |o. 19366| 25 5. 06584| --- |1.01930| & |0.98107| | 50
29 05809) 775 | 01936 9 | ` 98101 49
AETA .05037| 772 | 010411 9| 98096! 5 | 48
ja | 519453 - 29 .04267| 770 |:01947| 6 | 98001 9| 47
ü Base hs ` 03499 SE ` 01953 E ` 98084 S 46
5 lo. 1 45
16 |” 19838 29 VR E) R | ae
17 | : 19566] 28 01210 781 oan $ [98067 % | 43
18 | 19595] 29 5.00451 299 | .01977/ $|:98061| 9 | 42
19 | :19623| 28 4. 99695] 756 | 01983 9 |:98056| 5 | 41
19 | - 19623 25 Peale 4 4
2 4. 98940 1.01989 g |0. 98050] ( | 40
a "219880 28 | ` 08125 ` 98188 ve ` 01995 E .98044| Ë | 39
22 | . 19709] 29 | ` 07390 . 97438] 19 | .02001| § | . 98039] ¿| 38
23 | . 19737| 28 | ` 06657 - 96690] 748 |.02007| ê|. 98033| 6 | 37
24 | . 19766. 29 | ` 05926 -95945| 745 |.02013 0 |:08027 Ë | 36
25 lo. 19794. *% ls 05107 02019| ? |0. 98021 35
25 |0. 19794 5. 05197 4.95201| +4, |L at lo, 5 | 35
26 | . 19823| 29 |” 04471 944601 73) | 02025] 6 | .98016| 5
27 | . 19851, 28 | ` 03746 .93721| 739 |.02031| 6 |:98010| 6 33
28 | ` 19880| 29 | ` 03024 .92984 737 |:02037 6 |:98004| 6 32
29 | . 19908| 28 | ` 02303 .92249 735 | 02043) 6 |:97998 Ë
30 |0. 19937| 22 |5 01585 4. 91510 731 [L02049 |0. 979025 | 30
9965| 28 1 00869 ` 90785 .02055| 6 |.97987 5
ES 925202129 |. 729 2061 97981 28
32 | ` 19994| 29 |5. 00155 .90056 728 |.0 GE: dE
33 | : 20022] 28 |4. 99443 -89330 735 | 02067) G|-97975 g | 27
34 | 20051 29 | | 98733 .88605| 723 |02073| 6 |: 97969] $ | 26 |
35 |o. 200791 25 |Z 98025 187882 720 |1-02079 |0. 97963 | 25
36 | . 20108] 22 | ` 97320 .87162| 715 | 02085, g | .97958 & | 24
37 | 20136] 28 | . 96616 $6444] 717 |.02091| 6 | : 97952) | 28
38 |.20165| 22 | | 95914 Son 714 |.02097 g | . 979461 | 22
39 | -20193| 25 | : 95215 95013, 18 E qe
40 |0. 20222 4. 94517 154300 710 |1.02110 g |O. 97934 ¿[20
41 |.20250| 28 | ` 93821 83590) fog | : 02116) g |-97928| | 19
` 20279| 29 | 93128 .82882| 707 |.02122 g |.97922 e
2 | 02 28 | ; . 02128 . 97916 17
43 | ` 20307 92436 EE keet Ek
44 | 20336 22 | | 91746 281471) o [602164 g | -97810] | 16
45 |0. 20364! + |4 91058 4. 50769 791 |1. 02140) g |0. 97905) | 15
46 |. 29 |" 90373 . 80068 .02146| 2|.97899| g
A EIRA 79370 998 | 02153 .97893| 8 | 13
es | Seen? 27867959097 M 02160 128 | 59758786 | 12
7 17 6
49 |: 20478| 28 | : 38327 77976 28 |e 02160108. | 9788400 | 11
49 | | 2047 ` 88: ; | 6 : us =
29 1787649 4.77286) 591 [102171 7 |0.97875| | 10
e dones 76595 02178 ` 97869
28 . 76595 : 6 6
51 | .20535| 28 | . 86973 R e 9| s
52 | .20563 28 | . 86299 pu Se Edo 8| 7
54 | 20620. 28 | ` 84056 .74534| ees |. 02190 7 AS 6
— na 29 la 4 73851 203 0. 97
55 |0. 20649) 2g [1 84288 aq 681 eie 6" 97830) ê| 4
56 | .20677 28 | . 8362 73490] 680 |:o22ns| 8 |:oress 9| 3
57 | ` 20706, 22 | ` 82956 | 67 Cs sals) | Seger >
20734 28 | ` 82294 O MM ie 7 Gee rere | ga
355 29 | ` .71137 674 |.02228 & | .97821| 6
AE. 4. 70463 Di [1 02234| 9 |0. 97815 0
60 |0. 20791 4. 80973 . 7046: xii sr
i Diff m sin We o
1019» cos win sec tan 1” ese 1 1'€78

1324

TABLE 31

Natural Trigonometric Functions

12 «167° i
i Diff. Diff.
y sin | ese 1 tan 1⁄ cot y |
j F= 60
, 20791 4. 80973| az» |0. 21256 4. 70463 2 |
1 [^ 20820 29 | 880316 857 | .21286| 30 - 69791 6|59| `
2 |.20848 25 |.79661| $5, |-21316 3; |. 69121 6 | 88
3 | ` 20877 :79007| 0253 | 21347) 34 | . 6845 6 | 57
4 | 20905 28 | 78355 092 |.21377 3, |. 67786 7 1
28 |—7705 999 |o 21408 2! |4 67121 6 [l _
8 | 20062) 29 |. 77057) 948 |.21438 39 | 66458 dE
2e 28 | 76411) 949 | :21469| 31 |: 65797 e | 98
7 | :20990| 28 |. Sa E a 53
8 | ` 21019 ` 75766 ` 21499 ` 65138 S
9 | 21047) 28 | 75123 643 | .21529| 5) | - 64480 6 Lä
0.21076 5. |4. 74482 0. 21560 4. 63825 >
10 |0 21104 28 | 73843 639 |” 215901 39 | 63171 6 | 49 | 3
“21132 28 | "73205 638 | ` 21621) 31 | | 62518 7 | 48
13 | | 21161 29 | 72569 638 |:21651| 30 | : 61868 6 | 47
i . 6121
14 |:21189 28 | 71935] 33 |-21682 3) |. 61219 6 [6
15 |0. 21218 4. 71303 0.21712| 2, |4. 60572 S
21246 28 | 70673 930 |" 21743 31 |” 59927 Bi 44] 3
17 |: 21275) 29 | 70044] 929 |: 21773) 30 | | 59283 e | 43 | a
18 | ` 21303 2 ` 69417 2 ` 21804 a ` 58641 : 42 |
19 | :21331 28 |:68791| 626 |. 21834| 20 |. 58001 s 41] g
20 0.21360 25 |1. 68167| g2> |0-21864| a [i 57363 e [29] >
ST SE 5 ac Ge 321928 30 | : 56091 E 38 |
23 | ` 21445 66307 ` 21956 : 55458 d
29 617 30 36 PR
24 | 21474 29 | 65690) $17 |.21986| 30 | . 54826 6 [26
25 |0. 21502 4. 65074 0. 22017 4. 54196 2
26 |.21530| 28 |. 64461 013 |. 22047] 30 | . 53568 7 | 34
25 | 21887) 28 | ganas] 611. | -22108]-30 | : cose 6 | 32
29 | . 21616 e ` 62630 Ene ` 22139 CM ` 51693 e Lët
30 |0. 21644 4. 62023 0. 22169 4. 51071 7 | 30
31|.21672| 28 | 61417 9996 |” 22200 31 |” 50451 29
32 | 21701 29 |. 60813} 904 | ` 29931] 31 |: 49832 6 | 98
33 | .21729 28 |. 60211 Pot ` 22261 au ` 49215 : 27
34 | 21758) 59 | 59611] $00 | 22292] 24 |. 48600 6 | 2
35 lo. 21786| 5% |4. 59012 0. 22322 4. 47986 E
36 | .21814| 28 | 58414 998 | 99353] 31 |: 47374 24
37 | . 21843] 29 |. 57819) 595 | | 22383) 30 | ` 46764 7 | 93
38 |.21871| 28 | 57224 595 |. 22414 31 | ` 46155 6 | 22
39 | . 21899) 28 | . 56632) 292 |:22444| 30 | | 45548 da
40 |0. 21928 4. 56041 0. 22475 4. 44942 6 | 20
41|.21956| 28 | 554511 990 | 22505| 30 |” 44338 19
42 | .21985 29 | 54863| 938 | ` 99536) 31 | ` 43735 Ti Hiig
43 |.22013| 28 |: 54277 586 | 22567 31 | 43134 6 | 17
44 | 220411 28 | 53692 253 |:22597 30 | | 42584 $ | 16
45 |0. 22070 4. 53109 0. 22628 4. 41936 e | 15
46 |.22098 28 |. 52527 582 | 22658| 30 |” 41340 14
47 |.22126 28 |. 51947 980 1 ` 22689] 31 | ` 40745 M
48 |.22155 29 | 513681 9729 | 22719] 39 | ` 40152 6 | 12
49 | 22183 28 | .50791| 277 |:22750| 31 | : 39560 br
50 |0. 22212 4. 50216 0. 22781 4. 38969 10
51|.22240| 28 |" 49642 974 | 29811] 39 |” 38381 Ux e
52 | . 22268| 28 |. 49069 973 | :22842| 31 | ` 37793 7| 8
53 | :22297| 29 | 48498] 571 | :55879| 30 | ` 37207 SB
54 | .22325 28 |. 47028 370 | | 22903) 3! | : 36623 (| 6
55 [0.22353 59 |4. 47360, zey |0.22934 3, |4 36040 ZUR
56 |.22382 22 |.40793| 267 |.22064| 30 |. 35459 EZ
4E FB EAE EES dÉ
59 | . 224671 28 |.45102| 262 | :23056| 30 | | 33723 ak:
60 lo. 22495 4. 44541 0. 23087 4. 33148 0
^ E s Å : ^
1029. cos pi sec PE cot i tan Dif oe

1325

TABLE 31

Natural Trigonometric Functions

, 22495 | 4. 33148 1. 02630
` 22523 e i 30 |” 32573 ` 02637
` 22552 | ` 32001 ` 02644
` 22580 E ` 31430 ` 02651
` 22608 k è ` 30860 ` 02658
22637 : i 4. 30291 1. 02665
` 22665 | i ` 29724 ` 02672
` 22693 : : ` 29159 ` 02679
` 22722 i i ` 28595 ` 02686
22750 E i ` 28032 ` 02693

. 22778 f : . 27471 . 02700
. 22807 : i . 26911 . 02707
. 22835 : Á . 26352 . 02714
. 22863 : M .25795 . 02721
. 22892) < e ; . 25239 . 02728

. 22920 à i . 24685 . 02735
+ 22948] ša |: e . 24132 . 02742
. 22977 e : . 23580 . 02749
. 23005 e 5 „23030 . 02756
. 23033 s : . 22481 . 02763

. 23062 : À 4. 21933 . 02770
. 23090 5 3 . 21387 . 02777
. 23118 : 3 . 20842 . 02784
. 28146 : ; . 20298 . 02791
. 23175 z : . 19756 . 02799

. 23203 M ; . 19215 1. 02806
. 23231 , : . 18675 . 02813
. 23260 e 4 „18137 „02820
. 23288 e 3 . 17600 . 02827
. 23316 e : . 17064 . 02834

. 23345 ; E 4. 16530 1. 02842
. 23373 : ; . 15997 . 02849
. 23401 4 F „15465 „02856
. 23429 : ; . 14934 . 02863
. 28458 5 m „14405 „02870

. 23486 e ; . 13877 1. 02878
. 23514 S . 13350 . 02885
. 28542 5 F „12825 „02892
„23571 ; : . 12301 . 02899
. 23599 : s . 11778 . 02907

. 23627 : Á 4. 11256 1. 02914
. 23656 : 5 „10736 „02921
. 23684 : ; . 10216 . 02928
. 23712 : S „09699 „02936
. 23740 > : . 09182 . 02943

SE 6
. 23769 : E 4. 08666 1. 02950
. 23797 2 : . 08152 . 02958
. 28825 > : . 07639 . 02965
. 23853 ; . . 07127 . 02972
. 23882 ? . . 06616 . 02980

. 23910 : E 4. 06107 1. 02987
. 23938 : ; < . 05599 „02994
. 23966 : o . 05092 . 03002
. 23995 á 4 „04586 „03009
. 24023 : ` . 04081 . 03017

. 97072

. 97065
. 97058
. 97051
. 97044
. 97037

60 lo. 24192 £ i ` 01078 ` 03061 ` 97030

. 24051 À E . 03578 . 03024
. 24079 . ; . 03076 . 03032
.24108 52 |. 5 . 02574 . 03039
. 24136 : 1 . 02074 . 03046
59 24164 z 5 . 01576 . 03054

-100-1-100 NONON NONNO NNONN -100-I-I-I1 ONNNN ONNNN NONNN -I-I-1-I-] -I-I-I-I-] -I-I-I-1-1 NNNNN

sin

LY
E

103%» cos iff. iff. iff. tan iff. csc

TABLE 31
Natural Trigonometric Functions
pa o
02 T á . Diff Diff 165
14 sin PAT) we | DI | tan TI) cot 127 | see qae s Das
1’
0. 24933 4. 01078 1. 03061 0. 97030 60
dero e E Tu 482 |" 54984) 31 |“ 00582] 296 |:03069 8 | .97023| 7 | 59
29 |: 481 31 496 7 ges
2 | ` 24249 ` 12394 ` 24995 4. 000861 496 loo 7 | .97015 7
3 | 22427700S | 211916 479 |:25026 30 |8. 99592). 493 - 03084) 7 : 97008 7 | 37
4 | 24805) ze | 11487) arr | 28088) 31 A o o 7 [55
5 lo. i ; 7
6 | . 24362 29 |. 10484 FLA ee El | oga 400 [03106 4 -96987 7 | 54
7|.24390 28 |-10009] 474 | -25149 31 o iss | 03114) 7 - 96980 7 | 53
8 | | 24418 ` 09535 ` 251 l ; : :
28 472 31 488 8 i
10 |0. 24474) 29 |4 085911 470 _ |O. 25242] 3, |8: es AL 7 |0. 7 [5
11 | . 24503/ 29 veau 420 |.25273| 3) | .95680 484 |.03144 g | . 96952) 7 | 49
12 |:24531| 38 |:07652| 468 |. 25804] 31 | -95196 383 |-03152 7 | .96945| g 48
E
ia | 24887 28 | 1067171 467 | 125306) 3! | 104232. 481 | 08167) 8 | 96930) 7 | 46
15 |0. 24615| 59 |4 06251) 465 |0. 25397) 3] |3. 93751) ven |1 03175 y [096923 7 | 45
16 | . 24644] 2g | -05786 464 |-25428 31 | -93271| 478 |-03182 g | . 96916 7 44
la | 124872) 28 | -D5922 aea (| 20490081 cdo ad Ee as
28 |: 462 |: al 477 |: al: 8
19 |:24728 28 |:04398 465 |:25521 31 | 91839) 477 |-03205 $ |- 068094 7 | 41
20 [0.24756 og |4. 03938 459 0. 25552| 3, [3. 91364 474 |1 03213 , [096887 7 | 40
21 | .24784 28 | 03479] 459 |.25583| 31 | 90890 273 |.03220| g |.96880 7 | 39
ABRE Erro Seele embed
24 | : 24869 28 | 02107 456 |:25676| 3! |.89474| 471 |.03244 $ |.96858 7 | 36
ET, 28 |: 455 ges ail 470 | Tis 7
25 |0. 24897| >g H 01652 454 [0.25707 4, |8. 89004) 46g [103251 g [0.96851] „ [35] |
a ie Le | at GE a
28 | ` 24982| 28 |4 002031 452 | ` 25800) 31 | soen 497 | 03275 8 |:96829 8| 32] *
29 | | 25010] 28 |3. 99843) 49° | | 25831] 31 | | 87136) 465 |:03282 7 | . 96822) 7 | 31
28 |8: 450 |. 31 |: 465 | 8 7
30 |0. 25038| sg |3. 99393 449 |0.25862| 3, |3.86671| 463 |1.03290 g |0. 96815) g | 30
31 |.25066| 28 | 98044] 14» |.25893 31 |.86208| 463 |.03298| 8 |.96807 5 | 29
JECHEOEME HESESE dE
- 251221 59 |. 446 |: 31 | - 85284) 460 |.03313 g 7 :
34 | : 25151) 28 | .97604| 444 | .25986| 3, |.84824| 46° Lea 8 |.96786 7 | 26
35 |0. 25179) 28 |8.97160| 444 0. 26017| a |3. 84364) 45g |1 03329] g |0.96778| „ | 25
36 | . 25207| 58 | . 96716] 44> | . 26048] 31 | . 83006, 125 | 03337] 8 |.96771| 7 | 24
37 | . 25235) 28 | 96274) 142 | .20079 31 | .83449| 157 | . 03345] S |.96764| 7 | 23
39 | 125291 28 | 1653221 440 «| 20141121 | ess Ce R A
.39 |. 25291) 99 | -95392 440 |. 31 |- 454 (|2 g |- 7 |.
40 [0.25320 5, |3. 94952| 43g |0. 26172| 31 |8. 82083 453 |1.03368| g |0.96742| g | 20
41 |.25348 28 | 94514 43% |.26203 33 | aen 193 |:03376| 8 |.96734 5 | 19
42 | : 258761 28 | .94076| 136 | . 26235) 3; | 81177 457 |. 03384 8 |:96727| 7 | 18
44 | 128422, 28 | : 0829410536. EE EE Sjá na 00 ln n OLI ME
EL IIIS, ots 434 ¡| Betis] 4 90469 5449. EE AQUA NE, AO
45 |0. 25460) — |8. 92770| 433 [0.26328 3, |8.79827| 449 [103408 y [0.96705 g |75
46 | . 25488| 28 |.92337 433 |.26359| 31 | . 79378| 447 | 03410| 8 |.96697| B | 14
47 |.25516| 28 |.91904| 437 |. 26390] 31 |:78031| 147 |: 03424 ` 96690 13
48 |.25545 9g | mä 43] |.26421 3] |.78485 449 | 08432 a ` 96682 z 12
49 | . 25573] 3g [91042 259 | - 26452] 31 | 78040) 445 | 03439]. 7 |.06675 7 | 11
50 |0. 25601 — [3.90613] 499 0. 26483) 35 |3. 77595) 443 |L 03447 0.96667, 7 | 10
51 | . 25629) 28 | 90184) 453 | . 26515) 37 |.77152] 443 | 03455} 9 |. 96660 9
52 | . 25657] 3g | 89756 156 |.26546 31 | 76709 447 |:03463| 8 |:90653| 2] 8
53 | . 25685] 52 |.80330| 126 | . 26577| 51 | 76268 445 103471 "0664509 | amy
54 | . 25713) 3g |. 88904} 425 | . 26608] 31 |.75828| 340 |.03479| 8 | | 96638 T 6
55 |0. 25741) 59 |3.88479| 493 |0.26639| 3, |3. 75388 438 |1. 03487 0. 96630 Bs
56 | . 25769) 2g | 88056) 423 |: 26670) 31 | 74950 438 | 03495 8 | | 96623 A 4
ARS BAR ES EIE HE B
59 | . 25854] 28 | .86790| 121 |. 26764 * .73640| 425 | 03520 9 |:96600 Sd 1
60 |0. 25882 28 |3. 86370 0. 26795| % |3. 73205, 43° li 03528 9 |o.96593| "| 0
4 Diff a ; 1 6 T
1049» cos 1? sec De cot pis tan BH csc Y sin Dite Ed

1327

TABLE 31

Natural Trigonometric Functions

cot

. 25882 s Ë 3. 73205 . 03528
. 25910 Å à TP . 03536
. 25938 : à „72338 „03544
. 25966 e à . 71907 . 03552
. 25994 à 4 „71476 „03560

. 26022 3. . 26€ 3. 71046 . 03568
. 26050 a . 26€ . 70616 . 03576
. 26079 S À . 70188 . 03584
. 26107 > 3 . 69761 . 03592
. 26135 : : . 69335 . 03601

. 26163 3 Ņ 3. 68909 1. 03609
„26191 : : . 68485 „03617
„26219 Ý xi . 68061 . 03625
. 26247 y ^ . 67638 ; . 03633
. 26275 ^ A27 ? „67217 „03642

. 26303 : .27 3. 66796 1. 03650
. 26331 M : . 66376 . 03658
. 26359 : : < . 65957 . 03666
. 26387 : s . 65538 . 03674
. 26415 : : . 65121 . 03683

. 26443 3. : 3. 64705 . 03691 S
. 26471 e - 27 : . 64289 . 03699 . 96433
226500855 Ee 3 . 63874 . 03708 . 96425
. 26528 k : . 63461 . 03716 . 96417
. 26556 : h . 63048 . 03724 . 96410

25 |0. 26584. - ; c . 3. 62636 . 03732 . 96402
26 | . 26612 m 20 q . 62224 . 03741 . 96394
. 26640 : e . 61814 . 03749 . 96386
. 26668 3 E . . | . 61405 . 03757 . 96379
. 26696 : 20: : . 60996 . 03766 . 96371

30 |0. 26724 8. < | . 60588 . 03774 . 96363
. 26752 x < 3 „60181 . 03783 . 96355
. 26780 : Ë : . 99775 . 03791 . 96347
. 26808 e : . 59370 . 03799 . 96340
. 26836 : : , : „58966 „03808 . 96332

. 26864 3: Á i 3. 58562 . 03816 . 96324
. 26892 : : Mort : . 58160 . 03825 . 96316
. 26920 ! ` . 57758 . 03833 . 96308
. 26948 ^ : ; . 57357 „03842 „96301
„26976 : Å : . 56957 „03850 . 96293

. 27004 = j i J . 56557 . 03858 . 96285
. 27032 E | a .56159| : . 03867 . 96277
. 27060 * : A : .55761| : . 03875 . 96269
. 27088 : : s 2- | 28536409 . 03884 „96261
„27116 K : ; : .54968| 2: . 03892 . 96253

PTEN EOS
1
©

— A pl AB
A U DO
©

„27144 j i : 3.54573| 3. 1. 03901 0. 96246
97179 å 2 : 95 | 654179 086: . 03909 . 96238

. 27200 : oe > ; .53785| 2% . 03918 . 96230
.27228 ` 208297119 | 533931 02; 089971022 | 06222

i . 27256 - SE 893899 b= | 7530011059; . 03935 . 96214
0. 27284 > , 28: a A . 03944 . 96206

3] kt : . 28: A M: Os . 03952 . 96198

. 27340 ; k Jes E Josse „03961 . 96190

. 27368 ; m: . 28454| 25 | Si ; . 03969 . 96182

. 27396 : ot “Sa 306: . 03978 . 96174

7 : xi BBS AIS S . 03987 . 96166

ms ; ` 9 eea : ` 03995 . 96158

. 27480 : . 28: Sol: AOE: . 04004 . 96150

. 27508 : 1 : ; ; . 04013 . 96142

9 | . 27536 à DO. | le 294 R: S . 04021 . 96134
60 |0. 27564 : |3. . 04030 . 96126

10505 cos rija = vii, Pu ese | sin

1328

9
8
9
9
8
9
9
9
8
9
9
9
g
8
9
9
9
9
9
9
8
9
9
9
9
9
9
9
9
9

—

a
—
-

=

Pi

E

TABLE 31
Natural Trigonometric Functions
16?»
y sin cot
0 |0. 27564 3. 48741
1 |.27592 . 48359
2 | . 27620 . 47977
3 | . 27648 . 47596
4 | . 27676 _. 47216
5 |0. 27704 3. 46837
6 | . 27731 . 46458
7.427759 „46080
8 |.27787 „45703
9 |.27815 _- 45327
10 |0. 27843 3. 44951
I. 727871 „44576
12 |.27899 „44202
19215527921 . 43829
14 | . 27955 |. 43456
15 |0. 27983 3. 43084
16 | . 28011 „42713
17 |.28039 „42343
18 |. 28067 . 41973
19 | . 28095 . 41604
20 |0. 28123 3. 41236
21 | . 28150 . 40869
22 | . 28178 . 40502
23 | . 28206 . 40136
24 | . 28234 . 39771
25 |0. 28262 3. 39406
26 | . 28290 . 39042
27 | . 28318 . 38679
28 | . 28346 . 98317
29 | . 28374 .97955
30 |0. 28402 3. 37594
31 | . 28429 . 97234
32 | . 28457 . 36875
33 | . 28485 . 96516
34 | . 28513 . 96158
35 |0. 28541 3. 35800
36 | . 28569 . 95443
37 | . 28597 . 35087
38 | . 28625 . 94732
39 | . 28652 . 94377
40 |0. 28680 3. 34023
41 | . 28708 „83670
42 | . 28736 - 99917
43 | . 28764 . 32965
44 | . 28792 . 32614
45 |0. 28820 3. 32264
46 | . 28847 . 31914
47 | .28875 . 31565
48 | . 28903 . 91216
49 | . 28931 . 30868
50 |0. 28959 3. 30521
51 | . 28987 . 30174
52 | . 29015 . 29829
53 | . 29042 . 20483
54 | . 29070 . 20139
55 |0. 29098 3. 28795
56 | . 29126 . 28452
97 | . 29154 . 28109
58 | . 29182 . 27767
59 | . 29209 . 27426
60 |0. 29237

4
1062» cos

. 27085

OOOOO OO OO OO OO d Oud du OO OO S Oe EE CH O CH CH ECH GC

ODO RO -105dccoc

tan

1329

TABLE 31 |
e H ons
Natural Trigonometric Functi «162°
. Diff. cos . y
= i DE Si Diff, Ti pi sec 1’ p
“4 sin e] ee | OH i E A A no
1. 04569 0. 95 8 | 59
— 085 : 9 | 95622 :
; 0. 30573 3. 27 340 |” 04578 9 | 53
o lo. 29237 3. 42030 325 |” 30605 E "26745 339 |` 04588 d . 95613 8 | 57
1 | -29263| 2g | - 41705) 324 EE [uro EE SE ch RE
2 | . 29293 5. 41057 324 | ` 30660 31 | 25729] 338 |” 04606 10 | 2 8 |57
^ > 588
3 | . 29321) 57 40734 323 | 30700 32 Bd 04618 9 [0.95 9 | 54
` 392 95579
4 | . 29348) 58 428 iso 39 |8. 25 337 |” 04625 10 |: S 63
5 [0. 29376| 92 40089 . 30764. 35 24719 . 04 9 | 95562 52
` . 6 644 e 8 | 51
7 | 20432) 28 | ` 30768] 321 | ` 30796 32 | - 24383) 330 |. 04644]: 9 95554 5
: : 4 653 9 LH
7 | .29432| 22 39448| 320 | ` 30828 32 |'54049| 334 |` 04 10 50
: ` : 35 0. 95545 9
8 | . 29460 27 | ` 39198, 320 . 80860) 31 714 3 1. 04663) y 95536 49
9 | . 29487 A SVAN) 0. 30891 39 3. 23 333 . 04672 10 |: 28 3 48
10 |0. 29515) ze 38489 . 30923| 25 23048 : 9 | ` 95519 4
8 955 :2 333 |” 04691 e 8 | 46
11 | . 29543) 28 Seen 3! E MET, 22715 9 | 95511
5 : 1 987 : 331 04700 = == 9 Æ
12 | . 29571) 28 37854| 31 . 80987) 35 22384 i | 10 5 45
: 17 019 : =| Sol 10 0. 95502) y
` 16 3. 22053 331 19 . 954 8
14 |. 29626) 3g | .37537| 2 0.31051) 55 * . 04719] 10 485 43
"15 lo 29654 3.37221| 316 083 - 21722) 339 04729 . 95 Ü 179
15 |0. 29654| og 36905 go Io 21392 : 9 | 95476
k 15 1115 : 329 |” 04738 0 |: 9 | 41
a Ee .3 32 | ' 51063 10 | "95467 9 | 41 |
: 14 1147 : 329 | ` 04748 A ESS
17 | .29710| 57 36276 3 .3 31 | ` 20734 1 04757 H lo 95459 40
: 14 1178 : 328 757 0. 9 9
18 | . 29737 28 35962 3 £ 31178 GY) === 1. 04 10 450 39
: 13. a= 3. 20406 3097 767 .95 9
19 |.29765 55 |.35962| 3 0. 31210| 39 79 . 04 9 | 95441 38
| Ganas 3. 35649) 219 1242 . 200 327 04776 8 | 37
20 |0. 29793) 5. 35336 3 32 | ` 19752 : 10 | ` 95433 9
^ 11 1274 . 826 |` 04786 9 36
21 | . 29821) 5g 35025) ? .3 32 | ` 19426 .95424 y [36
Å 12 1306 : 326 | ` 04795 10 5
22 | . 298491 5» 34713| 3 .3 32 | 19100 95415 2
; 10 1338 Rene ki V 4805 0. sl
23 |.29876 28 34403 3 S3 32 1.0 10 5407 4
l 11 2 3. 18775| 394 815 . 9 9 | 33
24 | . 29904) 52 | . 34403. 3 0. 31370 39 51 . 04 9 | ^ 95398 3
5 ENEE 1402 SEU ME MEUM 10 |: 9 |32
25 |0. 29932 5. 33783 . 3 32 | ` 18127 3 |: j . 95389 y
$ 09 1434 : 32 .04834 “y 31
26 | . 29960 27 33474| 3 .8 82 17804 3 953801 g
h 08 1466 . 32 . 04843) 10 30
27 | . 29987) 5g 33166 3 .3 Bs | 217431 88252 iD*04843 95372
08 31498 Pa cred 04853 0. 9 | 59
28 | . 30015 28 32858 > , 32 9 1; 10 95363
: 307 | 3. 17159) 301 04863 : 9 | 28
29 |. 30043) 5g 0. 31530) 29 6838 i 2 | 705354 9
: 0 r dE des 350 SEH? 5 SN
BS lge 32244 305 |: 94| 32 |. 16517 320 | ` 04882 teli 26
31 |.30098| 28 |. 21939 . 31594 29 16197 399 |. 11 2 | 95337 9
306 |" 31626 : . 04891) 19 25
32 | . 30126) 55 31633) 205 |- 58 92 | | 15877 319 I. 04901 0. 95328| y
i Mi 24
33 | .30154 Ze 31328| 304 |-31658 35 3. 15558| 318 |1 04901) 10 „95819]1 4
: i : 911 23
34 | . 30182) 57 0. 31690) 29 15240 . 04 9 | ` 95310 9
Y 3. 31024| 203 31722 , 318 | ` 04920 10 01 22
35 |0. 30209) 5. 3072110508 |. 54 32 | 14922 317 04930 . 953 8 |31
S 3 10 293
oa EE 303 | ` 31786 32 | | 14605 317 | 04940 285 9
| ; 10 20
37 | . 30265) 27 tp. ti deta E Í 241348 316 0. 95284 y
i 1818| 35 1. 04950| 9 19
38 | . 30292) 38 295-2005 S anl Ms 3. 13972 216 959 . 95275] y 18
39 | 30320| 52 |. UE A A Ee ` 40969] 10 | ` 95266 9
= De 3. 29512 200 31882 : 315 | ` 04969 10 257 17
40 10. 30348 28 29212 300 . 4| 32 .18341| 214 979 . 95 9 | 16
` 1914 29 . 04 10 | ` 95248
41 | .30376 57 A Boat 32 | 213027 314 989 : 8 ie
: 1946| 55 „04 O KES 15
42 | .30403| 93 2801200556 Lë 32 | ` 12713 313 0. 95240] 9
: 1978| 95 1. 04998) 19 14
43 | . 30431) 52 28313} 59g |-3 3 3. 12400} 313 .95231| y
: : 05008 10 13
44 | . 30459) 57 |. 28313 MEA Pg E 2 |: . 95222) y
mus al 3. 28015) 298 32042 . 31 . 05018) 10 5213 12
45 |0. 30486) 28 271000257 128. 32 | 11775 311 5028 . 95: 9 | 11
. 2074| 39 .0 10 | ` 95204 E
46 | . 30514) 28 27420 297 |.3 22] 5114640850 05038 : 9
o 2106| 33 RU EO 5 10
47 | . 30542) 55 Pe 206 (ue 2220035 ei 311 0.95195 y
- C 2139| 39 | . 11153 1. 05047| 19 6 9
Kee Rites 296 |-32139 3 go FEAR no TU | 19
49 | . 30597 QS ES, 0. 32171 32 |? 10532 09 ane 7 10 O 9 >
| ss 3. 26531) 294 32203| 33 |. 3 . 05067) 19 95168
UE ECCE Bee 205 ses: 32 | 10228 309 05077 2-6
À 22851 39 : 10 | ` 95159
a 112 294 |-3 lee site cease = 9
52 |.30680 28 25648 293 -3 . 09606 308 0. 9515 8
; 8 2299 39 | . 09606 1. 05097 10 42 4
aros Ge EL e 3. 09298| 307 05107 TE 91-3
54 | . 30736 Pep tīšs 0. 82331 32 |? 08991 06 : 16 9 . 95133 9 2
SS SE 3. 25062) 292 32363) 33 |. 3 . 05116) 19 95124
a 6 VETERA 292 1239396152 | žosesslēšis 05126| 19 | - 9 ad et
3 g ( . 5115
56 | .30791 28 21478 10991 Br 32 | ` 08379 306 05136 30 91 o
5 ( 2428| 29 . 10 |o. 95106
7 | .30819 27 7 - $2428) 3 . 08073) 205 5146
58 | 308401 27 28897 290 32192 32 |3. 07768 =" Dit. ho
60 |o: 30902 i mr mean ege are
TC EE Diff. cot 1" +
(0705 cos Pi] see | V
1 >

1330

TABLE 31

Natural Trigonometric Functions

18°

y sin

~

©

. 30902 . 23607 . 32492
. 30929 . 23317 . 32524
. 30957 . 23028 „82556
„80985 . 22740 . 32588
. 31012 . 22452 . 32621

. 31040 . 22165 . 32658
. 31068 . 21878 . 32685
. 31095 . 21592 . 32717
. 31123 . 21306 . 32749
, 31151 . 21021 . 32782

. 31178 . 20737 . 32814
. 31206 . 20453 . 32846
. 31233 . 20169 . 32878
. 31261 . 19886 „82911
„81289 . 19604 „829483

„81316 3. 19322 . 32975
. 31344 . 19040 . 33007
. 31372 . 18759 . 33040
. 31399 . 18479 . 33072
. 31427 215199 . 33104

. 31454 . 17920 0. 33136
. 31482 . 17641 . 33169
. 31510 . 17363 . 33201
. 31537 . 17085 . 33233
. 31565 . 16808 . 33266

. 31593 3. 16531 . 33298
. 31620 . 16255 . 33330
. 31648 . 15979 . 33363
. 31675 . 15704 . 33395
. 31703 . 15429 . 33427

. 81730 . 15155 j . 33460
. 31758 . 14881 . 33492
. 31786 . 14608 . 93524
. 31813 . 14335 : . 93557
. 31841 . 14063 . 33589

. 31868 . 13791 . 33621
. 31896 . 13520 . 93654
. 31923 . 13249 . 33686
. 31951 . 12979 . 93718
. 31979 . 12709 . 33751

. 32006 . 12440 0. 33783
. 32034 A . 33816
. 32061 . 11903 . 33848
. 32089 . 11635 . 39881
. 932116 ..11367 . 338913

. 32144 3111011). 0. 33945 1 . 05604
132171 . 10834 . 33978 : . 05615

. 32199 . 10568 = |.34010 : . 05625
E072 . 10303 ; „34043 ` . 05636

. 32254 . 10038 3 . 84075 - „05646

. 32282 . 09774 . 34108 1. 05657

. 32309 .09510| 52 . 34140} : i . 05667

. 32337 . 09246 94179 , . 05678

. 32364 . 08983 . 34205 e . 05688

. 32392 . 08721 . 34238 R „05699

. 32419 . 08459 0. 34270 : 1. 05709

. 32447 . 08197 ) . 34303 H . 05720

. 92474 . 07936 . 34335 . 05730

. 32502 „07675 . 84368 : . 05741

59 | . 32529 „07415 „34400 e . 05751
| 60 |0. 32557 . 07155 0. 34433 . 05762

4 à ő ^ 5
1080, «os | sec i E ese

i=)

=

SE
OOO C «o tod oodo «(D cO «D cO «D «OD CO CO cO «D. cO cO cO cO co

pa

-

Hn
ooo oo OO

rk

m

[m

pi
«OD C d CO «d ODO O Od Odd OS GO O O O ODO ODO OO O

— Ru
[m
5

[20

[es
A sque

SE
Lë

NI
ji ->
| o

. 32557
. 32584
. 32612
. 32639
. 32667

TABLE 31

Natural Trigonometrie Functions

. 07155
. 06896
. 06637
. 06379
. 06121

. 32694
. 32722
. 32749
. 32771
. 32804

3. 05864
. 05607
. 05350
. 05094
. 04839

. 32832
. 32859
. 32887
. 32014
. 32042

. 04584
. 04329
. 04075
. 03821
. 03568

. 32969
. 32097
. 33024
. 33051
. 33079

20 |0. 33106
. 33134
. 33161
. 33189
. 33216

. 03315
. 03062
. 02810
. 02559
. 02308

3. 02057
. 01807
. 01557
. 01308
. 01059

. 33244
. 33271
. 33298
. 33326
. 33353

. 00810
. 00562
. 00315
. 00067
. 99821

. 33381
. 33408
. 33436
. 33463
. 33490

. 99574
. 99329
. 99083
. 98838
. 98594

. 33518
. 33545
. 93573
. 33600
. 33627

. 98349
. 98106
. 97862
. 97619
. 97377

. 33655
. 33682
. 38710
. 33737
„83764

. 97135
. 96893
. 96652
. 96411
. 96171

. 33792
. 33819
. 33846
. 93874
. 33901

. 33929
. 33956
. 33983
. 34011
. 34038

. 95931
. 95691
. 95452
. 95213
. 94975

2. 94737
. 94500
. 94263
. 94026
. 93790

. 34065

. 34093

. 34120
„84147

9 |.34175
60 |0. 34202

„93554
„93318
„93083
„92849
„92614
„92380

„84791
. 34824
. 34856
. 34889

. 34922
. 34954
. 34987
. 35020
. 35052

. 35085
. 35118
. 85150
. 95183
. 35216

. 35248
. 35281
. 35314
. 35346
. 35379

. 35412
. 95445
. 35477
. 35510
. 35543

. 35576
. 35608
. 35641
. 35674
. 95707
0. 35740
. 85772
. 35805
. 35898
. 35871

. 35904
. 35937
. 35969
. 36002) :
. 36035

. 36068
. 36101
. 36134
. 36167
. 36199
. 36232
. 36265
. 36298
. 96331
. 86364
. 36397, `

. 05762
. 05773
. 05783
. 05794
. 05805

. 05815
. 05826
. 05836
. 05847
. 05858

. 05869
. 05879
. 05890
. 05901
. 05911

. 05922
. 05933
. 05944
. 05955
. 05965

. 05976
. 05987
. 05998
. 06009
. 06020

. 06030
. 06041
. 06052
. 06063
. 06074

. 06085
. 06096
. 06107
. 06118
. 06129

. 06140
. 06151
. 06162
. 06173
. 06184

. 06195
. 06206
. 06217
. 06228
. 06239

. 06250
. 06261
. 06272
. 06283
06205
1. 06306
. 06317
. 06328
. 06339
. 06350

. 06362

T
1092. cos

sec

cot

1332

TABLE 31

Natural Trigonometric Functions

20?»
n sin

-

0 [0. 34202 27 2. 92380) 233 0. 36397 33 2.74748 249 1. 06418 11 0. 93969 10 s
1 | . 34229 . 92147 : . 74499 . 06429 . 93959) 19
28 233 33 248 11 949 58
2 | . 34257 .91914 555 . 36463 33 | - 74251) 547 . 06440) 39 |. 93 10
3 | . 34284 27 | : 91681 . 36496 33 | - 74004 248 |: 06452 31 |. 93939) 19 57
4 | . 34311 28 |_ 91449 . 36529 . 73756) 947 . 06463) 11 | - 939291 19 56
A 0. 343391 o7 |2. 91217 231 0. 36562 33 2.73509 946 |! 06474 12 0. 93919| 19 55
7
8
9
10

-34366 27 |”. 90986 ` 73263 -o6486 12 | 93909) 10 | 54
134393] 27 |:90754| 232 |:36628| 33 | 73017 246 | :06497| 11 | .93899| 19 | 53
:34421 28 |:90524 239 |:36601 33 | 172771) 249 |.06508 12 | - 93889| 10 | 52
34448 27 | ` 90293 .36694| 33 | 72526 249 | :06520 17 | . 93879) 10 | 51

0. 34475| 5. |2. 90063 0. 36727| z |2. 72281 1. 06531| ,, |0. 93869 50
11 | . 34503| 28 |. 89834) 229 |.36760| 33 |.72036| 24% | 06542 12 | . 93859] 19 | 49
12 | 34580] 27 | :89605 229 |.30793| 33 | 171792): 244 | .00554 12 | - 93849 10 | 48
13 | 34557 27 | . 89376 223 |-36826 33 | -71548 243 | 00505 1 | -93839 10 | 47
14 | 34584 27 |. go14s| 228 |:36859 33 | 71305 343 |-06577 12 | - 93829 19 | 46

15 |0. 34612) 5- |2. 88920 2.71062 943 |l 06588 12 0. 93819| 19 45
16 | .34639| 57 |. 88692 227 : 33 | - 249 . 06600| 11 | - 93809) 19 44
17 |. 34666 28 |: 88465 297 „86958 „70577. 249 „06611 11 |: 93799 10 43
18 |.34694 97 |- 88238 „86991 33 | - 70335 241 . 06622) i5]. 93789 10 42
19 | . 34721) 57 | -88011| 55, | . 37024 „70094. 24] .06634 11 |- 93779 10 41

20 |0. 34748 27 |2. 87785 : 33 |2. 69853] 941 (1.06645 19 |0. 93769 10 40
21 | . 34775 98 |: 87560 226 . 37090 33 | - 69612) 341 . 06657) 11 |. 93759 11 39
22 | . 34803 27 |: 87334 225 . 37123 34 |: 69371 240 . 06668 12 | - 93748 10 38 |
23 | . 34830 27 |: 87109 . 97157 33 | - 89131) 229 : tī [- 93738 10 |
24 | . 34857 27 | 86885 224 . 37190 33 | - 68892 299 . 06691 . 93728 36
25 |0. 34884 98 |? 86661 294 |0. 37223 33 2. 68653 239 1. 06703 12 |0- 93718 10
26 | . 34912 97 | - 86437 224 . 37256 33 |: 68414 239 . 06715 11 |: 93708 34

27 | 34939 ` 86213 ` 37289 ` 68175 ` 06726 ` 93698
28 | 34966 ti .85990| 223 |.37322 33 238

=a AA. ee kaa sg dic kāši

33 |: 67937 237 . 06738 11 |: 93688 11 32
29 | . 34993 28 | 85767 299 . 37355 33 | 67700 238 . 06749 19 | - 93677 10 31
30 |0. 35021 97 |2 85545 599 |0. 37388 34 |2 67462 937 |! 06761 12 0. 93667 10 30
31 | . 35048) 57 | . 85323 291 . 9/422 33 | - 67225 236 . 06773) 31 | - 93657 10 29
32 | . 35075 27 | - 89102 555 . 97455 33 | - 66989 237 . 06784 12 | - 93647 10 28
33 | . 35102 28 | - 84880 291 . 97488 33 | - 66752 236 . 06796) 11 | . 93637 11 | 27
34 | . 35130 97 | - 84659 220 . 97521 33 | - 66516 235 . 06807 12 | - 93626 10 26
35 |0. 35157 97 |2 84439 299 |0. 37554 34 |2 66281 235 |l 06819 12 |0. 93616 10 25
36 |.35184 27 | - 84219 220 . 37588 33 | - 66046 235 . 06831 11 | - 93606 10 24
37 | . 35211 98 | - 83999 219 . 37621 33 | - 65811 235 06842 12 | - 98596) 11 | 23
38 | . 35239 27 | - 83780 . 37654 . 65576 06854 . 93585 22

39 | .35266 27 | .83561/ 219 |:37687 33 | | 65342 234 | 06866 12 | | 93575) 10 | 21

40 |0. 35293 2. 83342 0. 37720 2. 65109 1. 06878 0. 93565
41 |. 35320 A ` 83124 ae . 87754) 34 | . 64875 EE -06889| 11 |` 93555| 19 | 19
42 | .35347| 3g | .82906| 218 |.37787 33 | 64642 233 |. 069011 12 | | 93544

43 | .35375 57 | . 82688, 217 |.37820 33 | 64410 232 | | 06913 12 | "93534 10 | 17
44 | .35402 57 | .82471| 21, |.37853 33 | .64177| 233 | 06925 12 |:93524| 19 | 16
45 |0. 35429 37 |2. 82254 0.93514| |, | 15

217 [V 33 |2 231 |. 12

46 | . 35456 ` 82037 ` 37920 ` 63714 ` 06948 ` 93503 14
47 | 35484 25 | ` 81821 SE šā .63483| 231 | | 06960 13 | | 93493 us 13
48 | .35511 27 | . 81605] 215 |-37980 34 | 63252 251 | 06972 12 | :93483| 10 | 12
49 | . 35538 27 | ` 81390 ` 38020 ` 63021 ` 06984 ` 93472 11

7 215 33 230 |.06984 41 | . 93472 19 | 11.
50 |0. 35565) 97 [2.81175 aa |0.38053 33 |2. 62791. 339 |i. 0699515, |0. 93462 10
51 | . 35592] 57 | .80960 214 |.38086 34 | . 62561) 259 |. o7007 12 | . 93452 H 9

| 52 | . 35619) 3g | . 80746 215 |. 38120) 33 | 62832 229 |. 07019) 12 |: 93441 8

53 | .35647 27 | . 80531] 913 |.38153 33 | 62103 229 | 070311 12 | :93431| 19 | 7
54 |. 35674) 57 | 80318 214 | 38186) 33 | 61874 229 | 07043 e ` 93420 i 6
55 |0. 35701| 5 |2. 80104 0. 38220| >. |2. 61646 1, 07055 0. 93410 5
56 | ` 35728 79891| 213 38 [76 228 12 10
5 KT 219 adas 61418 07067 ` 93400 4
57 | . 35755 79679 33 228 12 11

$i | 77661 ` 38286 61190 ` 07079 ` 93389 3
58 | ` 35782 79466| 213 21 227 12 10

2s ké 515 8620 ` 60963 ` 07091 ` 93379 2
59 |. 35810 79254 SS SE 12 | 03368 11

a7 (ST 211 |, 38353| 33 | . 60736) 22% | :07103| 1? | | 93368 1
60 lo. 35837 2. 79043 0. 38386 2. 60509 1. 07114 0.93358 10 | 0

| A ` n E ` :
110?» cos Diff. sec Diff. cot ¡DiR din Diff. Diff. a Diff

1333

TABLE 31
Natural Trigonometric Functions
21°>
Diff Diff Diff. “158°
y sin 1’ csc T tan v cot po sec B cos 158

j Å 1. 07114 . 93

.35864 27 | .78882 511 |.38420| 34 | 60283 SCH ` 07126 e Ls 3 B
27 | - 78621 21; |.38453 3% |.60057| 226 |.07138| 12 | :93337| 11 | 58

1 E 210 | 38487 33 | 59831] 222 | | 07150] 12 | 93327 10

35945] 28 | 78200] 319 |.38520 33 |. 59606 225 | :07162 ` 93316 56

L 07174 12 |0. 93306 ,,
k i i ` 93295 54
-36027| 27 | | 77571 aan ` 38620 E ` 58932 2 -07199 13 | | 93285 10 | 53
.36054| 97 |.77362| 552 | . 38654| 34 |.58708 .07211/ 12 | 93274] 11 | 52

9 | . 36081) 57 | .77154 50g |.38687| 33 | . 58484) 224 | 07223 12 | | 932641 10 | 51

10 |0. 36108| 2, |2 76945 ue |0.38721 33 |2 582611 554 |L.07235| ¡o |0. 93253

.38754| 33 | .58038 533 |.07247| 12 |.93243| 10 | 49
- 57815 223 |. 07259 93232 14 | 48
A i oie bs li S | ia53222/ 040
14 |.36217| 37 |.76116| 207 |:38854 ` 57371 ` 07283 ` 93211 46

15 |0. 36244 97 |2.75909| >0; |0. 38888| 34 |2. 57150 1.07295| 55 [0. 93201 ,, | 45
` 07307 ` 93190 44

221 1 ` 97320| 13 | ` 93180] 19
220 |: 12 |: 11

18 | | 36325 75292 38988 56487 ` 07332 ` 93169 42
19 | V 36352) 37 | 75086 206 |: 39022) 3% | : 562661 221 |:07341| 12 | 93159) 19 | 41
20 |0. 36379| 27 |2.74881| 55, |[0.39055 3, |2. 56046) 51, |1.07356 |2 [093148 ,, | 40
21 | . 36406] 52 | .74677 394 |.39089 33 | .55827 219 |.07368| 12 |: 93187) 1 | 39
22 | 36434 25 | 744738) 204 |.30122 33 | : 55608 :07380| 12 | | 93127| 19 | 38

- > : : 219
23 | . 36461 27 | - 74269 504 . 39156 34 | - 55389 . 07393 WER

24 | 36488 37 | -74065 203 | . 39190] 35 | . 55170 2E 07405 12 | : 93106] 19 | 36
25 |0. 36515| 2, [2.73862 2093 |0.39223 34 [254952 as |1.07417| 13 [0 93095| ,, | 35

26 | . 36542 . 73659 . 39257 | 54734 ` 07429 ` 93084 34

27 |:73456| 205 | .39290 33 |:54516| 218 |:07442 15 | . 93074 io iss
28 | | 36596| 27 |.73254| 205 | .39324| 53 | .54299| 217 |.07454 12 | .93063 1]
54082] 217 |:07466| 12 |: 93052 13 | 31
; 2. 53865 - 07479) 19 [0-93042 1, | 30
31 | . 36677 ` 72649 ` 39425 ` 53648 ` 07491 ` 93031

27 | 72448] 201 | | 39458] 82 | 53432 216 |:07503 12 | 93020) ue | 28
33 | - 36731 27 |.72247 29) |.39492 34 |.53217 519 |-07516 19 | : 93010] 11 | 27
34 | 36758 27 | 72047] 200 |:30526 34 | 530011 218 |.:07528| |2 | - 92999 |1

35 |0. 36785| s7 |2. 71847 0. 39559 3, |2. 52786 07540 74 |0.92988| 1, | 25

36 | . 36812] 37 | 71647 200 | 39593) 34 | 52571| 215 |:07553| 13 | .92978 37 | 24

h 27 | 71448] 199 | . 39626| 3% | :52357 215. |-07565 [3 | 92967 1, | 23

38 | 136867) 27 | 71249 199 |-39660 34 |.52142 213 | 07578) jj | . 92956] 11 | 22
39 | 36894 27 | 71050 |99 |. 39694) 34 |: 51929) 213 |.07590| 15 | - 92945 10

40 |0. 36921 ,- |Z. 70851 0.39727 3, |2. 51715 7076021 ,4 |0.92935| ,, | 20
41 |.36948| 27 |.70653| 198 |.39701 34 | 51502 213 [:07615 13 | - 92924) 11 | 19
42 | 569751 27 | awa 195 | 39795) 34 | .51289| 313 |.07627| 13 | > 92913] 11 | 18
43 | 37002 37 | : 70258] 197 |.39820 33 |-51076 319 | - 07640) 12 | - 92902 jg | 17
44 | 37029 27 | "70061 19% |.39862 33 |: 50864 212 |.07652| 3 |. T

45 |0. 37056| 5. |2. 69864 0. 39896 3, |2. 50652 07665 ,2 |0: 92881) ,, | 15
46 | . 37083| 27 |.69667 19; |.39930 33 |.50440| 311 | . 07677] ¡3 | - 92870) 31 | 14
47 | 37110) 27 |.69471| 198 |: 39963) 33 | 50229 21] |.07690| 15 | - 92859) 10 | 13
48 | | 37137) 27 | : 692751 196 |-39997 34 | - 50018] 211 |. 07702] 13 | 92849 11 | 12
49 | 37164 27 | 69079 195 |: 40031| 34 | 40807 210 |-07715| 12 | - 92838) 11

[Em

æT

=

E

50 |0. 37191 5 |2. 68884 0. 40065) 24 |2. 49597 1.07727| 44 |0. 92827, q | 10
51|.37218 27 |. 68689 199 |. 40008 33 |. 49386) 21! [:07740 13 |. 92810 3, | 9
52 | :37245| 27 | 68494 195 |:40132 31 | : 49177, 209 | 07752 13 | -92805 11 | 8
53 | |57272124 | :68299| 195 |:40166| 31 |: 489067 S59 | .07765| 13 | - 92794 19 | 7
54 | :37299| 27 | : 68105) 194 |:40200 34 |.48758 209 |-07778 12 | 92784 11 | $
55 |0. 37326| 97 |2. 67911 0.40234| 24 |2. 48549 „a |1.07790 13 |0. 92773| 11 | 5
AA 193 |: 40267| 93 | 48340| 202 |.07803 ` 92762 4
56 | . 37353 ` 67718 ` 40267 Å 07803] 13 e
2 25| 193 |:40301| 34 | 48132) 208 | .07816 :92751| 1! | 3
57 | aaen 27 |.67525| |93 |. 34 |. 48132) 208 |-07816| 12 | - 92751 3
58 | | 37407 ` 67332 Lanass s T7 20s CU 1217 927401
E 193 anio 07841 ` 02729 1
59 |:37434 27 | 67139) 193 |: 40369) 34 | 47716 207 | -07841] 13 | 92729 11 | |
60 lo: 37461 2” |2 66947 o. 40403| 34 |2. 47509 1, 07853| 12 |0. 92716 t
z i i i Diff. Dies. Dit,
111?» cs KC sec ps. cot n tan V csc 1 sin 1-6 82

1334

TABLE 31

Natural Trigonometric Functions

. 40403
. 40436 34 47302
. 40470 34 47095
. 40504 34 46888
. 40538 34 46682
0. 40572 34 2. 46476
. 40606 34 46270
. 40640 34 46065
. 40674 33 45860
. 40707 34 45655
0. 40741 34 2. 45451
. 40775 34 45246
. 40809 34 45043
. 40843 34 44839
. 40877 34 44636
0. 40911 34 2. 44433
. 40945 34 44230
. 40979 34 44027
. 41013 34 43825
. 41047 34 43623
0. 41081 34 2, 43422
. 41115 34 . 43220
. 41149 34 . 48019
. 41183 34 . 42819
„41217 34 . 42618
0. 41251 34 2. 42418
41285 34 42218
41319 34 42019
41353 34 41819
41387 34 41620
0. 41421 34 2. 41421
41455 35 41223
41490 34 41025
41524 34 40827
41558 34 . 40629
0. 41592 34 2. 40432
41626 34 40235
. 41660 34 40038
41694 34 39841
_. 41728 35 39645
0. 41763 34 2. 39449
41797 34 39253
41831 34 39058
41865 34 38863
41899 34 38668
0. 41933 35 2. 38473
41968 34 38279
42002 34 38084
42036 34 37891
_. 42070) 35 | . 37697
0. 42105 34 2. 37504
. 42139 34 ZI
242178 34 37118
. 42207 35 36925

. 42242
0. 42276
. 42310
. 42345
. 42379
. 42418
0. 42447

1. 07858
. 07866
. 07879
. 07892
. 07904

1. 07917
. 07930
. 07943
. 07955
. 07968

1. 07981
. 07994
. 08006
. 08019
. 08032

1. 08045
. 08058
. 08071
. 08084
. 08097

1. 08109
. 08122
. 08135
. 08148
. 08161

1. 08174
08187

. 08200
08213

. 08226

1. 08239
08252
08265
08278

. 08291

1. 08305
08318
08331

. 08344
08357

OÓ

. 08370
08383
08397
08410
08423

1. 08436
08449
. 08463
08476
„08489

IO

08503
08516
08529
. 08542
08556
1. 08569
. 08582
. 08596
. 08609
. 08623
1. 08636

0 |0. 37461| y,
1 | . 37488 66755
2 137515 27 | ` 66563
3|.37542| 27 | ` 66371
4 | -37569| 27 | 66180
dari
7|.37649 d 65609
peras
10 |0. 37730 2. 65040
11 |.37757 27 |. 64851
12 | | 37784| 27 | ` 64662
13 | 378111 27 | ` 64473
14 | | 37838 a 64285
15 |0. 37865 2, 64097
16 | . 37892 27 |. 63909
17 | . 37919 E 63722
a
20 |0. 37999 2, 63162
21 | . 38026! 27 |. 62976
22 | : 38053 de 62790
EE
25 |0. 38134 2, 62234
26 | . 38161 A 62049
AS EE
29 | . 38241 = 61496
30 |0. 38268 2. 61313
31 | . 38295 A 61129
js
34 | . 38376 24 60581
35 |0. 38403] 37 |2. 60399
37 | | 38456) 26 | 00033
Al |
40 |0. 38537 2. 59491
41 | . 38564| 27 |” 59311
42 | ` 38591 x 59130
dub
45 |0. 38671 2. 5
46 | 38698 27 |. EE
47 | . 38725 Á 58233
EE ERES
50 |0. 38805 2. 57698
2 - 38832 4 57520
` 38859 ` 57342
27 :
AE PE
DANA o ADOOS:
55 |0. 38939) 2. |2. 56811
AR di
JE CHE
60 |0. 39073 2. 55930
n
11295 cos p sec

cot

CSC

er! Sas Se id id: eS ee A ee V

E
=

. 39073
. 39100
„ 39127
. 39153
-. 39180

TABLE 31

Natural Trigonometric Functions

. 39207
. 39234
. 39260
. 39287
. 39314

. 39341
. 39367
. 39394
. 39421
. 39448

. 39474
„89501
. 39528
. 39555
. 39581

. 99608
. 39635
. 39661
. 39688
. 89715

. 39741
. 39768
. 99795
. 99822
. 39848

. 39875
. 39902
. 39928
. 39955
. 39982

. 05057
. 94883
. 54709
. 54536
. 04363

2. 54190
. 94017
. 93845
. 03672
„53500

. 53329
. 53157
. 52986
. 52815
. 52645

. 52474
. 52304
. 52134
. 51965
. 51795

. 51626
. 51457
. 51289
. 51120
. 50952

2. 50784
. 50617
. 50449
. 50282
. 90115

. 40008
. 40035
. 40062
. 40088
. 40115

. 49948
. 40782
. 49616

. 49450

. 49284

. 40141
. 40168
. 40195
. 40221
. 40248

. 49119
. 48954
. 48789
. 48624
. 48459

. 40275
. 40301
. 40328
. 40355
. 40381

. 40408
. 40434
. 40461
. 40488
. 40514

„40541
. 40567
. 40594
. 40621
59 | . 40647
60 |0. 40674

. 48295
. 48131
. 47967
. 47804
. 47640

. 47477
. 47314
. 47152
. 46989
. 46827

2. 46665
. 46504
. 46342
. 46181
. 46020
. 45859

1335

. 32570
. 32383
. 32197
. 32012

. 31826
. 31641
. 31456
. 931271
. 31086

. 30902
. 30718
. 30534
. 30851
. 30167

2. 20984
. 20801
. 29619
. 20437
. 20254

. 29073
. 28891
. 28710
. 28528
. 28348

2. 28167
. 27987
. 27806
. 27626
.27447

. 27267
. 27088
. 26909
. 26730
. 26552

. 26374
. 26196
. 26018
. 25840
. 25663

„25486
. 25309
425182
. 24956
. 24780
„24604

„08636
„08649
„08663
„08676

. 08690

. 08703
. 08717
. 08730
. 08744
. 08757

. 08771

. 08784
. 08798
. 08811
. 08825

1. 08839
. 08852

. 08866)

. 08880
. 08893

. 08907
. 08920
. 08934
. 08948
. 08962

. 08975
. 08989
. 09003
. 09017
. 09030

. 09044
. 09058
. 09072
. 09086
. 09099

. 09113
. 09127
. 09141
. 09155
. 09169

. 09183
409197
. 09211
„09224
„09238

„09252
„09266
„09280
„09294
„09308

„09323
. 09337
. 09351
. 09365
. 09379
1. 09393
. 09407
. 09421
. 09435
. 09449
1. 09464

4
113?» cos

sec

tan

csc

1336

TABLE 31
Natural Trigonometric Functions
Dä ¿ 5 ; `

24 sin Dit. esc E tan p | cot pue sec
o |0. 40674 oa |2. 45859 0. 44523 2. 24604 . 09464
1 | 20700 26 | 45699 190 |” 44558] 35 | 24428 176 |. 09478
2 | 40727 27 | 45530 160 | ` 44593) 39 | 24252 176 |. 09492
3 | ` 40753 4 ` 45378 ti ` 44627 2 24077 ne ` 09506
4 |. 40780] 27 | 45219) 159 |. 44662 35 |. 23002, 173 | . 09520
5 |0. 40806 2. 45059 0. 44697 2, 23727 709535
6 | . 40833 27 |” 44900] 159 | 44732] 35 | 235538 17% |” 09549
7 | 208601 27 | ` 44741) 199 | 44767 39 | 23378 175 |: 09563
8 |. 40886 a0 ` 44582 a ` 44802 ds ` 23204 d. ` 09577
9 |. 40913 5 ` 44423 m? . 44837| 35 |. 23030 173 | 09592
10 |0. 40939 2. 44264 0. 44872 3; |2. 22857| ¡74 |l. 09606
11 | . 40966 27 |” 44106) 198 | 44907| 35 |” 22683 ` 09620
12 | | 40992 25 | 43948 158 |:44942 35 |:22510 172 | .09635
13 | 41019] 27 |. 43790| 158 |: 40977] 35 | 22337 |73 | . 09649
14 | 41045 25 |. 436838] 197 |:45012 32 | 22164 373 |. 09663
15 |0. 41072 2. 43476 0. 45047 a 21992 52 |i. 09678
16 | . 41098 2 ` 43318 D ` 45082 ` ` 21819 ie 09692
17 |. 41125] 27 | 43162) 188 Laun 32 | 21647) 172 |. 09707
18 | ` 41151 ` 43005 ` 45152 21475) 172 | ` 09721
19 |. 41178 54 ` 42848 ag 45187 25 ` 21304 i ` 09735
20 |0. 41204 2, 42692 0. 45222 2. 21132 - 09750
21 | . 412311 57 |. 42536 158. 0145257 Se ` 20961 i ` 09764
22 |.41257| 29 | | 49380| 156 |.45202 33 |:20790| 17! [09779
23 |.41284 24 |. 42225| 195 |.45327 32 |.20619| 175 | 09793
24 |. 41310) 3° | 42070, 155 |:45362| 32 |. 20449] 179 |:09808
25 |0. 41337 2. 41914 0. 45397 2. 20278 ` 09822
26 |.41363 29 |.41760| 15% |.45432| 32 |”: 20108] 170 |:09837
27 |.41390 26 |.41605| 185 | .45467| 32 |. 19938] 170 |. 09851
28 |.41416| 27 | 41450 195 |.45502 32 | 19769] 199 | 09866
29 |.41443 2; | 412061 13% |:45538 39 |. 19590] 170 |: 09880
30 |0. 41469 2. 41142 0. 45573 2.19430 "IT |i. 09895
31 |. 41496| 2^ | . 40988 155 | . 45608 Se [19261 mh ` 09909
32 |.41522| 27 |.40835| 153 |:45643 35 |:19092| 169 |: 09924
33 |.41549 26 | 406811 15% |. 45678) 22 | 18923 169 | 09939
34 |. 41575 27 | 40528 193 |. 45718| 33 | 18755 168 |: 09958
35 |0. 41602 2. 40375 0. 45748 2.18587| "II [L 09968
36 |. 41628 26 |” 40222) 153 |” 45784 36 |” 18419 198 |” 09982
37 | : 41655) 27 | ` 40070 152 |: 45819 = 182511 165 | 09997
38 | . 41681 26 | . 39918 ee . 45854] 32 | . 18084 mi ` 10012
39 |.41707 27 |.39760 132 |:45889 35 |. 17916] 168 |: 10026
40 |0. 41734 2. 39614 0. 45924 2. 17749 . 10041
41 |.41760| 29 |^ 39462| 152 |” 45960 36 |^ 17582 167 10056
42 |.41787| 27 | ` 39311; 151 | ` 45095) 39 | 17416. 199 | 10071
43 | 41813 ge ` 39159 SE ` 46030 HE ` 17249 e ` 10085
44 | .41840 56 |.39008 |5; |.46065 ze |.17083 166 |.10100
45 |0. 41866 2. 38857 0. 46101 2.16917| 322 |L 10115
46 | .41892| 2% |" 38707, 190 |"146136| 35 |“ 16751| 199 1" 10130
47 |.41919 27 | : 38556. 151 |” 461711 39 | 16585 166 | ' 10144
48 | . 41945 25 | ` 38406 150 | 46206 es 16420 195 |” 10159
49 | 41972 56 | . 38256] 13) |. 46242] 3° | 16255 162 | 10174
50 |0. 41998 „g [2.38106] | 0. 46277 2. 16090 . 10189
51 | . 42024 25 |. 37957 Y ` 46312 a 15925 199 |" 10204
52 | . 42051) 27 | ` 37808 ` 46348 .15760| 199 |'10218
53 | . 42077 57 | . 37658 190 |.46383| $2 |.15596| 164 |: 10233
54 | 42104) 36 | 37509] 13% |. 46418] 36 |. 15432 16% |: 10248
55 |0. 42130. 6 |2. 37361 0. 46454 2. 15268 . 10263
56 | . 42156| 28 |" 37212 m ` 46489 a ` 15104| 16% |” 10278
57 | . 42183) 36 | 37064 148 |.46525 39 | 14940) 16% |: 10298
| 58 |. 42209 26 | ` 36916 465601 39 | ` 14777 193 | ` 10308
59 | ` 42235 36768 148 35 163 | 10308
59 | 27 |, 36768 173 |.46595 38 |.14614| 163 |” 10328
` 42262 2 36620 0. 46631 2. 14451 ` 10338

4
D ff . "
1140, cos T sec Dit cot pi. tan dur csc

1337

TABLE 31
Natural Trigonometric Functions
Diff, Diff, Diff. Diff. «154°
CSC 1’ tan 1 cot 1 sec i’ cos Dit. y
1”
2. 36620 0. 46631 2. 14451 1. 10338 0. 90631 60
` 36473 ns 46666 2° |” 14288 ia 10358 19 | ` 90618) 13 | 59

` 36325 46702 39 | ` 14125 „10368| 19 | ` 90606 12 | 58
` 36178 Sid ` 46737 22 ` 13963 n ` 10383 E .90594| 12 | 57
.36031| 346 |.46772| 36 | 18801 789 |. 10398] 15 | 90582 12 | 56
2. 35885] 147 |0. 46808) 35 |2 13639 |62 |T. 10413 ¡2 |0.90569| 15 | 55
-35738 146 | - 46843) 36 |.13477 10% |. 10428 15 |.90557, 12 | 54

` 35592 ` 46879 ` 13316 ` 10443 90545 53
- 35446 i 46914 He ` 13154 ach ` 10458 Ë : 90532) 13 | 52
.35300| 146 |.46950| 35 |. 12993] 161 |:10473| 15 | : 90520 12 | 51

2.35154 145 |0. 46985 ze |2. 12832) jẹ] |I 10488 0. 90507, 19 | 50
.35009| 146 |.47021| 35 |.12071| 181 |:10503 19 | 90495 12 | 49
- 34863 145 |-47056 38 | 12511 160 |:10518 15 |: 90483 12 | 48
.34718| 148 |-47092 36 | 12350 165 |:10533 19 | 90470 13 | 47
34573) |44 |.47128| 35 | 12190 100 |: 10549 18 |: 904581 12 | 46

2, 34429 : dec P I2080|9/ 389 A R i
.34284| 132 |.47199| 35 | 11871) 15% | 10579] 13 |. 90433 13 | 44
` 34140 ` 47234 ` 11711 ` 10594 ` 90421 43

144 36 159 15
same e a let AS
.33852| 124 |.47305| 50 |. 11392) 160 |:10625| 16 | : 90396 12 | 41

2. 33708| 143 |0. 47341| ze .11233 ¡58 |L
.33565 143 |.47377 36 | 11075) 158 |.10655 15 i;
.33422 144 |.47412 35 |: 109161 152 | 10670 ` 90358 38
.33278 144 |.47448| 36 | :10758 158 |:1068e 18 |.
.33135| 149 |.47483| 59 | : 10600 . 10701| 12 | :90334| 12 | 36

2. 32993 0. 47519 2. 10442 1. 10716 0. 90321 35
` 32850 id ` 47555 ER ` 10284 E ` 10731 i 90309 12 | 34
32708 172 |.47590| 38 |. 10126 155 | :10747| 18 |: 90296) 13 | 33
.82566| 145 |.47626| 36 |. 09969 192 |.10762| 12 | - 90284 12 | 32
.32424 1412 | | 47662| 29 | 00811 128 |:10777| 12 | : 90271 13 | 31

2. 32282 |43 |0. 47698| 35 |2. 09654) |56 |1.10793| |; |0. 90259) ¡3 | 30
32140 142 |.47733| 35 |.09498 155 |:10808| 19 | . 90246) 13 | 29
.31999 11 |:47769 36 | 09341 157 |:10824| 18 |: 90233) 13 | 28
31858 141 |:478o5| 36 | wa 157 |. 10839] 15 | .90221| 13 | 27
31717 !4! |:47840| 38 |: 09028 126 |. 10854) 13 | - 90208) 15 | 26

2, 31576 0. 47876 2, 08872 I. 10870 0. 90196 25
31436 120 |.47912 4 ` 08716 tee . 10885| |? |. 90183 7 | 24
31295 141 |.47948| 36 | 08560] 199 | 10901] 15 | . 90171) 13 | 23
(31155, 140 |.47984| 3% | mann 195 |.10916] 18 | - 90158| 15 | 22
31015 110 |. 48019] 38 | 08250] 156 |-10932 |5 |.90146| 13 | 21

2. 30875 |4) |0 18055 ze |2. 08094| |55 |i. 10947) „g [0.90133| ¡3 | 20
.30735| 140 |.48091| 36 |.07939| 133 |. 10963) |5 | . 90120) 5 | 19

` 30596 ` 48127 ` 07785 ` 10978 90108 18
` 30457 A ` 48163 ge 07630 i . 10994| 19 | : 90095 2 17
.30318| 139 |:48198 36 |. 07476] 155 |.11009| 1$ | . 90082) 15

2. 30179 0. 48234 2, 07321 1. 11025 0. 90070 15
"20040 139 | 48270 36 |“ o7167 194 |” 110411 16 |. 90057 13 | 14
139 36 153 15 12
29901 199 |: 48306ļ 36 |.07014| 154 |. i
29763 138 |:48342 36 |. 06860] 124 |-11072 15 | - 90032 13 | 12
20625 138 | 48378 36 |. 06706| 153 |.11087 jg | 90019 13 | 11
2.29487 e |0. 48414) 35 [206553 153 |T. 11103 je [0 90007) ¡3 | 10
20349 138 [ [48450 36 [.06400 |53 |-11119 5 | - 89994 13
292111 138 48486 35 | 06247 153 |.11134 jg | - 89981 13
200741 137 | 148521) 33 |.00094 123 |-11150 jg | - 89968 12
` 28937 : 48557) 36 | 05942] 152 |.11166| 15 | - 89956 13

9

8

7

6

2. 28800 0. 48593 2. 05790 1. 11181| ue |0. 89943) 4 5
2 137 36 153 16 3

. 28663 137 . 48629 36 . 05637 152 .11197| 16 . 89930} 15 4

2

1

0

1

` 28526 ` 48665 ` 05485 ` 11213 ` 89918) 13
` 28390 E ` 48701 ee ` 05323 T1 ` 11229 e -89905 13
Å 28258 137 | 148737) 30 |. 05182) 123 | - 11244) 16 | - 89892 13
60 |0. 43837 2 28117 2. 05030 |

1152. cos iff. sec ck cot Ü tan 17 ese 1

1338

TABLE 31

Natural Trigonometric Functions

26%.

y sin

. 43837
. 43863
. 43889
. 43916
. 43942

. 43968
. 43994
. 44020
. 44046
. 44072

«c0 -1oo|mmcot-0:^

2. 27439
. 27304
. 27169
. 27035
. 26900

. 44098
. 44124
. 44151
„44177
. 44203

. 26766
. 26632
. 26408
. 26364
. 26230

. 44229
. 44255
. 44281
. 44307
. 44333

. 26097
. 25963
. 25830
. 25697
. 20565

„44359
„44385
„44411
. 44437
. 44464

. 20432
. 25300
. 25167
. 25035
. 24903

. 44490
. 44516
. 44542
. 44568
. 44594

. 24772
. 24640
. 24509
. 24378
. 24247

. 44620
. 44646
. 44672
. 44698
. 44724

. 24116
. 23985
. 23855
. 23724
. 23594

. 44750
. 44776
. 44802
. 44828
. 44854

. 23464
. 28334
. 23205
. 28075
. 22046

. 44880
. 44906
. 44932
. 44058
. 44984
. 45010
. 45036
. 45062
. 45088
. 45114
„45140
. 45166
. 45192
. 45218
. 45248
55 |0. 45269
„45295
„45321
58 |. 45347
59 |.45373
60 |0. 45399

7
116°» cos

. 22817
. 22088
. 22559
. 22430
. 22302
2. 22174
. 22045
. 21918
. 21790
. 21662

2. 21535
. 21407
. 21280
. 21158
. 21026

2. 20900
. 20773
. 20647
„20521
„20395

|2. 20269

. 48773
. 48809
. 48845
. 48881
. 48917

. 48953
. 48989
. 49026
. 49062
. 49098

. 49134
. 49170
. 49206
. 40242
. 49278

. 03376
. 03227
. 08078
. 02929

. 49315) .

. 49351
. 49387
. 49423
. 49459

. 02780
. 02631
. 02483
. 02335
. 02187

„49495
„49532
„49568
. 49604
. 49640

. 02039
. 01891
. 01743
. 01596
. 01449

. 49677
. 49713
„49749
„49786
„49822

„01302
. 01155
. 01008
. 00862
. 00715

. 40858
. 49894
. 49931
. 49967
. 50004

. 00569
. 00423
. 00277
. 00131
. 99986

. 50040
. 50076
„50113
„50149
„50185

0. 50222
„50258
„50295
„50331
„50368

0. 50404
. 90441
. 00477
. 50514
. 50550

0. 50587
. 00623
. 50660
. 00696
. 50733

. 99841
. 99695
. 99550
. 99406
. 99261
1 99116
. 98972
. 98828
. 98684
. 98540

1. 98396
. 98253
. 98110
. 97966
. 97823

1. 97681
. 97538
. 97395
. 97253
97411

0. 50769
. 50806
. 50843
. 50873
. 50916

0. 50953

1. 96969
. 96827
. 96685
. 96544
. 96402

1. 96261

. 11260
. 11276
. 11292
. 11308
. 11323

1. 11339
. 11355
„11374
„11387
„11403

. 89879
. 89867
. 89854
. 89841
. 89828

0. 89816
. 89803
. 89790
. 80777
. 89764

. 11419
. 11435
. 11451
. 11467
. 11483

. 89752
. 89739
. 89726
. 89713
. 89700

. 11499
. 11515
. 11531
. 11547
. 11563
. 11579
. 11595
. 11611
311627
. 11643

. 89687
. 89674
. 89662
. 89649
. 89636

0. 89623
. 89610
. 89597
. 89584
. 89571

. 11659
. 11675
. 11691
. 11708
. 11724

. 89558
. 89545
. 89532
. 89519
. 89506

. 11740
.11756
. 11772
. 11789
. 11805
1. 11821
. 11838
. 11854
. 11870
. 11886
„11903
. 11919
. 11936
. 11952
. 11968

1. 11985
. 12001
. 12018
. 12034
„12051
1. 12067
. 12083
. 12100
. 12117
. 12133
1. 12150
. 12166
. 12183
. 12199
. 12216
. 12233

. 89493
. 89480
. 89467
. 89454
. 89441

. 89428
. 89415
. 89402
. 89389
. 89376
0. 89363
. 89350
. 89337
. 89324
„89311

. 89298
„89285
. 80272
. 89259
. 89245

. 89232
. 89219
. 89206
. 89193
. 89180

0. 89167
. 89153
. 89140
. 89127
. 89114

0. 89101

A 5858

tan

csc

Q2

o

1339

TABLE 31
Natural Trigonometric Functions

å i , -1520

y sin 1 csc 1’ tan 1 | cot pig. sec id co 152
EM ae, te Pn | i?

0 |0. 45399] „„ |2. 20269 0. 50953 1. 96261 1. 12233 0. 89101 60
1 | . 45425] 26 |.20143| 129 |.50989 36 | 06120 141 [:12249| 16 | 80087 14 | 59
2 | ` 45451 .20018| 129 | 51026 37 | 95979, 141 1 192266 17 | ` 89074| 13 | 58
3 | ` 45477 2 ` 19892 T ` 51063 E .95838| 1%) |:12983| 17 | 80061 13 | 57
4 | . 45503] 55 | 19767| 125 |.51099 38 | 956081 119 |:12299 e ` 89048 E 56
5 |0. 45529 2. 19642 0. 51136 1. 95557 1.12316| ,- lo. 89035 dé

GER 125 37 7^ 140 16) 17 14
6|.45554| 28 |.19517| 154 |.51173| | 95417) 140 |.12333 1 |. 89021 54
7 | .45580| 26 |.19393| 12: |.51209 39 | 195277): 140 |.12349 19 | :89008| 13 | 53
8 |.45606| 26 | .19268| 12; | . 51246) 32 | 95137, 140 |. 12366 Ww ` 88995. 19 | 52
9 | 45632 56 | .19144| 152 |.51283| 34 | 94997] 130 |.12383 17 | 88981 i 51
10 0.45658 ze |2. 19019 194 |0. 51319 37 |1. 94858 140 1. 12400) 16 0. 88968 50
11 | . 45684] 26 | . 18895) 123 | 51356) 37 | 94718 130 |. 12416 19 |. 88055 13 | 49
121 ?45710|.29 | 18772 151398 ase || 694570 enc: 12433 17 | 88942 13 | 48
13 | . 45736 de . 18648 Tak ` 51430 d 94440] 139 | . 12450 17 | | 88928 E
14 |.45762| 25 |.18524| 153 |-51467 34 |.94301| 139 |. 12467 17 | 88915 13 | 46
15 |0.45787| 5; |2. 18401| |94 |0. 51503] 37 |T. 94162 |39 [1.12484 |; |0. 88902 ,, | 45
16 | . 45813 .18277| |23 |.51540 .94023 vs |. 12501 ` 88888 44

17 | . 45839 de Eege ek |9 51573 de .93885 138 |. 12518 M ` 88875 15 43
18 | . 45865] 26 | -180311 153 |.51614| 37 | .03746| 13% |:12534 . 88862] 13 | 42
19 | . 45891] 38 |.17909| 353 |.51651| 37 |.93608| 13% |: 12551 17 |: 88848 41

20 |0. 45917 25 2. 17786 123 |0. 51688 36 1. 93470 138 |. 12568 17 |0. 88835 13 40
21 |.45942 26 |: 17663| 155 . 51724 37 |- 93332 137 . 12585| 17 | - 88822 14 39
22 | . 45968 26 |: 17541 122 „51761 37 |: 93195 138 „12602 17 |: 88808 13 38
23 | . 45994 26 |: 17419 122 . 51798 37 | : 93057 137 . 12619 wl 88795 13 37
24 | . 46020 26 | 17297 129 . 51835 37 | 92920 138 „12636 TVAE 88782 14 36
25 |0. 46046 26 2.17175} 199 |0. 51872 37 |! 92782) , 137 |l 12653 17 0. 88768 13 35
26 | . 46072 25 |- 17053| 151 . 51909 37 |: 92645 137 . 12670) iz |. 88755 14 34
27 | . 46097 26 |- 16932 122 . 51946 37 |: 92508 137 „12687 17 . 88741 13 33
28 | . 46123 26 |: 16810 191 . 51983 37 . 92371 136 . 12704 17 |: 88728 13 32
29 | . 46149 26 |: 16689! 191 . 52020 37 . 92235 137 .12721| 17 | - 88715 14 31
30 |0. 46175 26 2.16568} 191 0. 52057 37 1. 92098 136 1. 12738 17 0. 88701 13 30
31 | . 46201 25 |: 16447| |9] „52094 37 | - 91962 136 . 12755) iz |. 88688 14 29
32 | . 46226 26 |: 16326) 150 . 52131 37 |: 91826 136 . 12772) 17 |. 88674 13 28
33 | . 46252 26 |: 16206| 151 . 52168 37 . 91690 136 . 12789 ig |. 88661 14 27
34 | . 46278 26 | 16085 150 . 52205 37 . 91554 136 . 12807 TVAE 88647 13 26
35 |0. 46304 26 2.15965! 1959 JO 52242 37 |! 91418 136 1. 12824 17 0. 88634 14 25
36 | . 46330 25 |: 15845| 120 . 52279 37 . 91282 135 . 12841 17 |: 88620 13 24
37 |. 46355 „15725| 120 „52316| 32 |.91147 : .12858| 17 |. 88607 23

26 37 à
38 | . 46381 . 156051 159 . 02353 . 91012 136 . 12875) i7 . 88593) 14 22

39 | ` 46407 a .15485| 179 |. 52390 A med 139 |. 12899) |4 | -88580| 14 | 21
40 |0. 46433 3p |2. 15366 van |0-52427| 37 |1. 90741] ¡34 |I 12910] |7 [0.88566| ¡3 | 20
41 |.46458| 29 |. 15246] 120 | 52464) 37 |.90607| 13$ |.12927| 17 | . 88553] 14 | 19
42 | :46484| 26 |. 15127] 119 | 52501) 37 | 90472 155 |. 12044) 17 | . 88539 13 | 18
43 | :46510| 26 | :15008| 119 |.52538| 37 |.90337| 134 |-12961| jg | . 88526] 14 | 17
44 | :46530 29 | 14889] 119 [|:52575 34 | 90203) 134 |.12979 j7 | -88512 13 | 16
45 |0. 46561| 5c |2. 147701 vun |0. 52613] 37 |T. 90069 |34 |1. 12096] ¡7 |0. 88499] 14 | 15
46 | .46587| 20 [14651] 119 |. 52650) 37 |.89935| 134 |-13013| jg | -88485 13 | 14
47 | :46613 20 | "145331 118 |. 52687) 37 |.89801| 134 |-13031 17 | 88472 14 | 13
48 | .46639| 20 | ` 14414] 119 | 52724 37 | 809667 134 |-13048| 1, | 88458 ¡3 | 12
49 | : 46664] 25 |. 14296] 118 | 52761) 37 [80533 |33 |.13065 jg | 88445 ¡7 | 11
50 |0. 46690 5, D. 14178| |18 |0.52798| 3g |1. 89400 ¡34 [1 13083) 17 [088431 14 | 10
51 | . 46716] 26 | 14060] 118 |. 52836, 37 |.89200 133 |-13100 17 | . 88417) 13 9
7 3 92661 |3; :
52 | :46742 29 | 13942] 115 |.52873 32 |.89133| 133 |. 13117) 18 |- +

53 | 146767 ` 13825 ` 52910] 37 | ` 89000) 133 | ` 13135 . 88390) 13
54 | ` 46793| 26 | ` 13707) 118 | ` 52947 Ka ` 88867 tās .13152 12 |.88377] |4
55 |0. 46819 2, 13590 0.52985| *- |1.88734 |45 |i. 13170| v [0 88363| 14
56 | 26844 29 | 13473] 117 |. 53022 37 | 88602 132 [13187 ¡8 | . 88349] ¡3
57 | ` 46870 133560 147 | 53059 27 | 88469 n 13205] 15 | . 88336) 14
58 | 46896, 29 | 13239 11% |:53090 32 | 883371 135 |.13222 17 | - 88322] ¡4
59 | 469211 29 | 13122 17 |:53134 28 | 88205 1: .13239| 12 | -88308| 13
60 lo 46947) 29 |2 13005. 117 lo 531711 37 |i 88073| 192 fī. 13257 0. 88295

4 i i i Diff. Ditiļ ge! Dit...
117?» cos s sec p cot SCH tan l' csc 1 sin 29

O? NO OTU O SO

1340

. 47204
. 47229
. 47255
. 47281
. 47306

15 |0. 47332
. 47358
. 47383
. 47409
. 47434

0. 47460
. 47486
. 47511
. 47537
. 47562

. 47588
. 47614
. 47639
. 47665
. 47690

. 12889
. 12773
. 12657
. 12540

. 12425
. 12309
. 12193
. 12078
. 11963
2. 11847
. 11732
. 11617
. 11503
. 11388

2. 11274
. 11159
. 11045
. 10931
. 10817

2. 10704
. 10590
. 10477
. 10363
. 10250

2. 10137
. 10024
. 09911
. 09799
. 09686

. 47716
. 47741
„47767
. 47793
. 47818

. 09574
. 09462
. 09350
. 09238
. 09126

. 47844
. 47869
. 47895
. 47920
. 47946

. 09014
. 08903
. 08791
. 08680
. 08569

„47971
. 47997
. 48022
. 48048
. 48073

45 |0. 48099
. 48124
. 48150
. 48175
. 48201

. 08458
. 08347
. 08236
. 08126
. 08015

. 07905

. 07795
. 07685
. 07575
. 07465

. 48226
. 48252
. 48277
. 48308
. 48328

. 07356
. 07246
. 07137
. 07027
. 06918

„48354
. 48379
. 48405
. 48430

BOND
1189. cos

. 06809
. 06701
. 06592
. 06483
. 06375
. 06267

TABLE 31

Natural Trigonometric Functions

0. 53171
. 53208
. 03246
. 03283
. 03320

. 53358
. 53395
. 03432
. 53470
. 53507

0. 53545
. 53582
. 53620
. 53657
. 03694

0. 53732
. 03769
. 53807
. 53844
. 53882

. 53920
. 03957
„53995
„54032
„54070

. 04107
. 04145
. 04183
. 54220
. 54258

. 04296
. 04333
. 54371
. 54409
. 04446

. 04484
. 04522| :
. 54560
. 54597
. 04635
. 04673
„54711
„54748
. 54786
. 04824

. 54862

. 54900

. 04038

. 54975) :
„55013
„55051
„55089
. 55127
. 55165
.55203| :

„55241
. 55279) :
. 55317
. 05355
. 55393} :
. 55431

` 13275
` 13292
` 13310

. 13362
. 13380
. 13398
. 13415

. 13433
. 13451
. 13468
. 13486
. 13504

. 13521
. 13539
. 13557
. 13575
. 13593

. 13610
. 13628
. 13646
. 13664
. 13682

. 13700
. 13718
. 13785
. 13753
. 13771

. 13789
. 13807
. 13825
. 13843
. 13861

. 13879
. 13897
. 13916
. 13934
. 13952

. 13970
. 13988
. 14006
. 14024
. 14042

. 14061
. 14079
. 14097
. 14115
. 14134
. 14152
. 14170
. 14188
. 14207
. 14225

. 14243
. 14262
. 14280
. 14299
. 14317
. 14335

cot

csc

Ra Fei
DU Ha

T
O NDOO

z
q
a
[M Ot o ds Cn

1341

TABLE 31
Natural Trigonometric Functions
29%
4 7 ` € [e]
y sin ps csc pin tan pia cot pit. sec pis. cos 150
7 E i 1
o lo. 48481 2. 06267 0. 55431 1. 80405 1. 14335 0. 87462 ,
1 | . 48506 ae ` 06158 R - 55469 3 ` 80281 E ` 14354| 19 | 37448) 14 E
2 | .48532 25 | 06050) 108 |.55507 38 | .80158| 1 14372 18 | 37434 14 | 58
3 | .48557 26 | . 05942] ¡97 | . 55545] 38 | . 80034 D. ` 14391, 19 | 87420 14 | 57
4 | ` 48583 ` 05835 ` 55583 ` 79911 ` 14409, 18 | 187406. 14 | 56
LOS | 20099195 | 0983917 im | .99988| 38 | 199111 193 | 14409 15 | -87406/ 15 | 56 |
5 |0. 48608 55 |2. 05727] jog |0. 55621 1. 79788 1. 14428 0. 87391 55
6 |.48634 05619 55659 88 128 18 14
SI EE 9 35 |.79665| 125 | . 14446) 18 | 87377) 14 | 54
7 | . 48659] 22 |.05512| 107 | . 55697] 38 | 79542 123 |” 14465 ` 87363 53
8|.48684 28 | .05405| |07 |.55736| 38 | .79419 125 |.14483 18 | ` 97349] 14 | 52
9|.48710 22 | .05298| |07 |.55774| 38 | 79290 123 |.14502 ña ` 87335 i 51
10 [0.48735 5, |2. 05191 0. 55812 1. 79174 I. 14521 0. 87321 50
1 11 | 48761 29 | 05084| 197 |” 55850] 38 |. 79051) 123 | 14539| 18 15
25 |: 21107 In 38 |:/ 122 |: 19 | :87306| 14 | 49
12 |.48786| 25 | 104977) 107 |.55888 38 | : 78929] 122 |: 14558 ` 87292 48
13 | . 48811) 22 | :04870| 10% |.55926| 38 | "78807 122 |* 14576 18 | ^ 87278| 14 | 47
14 | . 48837 5° | . 04764 |07 | 55964 35 |. 78685| 122 |. 14595 e ` 87264 bi 46
15 |0. 48862| — |2. 04657| |06 |0. 56003 38 |ī.78563| |92 |I 14614 ve |0.87250| ,5 | 45
16 |.48888| 28 | .04551| 108 |.56041 38 | . 78441) 122 |. 14032] 18 |. 87235] 15 | 44
17 |.48918| 25 | .04445| 108 | .56079] 38 | 783101 122 |. 14651 87221| 14 | 43
18 |.48938 22 | .04339| |06 |-56117| 33 | .78198 |2| |.14670 19 | "87207 14 | 42
19 |.48964| 28 |. o4288| 109 |. 56156] 38 |. 78077] 129 |.14689| 13 |.87198| 15 | 41
20 |0. 48989| „5 |2. 04128] |06 |0. 56194] 3g |1. 77955, van |L. 14707! ,9 |0.87178| 14 | 40
21 | . 49014 25 | .04022| |06 |.56232| 38 |. 77834 121 | . 14726 19 |.87164 14 | 39
22 |. 49040) 26 | mag 109 |.56270| 38 oa lai |. 14745 ` 87150 38
23 | . 49065 ` 03811 9 | ` 56309 ` 77592 :14764 191 ` 87136| 14 | 37

25 105 38 18 |á 15
24 | . 49090 . 03706 . 56347 . 77471 120 . 14782) 19 .87121 14 | 39

25 10. 49116 25 |?- 03601 105 p 39 . 14801
26 | . 49141 25 |: 03496 105 „56424 38 |: 120 . 14820 :
27 |. 49166 26 |: 03391 105 . 56462 39 |: 77110 120 . 14839 19|: 87079 15 33
28 | . 49192 25 |: 03286 104 „56501 38 |: 76990) 191 . 14858| 39 | - 87064 14 | 32
29 | . 49217 . 03182 . 56539 . 76869 120 . 14877 19 |: 87050 14 31

em

to

30 |0. 49242 26 2. 03077) 104 |0 56577 39 1.76749| 159 |l 14896 18 0. 87036 15 30
31 | . 49268 25 |: 02973 104 „56616 38 |: 76629 119 „14914 119 | . 87021 14 29
32 | . 49293 25 |: 02869 104 . 56654 39 |: 76510 120 . 14933) 39 |. 87007 14 28
33 |. 49318 . 02765 . 56693 . 76390 119 . 14952) 19 |. 86993 15 27

34 | :49344 26 | 02661 104 |. 56731) 38 | -76271 120 |-14971 19 | -86978| 1j | 26
35 |0. 49360| 55 |2. 02557] 194 |0. 56769 39 |T. 76151) ¡19 |1 14990| ¡9 |0. 86964) ,5 | 25
36 | . 40394 25 |. 02453 10% |.56808| 32 | .76032 119 |- 15000) 19 | -86949| 14 | 24
37 | 40419 25 | 02349 |03 |.56846| 39 | 75913) 119 |-15028| ¡9 | - 86935 14 | 23
38 | | 49445] 26 | 102246) 109 |.56885 38 | - 75794 jjo |. 15047 i
39 | | 49470 02143) 103 | . 56023) 38 | :75675| 119 |. 15066) jg | 86906) 14 | 21

¡AA SE e i
40 |0. 49495 2. 02039 103 0. 56962 38 5500 119 „15085 20 0. 86892 14 20

26 6
41 | . 49521 ` 01936 ` 57000 ` 75437 ` 15105 i
42 | | 49546 p ` 01833 ie ` 57039 a Dfsatgn iis |. 15124 19 | . 86863) 15 | 18
43 | . 49571) 25 | 01730 l 275200 119 |:15143 19 | 86849] 15 | 17
44 | ` 49596) 25 | | 01628) 102 | 57116 35 | -75082 us [15162 jg | . 86834) jj | 16
45 |0. 49622| 95 [2. 01525) 103 0. 57155) 3g |1 74962 us |L 15181] 19 0. 86820) 15 | 15
46 | . 49647| 25 |.01422| 109 | .57193 38 | mm us |: 15200) 19 | - 86805) 14 | 14
47 | .49672| 25 | 01320] 102 |.57232 39 | . 74728) us | - 15219) 20 791| 14
48 | 49697 25 | .01218 |02 |. 39 | 74610] 115 |- 15239] 19 | -86777| 15 | 12
49 | ` 49723 101116 ` 57309 :74492| 118 | | 15258) 19 | -86762] |4 | 11

[em

ES

E EE E 11.09

50 |0. 49748 d: 2. 01014 |0) |0. 57348 x“ 1.74875 us |l 15277] ¡9 |0- 86748) ¡5 | 10
51 | . 49773 25 | .00912 |02 | -57386 39 | -74257| 117 | - 15296 19 86733 54 | 9
52 |. 49798] 25 | 00810] |02 | .57425| 39 | .74140| 118 .15315 39 | -86719 |5| 8
53 | . 49824 26 | .00708| |01 | -57464 39 | -74022 117 .15335| 19 | -86704 13 | 7
54 | . 49849] 25 | - 00607 |02 |.57503 3g | - 73905 117 ` 15354 39 | -86690| |5 |_6
55 |0. 49874] „5 [2.00509 101 0. 57541) 39 |1- 73788] 117 1. 15373| 20 |0. 86675| ¡4 | 5
56 |. 49899) 25 | 00404} 10i | - 57580) 59 | -73671 116 .15393| 15 | -86661 ¡5 | 4
57 | . 49924 Se .00303| 10i |. 57619) 38 | .73555 117 |-15412 19 .86640| 12 | 3
58 |. 49950 26 | 00202 ¡91 | - 57657] 39 | .73438 117 . 15431] 29 | - 86632) 15 | 2
59 |. 49975] 25 |. 00101, 101 | -57696 39 | .73321 116 | 15451 19 16617 154 | 6
60 lo. 50000] 2° |2. 00000 0. 57735 1. 73205 1. 15470 0. 86603 0
t i i : i Dif| . Dig
119%, cos p sec BE cot SCH tan jās esc 1 sin re 092

TABLE 31

Natural Trigonometric Functions

30221

y sin

,

0. 50000 2. 00000 Ë 1. 73205 . 15470

0

1 | . 50025 1599899 , . 73089 . 15489
2 | . 50050 299/99 4 . 72973 . 15509
3 | . 50076 . 99698 : „72857 „15528
4 | . 50101 . 99598 ; „72741 „15548
5

6

[í

8

0. 50126 1. 99498 7 . 72625 1. 15567

. 50151 . 99398 . 57968 . 72509 . 15587

. 50176 . 99298 . 58007 . 72393 . 15606

. 50201 . 99198 . 58046 . 12278 . 15626

9 | . 50227 . 99098 . 58085 . 72163 . 15645

10 |0. 50252 . 98998 . 58124 1. 72047 . 15665
11 |.50277 . 98899 . 58162 . 11932 . 15684
12 | . 50302 . 98789 . 58201 sal „15704
13 |. 50327 . 98700 . 58240 . 71702 . 15724
14 | . 50352 . 98601 . 98279 . 71588 . 15743

15 |0. 50377 „98502 „58318 „71473 1. 15763
. 98403 . 58357 . 71358 . 15782
. 98304 . 58396 . 71244 . 15802
. 98205 . 58435 . 11129 . 15822
. 98107 . 58474 . 71015 . 15841

0. 50503 . 98008 . 98518 . 70901 1. 15861
. 50528 . 97910 „58552 „70787 „15881
„50553 „97811 „58591 „70673 „15901
„50578 . 97713 . 58631 . 70560 . 15920
. 90603 . 97615 . 58670 . 70446 . 15940

0. 50628 „97517 . 58709 . 70332 1. 15960
. 50654 . 97420 „58748 „70219 „15980
„50679 . 97322 „58787 „70106 „16000
„50704 . 97224 „58826 „69992 . 16019
. 90729 . 97127 . 58865 . 69879 . 16039

30 |0. 50754 . 97029 . 58905 . 69766 1. 16059
31 100/7985: | . 96932 „58944 . 69653 . 16079
32 | .50804 5z | . 96835 „58983 „69541 „16099
33 | . 50829 . 96738 . 59022 . 69428 . 16119
34 | . 50854 . 96641 „59061 „69316 „16139
35 |0. 50879 1. 96544 0. 59101 1. 69203 1. 16159
36 |. 50904 . 96448 . 59140 . 69091 -16179
37 | . 50929 . 96351 „59179 „68979 „16199
| 38 |.50954 „96255 „59218 „68866 „16219
39 | . 50979 „96158 . 09258 . 68754 . 16239

40 |0. 51004 . 96062 „59297 1. 68648 1. 16259
41 | . 51029 . 95966 . 09336 . 68531 . 16279
42 | . 51054 . 95870 . 59376 . 68419 . 16299
43 | . 51079 . 95774 . 09415 . 68308 . 16319
44 | . 51104 5 | - 95678 . 59454 . 68196 . 16339

45 |0. 51129 . 95583 0. 59494 1. 16359
46 | . 51154 . 95487 . 59533 . 16380
47 | .51179 32 | | 05392 . 59573 A . 16400
48 | . 51204 . 95296 . 59612 : . 16420
49 | . 51229 . 95201 > | -59651 . „16440
50 |0. 51254 1. 95106 0. 59691 1. 67530 1. 16460
BL 51279) 22 | 395011 . 59730 „67419 „16481

s6130405%:| 204916 . 59770 . 67309 „16501
151829529" | 04391 „59809 „67198 „16521

. 51354) 55 | . 94726 4 | - 59849 . 67088 . 16541

ee E — EE PA E dy OS 0 fier
55 |0. 51379 1. 94632 0. 59888 1. 66978 1. 16562
. 51404 . 94537 : „59928 . 66867 . 16582

. 51429 52 | . 94443 . 59967] * „66757 „16602

. 51454) 5° | . 94349 -| . 60007 „66647 „16623

59 | .51479| 52 | . 94254 . 60046 . 66538 . 16643
60 |0. 51504 1. 94160 0. 60086 . 66428 . 16663

4
120°- COS | sec | tan ^ ese

1343

TABLE 31

Natural Trigonometric Functions

0. 51504
. 51529
. 51554
. 51579

-. 51604

0. 51628
. 51653
. 51678
. 51703
. 51728

. 51753
. 51778
. 51803
. 51828
. 51852
0. 51877
. 51902
. 01927
. 51952
. 51977

. 52002
. 52026
. 52051
. 52076
. 52101
25 |0. 52126
. 52151
. 52175
. 52200
. 52225

. 52250
. 52275
. 52299
. 52324
. 52349

. 52374
. 52399
. 52423
. 52448
, 52473
0. 52498
. 52522
. 52547
. 52572
. 52597

. 52621
. 52646
. 52671
. 52696
. 52720

. 52745
. 52770
. 52794
. 52819
. 52844

. 52869
. 52893
. 52918
. 52943
59 | . 52967
60 |o. 52992

t
12] cos

. 90845
. 90755
. 90665
. 90575

. 90485
. 90395
. 90305
. 90216
. 90126

1. 90037
. 89948
. 89858
. 89769
. 89680

1. 89591
. 89503
. 89414
. 89325
. 89237

. 89148

. 89060
. 88972
. 88884
. 88796
. 88708

0. 60086
. 60126
. 60165
. 60205
. 60245

cot

. 66428
. 66318
. 66209
. 66099
. 65990

. 60284
. 60324
. 60364
. 60403
. 60443

. 65881
. 65772
. 65663
. 65554
. 65445

. 60483
. 60522
. 60562
. 60602
. 60642
0. 60681
. 60721
. 60761
. 60801
. 60841

. 65337
. 65228
. 65120
. 65011
. 64903
1. 64795
. 64687
. 64579
. 64471
. 64363

. 60881
. 60921
. 60960
. 61000
. 61040
0. 61080
. 61120
. 61160
. 61200
. 61240

. 64256
. 64148
. 64041
. 63934
. 63826
1. 63719
. 63612
. 63505
. 63398
. 63292

. 61280
. 61320
. 61360
. 61400
. 61440
0. 61480
. 61520
. 61561
. 61601
. 61641
0. 61681
. 61721
. 61761
. 61801

. 63185
. 63079
. 62972
. 62866
. 62760

. 62654
. 62548
. 62442
. 62336
. 62230

1. 62125
. 62019
. 61914
. 61809
. 61703

1. 61598
. 61493
. 61388
. 61283
6179

1. 61074
. 60970
. 60865
. 60761
. 60657

1. 60553
. 60449
. 60345
. 60241
. 60137

1. 60033

1. 16663
. 16684
. 16704
. 16725
. 16745

1. 16766
. 16786
. 16806
. 16827
. 16848

0. 85717
. 85702
. 85687
. 85672
. 85657

0. 85642
. 85627
. 85612
. 85597
. 85582

. 16868
. 16889
. 16909
. 16930
. 16950

. 85567
. 85551
. 85536
. 85521
. 85506

. 16971
. 16992
. 17012
. 17033
. 17054

1. 17075
. 17095
. 17116
. 17137
. 17158

1. 17178
s HIT)
. 17220
. 17241
. 17262

. 85491
. 85476
. 85461
. 85446
. 85481

. 85416
. 85401
. 85385
. 85370
. 85355

. 85340
. 85325
. 85310
. 85294
. 85279

. 17283
. 17304
. 17325
. 17346
. 17367

1. 17388
. 17409
. 17430
. 17451
. 17472

. 85264
. 85249
. 85234
. 85218
. 85203

. 85188
. 85173
. 85157
. 85142
. 85127

. 17493
. 17514
. 17535
. 17556
SAUDI

1. 17598
. 17620
. 17641
. 17662
. 17683

. 85112
. 85096
. 85081
. 85066
. 85051

. 85035
. 85020
. 85005
. 84989
. 84974

. 17704
. 17726
. 17747
. 17768
215090

ALAS
. 17832
. 17854
. 17875

. 17896, <

. 17918

. 84959
. 84943
. 84928
. 84913
. 84897

. 84882
. 84866
. 84851
. 84836
. 84820
„84805

sec

cot

tan

csc

sin

1344

TABLE 31

Natural Trigonometric Functions

keem pg FE TI FE RENE DE E E
Dä E ; Á e ;
32 sin ee esc E tan e cot pu sec
0 |0. 52992 1. 88708 0. 62487 1. 60033 1. 17918
1|.53017 25 |.88620| 53 |.62527| 40 |.59930| 109 |.17039
2 |.53041 25 |: 88532 87 . 62568 40 |: 59826 103 . 17961
3 | . 53066 25 |: 88445 88 . 62608 Al 59723 103 17982
4 | . 53091 . 88357 . 62649 . 59620 18004
PEA 24 sy MASA, | 103
52102591015 25 1. 88270 87 0. 62689 41 1. 59517 103 1. 18025
6 | . 53140 24 |: 88183 88 . 62730 40 |: 59414 103 . 18047
7 | -53164 25 |: 88095 87 „62770 41 |: 59311 103 . 18068
8 | . 53189 25 |: 88008 87 . 62811 TY Tu 59208 103 . 18090
9 | . 53214 24 |: 87921 87 . 62852 40 |: 59105 103 SLS
10 |0. 53238 1. 87834 0. 62892 1. 59002 1. 18189

11 | . 53263 Se ` 87748 m ` 62933 Se ` 58900 d ` 18155
12 | . 53288) 24 | 87661 7 |.62973 49 |.58797 103 |: 18176
13 | .53312 25 | .87574 $& |.63014 4 |. 58695 102 |: 18198
14 | 53337 ` 87488 ` 63055 ` 58593 ` 18220

15 |0. 53361 25 |! 87401 g6 |0. 63095| 4, |l. 58490 102 S
16 |. 53386 25 | - 87315 86 . 63136 . 58388 102 . 18263
17 | . 53411 94 | - 87229 87 . 63177 40 | : 98286 102 . 18285
18 | . 53435 25 | - 87142 86 . 63217 41 | - 98184 101 . 18307
19 | . 53460 94 | - 87056 . 63258 . 58083 . 18328

20 |0. 53484 25 |1. 86970 g5 |0. 63299 , |l. 57981 102 z
21 | . 53509 25 | - 86885 86 . 63340 40 |: 57879 101 . 18372
22 | . 53534 24 | - 86799 86 . 63380 „57778 102 „18394
23 |. 53558 25 | - 86713 86 . 63421) 41 |. 57676 . 18416

24 |. 58583) 57 | .86627| $$ |. 63462| 41 | 57575) 101 | | 18437
25 |0. 53607 95 |1. 86542) g; |0.63503| 4, |1.57474| |02 |L 18459
26 | . 53632 . 86457 ` 63544 . 57372 18481

21 | | 53656 E ` 86371 2: ` 63584 +| ` 57271 iu ` 18503
28 | . 53681) 52 | seg 85 | 63625 .57170| 101 | | 18525
29 |. 53705 ` 86201 ` 63666 ` 57069 ` 18547

30 10. 53730 94 |1. 86116 g5 |0. 63707 41 |! 56969 101 :
31 | .53754 25 | - 86031 85 . 63748 41 | - 96868 101 . 18591
32 | . 53779 25 | - 85946 gm. | - 63789 41 |: 56767 100 :
33 | . 53804 . 85861 . 63830 . 06667 . 18635

; 24 84 41 101
34 |. 53828 25 | - 85777 . 63871 41 | 56566 100 . 18657

35 [0.53853 24 H. 85692, g4 1.63912 41 [1.56460 509 |L 18679
36 |.53877 25 | 85608, $5 |.63953 41 | 56366 109 | ` 18701
37 |.53902 24 | . 85523) $4 |.63994 41 |.56265 101 |. 18723
38 | . 53926) 35 |.85439 $4 |.64035| 21 |.56165| 100 | 18745
39 |. 53951) 22 | | 85355 ` 64076 56065 100 |” 18767

A ER MA ed 84. MA eae ae
40 |0. 53975 1. 85271 0. 64117 1. 55966 xis 1. 18790

41 | . 54000) 25 | ` 85187 Ši . 64158| 11 | . 55866 de ` 18812
42 | 54024 ` 85103 ` 64199 ` 55766

` 18834
43 |.54049 25 |. 85019] 84 |:64240| 41 | ` 55666, 100 18856

-44 | 54073 5, | 84985] ga |.64281 41 |:55567| DN |. 18878
45 |0. 54097

< |1. 84852 0. 64322 1. 55467 1. 18901
46 | . 54122] 25 | ` 84768 Ss |.64363 41 | - 55368 E ` 18923
47 | .54146 27 | . 84685 . 64404 . 55269 . 18945

48 |.54171 57 |.84601| $ |:64446 12 | 55170 99 |: 18987
49 |.54195 25 |:s4518| 83 | | 64487] 41 |: 55071 2 ` 18990
50 |0. 54220) 7, [184435 -.. |0. 64528 1. 54972 1. 19012
51 | .54244| 21 | 84352 = 64569 n .54873 99 |” 19034
52 | . 54269) 24 |.84269] $5 |:64610 1l |:54774 a . 19057
53 |. 54293 84186 64652 . 54675) 99 | ` 19079

54 |. 54817) 25 | 84103) 53 | 64603 41 | 54576 99 |:19102
55 |0. 54342 1. 84020 0. 64734 14544789 152

d 24 s2 [e 41 H gg |l 19124
56 | . 54366) 25 |.83938 — 82 |. 64775) 41 |. 54379 ` 19146
57 | . 543911 24 | . 83855, $9 |.64817| 4? | | 54281 ER ` 19169
58 | . 54415) 25 |. 83773) ¿3 |.64858 41 | 54188 98 |: 19191
59 | 54440) 24 | . 83690, 25 |.64899 41 |. 54085, 98 |' 19214
60 |0. 54464) ^" |1. 83608] %% lo 64941| 42 |1. 539086 99 |1 19236
A M d ; ;

1222. cos pr sec es cot ur tan py. ese

1345

TABLE 31

Natural Trigonometric Functions

L : 0. 64941 . 03986 . 19236 ;
. 04488 ; . 64982 „58888 „19259 . 83851
. 54513 : . 65024 . 53791 . 19281 . 83835
. 04537 d . 65065 . 53693 . 19304 . 83819
. 54561 : . 65106 . 53595 s . 83804
. 54586 : . 65148 . 53497 : . 83788
. 54610 à . 65189 . 53400 . 19372 . 83772
. 54635). á . 65231 . 53302 . 19394 . 83756
. 54659 : . 65272 . 93205 . 19417 . 83740
. 54683 : . 65314 . 58107 . 19440 . 83724

0. 54708 k . 65355 . 53010 . 19463 . 83708
. 54732 i . 65397 . 52913 . 19485 . 83692
. 54756 : . 65438 . 52816 . 19508 . 83676
. 54781 : . 65480 . 52719 . 19531 . 83660
. 94805 : . 65521 . 52622 . 19553
15 |0. 54829 , 0. 65563 . 92525 1. 19576 i

. 54854 : . 65604 . 52429 . 19599 . 83613

. 54878 : . 65646 . 52332 . 19622 . 83597

. 54902 : . 65688 . 52235 . 19645 . 83581

. 54027 : „65729 . 52139 . 19668 . 83565

20 |0. 54951 E 0. 65771 . 52043 1. 19691 . 83549
2 . 54975 e . 65813 . 51946 . 19713 . 88533
. 54999 : . 65854 . 51850 . 19736 . 83517
. 55024 d . 65896 . 51754 . 19759 . 83501
. 55048 : . 65938 . 51658 . 19782 . 83485

25 |0. 55072 R 0. 65980 . 51562 . 19805 . 83469
2 . 55097 : . 66021 „51466 „19828 . 88453
. 55121 3 . 66063 . 51370 . 19851 . 83437
. 90145 : „66105 . 51275 . 19874 . 88421
. 55169 : . 66147 - 51179 . 19897 . 83405

30 |0. 55194 E 0. 66189 - 51084 . 19920 . 83389
. 55218 : . 66230 . 50988 . 19944 . 88378
. 55242 : . 66272 . 50893 . 19967 . 88356
. 55266 : . 66314 . 50797 . 19990 . 83340
295291054 Es . 66356 . 50702 . 20013 . 83324

. 55315 : 0. 66398 1. 50607 1. 20036 . 83308
. 55339 , . 66440 . 50512 . 20059 . 83292
. 55363 : . 66482 . 50417 . 20083 . 83276
. 55388 d . 66524 . 50322 . 20106 . 83260
. 55412 4 . 66566 . 50228 . 20129 . 83244

| 40 |0. 55436 ; . 66608 . 50133 1. 20152 94 |0. 83228
41 |. 55460 2 „66650 „50038 „20176 . 83212
. 55484 : „66692 „49944 „20199 „83195
„55509 t . 66734 . 49849 . 20222 . 83179

. 55533 E . 66776 . 49755 . 20246 . 88163

45 |0. 55557 : „66818 „49661 1. 20269 . 83147
. 55581 : . 66860 . 49566 .20292 94 | . 83131
. 55605 : „66902 . 49472 . 20316 . 83115
. 55630 : . 66944 . 40378 . 20339 94 | . 83098
. 55654 : . 66986 . 49284 . 20363 93 |. 83082

50 |0. 55678 , 0. 67028 1. 49190 1. 20386 0. 83066
. 55702 m „67071 „49097 „20410 . 88050
. 55726 3 „67113 . 49003 . 20433 . 83034
. 55750 d . 67155 . 48909 . 20457 . 83017
. 55775 4 . 67197 . 48816 . 20480 . 83001

99 OLIN) 49 4
| 55 |0. 55799 4 0. 67239 1. 48722 1. 20504 . 82985
6 . 55823 E . 67282 . 48629 . 20527 . 82969
57 | . 55847 1 . 67324 . 48536 . 20551| 4* | . 82953
58 | . 55871 i . 67366 . 48442 . 20575 . 82936
59 | . 55895 1 . 67409 . 48349 . 20598 . 82920
60 |0. 55919 1 0. 67451 1. 48256 . 20622 . 82904

Ex nez.
co

+
HO

123°> cos VT: x cot if) tan iff. ese if] gin

1346

TABLE 31
Natural Trigonometric Functions
€ o

Da y e : Diff. 145
34 sin me csc DT tan A DR cot K sec 1 cos [Dir 4

1^
0 0. 55919 1. 78829 > |0. 67451 1. 48256 1. 20622 0. 82904 17 60
1 |.55943| 2: |:78752 77 |.67493 42 |.48163| 93 |. 20645) 23 | .82887| [4 | 59
2 | . 55968 5 . 78675 hes . 67536 . 48070 . 20669 . 82871 16 58
24 (i "pm 42 - 93 24 82855 57
3 | . 55992 24 |: 78598 77 67578 42 |: 47977 92 f 20693 24 | - 8! 16 7
4 56016 24 |: 78521 76 67620 43 |: 47885 93 . 20717 23 | 82839 17 56
5 10. 56040 1. 78445 25 10067605 1. 47792 1. 20740 0. 82822 16 55
= 24 ta = 42 98 24 82806 54

6 56064 24 |: 78368 77 . 67705 43 |: 47699 92 . 20764 24 |: 8 16
7 | . 56088 94 |: 78291 76 . 67748 42 |: 47607 93 . 20788 24 |: 82790 17 58
8 | . 56112 94 |: 78215 77 . 67790 42 |: 47514 92 . 20812 94 |: 82773 16 52
9 | . 56136 24 |: 78138 76 . 67832 43 | - 47422 92 . 20836 23 | 82757 16 51

10 |0. 56160 1. 78062 0. 67875 1. 47330
24 m 76 42 ` 47238 92

=

-20859 0. 82741 50
20883, 24 | ` 82724 de 49

12 |.56208| 24 | 77910) 76 |: 67960 a ` 47146 Mc ` 20907 Ss -82708| 18 | 48
13 | . 56232) 24 | .77833 7% |.68002 43 |.47053 93% |.20931 24 | 82692 16 | 47
14 | . 56256) 5, | .77757 76 |. 68045] 43 | 46962 34 |:20955| 24 |.82075 14 | 46
15 |0. 56280 95 [177681 ` „> |0. 68088) 43 |T. 46870 55 |1-20979| 5, |0.82659| e | 45
16 |.56305| 5° |. 77606 .68130| 43 | . 46778] 92 |.21003 24 |.82643 16 | 44

cs a ` :

17 |.56329 77530) oe |.68173 . 46686 . 21027 . 82626
18 | -56853 24 | 77454 76 |:68215 12 | 46595, 91 |:21051| 24 |: 82610 19 | 42
19 |.56377 54 | .77378| 75 |:68258 43 |.46503| 93 |: 21075 82593

LE RAZR AAA AA ZAS AAA
20 |0. 56401 94 |1- 77303 ze | 68301 49 |l. 46411 91 |l 21099 0. 82577 16 40

21 | . 56425] 5, |.77227| 75 |.68343 43 |.46320| au |.21123 Ce . 82561) 17 | 39

22 | . 56449) 34 |. 77152 75 |.68386 43 | . 46229) 99 |.21147 24 | -82544 16 | 38

23 | . 56473) 94 | -77077 7g |.68429 42 |.46137 9; |.21171 34 | -82528 19 | 37

24 |. 56497 .77001 <2 | .68471| 24 | . 46046 . 21195 . 82511 36
24 75 43 91 25 16

25 |0. 56521 94 |1. 76926 75 |0. 68514 43 |l. 15955 oj |l 21220 94 |0. 82495) ,7 | 35
26 | . 56545 94 | - 76851 75 . 68557 43 | - 45864 . 21244) 5, | . 82478 16 34 |
27 | . 56569 94 | : 76776 75 3 49 | - 45773 91 . 21268 . 82462 16 33
28 | . 56593 94 | - 76701 75 . 68642 43 | - 15682 90 . 21292 94 | - 82446 17
29 | . 56617 94 | : 76626 74 . 68685 43 | - 45592 91 . 21316 . 82429 31
30 |0. 56641 94 |l. 76552 75 |0. 68728 43 |l. 45501 91 |i 21341 24 |0. 82413 17 30
31 | . 56665 oul, 76477 75 . 68771 43 | - 45410 90 . 21365 94 | - 82396 16 29
32 | . 56689 94 | - 76402 74 : 43 | - 45320 91 . 21389 25 | - 82380 17
33 | . 56713 93 | - 76328 75 . 68857 . 45229 . 21414 . 82363 27

34 | 56736 24 |.76253 z4 |.68900 43 [:45139| 30 |.21438 24 |: 82347 19 | 26
35 0.86760 24 |L76179| 74 0. 68942) 43 [1.45049 gı |T. 21462] 5. [0.82330 14 | 25
36 |. 56784 5, |.76105| 74 |- 68985] 43 |:449058 93 |:21487| 25 | . 52314) 19 | 24
37 | - 56808) 24 |.76081| 75 |.69028 43 |:44868 90 |:21511| 24 | 82297| 17 | 23
38 |.56832| 24 |.75950| 7 |.69071 23 |:44778| 90 |:21535 24 |: 82281] 19 | 22

> 25
39 | . 56856 94 | - 75882 74 . 69114 43 | - 44688 90 21560

: 94 | - 82264 16 21

40 |0. 56880) 5, |1. 75808) -, |0. 69157 43 |}. 44998 go |L. 21584] 35 |0. 82248| ,- | 20
11 | 36904 24 |.75734 74 |.69200 43 |.44508|. 90 |.21609 24 | - 82231] i7 | 19
42 | .56928| 54 |.75601 71 |.69243 . 44418 . 21633 . 82214 56 | 18
43 | . 56952 q 25 oe

PROF 5 25 16 >
92 94 | - 75587 74 . 69286 43 |: 14329 90 s 21658 24 | - 82198 17 17
44 | . 56976 94 |_- 75513 73 „69329 43 |__11239 90 . 21682 25 | 82181 16 16

45 |0. 57000 24 |1. 75440 74 |0. 69372 44 H. 44149 so |l. 21707 24 |0. 82165 17 15

46 | . 57024 „75366 - . 69416 . 44060 21731 82148 14
" "nas 28 z 73 43 K 90 STR 16
ed | P 94 | - 75293 74 . 69459 43 | - 43970 89 . 21756 . 82132 13

7 .75219| / . 43881 . 21781| 2° | 82115 17 | 12
49 | 57005 34 | :75146| 73 |. 69545 43 | | 43792) 89 | 21805] 22 | “82095 17 | 11 |

50 |0. 57119 94 1. 75073

57 73 |0. 69588 1. 43703 1. 21830|-5- |0. 82082 ,- | 10
51 |. 57143) 94 | . 75000) 73 |.69681| 4% | 43614] 89 (21855 55 | 82065 17 | 9
52 |.57167 34 | .74927 7% | . 69675 . 43525] $9 |.21879 . 82048 8
es | eodd E E 89 25 16
zl: 22291) 24 | - 74854) 73 |.69718| 43 | ..43436 29 | | 21904 25 | 82032 37 | 7
34 |..97215 93 | 74781) 73 |.69761 23 | 48347] 88 |. 21929 24 | -82015| 16 |. 6
$6 |0: 87288) 24 |. 74708 73 |0. 69804| ,. |1. 43258 go [1.21953 25 |0. 81999 ,, | 5
56 |.37202/ 24 | 74035. 73 |.69847 44 |.43169 89 |.21978 25 | 81982 37 | 4
Sg | :57250 24 | 74562 72 |.69891| 43 | 43080 $2 |. 22003 25 | - 81965) 36 | 3
35 |:2:310 24 | -74490 73 | . 69934) 43 | 42002 88 |: 22028 25 | - 81949] 37 | 2
do Wäsch 24 |- 74417. 72 |. 60977] 44 | 42008 29 .22053 54 | .81932 i2 | 1
60 |0. 57358 1. 74345 0. 70021 1. 42815 1. 22077| ^^ |0. 81915 0
T Diff. Diff i i i Tem
124°- cos 1 sec 0^ cot p tan E S ese Rim sin RAR

1347

TABLE 31
Natural Trigonometric Functions

Y . Á 5 e " € o

y sin 1’ csc 1’ tan 1’ cot pi sec p cos NS

L 14

0 |0. 57358| „2 |1. 74345 0. 70021 1. 42815 1. 22077 0. 81915 60
1 |.57381 e ` 74272 Ls 70064 4 ` 42726 e 22102) 22 |. 81899] 16 | 59
2 | .57405 24 | .74200 75 |.70107 44 | 42638 $8 |:22127 29 | | 81882 17 | 58
3|.57429 24 | 74128. 75 |.70151 43 |. 42550 88 |.22152 29 | 81865) 17 | 57
| 4 | . 57453) 34 |.74050 73 |.70194 44 |. 42462 8 |.22177 25 | : 81848 i 56
5 |0.57477| 4 |1. 73983) „2 |0.70238 43 |1. 42374 gg [122202 5. |0. 81832 55
6 | .57501| 23 |.73911] ze |.70281| 13 |. 42286 22227 29 | 81815| 17 | 54
7 |.57524| 24 |.73840| 7% |7 70325) 4% | . 42198 a 22252 a 81798 17 | 53
8 | . 57548) 54 | 73768 72 | . 70368) 44 |.42110| 58 |.22277 25 | 81782 16 | 52
| 9 | . 57572) 24 | 73696 72 |.70412 43 |.42022| 88 |:22302 25 | | 81765 Ke 51
10 |0. 57596) 93 |1.73624| 79 |0. 70455 44 |1. 41934 87 |l 22327| 95 |0. 81748 i- 50 |
11 | . 57619] 24 |.73552| 71 |.70499 43 |.41847| 8% |:22352 25 | sizai| 17 | 49
12 | . 57643) 24 | 734811 79 | - 70542) 44 | 41759 88 |.22377 25 | 81714 17 | 48
13 | . 57667| 94 | 73409 7; | - 70586) 43 | 41672) 8% |:22402 2 | s1698 18 | 47
14 | . 57691| 24 |.73338| 7] |.70629 44 |.41584 SS |:22428 26 |. g1681| 17 | 46
15 |0. 5715] 23 |. 73267| 79 |0.70673| 44 |1. 41497] gg |i. 22458] 25 |0.81664| |, | 45
16 |.57738 4 | 73195 75 |.70717 43 |. 41409) 55 |:22478 25 | 81647] 17 | 44
17 | ¿57762 | .73124| 71 | . 70760] 43 | 141322155 87 |: 29503) 22 | 81631 18 | 43
18 |.57786| 24 | 73058 — 71 | . 70804) 44 | 412835 87 |:22528| 25 | 81614 17 | 42
19 | . 57810 23 | 72082 71 |.70848 43 | .41148| Sr |:22554 26 | 81597. 17 | 41
20 |0. 57833| 94 |1. 72911) 7, |o 70891 4 |ī. 41061) ` gy |1.22579 5 |o. 81580) ,, | 40
21 | . 57857| 24 | 72840. 71 | . 70935] 44 |. 40974| 87 |.22604 25 | . 81563) 17 | 39
22 | .578811 25 | 72769 71 | . 70979| 44 |.40887| áp |.22629 30 | : 81546| 17 | 38
23 | 57904 53 |. 72698 7) | 71023) 43 |. 40800, 84 | | 22655) 29 | .s1530 18 | 37
24 |.57928| 24 | 72628 7) |.71066| 44 | 40714, 55 |:22680| 29 | | 81513) 17 | 36
25 |0. 57952) 5, |1.72557| oa |0.71110| 44 |i. 40627| gy |1 22706 25 |0. 81496| ,, | 35
26 | 15797625 | 72487) < 7, |. 71154| 44 | 205401) SL |” 20731) 25 | .81479 17 | 34
27 |.57999 24 | .72416 7L |:71198| 44 |. 40454) 85 |:22756 zl. 81462] 17 | 33
28 | .58023 24 | .72346 79 |.71242 4% | 40367| 84 |.22782 5? | 81445 17 | 32
BE E 7) "V. asa | aozet 25 |) 22807020 | 81428070 | St
30 |0. 58070| 24 |i. 72205| 0 |0.71329| ,, |1. 40195| gg |i. 22833 2; |0. 81412 ¡7 | 30
509455, | 172135 kú £o |. 71873) 4, | ¿2010910 29 |2. 22858520 | 131305) 77 | 29
32 | ¿bss 22 | 72065) 70 |. 71417| 44 | 140022, - 84 |. 2288435 | 81878] 47 | 28
Bs sardo. | 7199510 70 4%. 71400 O, | 53993041 Se ||. 22009] e35 | 8186117 | 27
34 | 58165) 24 | 71925 70 |.71505| 44 | .39850 Sg |.22935 25 |. 81344] 17 | 26
35 |0.58189 23 |1.71855| yọ |0. 71549] 44 [139764 g; |i. 22960 96 |0. 81327 ¡7 | 25
36 | 58212 23 | 71785 70 | 71593) 44 | 39679 83 |.22980 26 | . 81310] 17 | 24
37 | 582361 24 |: 71715 20 |. 71637| 44 | 30598 Ž6 |-23012 25 | .81293| 17 | 23
38 | 58260 23 | 71640, % |.71681 44 |.39507| ze |.23037 5¢ | . 81276) 17 | 22
39 | 58283 23 |. 71576] 70 | | 71725) 44 | 394211 $5 |.23063 26 | 81259] 17 | 21
40 |0.58307| 54 |L 71506) gg |0 71769 4, |1.39336| gg [1.23089 55 |0. 81242 ,; | 20
41 | 58330 2% |: 71437 8° |.71813| 44 | 392501 85 | . 23114) 2 | . 81225) ¡7 | 19
42 |: 58354 24 | 71368 $9 |:71857 44 | -39165 gà |.23140 56 | 81208 ¡7 | 18
43 | 58378 24 | 71208 40 |:71901| 45 | 39079 $$ |.23166] 38 | - 81191! 17 | 17
44 | 584011 2% |. 71229. 68 |:71946| 4% |.38994 $g |.23192 25 | .81174 ¡7 | 16
45 |0. 58425| 5, |1.71160 gg |0. 71990) 44 |1. 38909 gs |1.23217| ze |0. 81157) 17 | 15
46 |.58449| 24 | 71091 89 |.72034 44 | - 38824 gg |. 23243) 26 | . 81140] 17 | 14
47 | 58472 22 | 71022 69 |. 72078) 44 |-38738 g5 |.23269 55 | -81123 17 | 13
48 | 58496 24 | : 70953) Q9 |.72122 45 | . 38653] el 23295] 26 | - 81106) 17 | 12
49 | 58519 23 | 70884 $8 |.72167 44 |-38568 g4 |.23321 26 | 81089 ¡7 | 11
50 |0. 58543 94 |L 70815 gg [0.7211 44 |1. 38484 gs |L 23347 25 [0. 81072 17 | 10
51 | 58567 24 |. 70746] 8 | 72255) 44 | 38399, ge | .23373 25 | -S1055 17 | 9
52 | . 58590 70677) 69 |:72299 12 | 38314 $$ |.23398| 2; | - 81038 17 | 8
53 |. 58614] 24 |. 70609 88 |:72344 45 | - 38229] $4 | 23424 2; | 81021 17 | 7
54 | 58637 23 | 70540) 62 |.72388 44 | 38145 g5 |.23450 55 | . 81004) 17 | 6
55 |0. 58661 1. 70472 0. 72432 1. 38060 1. 23476 0.80987 |, | 5
56 | . 58684 m ` 70403 4 72477| 43 | . 37976 2c || 23502 26 |.80970] I| 4
57 | . 58708 170335) OS | 72521 44 | 37891) $4 | - 23529) 26 | - 50953 ¡7 | 3
58 |.58731| 2% | 70267 68 |:72565 45 | . 37807) e |.23555 26 | - 80936 ¡7 | 2
59 | 58755 24 |. 70198 89 |:72610 43 |.37722| g4 |- 28581) 5g | 80919 ¡7 | 1
60 |0. 58779) 24 |1. 70130 0. 72654 1. 37638 1 23607 0. 80902 0

: : ; i Diff 3 Diff. = î
1250 cos B. sec ru cot E tan v csc V sin (e 5429

1348

EA

(=`
o
y

€

TABLE 31

Natural Trigonometric Functions

e

58779
. 58802
. 08826
. 58849
. 58873

. 70062
. 69994
. 69926
. 69858

. 58896
. 58920
. 58943
. 58967
„58990

OO O TS: Cal, ODO `
S

. 69790
. 69723
. 69655
. 69587
. 69520

©

. 59014
. 59037
. 59061
. 09084
. 59108

. 69452
. 69385
. 69318
. 69250
. 69183

. 59131
„59154
„59178
„59201
„59225

„69116
. 69049
. 68982
. 68915
. 68848

. 09248
. 59272
. 59295
. 59318
. 59342
25 |0. 59365
2 . 59389
. 59412
. 59436
. 09459
30 |0. 59482
. 09506
. 59529
. 59552
. 59576

. 68782
. 68715
. 68648
. 68582
. 68515

1. 68449
. 68382
. 68316
. 68250
. 68183

1. 68117
. 68051
. 67985
. 67919
. 67858

. 09599
. 00622
. 59646
„59669
„59693
40 |0. 59716
41 |.59789
42 |. 59763
43 |.59786
44 |. 59809
45 |0. 59832
46 | . 59856
47 | . 59879
48 | . 59902
49 |. 59926
50 |0. 59949
. 09972
. 59995
. 60019
. 60042

| 55 |0. 60065 X

56 | . 60089
57 | . 60112
58 | . 60135
59 | . 60158
60 [0. 60182

. 67788
. 67722
. 67656
. 67591
. 67525
1. 67460
. 67394
. 67329
. 67264
. 67198

1. 67133
. 67068
. 67003
. 66938
. 66873

1. 66809
. 66744
. 66679
. 66615
. 66550

1. 66486
. 66421
. 66357
. 66292
. 66228

1. 66164

1. 37638
. 97554
. 97470
. 97386
. 37302

. 37218
. 97134
. 97050
. 36967
. 36883

. 36800
. 96716
. 36633
. 96549
. 36466

1. 36383

1. 34323
. 94242
. 34160
. 34079
. 33998

1. 33916
. 33835
. 33754
. 33673
. 33592

1. 33511
. 33430
. 33349
. 33268
. 33187

1. 33107
. 33026
. 32946
. 32865
. 92785

1. 32704

1. 23607
. 23633
. 23659
. 23685
. 23711

1. 23738
. 23764
. 23790
. 23816
. 23843

0. 80902
. 80885
. 80867
. 80850
. 80833

0. 80816
. 80799
. 80782
. 80765
. 80748

. 23860
. 23895
. 23922
. 23948
. 23975

1. 24001
. 24028
. 24054
. 24081
. 24107

1. 24134
. 24160
. 24187
. 24213
. 24240

1. 24267
. 24203
. 24320
. 24347
. 24373

1. 24400
. 24427
. 24454
. 24481
. 24508

. 80730
. 80713
. 80696
. 80679
. 80662

. 80644
. 80627
. 80610
. 80593
. 80576

0. 80558

. 80455
. 80438
. 80420
. 80403

0. 80386
. 80368
. 80351
. 80334
. 80316

. 24534
. 24561
. 24588
. 24615
. 24642
1. 24669
. 24696
. 24723
. 24750
. 24777

1. 24804
. 24832
. 24859
. 24886
~ 24913

. 80299
. 80282
. 80264
. 80247
. 80230

0. 80212
. 80195
. 80178
. 80160
: 80143

. 80125
. 80108
. 80091
. 80073
. 80056

. 24940
. 24967
„24995
. 25022
. 25049

1. 25077
. 25104
. 25131
. 25159
. 25186

1. 25214

. 80038
. 80021
. 80003
. 79986
. 79968

. 79951
. 79934
. 79916
. 19899
. 79881
. 79864

(4
126?» cos

tan

sin

irr C A to R OO» 100 O

1349

TABLE 31

Natural Trigonometric Functions

0 10. 60182
1 | . 60205
2 | . 60228
3 | . 60251
4 | . 60274
5 |0. 60298
6 | . 60321
7 | . 60344
8 . 60367
9 | . 60390

10 |0. 60414
|! 11 | . 60437
12 | . 60460
13 | . 60483
14 | . 60506

15 |0. 60529
. 60553
. 60576
. 60599
. 60622
20 |0. 60645
21 | . 60668
. 60691
. 60714
. 60738

25 |0. 60761
. 60784
. 60807
. 60830
. 60853

30 |0. 60876
3 . 60899
. 60922
. 60945
. 60968

35 |0. 60991

40 |0. 61107
41 | . 61130
42 | . 61153
43 | . 61176
44 | . 61199

45 |0. 61222
46 | . 61245

47 | . 61268) <

48 | . 61291
49 | . 61314

50 |0. 61337
. 61360
. 61383
. 61406
. 61429

55 |0. 61451

` 61474, :

. 61497
. 61520
. 61548
60 |0. 61566

1. 66164
„66100
„66036
„65972
. 65908

1. 65844
. 65780
. 65717
. 65653
. 65589

ANS
1. 65526

. 65462
- 65399
. 65335
. 65272
1. 65209
. 65146
. 65083
. 65020
. 64957

1. 64894
. 64831
. 64768
. 64705
. 64643

1. 64580
. 64518
. 64455
. 64393
. 64330

1. 64268
. 64206
. 64144
. 64081
. 64019

ade
1. 63957

. 68895
. 68834
. 63772
. 63710

1. 63648
. 63587
. 63525
. 63464
. 63402

1. 63341
. 63279
. 63218
. 63157
. 63096

1. 63035
. 62974
. 62913
. 62852
. 62791

1. 62730
. 62669
. 62609
. 62548
. 62487

1. 62427

0. 75355
. 75401
. 75447
. 75492
. 75538

. 75584
. 75629
. 75675
. 15721
. 15767

0. 75812
. 75858
. 75904
. 75950
. 75996

0. 76042
. 76088
. 76134
. 76180
„76226

0. 76272
„76318
„76364
„76410
„76456

0. 76502
„76548
„76594
. 76640
. 76686

0. 76733
. (6779
. 76825
. 76871
. 76918

0. 76964
. 77010
. 17057
. 77103
. 44149

0. 77196
. 44242
„77289
. 77335
. 77382

` 29229

. 77428
. 77475
. 17521
. 77568
„77615
0. 77661
„77708
„77754
„77801
„77848

0. 77895
„77941
„77988
„78035
. 78082

0. 78129

. 29152
. 29074
. 28997
. 28919
. 28842
1. 28764
. 28687
. 28610
. 28533
. 28456
1. 28379
. 28302
. 28225
. 28148
. 28071
. 27994

. 25214
. 25241
. 25269
. 25296
. 25324

. 79864
. 70846
. 19829
VISU
. 79793

. 25351
. 25379
. 25406
. 25434
. 25402

79000
. 79758
. 79741
. 79723
. 79706

. 20489
. 25517
. 25545
. 25572
. 25600

. 79688
. 79671
. 79653
. 79635
- 79618

. 25628
. 25656
. 25683
. 25711
. 25739

1. 25767
. 25795
. 25823
. 25851
. 25879

1. 25907
. 25935
. 25963
. 25991
. 26019

1. 26047
. 26075
. 26104
. 26132
. 26160

. 26188
. 26216
. 26245
. 26273
. 26301

. 79600
. 79583
„79565
„79547
„79530

„79512
„79494
„79477
. 79459
. 79441
0. 79424
. 79406
. 79388
. 79371
„79353
0. 79335
„79318
„79300
. 19282
. 79264

g a A
0. 79247

. 79229
. (9211
. 79193
. 79176

. 26330) .

. 26358
. 26387
. 26415
. 26443

. 26472
. 26500
. 26529
. 26557

. 26586) :

1. 26615
. 26643
. 26672
. 26701
. 26729

1. 26758

. 26787| 5

. 26815
. 26844
. 20873
. 26902

. 79158
. 19140
. 79122
. 79105
. 79087

. 79069
. 79051
. 79033
. 79016
„78998

„78980
„78962
„78944
„78926
„78908

) melu eerie ae
0. 78891

. 78873
. 78855
. 78837
. 78819
0. 78801

T
127% cos

tan

csc

1350

TABLE 31

Natural Trigonometric Functions

. 61566 1. 62427 0. 78129 . 27994
. 61589 . 62366 „T8175 27917
„61612 „62306 . 78222 . 27841
. 61635 . 62246 . 78269 . 27764
. 61658 . 62185 . 78316 . 2/688

. 61681 1. 62125 . 78363 . 27611
. 61704 . 62065 . 78410 . 27535
. 61726 . 62005 . 78457 . 27458
. 61749 . 61945 „78504 . 27382
„61772 „61885 „78551 . 27306

. 61795 . 61825 . 78598 . 27230
. 61818 . 61765 . 78645 . 27153
. 61841 . 61705 . 78692 . 27077
. 61864 . 61646 . 78739 . 27001
. 61887 . 61586 . 78786 . 26925

. 61909 . 61526 0. 78834 1. 26849
. 61932 „61467 „78881 . 26774
. 61955 55 | . 61407 . 78928 . 26698
. 61978 . 61348 . 78975 . 26622
. 62001 . 61288 . 79022 . 26546

. 62024 . 61229 . 79070 . 26471
. 62046 . 61170 ( 249147 . 26395
. 62069 KOLLI ( . 79164 . 26319
. 62092 . 61051 . 79212 . 26244
. 62115 . 60992 . 79259 . 26169

. 62138 1. 60933 . 79306 . 26093
. 62160 . 60874 . 79354 . 26018
. 62183 . 60815 . 79401 . 25943
. 62206 . 60756 E . 79449 . 25867
. 62229 . 6069? . 79496 . 25792

. 62251 . 60639 . 79544 HST
. 62274 . 60580 . 79591 . 25642

. 62297 . 60521 = 21 279839 . 25567

. 62320 . 60463 . 79686 . 25492

. 62342 . 60404 ; . 79734 . 25417

35 |0. 62365 1. 60346 . 79781 . 25343
36 | . 62388 . 60287 ; . 79829 . 25268

. 62411 . 60229 . 79877 . 25193

. 62433 „60171 .79924| ^ . 25118

. 62456 . 60112 „79972 . 25044

| 40 |0. 62479 1. 60054 . 80020 . 24969
. 62502 . 59996 . 80067 . 24895

. 62524 . 59938 . 80115 . 24820

. 62547 . 59880 . 80163 . 24746

| . 62570 . 59822 O 7| A . 24672
| 45 |0. 62592 1. 59764 0. 80258| |. |1. 24597
| 46 |.62615|: . 59706 . 80306 . 24523
. 62638| : . 59648 . 80354 . 24449

. 62660 . 59590 . 80402 ` . 24375

| . 62683 . 59533 g | - 80450 . 24301

0. 62706 1. 59475 0. 80498 . 24227

. 62728 We .59418| * . 80546 . 24153

. 62751 . 59360 . 80594 . 24079

. 62774 150309 I: . 80642 . 24005
.62796 23 |.59245 ; . 80690 . 23931

55 [0.62819 54 |1.59188| ` . 80738 . 23858

| . 62842 . 59130 . 80786 . 23784
. 62864 . 59073 . 80834 . 23710

. 62887 . 59016| | . 80882 . 23637
.62909| 22 |. 58959: . 80930 . 23563

62932 1. 58902 . 80978 . 23490

Im í e
128°- cos i cot | tan

1351

TABLE 31

Natural Trigonometric Functions

9»
1^
0 |0. 62932 »a |l. 28676 0. 77715 60
1 | . 62955 74 | 287061239 [ 77696 18 | 59
2 | . 62977 73 | - 28737] 39 | . 77678] ¡g | 58
3 | . 63000 "4 | - 28767 30 | -77660| 19 | 57
4 | . 63022 73 28797] 31 | -77641| jg | 56
5 10. 63045 73 |1. 28828) 30 |0. 77623| ig | 55
6 |.63068 73 | . 28858) 31 |.77605| 39 | 54
7 | .63090 73 . 28889 39 | . 77586| ig | 53
8 | . 63113 73 . 28919) 31 | . 77568) |8 | 52
_9|.63135 73 |.28950 39 |-77550| 19 | 51
- sels
10 |0. 63158 73 _|1. 28980] >} [0.77531] jg | 50
11 | . 63180 73 | - 29011] 37 | .77513| ¡9 | 49
12 | . 63203 73 |.29042 35 | .77494| 1g | 48
13 | . 63225 79 | - 29072 31 . 77476) 1g | 47
14 | . 63248 73 . 29103] 29 | -77458| ¡9 | 46
15 |0. 63271 73 |1-29133| 3, |0. 77439] jg | 45
16 | . 63293 79 29164| 51 | .77421 ¡9 | 44
17 | . 63316 73 |.29195 37 | .77402| ¡g | 43
18 | . 63338 79 . 29226) 59 | -77384 jg | 42
19 | . 63361 73 29256) 3, | -77366 19 | 41
20 |0. 63383 72 |1.29287| 3, |0. 77347| jg | 40
21 | . 63406 73 | - 29318 31 | -77329| 19 | 39
22 | . 63428 29 29349] 21 | .77310| |8 | 38
23 | . 63451 72 29380 3, | 77292 ¡y | 37
24 | . 63473 72 |.29411| 57 | -77273| ¡g | 36 |
25 |0. 63496|. 72 |1. 29442) 3, |0.77255| ¡9 | 35
26 | . 63518 72 |.29473 3, | . 77236) ¡g | 34
27 | . 63540 79 . 29504) 51 | -77218 19 | 33
28 | . 63563 79 .29535| 3, |.77199| ¡g | 32
29 | . 63585 72 |.29566| 3, | .77181| ¡9 | 31
30 |0. 63608 72 |L 29597] 3, |0. 77162| ¡g | 30
31 | . 63630 72 |- 29628) 51 | -77144| ¡9 | 29
32 | . 63653 72 | . 29659) 3, | 77125 18 | 28
33 | . 63675 71 |.29690 3, | .77107| 19 | 27
34 | . 63698 79 |.29721| 3, | -77088| ¡g | 26
35 |0. 63720 72 |1- 29752] 39 |0. 77070) 19 | 25
36 | . 63742 71 |.29784 31 | - 77051) ¡g | 24
37 | . 63765 72 | - 29815] 3, | - 77033) 19 | 23
38 | . 63787 71 |.29846 3, | 77014 ¡3 | 22
39 | . 63810 72 |-29877 35 | -76996| 19 | 21
40 |0. 63832 71 |1-29909| 3; |0. 76977| ig | 20
41 | . 63854 71 | - 29940 31 | - 76959] 19 | 19
42 | . 63877 72 | . 29971) 39 | -76940| 19 | 18
43 | . 63899 71 | - 30003] 21 | - 76921) 43 | 17
44 | . 63922 71 30034| 35 | -76903| 19 | 16
45 |0. 63944 71 |1-30066| 3, |0. 76884) ig | 15
46 | . 63966 i .30097 33 | .76866| ¡9 | 14
47 | . 63989 "1 . 30129) 37 | -76847 19 | 13
48 | . 64011 a . 30160] 25 | -76828 15 | 12
49 | . 64033 7| |.30192 37 | 76810 ¡9 | 11
50 |0. 64056 71 |1.30223 20 |0.76791| ¡9 | 10
51 | . 64078 71 .30255| 39 | -76772 19 | 9
52 | . 64100 br |.30287 37 | -76754 ¡9 | 8
53 | . 64123 70 | - 30318] 32 | -76735| 18 | 7
54 | . 64145 71 30350| 35 |. 76717| ¡9 | 6
55 |0. 64167 71 |1-30382| 31 |0.76698| 19 | 5
56 |.64190 zo |:30413| 39 | -76679 ig | 4
57 | . 64212 2j |-30445 35 | - 76661) ¡9 | 3
58 | . 64234 so |-30477| 32 | - 76642) ¡9 | 2
59 | . 64256 71 | . 30509] 32 | .76623| 19 | 1
Á 0. 64279 GL" 305411 42 |0 76604 == | +0
A DI
1290, cos rus csc a sin e BUS

1352

Natural Trigonometric Functions

TABLE 31

HH SL gd
40°> ; ; s r Å «139°
y sin pir csc pie tan pi. cot pi sec pr cos Ing A
T4
o lo. 64279 1. 55572 0. 83910 1.19175] „, IL. 30541 0. 76604 60
1 | . 643011 22 | 55518 ¿3 | . 83960) 39 | . 19105 70 1" 30573| 32 | . 76586, 13 | 59
2 |:64323| 22 | :55465| 5% | :84009| 50 |. 19035 70 |:50605| 32 | : 76567. 19 | 58
3 |:64346 23 | :55411| 54 |.84059| 50 |. 18064 Ae | . 30636 21 |.76548| 19 | 57
4|:64368| 22 |.55857| 3% |.84108 20 |.18894 7) |.30668 35 |.76530 ¡9 | 56
5 |0. 64390| 20 |T. 55303) 23 0. 84158| zo |T. 18824 79 |1 30700 35 |0. 76511] ¡9 | 55
6 | 64412 22 | 552501 5% |.84208| 50 |. 18754 7) | . 30732) 35 | - 76492] 19 | 54
7 |. 64435 23 |.55196| 53 |.84258 20 |. 18684 45 | . 30764) $5 | . 76473) 13 | 53
8 |-64457 25 | . 55143) 54 |.84307 5o | -18014 70 .80796| 33 | .76455| 19 | 52
. 64479) 22 | 55089) 53 |.84357| 50 | 18544 7) |.30829| 35 |. 76436) jọ | 51
10 |0. 64501| 54 |1. 55036) 4 |0.84407 =o |L 18474 zo |1 30861 z 0. 76417 R 50
11 |. 64524 53 | 54082 53 |.84457 20 | 18404 70 |.30893| 33 | . 76308) 12 | 49
12 | 645461 22 | 54929 23 |.84507 50 |. 18334 mp |.30925| $5 | . 76380 48
13 | . 64568] 3 | - 54876] 54 |: 845561 59 |.18204 70 |-30957 32 |. 76361 m 1142
5 b O 3 | BSCS ap .18194| <0 | . 30989) 33 | .76342| 19 | 46
15 9.64612 53 [L54769] 53 [0. 84056) 50 [1.18125| 70 |1-31022 35 |O. 76323) 19 | 45
17 | 6de57| 22 | 54668] 3 |: Saree] 50 "17980 99 |: 51086] 32 | : easel 18 | as
18 |. 64679 25 | 54610 53 |: 84806] 20 ` 17916 a “3193 | ONE
19 | . 64701 . 54557 84856 . 1784 EU EXE. E
| 19 |. 64701) 55 AE so Leder co d SINE ` 76248 41
2 0. care 23 |1. 54504 5g 10. 84906] 50 |1. 17777| gg |1.31183 ša 0. 76229 ma 40
23 |.54451| 53 |.84956 177081 © |” 31216 762101 19 | 39
22 | .64768 55 | 54308] 5% |.85000 54 |.17638 10 |:31248 32 | 76192 18 | 38
23 | 647001 22 | - 54345] 53 | - $5057) 5o | 17509 eo JL. aen: | Arora dës
Ë FBI olan DA ET 76154 36
k SRI Eom eet 4 i13 3 0. 76135 iá 35
i SR dpi |4 217 31378 O | e
27 | | 64878 ` 54134 85257, 90 69 33 KC 19
2t oe ale ` 17292 ` 31411 6097 3
28 | . 64901 . 54082 x 51 d 69 9 | - 76097 3
29 | .64923 22 | 54029, 93 EE Kee D 33 | 76078 |9 | 32
"30 |0. 64945! ~~ |1 53977 52 YESO] si 69 |-31476 33 | -76059| jg | 31
Aīda 4d 0. 85408) 59 [I 17085) gg |ī 31509| 33 |0. 76041| 19 |30
32 | . 64989] 22 |. olu 02 E 5115 6 o | - 31541 . 76022 29
33 | 65011 22 Ee ek Ee 69 | 31974 33 |. 76003] 19 | 28
34 | . 65033) 55 | 53768 5% | | 85609 a k Msi (15983 19 | 27.
35 |0. 65055 0. 85660 ee ii E ss — Ë
35 |0. 65055) >> |1.53715| 55 |0. 85660) zo |L 16741 1. 31672| ** |0. 75946) 19 [5
5077| 53 | . 53663 85710 16672 69 veel 33 IE
37 | .65100| 2 ` 53611 52 : 0f 51 |: 16672 69 tm 24992709 1 24
22 59803595170) 16603 > 33 Ë 19
39 | . 65144) 55 | 53507 22 | 85862, 51 “ese 89 po Sh TE 3a | 15359 eco] eS
40 |0. 65166 1.53455, 7^ loss 2° |, 68 EEN EE Et,
A 22 52 . 85912 1. 16398 1. 31837 = XU d DATI
` 53351 lacas . 3187 7 19
43 | 65232 22 | ` 53299] 52 Erde pur 8b ege eko
alem 22 | 153247) 52 | 80119 51 | 16194] 68 |-31936 33 | 757941 19 | 17
45 |0. 65276| 5, |1.53196 5! lo soree *! lena 68 _: 81969) 33 | .75775 19 | 16
E. 22 zo |0. 86166 I. 16056 1. 32002 E l
5 |. 65298 53144 2610 D 50 02 0. 75756 15
47 | 65390) 22 2 52 . 86216 51 | - 15987 ` 32035| 33 GE 18
| 29 | - 53092 . 86267 15010) 68 |:325099| 33 | 25738179 | 14
48 | . 65342 Vi oe SEDI E . 32068 . 15719 13
29 ` 86318 15851) 68 33 19
49 | . 65364 .59989| 92 RAGU E . 32101 . 75700 19
49 | . 65364) 55 51 |.80368 15783| 98 33 Ki 20
50 |0. 65386) 55 |1. 52938 0.86419 *! lī ī5715| $ ..92184 34 | .75680| 19 | 11
510 ES 59886 B2 DER A are L. 32168 0. 75661| 44 | 10 |
52 | 65430) 22 | 528351 51 | 88290) 51 | - 15647 ba |.32201| 33 | 75642] 19 | 9
53 | 65452 22 | 52784] 51 | 865211 51 |-15579] gg |.32234 33 | 75623 19 | 8
54 | .65474 22 | 52732 52 Ey ud 68 |-32267| 33 |.75604| 19 | 7
55 [0. 65496] >> |i.5268:| Š! lema *' ise 8 | 328011 33 | .75585 19 |_6
SK 51 [0 86674 1.15375| ZZ |1 32 PASO
$6 Jo 0551525 | 52630) Ey ||. 86725) 2l | isos] 07 UIE asrakal T TOS
. 65! 7 28 . 13996 = =
58 | . 65562 22 (52527 52 | sl ee ES ` 32401 ES ` 75528 19 | 3
59 | . 65584 5294761 91 | ges 51 |: 19172 523168 19 |
: 99 | - 52476; . 86878 “15104 68 434| 34 | . 75509 2
60 |0. 656061 ^^ |1. 52425 5! |0. 86929 51 |1 15087] 67 y 32468) 33 | .75490 ek:
n ; . 32501 0. 75471 0
130? cos Pif se Diff Diff i
2 j^ x 1’ cot 1’ tan Diff ese Diff Sin Diff. , Â

WT Eeer"

1353

TABLE 31

Natural Trigonometric Functions

cot

0 |0. 65606 5, |1. 52425 0. 86929 . 15037 ! 0. 75471
1 | . 65628 . 52374 . 86980 . 14969 : . 75452
2 | . 65650 . 52323 . 87031 . 14902 j . 75433
3 | . 65672 . 52273 . 87082 . 14834 . 75414
4 | . 65694 52222} ou |.87188 . 14767 . 75395
5 |0. 65716| 2» |1. 52171 0. 87184 = |i. 14699 : 0. 75375|
6 | . 65738 . 52120 . 87236 . 14632 . 75356

. 65759 . 52069 . 87287 . 14565 Å . 75337

. 65781 . 52019 . 87338 . 14498 i . 75318

. 65803 . 51968 . 87389 . 14430 . 75299

. 65825 . 51918 0. 87441 1. 14363 0. 75280
. 65847 . 51867 . 87492 . 14296 . 32872 . 75261
. 65869 . 51817 . 87543 . 14229 . 32905 . 75241
. 65891 . 51766 . 87595 . 14162 . 32939 . 15222
. 65913 . 51716 . 87646 . 14095 . 32973 . 75203

. 65935 . 51665 0. 87698 1. 14028 1. 33007 0. 75184
. 65956 „61615 . 87749 „13961 „83041 „75165
. 65978 . 901565 . 87801 . 13894 . 33075 . 75146
. 66000 . 51515 . 87852 . 13828 . 33109 . 15126
. 66022 . 51465 . 87904 . 13761 . 33143 . 15107

20 |0. 66044 1. 51415 0. 87955 1. 13694 1. 33177 0. 75088
. 66066 . 51364 . 88007 . 13627 . 33211 . 75069
. 66088 . 51314 . 88059 . 13561 . 33245 . 75050
. 66109 . 51265 . 88110) = . 13494 . 33279 . 75030
. 66131 . 51215 . 88162 . 13428 . 33314 . 75011

. 66153 1. 51165 0. 88214 1. 13361 1. 33348 . 74992
. 66175 . 91115 . 88265 . 13295 . 33382 „74973
„66197 „51065 . 88317 . 13228 . 33416 . 74953
. 66218 . 51015 . 88369 . 13162 . 33451 . 74934
. 66240 . 50966 . 88421 . 13096 . 93485 . 74915
30 |0. 66262 1. 50916 0. 88473 1. 13029 . 33519 . 74896
. 66284 . 50866 . 88524 . 12963 . 93554 . 74876
. 66306 . 50817 . 88576 „12897 . 33588 . 74857
. 66327 . 50767 . 88628 . 12831 . 33622 . 74838
. 66349 . 50718 . 88680 . 12765 . 33657 . 74818

0. 66371 1. 50669 0. 88732 1. 12699 . 33691 . 74799
. 66393 . 50619 . 88784 . 12633 . 33726 . 74780
. 66414 . 50570 . 88836 . 12567 . 33760 . 74760
. 66436 . 50521 . 88888 . 12501 . 33795 . 74741
. 66458 . 50471 . 88940 . 12435 . 33830 . 74722

40 |0. 66480 1. 50422 . 88992 „12369 „83864 . 74703
. 66501 . 50373 . 89045 . 12303 . 33899 . 74683
. 66523 . 50324 . 89097 . 12238 . 33934 . 74664
. 66545 . 50275 . 89149 "212 . 33968 . 74644
. 66566 . 50226 . 89201 . 12106 . 34003 . 74625

. 66588 . 50177 . 89253 . 12041 . 34038 . 74606
. 66610 . 50128 . 89306 111975 . 34073 . 74586
. 66632 . 50079 . 89358 21900 . 34108 . 74567
. 66653 . 50030 . 89410 . 11844 . 34142 . 14548
. 66675 . 49981 . 89463 s . 34177 . 74528

. 66697 1. 49933 . 89515 . 11713 . 34212 . 74509
. 66718 . 40884 . 89567 . 11648 . 94247 . 74489
. 66740 . 49835 . 89620 . 11582 . 94282 . 74470
. 66762 . 40787 . 80672 . 11517 . 34317 . 74451
. 66783 . 49738 . 89725 . 11452 . 34352 . 74431

. 66805 . 49690 . 89777 . 11387 . 94387 . 74412
` 60827 . 49641 . 89830 . 11321 . 34423 . 74392
. 66848 . 49593 . 89888 . 11256 : . 14373
. 66870 . 49544 . 89935 21191 : . 74353
59 | . 66891 . 49496 . 89988 . 11126 S $ . 74334
60 10. 66913 . 49448 . 90040 . 11061 d |9. 74314

13195 cos HT. sec us cot hz tan i | sin

1354

TABLE 31

Natural Trigonometric Functions

0 |o. 66913 — |1. 49448| 49 (0. 90040] ¿2 |1. 11061) ¿5 |1.34563| 36 |0. 74314] ¡a | 60
1 | . 66035] 22 | mea 9 |.90093| 23 |: 10996) $2 |.34599| 35 | . 74295) 19 | 59
2|:66956 21 |:49351| 48 |.90146 23 |: 10031] $4 |.34634 35 | .74276| 20 | 58
3 |.66978 22 | meng 48 |:90199 53 |. 10867] 65 |.34669| 52 | . 74256) 19 | 57
4 |. 66999) 21 |:49255| 48 |:90251 22 |. 10802 68 | . 34704) $2 | .74237 20 | 56
TERR is Pie a mg as izan 19 |
7 | 67064) 21 | 49111) 48 |: 90410] 23 [10607 65 |.34811| 36 |. 74178] 20 | 53
8 | 67086 57 |.49063| 1$ |.90463 23 |:10543 ê% | .34846| 35 | .74159| 30 | 52
9 |.67107| 23 |.49015| 48 |: 90516) $3 |. 10478 65 | | 34882) 38 |. 74139) 70 | 51
10 |0. 67129) 55 |I. 48967 0. 90569| +» |T. 10: i
11 [erigi 22 | ear 48 |” boosi) 52 |:10349, 65 |” 31953 36 | 7a1o0l 20 | ag
era de E 58 |" 10285 D |:34988| 39 |: 20
12 | . 67172) 55 | : 47 |-90674| 5% |.10285| 02 |.34988 2° |.74080| 19 | 48
13 |. 671941 5) |.48824| 4g |.90727 54 |.10220 Gy |.35024 36 |. 74061 39 | 47
4 |.67215| 52 | 48776 48 |.90781| 53 | 10150 64 |.35060| 39 |. 74041| 20 | 46
15 067237 5, |1.48728 4, |0.90834| sa [i.10091| ¿y |L. 35095| ze |0. 74022 45
16 | . 67258) 21 |: 48681 90887 10027 35131| 96 20
17 |.67280 22 |.48633| 48 |:90940| 23 |.09963| 64 |:35167| 39 :73083| 19 | 43
18 | . 67301) 25 | . 48586, 44 |.90993| 23 |:09899| 614 |:35203| 36 |:73968| 20 | 42
19 | _ 67823] 71 | 48588) 17 | . 91046 $3 | 00834 69 | | 35238| 38 |.73944| 19 | 41
0. 67344| 5. |i. 48491 0. 91099 1. 09770 5
21 |. 67366 E - 48443 le oleae. ` 09706 dl ': $5310 A o 73004 1o 39
i ` 91206 ` 09642 i e
23 | . 67409| 22 | . 48349] 47 |:91259| 53 | 09578 64 35382 36 | ` 7380 20 37
24 | . 67430] 55 | 48301] 4% |.91313 23 |.09514| 94 |'35418 36 | : 73846] 19 | 36
25 |0. 67452 1. 48254 0. 91366 10050 94 1.35454| 29 lo 73826| 29
26 | . 67473 23 | . 48207 a .91419 5% |. 09386| 64 35490, 36 |0 73808 20 | 3?
„67495 . 48160 91473 0 64 | ` 35526| 36 | ` 19
A N ` 09322 ` 35526 .73787 3
28 |. 67516 53 6 3
28 | 67516) 55 |. 48113) 47 |-91526 34 | - 09258 e |.35562| 56 | 7376720130
21 | - 48066) 47 |:91580| 24 |: 09195 35598 30 |: 73747| 20 | 31
30 |0. 67559| 5, |1. 48019 0. 91633 L09131| D 1. 35634| 29 Io. 5
31 | . 67580) 23 |.47972 47 |. 91687| 2$ |.09067| 64 35670, 30 |" 73708 20 | 39
. 67602 . 47925 64 Ml ST its
JE HE-ESE- EIE MIR HE EIE
34 |.67645 27 |.47831 4, |.91847| 53 |:08s76| 94 |:35779 36 ` 73649) 20 | 26
E d Ai 22 |1 47784) 46 |0.91901| +, |1. 08813 D Casel 0.73629| 29 [35
. 67688) 22 | . 47738 91955 .08749 | 64 |" 35852 37 |. 19 |24
37 |. 67709 547691 17 53 63 |: . 73610 24
21 7 |.92008| 95 | 08686 35888| 90 20
38 |. 67730 .47644 4 54 Či Ë 8 . 73590) 24 | 23
39 | ` 67752| 22 46 | :92002 54 | . 08622 35924| 39 | | 73570) 20
. 67752] 21 | 47508 49 |.o2116 54 |‘ 08559 63 | 350611 37 |: 73551] 19 | 21
40 |0. 67773) 55 |1. 47551 47 |0. 92170 1.08496) °° mer he oie 20
41 |. 6795] 31 |. 47504) 47 [.92224 94 |: 084321 64 350997 37 |0. 73581) 20 | 20
42 | 67816 2; |.47458 19 | 92277| 53 | 08360 63 |:36070 36 |: 73491] 20 | 18
m 22 „47411 46 . 92331) 77 | . 08306 63 ` 36107 37 |: 19 18
44 |.67859| 37 |.47365 46 | | 92385 E 08243, 63 | Saal 36 RV 20 | 17
45 |0. 67880| 5, |1. 47319 47 |0. 92439 1. 08179 64 TE 37 | -73452 59 | 16
E . 67901) 99 |. 47272 16 |. 92493 54 M GE T 37 |0. 73432| 19 | 15
a o ae MEET) reet 36253 36 | ` 789881 20 | 13
48 | . 67944] 31 |. 47180) 46 |. 92601 "o7990]- 99 "|* 36200 37] | 05952-19200 eee
9 |.67965 99 | - 47134 E . 92655| 94 07927 63 . 90 37 UE 20 12
50 [0. 67987 3; [147087 e [o.92700 ** rose 99 36327 36 | .73353| 20 | 11
51 |. 68008 21 | 47041 Í ` 92763 | 94 ora 63 j} 36363 37 0. 73333 19 10
52 | . 68029) „2 | . 46995, 46 |:92817 54 | 07738 63 | 36489/ 37 | 23314| 20.| 9
53 | 68051) 57 |. 46040) $e |. 92872), 25 |“ ovevo| 62 |: zeara 37 73234 200 ame
| | - 68072) 2: |. 46003) 46 | | 92026) 54 |:07618| 63 |:30s11 37 | 73214 20 | 7
55 10. 68093| 55 [1. 46857| |6 D 92080 S4 šoka (09 _+ 365111 37 |. 73254| 59 | 6
. . 46765 . 93088 i 62 ao 532156 4
58 |. 68157| 21 | ` 46719) 46 | : as. | . 07425 . 36622| 37 20
å $ 63 . 73195 3
SIE BEE 36606 Esse -
1. 46628 0. 93252| 95 : 62 |.936696 . 73155 1
A Jo. 93252) °° |1: 07237 1. 36733| 37 lo. 73135| 20
1320, cos Pit pin Dis D TENTE.
> 1’ sec P cot F iff i i T
1 1 tan 1’ ese pn sin Din 470

1355

TABLE 31

ic Functions
igonometric
Natural Trig

«136?
iff. MALES,
Diff. sec D co Din
i ESCH d !
i Diff. tan di :
= 1. 36733) 37 Sil 2
y 07237 e : 367701 37 ja H 3
a a oz112| 9? . 36807. 37 73076| 20 56
| à q i | pae 55 | <07112 63 | ` 36844 37 | ` 73056 DOES
Å E : e? 2 sns 54 dies 62 Í ` 36881 38 [73036 20 | 25
CH 46 SB e 9: 22 | ` 070 S T
: I. 36919} 37 HE
RSA 45 E E. 1 D
4 | ` 68285| 21 146400 4e da TER LM BLUE 37 72976 AE
E i a i p 51 EE 62 | 37068 37 (72937 20 Hs
6l. 46 4 .9 54 0667 63 x d m ;
7 | . 68349 21 46263 45 . 93742 55 06613 62 1. 37143 p. 2917 20 49
8 | . 68370 21 46218 45 . 93797 gs 6551 62 m ; 7 ; 3 :
9 | . 68391 21 1. 46173 46 ERU 54 Dee 62 odd 38 72877 2 17
: E. : 16082 45 Tra Se rt 62 | ` 37255 38 72837| on 4d
Ta 4 uet 55 | 064 02 ds :
: RU UE 45902 16 | 94016) 55 Vno. Pd 12797 20 E
r^ Aa a5 Dun 55 | - 06241 62 | 37368 38 | ^ 70777 GR 41
14 | og 21 1. 45946 ys - 94125) 55 06179 65 . 37406) 57 72757 2
HE E 45 | - 94180 55 | ` 06117 61 | ` 37443 Hl 20 | 40
i Do 2 45811 E - 94235 55 06056 62 1. 37481| 28 72717) 50 oh
F ES n 45766 45 | 94290 55 05994 62 . 37519 37 72697 50 37
A ae ; 15721 15 o 55 05932 62 . 97556 38 72677 20 36
19 | . 68 21 1.45721| ¿5 - 94400) 55 05870) oi . 37594) 38 72667] 20 | ë
a BE GES 44 | 94455 55 | ^ 05809 02 16 37092 38 1072637 20 | 35
T I > | beet 45 | - 94510 55 | 05747 lesen 38 |" 29617 20 25
5 ques db ees T . 94565) 55 1.05085 e ` 37708 38 | ` 72597 20 | 39
: E au jR 0. 94620) ce 05624 ¿9 . 37746 38 | ` 79577 20 | 31
ARE 145452] 45 - 94676) 55 05562) ` 61 SE SE 204
degt 4540, H - 94731) 55 05501 65 . 97822 38 72537 9) >
z E n 15363 ú - 94786) 55 05439 61 1. 37860) 38 72517) 99 28
JR EIE 45 | 94941| 55 A TEL E 38 | 272497) 20 27
: C ne 15 |0. 94896 56 |” 05317 62 | ` 37936 38 | 79477 20 | 26
29 | . 68814) 51 1.45274| 45 . 94952) 55 05255 g] . 37974| 32 72457, 20 A
ac ii | 99007 55 ares q Etre 25 [0.72437| 20 24
31 |.68857| 51 45185 44 . 95062) 54 05133) $1 i 38051 32 cb E
: bee n 15096 Á S25 cin 55 05072 62 . 38089 38 72397 20 22
s som n eo a 0. 95173 56 05010 61 . 38127| 32 12377 99 21
34 | . 68920| 51 E ele 25 | 0494940 De 38165 39 | 72877 AE
HE LE "EDEN 95284 36 | 04888] 6! . 38204 58 E cna bee
36 . 68962 21 44963 44 . 95340 55 04827 61 AT R SE i
S Mós 052902 44 | | 95395) 95 Eege uE t
38 : 69004 S DEE a E | Bacon 61 |: 38319] 39 sal |
CE ids d . 95506) 56 04644| 61 e | lite 21 5
40 |0. 69046| 2, 44787) 45 -95562| Ze 04583 o . 38396 38 2255 7! i
41 | . 69067! 51 4474201 44 . 95618) 55 04522) 0l SE SE
EARS n E 44 | 95678] 2 ME 39 | 721061 20 12
: pas a j 43 [0.95729 56 |” 04401 61 | 38512 SS. PT ee 11
EE "os E 95785. 56 04340 gy . 38550 39 72156) 20 10
45 |0. 69151) 9, 44567 44 05841 56 | 04279 Is 39 E
NEC d) dH . 95897) 55 04218) ` ou 1. 38628) 38 72116] 2; 8
dE 14435) 44 . 95952) 56 04158 o -38666 39 72095 2 ii
49 | 100255 21 | taisa 44 ^ 90004 26 | 04097 9 PECE
49 | .69235| 51 1. 44391 44 | 96064 56 04036 60 (38744. 39 Sch E
AB wp mE . 96120) 56 03976 oi . 38783| 39 UM EL d
Ox kosten 45 |--96176| Ze 03915| ` ou Ce 3g 0 72005 sl?
3 E n ` 44217 44 | 962821 Ze EN 39 | "71995 20 2
a ama 1 0. 96288) 56 03794 80 . 38899 39 Āā p
ag >) SE GE On . 38938 39 71964) 20 ke?
ze |: e082 2i 44086) 43 | 96400 IE 61 - 38077 39 |0 71934 SC SE
BE 11012 44 . 96457 56 |” 93613 60 |i 3901 Diff. 6?
dE n 13999 B . 96513 56 03553 Diff sin 1⁄44
ah i 15080 - o Diff esc 1’
59 | . 69445) 21 E ze :
60 |0. 69466) * _ EC
Diff sec 1/
13355 cos 1”
iev EA ES EA A ee

1356

TABLE 31

Natural Trigonometric Functions

1. 43956 0. 96569 1. 03553 1. 39016 39 0. 71934
. 43912 . 96625 . 03493 . 39055 . (1914
. 43869 . 96681 . 03433 . 39095 . 71894
. 43826 . 96738 . 03372 . 89134 . 71873
. 43783 . 96794 . 03312 . 39173 . 71853

1. 43739 0. 96850 1. 03252 1. 39212 0. 71833
; . 43696 . 96907 . 03192 . 39251 . 71813
. 69612 . 43653 . 96963 . 03132 . 39291 . 11792
. 69633 . 43610 . 97020 . 03072 . 39330 „71772
. 69654 . 43567 . 97076 . 03012 . 39369 . 71752

. 69675 . 43524 ? 0. 97133 1. 02952 . 39409 . 71732
. 69696 . 43481 . 97189 . 02892 . 39448 . 71711
. 69717 . 43438 . 97246 . 02832 . 39487 . (1691
. 69737 . 43395 . 97302 . 02772 . 99527 Tw 1671
. 69758 . 43852 . 97359 . 02713 . 39566 . 71650

15 |0. 69779 1. 43310 . 97416 . 02653 1. 39606 0. 71630
6 | . 69800 . 43267 . 97472 . 02593 . 39646 . 71610
. 69821 . 43224 . 97529 . 02533 . 39685 . 71590
. 69842 . 43181 . 97586 . 02474 . 99725 . 71569
. 69862 . 43139 . 97643 . 02414 . 39764 „71549

20 |0. 69883 : 1. 43096 P 0. 97700 f 1. 02355 . 99804 . 71529
2 . 69904 . 43053 . 97756 . 02295 . 39844 . 71508
. 69925 . 43011 . 97813 . 02236 . 99884 . 71488
. 69946 . 42968 . 97870 . 02176 . 39924 . 711468
. 69966 . 42926 . 97927 . 02117 . 39963 „71447

25 |0. 69987 å 1. 42883 P 0. 97984 f 1. 02057 2 . 71427
. 70008 . 42841 . 98041 . 01998 : . 71407
. 70029 . 42799 . 98098 . 01939 s „71386
„70049 . 42756 . 98155 . 01879 : „71366
„70070 . 427714 . 98213 . 01820 : . 71845

|L-— iem Horus de 2 PA
30 |0. 70091 : 1. 42672 0. 98270 d 1. 01761 : . 71325
3 . 70112 . 42630 . 98327 . 01702 S „71305
. 70132 . 42587 . 98384 . 01642 x . 71284
. 70153 . 42545 . 98441 . 01583 : . 71264
. 70174 . 42503 . 98499 . 01524 : „71243

9 |98 ER
. 70195 1. 42461 0. 98556 d 1. 01465 d . 71223
-70215 . 42419 . 98613 . 01406 ; 241209
. 70236 . 42377 . 98671 . 01347 Ë STORE
. 70257 . 42335 . 98728 . 01288 : . 71162
. 10277 1 . 42293 . 98786 . 01229 : . 71141
40 |0. 70298 1. 42251 . 98843 . 01170 : eC LUZ
. 70319 . 42209 . 98901 TOnZ ? „71100
. 70339 . 42168 . 98958 . 01053 : . 71080
. 70360 . 42126 . 99016 . 00994 : . 71059
. 70381 0 . 42084 . 99073 . 00935 A . 71039
. 70401 1. 42042 . 99131 . 00876 ; „71019
„70422 . 42001 . 99189 . 00818 : . 70998
. 70443 . 41959 . 99247 . 00759 3 . 70978
. 70463 „41918 . 99304 . 00701 > „70957
. 70484 1 „41876 1 „99362 8 „00642 + . 70937
. 70505 1. 41835 0. 99420 1. 00583 . 70916
. 70525 . 41793 . 99478 . 00525 S „70896
„70546 „41752 „99536 „00467 : „70875
„70567 . 41710 . 99594) ` . 00408 k . 70855
. 70587 . 41669 . 99652 8 „00350
55 |0. 70608 1. 41627 „99710 1. 00291
„70628 . 41586 . 99768 . 00233
. 70649 . 41545 . 99826 . 00175
. 70670 . 41504 . 99884 . 00116
. 70690 . 41463 . 99942 . 00058
60 |0. 70711 1. 41421 . 00000 1. 00000

1 `
1340, cos F," ` | cot | tan

Logarithms of Numbers

TABLE 32

1357

emm

1-250

a BRM

No. Log No. Log No. Log No. Log No. Log
1 0. 00000 51 1. 70757 101 2. 00432 151 2. 17898 201 2. 30320
2 0. 30103 52 1. 71600 102 2. 00860 152 2. 18184 202 294950590
3 0. 47712 58 1. 72428 103 2. 01284 153 2. 18469 203 2. 30750
4 0. 60206 54 173289 104 2. 01703 154 2.18752 204 2. 30963
5 0. 69897 55 1. 74036 105 2. 02119 155 2. 19033 205 29: 05075
6 0. 77815 96 1. 74819 106 2. 02531 156 2. 19312 206 2. 31387
7 0. 84510 57 1. 75587 107 2. 02938 157 2. 19590 207 2. 31597
8 :0. 90309 58 1. 76343 108 2503342, 158 2. 19866 208 2. 31806
9 0. 95424 59 1. 77085 109 2. 03743 159 2. 20140 209 2532015
10 1. 00000 60 77815 110 2. 04139 160 2. 20412 210 22322022
11 1. 04139 61 ISS ibl 2. 04532 161 2. 20683 2171 2. 32428
12 1.07918 62 1. 79239 CH 2. 04922 162 2. 20952 212 2. 32634
13 1. 11394 63 1. 79934 113 2. 05308 163 2. 21219 213 2. 32838
14 1. 14613 64 1. 80618 114 2. 05690 164 2 21484 214 2. 33041
Kð 1. 17609 65 1481291 3/4115 2. 06070 165 DS 215 2. 33244
16 1. 20412 66 1. 81954 116 2. 06446 166 2. 22011 216 2. 33445
17 1. 23045 67 1. 82607 17. 2. 06819 167 24522212 2i 2. 33646
18 1. 25527 68 19892519 IES 2. 07188 168 232959 218 2. 33846
19 1. 27875 69 1. 83885 119 2107599 169 2. 22789 219 2. 34044
20 1. 30108 70 1. 84510 120 2. 07918 170 2. 23045 220 2. 34242
21 11532222 zl 18851200121 2. 08279 Íl! 2. 23300 221 2. 34439
22 1. 34242 | 72 1. 85733 122 2. 08636 172 2429509 222 2. 34635
2 130175 73 1. 86332 123 2. 08991 lio 2. 23805 223 2. 34830
24 1. 38021 74 1. 86923 124 2. 09342 174 2. 24055 224 2. 35025
25 1. 39794 LD 1. 87506 125 2. 09691 175 2. 24304 229 2. 35218
26 1. 41497 | 76 1. 88081 | 126 2381003 176 282755] 226 21354171
20 1. 43136 "id 1. 88649 127 2. 10380 177 2. 24797 22 2. 35603
28 1. 44716 78 1. 89209 128 210724 178 2. 25042 228 2. 35798
29 1. 46240 79 1. 89763 129 231059 179 2. 25289 229 2. 35984
30 ]. 47712 80 1. 90309 | 130 2. 11394 180 2525021 230 2. 36173
Sul 1. 49136 81 1. 90849 | Bil 281727 181 2. 25768 231 2. 36361
32 150515 82 1. 91381 132 2, 12057 182 2. 26007 232 2. 36549
33 1. 51851 83 1. 91908 133 2. 12385 183 2. 26245 299 2. 36736
34 1. 53148 84 1. 92428 134 2. 12710 184 2. 26482 234 2. 36922
35 1. 54407 85 1. 92942 135 2. 13033 185 226174 235 22. O
à 86 1. 93450 136 2. 13354 186 2. 26951 236 285129
2e + A 87 1. 93952 | lo 2. 13672 187 2. 27184 23 2. 37475
38 1. 57978 88 1.94448 || 138 2. 13988 188 2. 27416 238 2. 37658
1 | 139 2. 14301 189 2. 27646 239 2. 37840

39 1. 59106 89 1. 94939 :
40 1. 60206 90 1.95424 140 2. 14618 190 2. 27875 240 2. 3802]
. 95904 141 2.14922 | 191 2. 28103 241 2. 38202
e i 03535 2 A SE 142 2. 15229 192 2. 28330 242 2. 38382
43 1. 63347 93 1. 96848 143 215534 193 2. 28556 243 2. 38561
44 1. 64345 94 1. 97313 144 2. 15836 194 2. 28780 244 2. 38739
45 165321 95 07472 145 22: MIT 195 2. 29008 | 245 2. 38917
| "e c |246 | 2.39094
49 | 1.66276 | 96) 198227. 146 | 2 16733 | 197 | 2.29447 |247| 2 30270
48 1. 68124 98 1. 99123 148 2. 17026 198 2. 29667 Z 2. Se
49 1. 69020 99 1. 99564 149 257.319 199 2. 29885 249 2. ag;

50 1. 69897 100 2. 00000 150 2. 17609 200 2. 30103 | 250 2. 39

1358

TABLE 32

Logarithms of Numbers

1000-1500

Noe 1.10 Jal. ti ¡24 dis 32d 4. wid]. 5 «apt 6 [dle 7: ales? [dio od cR

100 |00000/43[00043 4400087 (4300130 43100173 44100217 43|00260|43|003808 43|00346 43|00389 43 44 43
101 |00432|43|00475|43|00518|43|00561!43|00604|43|00647 42100689 43100732 43|00775|42]00817 |43
102 |00860/43/00903 42100945 43|00988 42/01030.42101072 43|01115/42]011577/42]01199 43[01242 42
103 [01284/42]01326 42101368 42101410/42]01452 42101494 42]01536 42101578 42101620 4210166241
104 [0170342]01745/42]01787/41]01828/|42]01870 42]01912/41]01953/42]01995 41102036 42020778 41

105 [0211914102160 42102202/41/02243 41102284 41102325 41102366/41]02407 42102449 41102490 41
106 |02531|41|02572|40|02612|41|02653|41|02694|41|02735|41|02776|40|02816|41|02857|41|02898|40
107 [02938441]02979/4003019/4103060 40103100 41/0314 14003181 44103222 40103262. 4003302 40
108 [03342/41103383|40/03423 4003463 40103503 40103543 40]03583 4003623 40103663 40|03703 40
109 |03743/39]03782/4003822 4003862 40103902 3910394 1|40]0398 1 40104021 |39]04060 40[04 10039
110 [04139/10/04179 39/04218|40/04258 391042977 39104336 401043776 39104415 39104454 3904493 |39
111 [0453239104571 39/04610|40/04650 39104689 38/047 27 39104766 39104805 |39]04844.|39|04883 39
112 |0492239]04961/38[04999 3905038 39/0507 7/38|05 1 15/3905 154 38/05 192/39]05231 |38105269/39
113 |05308|38|05346|39105385'38|05423|38|05461|39[05500|38|05538|38|05576|38|05614|38|05652|38
114 [05690/39]05729 38[05767 ¡3805805 38[05843 3805881 |37|05918 38]05956 38]05994 380603238

OWNS ou otl
D
D
N
t2

115 [0607053806108 /37]06145/38|06183/38]06221/37106258/38]06296 37106333 381063 713710640838
116: [064463706483 3806521 |37106558|37106595 3806633371066 70/37106707/37106744 37106 78 1138
117 |06819|37|06856|37|06893|37|06980|37|06967|37|07004|37|07041 3710707837107 1 15/36]07 15 1127
118 |07188|37|07225|37|07262|36|07298|37|07335|37|07372|36|07408|37|07445|37|07482!36|07518|37 740 39 |
119 |07555|36|07591|37|07628|36|07664|36|0'7700|37|07737|36|07773|36|0'7809!37|07846|36|07882!36 sto

c 00-10 ou o Nal
N
—
Lä
©

120 |07918|36|07954|36|07990|37|08027|36|08063|36|08099|36|08135'36|08171|36|08207!36|08243|36
121 |08279|35|08314|36|08350|36|08386|36|08422|36|08458|35|08493|36|085291|36|08565|35|08600136
122 |08636|36|08672|35|08707|36|08743|35|08778|36|08814|35|08849|35|08884|36|08920!35|08955|36
123 [089913509026 35/09061/35[09096 36/09132|35109167|35/09202 35109237 35109272 35109307|35
124 1093423509377 3509412 35[09447 35/09482|35/09517|35109552|35109587 (34109621 35109656 35

125 |09691)35/09726/3409760/35]09795 35|09830/34]09864/35]09899 35109934 3410996835 10003134
126 |10037|35|10072|34|10106|34|10140/35|10175|34110209|34|10243|35|10278!34|10312!34 10346/34[[ 2/90/99 |
127 |10380/35|10415/34/10449|34/10483 34110517|34/10551 34110585 34110619 34110653 34 10687 34 38137

128 [1072134110755 34110789 34110823 34|10857 33|10890 34|10924 34|10958 3411099233 11025 34 |
129 |11059/3411093 33] 1 1126/|34]11160/33}1 1193/34] 1 1227/3411 1261 33]11294 3311 132 734 1136133

0 01D Oui 02 A!
t2
e
t2
e

130 |11394|34|11428|33|11461|33|11494 34|11528[33|11561/33|11594 34/11628 3311 1661 l3 1169433
131 |1172733|11760/33|11793 33|11826 34/11860/33111893|33111926 33 11959/33]11992 32]12024 33
132 |12057/33]12090 33|12123 33|12156 33|12189/33|12222/32| 19254 33 12287 33|12320/32]12352.33
133 [12385/33|]12418/32]12450/33]12483 33|12516 32 12548|33|12581|32|12613!33|12646|32/|12678|32
134 |12710|33|12743|32|12775|33|12808|32|12840|32|12872|33|12905|32 12937|32/|12969|32|13001/32|

c 0010 ou wy HI
mm
o
—
00

135 [13033|33113066 32/13098|32113130 32/13162/32113194 3| 13226 3013258 3013290 30 13322 s0l| 9/34/33 |
136 [1335432113386 3213418|32)13450'31113481 (32113513 3211354522 13577/32113609|31113640|32 36/35

137 |1367232113704 31/13735 32)13767/3213799|31113830 32113862 31/13893 32113925 3111305630
138 [139881114019 3214051 31114082 22] 14114 31/14145 31/14176 32/14208 31/14239 m 14270 1
139 114301 5214333 31/14364 31114395 31/14426 31/14457 32/14489 31/14520 31/14551 31/14582 31

140 114613 31/14644/31114675 31114706 31114737/31114768 31 14799/30/14829/31114860|31114891!31
141 [1492231114953 30/14983 31115014 31115045|31115076 30/15106/31115137/31115168/30 tt 31
142 [1522930/15259 2115290/30|15320/31]15351/30|15381 3115412 30/|15442/31|15473/30] 1550321
143 [15534 30115564 30/15594/31115625 30115655 30 15685/30|15715/31]15746/30]15 776/30] 1580630
144 [15836[30]15866/21|15897]30]15927/30]15957 30 15987 /30|16017/30|16047/30|16077 30] 16107 30

CONSE otl
um
00
mÓ
Qo

145 |1613730|16167/30|16197/30|16227 29|16256/30]116286 30116316 30116346 30|16376/|30] 16406 2 34/33
146 |16435/30]16465 30|1649529]16524130 1655430|16584/29|16613 30 16643 30 16673|29 Ta x

147 |1673229]16761 30116791 |29116820 30116850 29 16879 30116909/29116938 29116967 30116997/29
148 117026 30117056 29117085 29117114 20117143 30 17173 29|17202|29]1'7231 29|17260/29| 17289130
149 |1731929|17348 29|17377 2917406 29117435 29 17464 29]17493 2917522 29]17551 29] 1 7580/29

150 [17609 29]17638 29|17667 29]17696 29|17725 29117754 2811778229 1781129 17840 2 17869)/29

CONS oU ot nl
—
Ó
—
c

No. |, 0 jap (ted), 2 |a. 3 fai ða

1359

TABLE 32

Logarithms of Numbers

1500-2000

0 ld 1 d 2 d 3 jaq 4 ld 5 jd 6 Jal 7 | 8 Ja] 9 lalf Prop. parts

17609 29117638 |29] 17667 [2917696 29/17725 29/17754 2817782 20117811 29|17840 29 1786929 3231

17898 28] 17926 2917955 29|17984/29|18013/23| 18041 29|18070 29| 18099 28118127 20 18156 28 ED!
18184 29118213 23|18241 29|18270 23|18298 29| 18327 |28] 18355|29] 1838428] 18412 29| 184411 28
18469 2918498 |28] 18526 28|18554 29|18583 28| 18611 28|18639/28|1866729| 18696 28] 18724 28
18752 28|18780 23|18808 29|18837 2818865 28|18893 2818921 2s|18949/28| 1897 7/28]19005 28

19033 28|19061 2319089 28|19117/285|19145/28|19173 23|19201 528|19229 2s|19257 23] 1928527
19312|28|19340|28|19368|28|19396|28|19424|27|19451|28|194'79|28|19507|28|19535|27119562.28
19590|28|19618|27|19645|28|19673|27|19700|28|19728|28|19756|27|19783!28|19811|27|19838|28
19866|27|19893|28|19921|27|19948|28|19976|27|20003|27120030|28|20058!27|20085|27|20112'28
20140|27|20167|2720194 |28|20222|27|20249|27|20276|27|20303|27]20330!28|20358!27120385|27

CO o TO Ab
=
O
=
O

20412/27|20439 27|20466 27/20493 27120520 28/20548|27120575|27120602 27120629 27120656 25
20683 27|20710/27|20737 [26120763 27|207 90 27|20817 27|20844 27|20871/|27120898 27|2092527
20952 26|20978 27|21005 27|21032 27|21059 26|21085 27|21112/27|21139/26|21165/27|21192 27
21219 26|21245 27|21272/27|21299/26|21325 27|21352 26|21378/27|21405 |26| 2143 1/27|214.58 26
21484/27|21511/26|21537]27|21564/26|21590/27| 21617 26|21643/26|21669 27|21696/26|21722/26

21748 27|21775 26|21801 26[|218277/27|21854.|26| 21880 26|21906/25|21932 26|21958/27| 21985 26
22011/26|22037 26|22063/26|22089/26|22115/26|22141 26|22167 27|22194/26|22220 26| 2224626
222772/26|22298|26|22324 26|22350 26|223'76 25| 22401 |26| 224277 26| 22453 26|22477926| 22505 26
22531/26|22557 26|22583 25|22608 |26| 22634 26| 22660 |26|226806 |26| 22712. |25| 2273 '7 26| 22763 6| 2827

22789 25/22814 26|22840/|26|22866 25|22891 26|22917 |26| 22943 25| 22968 |26| 22994 25|23019 26]

0-10 ou oto dl
i
a
—
cs

23045/25|23070/26|23096 25123121 |26/23147/25/23172 26123198 25|23223 |26| 23249 25| 23274. 26
23300/25|23325/25|23350 26123376 25|23401 25|23426 26|23452/25| 23477 25|23502/26| 23528 25
23553 25|235'778/25|23603 26|23629/25|23654 25123679 25123704 |25| 23729 25|237 54 25|23 77 9 26
23805/25|23830/25|23855 25|23880 25|23905 25|23930/25|23955 |25|23980/|25| 24005 25|24030 25
24055/25|24080/25|24105/25|24130 25|24155 25|24180/24|24204 25|24229 25|24254 25/24279|25

24304/25|24329/24|24353 25|24378 25| 24403 /25|24428 |24|24452|25| 2447 7 |25| 24502 25|245 277 24
24551|25|24576|25|24601!24|24625|25|24650|24|24674 25|24699/25|24 724 24|247 48 /25124773 24
24797 25|24822 24124846 25|248771|24|24895 25|24920 24|24944 |25|24969 |24| 24993 25|25018 24 26

25042124|25066 25|25091/24|25115/24|25139/25|2516424|25188 24125212/25|2523 7 |24| 2526 1|24 Bo
25285 2525310 2125334 .24|25358 24/25382/24/25406 25| 25431 24|25455 24|254 79 24|25503 24

—
A

25527 24125551 |/24125575 25125600 /24125624 24|25648/24|256'72|24|25696 24125720 24| 25744 24
25768 24125792 24125816 24125840 2425864 [24125888 24|25912 23| 25935 |24|25959 24|25983 24
2600712426031 /24|26055/24|26079 23126102/24/26126/24126150 24126174 24126198 23126221 24
26245/24|26269/24|26293/23|26316 24|26340/24|26364 [23126387 |24]264 1 1 [24126435 23| 26458 24
26482 23126505 |24/26529 24126553 |23/26576/24/26600|23/26623 2426647 23|266 70 24|26694 23

26717 /24|26741123|26764./24|26788 23126811 23/26834 2426858 23/26881 |24|26905 23|26928 23]| — —— —
26951124|26975123|26998/23|27021 24127045 23| 27068 23|27091 23|27114 |24|27138 23|27 161 23 24

27184 /23127207 24|27231 123127254 23| 27277 23| 27300 23|27323 23| 27346 24|27370 23| 2/7393 23
27410/23|27439/23|27462 23|27485 23|27508 23127531 |23|27554 23|2'75 77 23| 27600 23|27623 23
27646 23127669 23127692 23|27715 23|27738 23/2776 1 23|27784.23| 27807 [23/27830 22]|27852 23

27875 2327898 23|27921/23|27944.23|27967 22|27989 23128012 23|28035 23|28058 23|28081 22
2810323128126 23|28149/22|28171 23|28194[23|28217 |23|28240 22|28262/23|28285 22|2830 7/23
28330 23|2835322|28375|23|28398 23|28421 22128443 23| 28460 22|28488 23|2851 1 22/28533 23
28556 2928578 23|28601 22|28623 23|28646 2228668 23|28691 22|287 1322/28735 23|28758 22
28780/23|28803 2228825 22128847 23| 28870 22|28892 2228914 23|28937 [22|28959 22|2898 1 22

O E
Re
oo
pi kel Fei ke NINN = kel bech Fei DN IND

Sora cal
—
D

29003!23|29026|22|29048!22|29070|22|29092!23|29115|22|29127|22|29159|22|29181|22|29208
221 25|2024822|29270/22|29292 22| 2931422] 20336 2229358 |22|29380/23| 29403 22 2042522
29447 22|29469/22|2949122|29513/22|29535 2229557 22| 29579 22| 29601 2229623 22 29645 22
29667|21|29688|22|29710|22|29732|22|29754|22|29776|22 29798/22|29820/22| 29842 21 29863 22
29885 2229907 22|29929 22|29951 |22| 29973 21129994 2230016 22130038 22|30060 21 30081 22

3010322130125 2130146/22|30168/22|30190|21|30211 |22|30233 22/3025 5 21 3027622130298 22

|
0D OUR DNA

Ra

=
a pl pl ee |
sl EN Dä C O OH DO

GIN sata dð (dl: Zeid, Sosa]: 9» id

e
D
e
=
e

1360

0

d

1

AZ UA dl

4

TABLE 32

Logarithms of Numbers
A EE

2000-2500

d 5

|

AA

dj 8

d| 9

30103
30320
30535
30750
30963

122130125
21130341

22130557
21130771
21130984

21130146
22130363
21130578
21130792
22131006

21130384
22130600
22130814
21131027

22130168 22130190
22130406
21130621
21130835
21131048

21130211
122130428
22130643
21130856
21131069;

22130233 22130255
21130449 22130471
21130664 21130685
22130878 21130899
22131091/21131112

21130276
21130492
22130707
21130920
21131133

22130298
22130514
21130728
22130942
21131154

31175
31387
31597
31806
32015

22131197
21131408
21131618
21131827
20132035

21131218
¡21131429
21131639
21131848
21132056

2131239)
21131450
21131660
21131869
21132077

21131260
21131471
21131681
21131890
21132098

21131281

21131702
21131911
2032118

21131492 21131513

21131323
21131534
21131744
21131952
21132160

2131302

21131723
20131931
21132139

22131345
21131555
21131765
21131973
21132181

21131366
21131576
20131785
21131994
20132201

32222
32428
32634
32838
33041

21132243
21132449
20132654
20132858
21133062

20132263
20132469
21132675
21132879
20133082

21132284
21132490
20132695
20132899
20133 102

21132305
20132510
20132715
20132919
20133122

20132325
21132531
21132736
21132940
21133143

21132346
21132552
20132756
20132960
20133163

20132366)
20132572
21132777
20132980
20133183

21132387
21132593
20132797
21133001
20133203

21132408
20132613
21132818
20133021
21133224

33244
33445
33646
33846
34044

20133264
20133465
20133666
20133866
20134064

20133284
21133486
20133686
19133885
20134084

20133304
20133506
20133706
20133905
20134104

21133325
20133526
20133726 20133746
20133925
20134124

20133345
20183546

20133945
19134143

|
20133365 20|33385
20133566 20133586
20|33766/20|33786
20|33965/20]|33985
20|34163/20|34183

20133405
20133606
20133806
20134005
20134203

20133425
20133626
20133826
20134025
20134223

34242
34439
34635
34830
35025

20134262
20134459
20134655
20134850
19135044

20134282
20134479
19134674
19134869
20135064

19134301
19134498
20134694
20134889
19135083

20134321
20134518
19134713
19134908
19135102

20134341
19134537
20134733
20134928
20135122

20134361
20134557
20134753
19134947
19135141

19134380
20134577
19134772
20134967
19135160

20134400
19134596
20134792
19134986
20135180

20134420
20134616
19134811
19135005
19185199

35218
35411
35603
35793
35984

20135238
19135430
19135622
20135813
19/36003

19135257
19135449
19135641
19135832
18136021

19135276
1935468
19135660
19135851
19136040

19135295
20135488
19135679
19135870
19136059

20135315
19135507
19135698
19135889
19136078

19135334
19135526
19135717
19135908
19136097

19135353
19135545
19135736
19135927
19136116

19185372
19135564
19135755
19135946
19136135

20135392
19135583
19135774
191385965
19136154

36173
36361
36549
36736
36922

1936192
19/36380
19/36568
18/36754
18/36940

19/36211
19136399
18136586
19136773
19136959

18136229
19136418
19136605
18136791
18136977

191386248
18136436
19136624
19136810
19136996 18137014

19136267
19136455
18136642
19136829

19136305
19136493
19136680
19136866
18137051

19136286
19136474
19/3666 1
18136847
19137033

19136324
18136511
18136698
18136884
19137070

18136342
19186530
19136717
19136903
18137088)

37107
37291
37475
37658
37840

18137125
19137310
18137493
18137676
18137858

19137144
18137328
18137511
18137694
18137876

18137162
118137346
19137530
18137712
18137894

19137181
19137365
18137548
19137731
18137912

18137199
18137383
18137566
18137749
19137931

1937218
18137401

18137236
19137420
1937585118137603
18137767 18137785
18137949 118137967

18137254
18137438
18137621
18137803
18137985

19137273
19137457
18137639
19137822
18138003

38021

38561

18138039
3820218138220
38382/17138399
17138578
38739 18138757

18138057
18138238
18138417
18138596
18138775

18138075
18138256
18138435
18138614
17138792

18138093
18138274
18138453
18138632
18138810

19138112
18138292
18138471
18138650
18138828

18138130 18138148
18138310 18138328
18138489 18138507
18138668 18138686
118138846 17138863

18138166
18138346
18133525
17138703
18138881

18138184
18138364
18138543
18138721
18|38899|

38917
39094

39445

17138934
17139111
39270 17139287
18139463
39620 17139637

18138952
18139129
18139305
17139480
18139655

18138970
17139146
17139322
18139498
17139672

17138987
18139164
18139340
17139515
18139690

18139005
18139182
18139358
18139533
17139707

18139023
17|89199|18|39217

1839041

17139058
18139235

17139375 18139393

17139550 18139568

17139724 18139742

17139410
17139585
17189759

18139076

17139602
18139777

17|39252|18
18139428117

18
17

39794

17139811

18139829 17139846

17139863

18139881

117189898 17139915

1839933

17|39950

17

0

d

jl

Cll el) gt

|

4

dj 5

d 6 ld| 7

dj 8

d | 9

d

SAS Ee (O 00 -IO VT H+ OO DD

1361

TABLE 32

Logarithms of Numbers

_ án

2500-3000

d 5 ae d| 9 Prop. parts

18|39881 17139915 17139950
17140054 17140088 17140123
17140226 18140261 17140295
17140398 17140432 17140466
5117|40552/17|40569 17140603 17140637

17|40722/17|40739 17140773 17140807
17140909 1740943 16/4097 6
17141078 16/41111 1741145
17141246 17141280 1741313
1741414 17141447 1741481

coo oue cose

17141581 17141614 16141647
1641747 16141780 17141814
17141913 17141946 1641979
1642078 9511642111 17142144
1642226 17|42243 16/42275/17|42292 16|42308

1642390 16|42406 1642439 /16|42455|17|42472
17142570 16/42602 16142635
16142732 16142765 16142797
16142894 16142927 1642959 16
16|43040!16|43056 16|48088|16|43104|16|43120

com oue toto H|

16143201 16143217 16/43249|16/43265|16/43281
16143377 16143409 1643441
1643537 1643569 16143600
16143696 15143727 16143759
15143838 16143854 16/43870|16/43886|16/43902/1543917

15143996 16|44012./16|44028 16/44044 15|44059 16|44075
16|44154/16|44170 1644201 15|44232
15144326 16144358 16144389
16144483 16144514 1644545
15|44638!16|44654|15|44669|16|44685|15|44700

IO oue coto |

1544793 16/44809 15|44824 1544855
16144948 16144979 1645010
16145102 16145133 1545163
15145255 1545286 1645317
1545408 15|45423 1645439 1545469

15145545 16|45561 15|455 776 15|45591/15|45606/15|45621
1545712 15145743 1545773
1545864 1545894 15/45924
15146015 1546045 15/46075
15|46150|15|46165|15|46180|15|46195|15|46210|15|46225

|P AUD eue eoi |

15146300 15|46315/15|46330/15]46345 1446359 1546374
1546464 15146494 14146523
151466153 1546642 1546672
15146761 14146790 1546820 1:
1546894 15|46909 1446923 15/46938 15146953 1446967

1547041 15|47056 14|47070/15|47085 1547100 1447114 15
14147202 1547232 1547261
1547349 15147378 15147407 15
14147494/15147509/15/147524 1547553
14147625 1547640 14|47654 15147669 1447683 1547698

«O O RIO OU i» 00 DO e

14147770 14|47784!15|4'7799|14|47813|15|47828|1414784215
di 5 el. 7 al %

1362

TABLE 32

Logarithms of Numbers

3000-3500

No.| 0 ld] 1 ld] 2 ld 3 jd 4 ld] 5 ld] 6 jd vd 8 ld] 9 Lal Prop. parts

300 [47712 1547727 14|47741 15J47756/14147770 14147784 15|47799 14|47813 15|47828 14|47842 15 m
301 [47857 14|47871 14|47885 1547900 14|47914 15|47929 14|47943 15|47958 14| 47972 14|47986 15

302 |48001 14|48015/14|48029/15|48044 14|48058 15|48073 14|4808 7 14|48101 15|481106|14|48130 14
303 |48144 15|48159/14|48173 14|48187 15|48202 14|48216/14|48230 14|48244 1548259 14|4 8273 14
304 148287 15|48302|14|48316 14|48330 14|48344 15|48359/14|48373 14|4838 7 14] 48401 15148416 14

305 |48430 14|4844414|48458 15|48473 14|4848 7 14|48501 14|48515|15|48530|14|48544 14|48558 14
306 |48572/14|48586 1548601 14|48615/14|48629 14|48643 14|4865 7 |14148671 15| 48686 14148700 14
307 |48714/14|48728/14|48742/14|48756/14|4877015|48785 14|48799 1448813 14|488277 (1448841 14
308 |48855/1448869/14|48883 14|48897 14|48911 15|48926 14|48940 14|48954.[14|4 8968 1448982 14
309 |48996/14|49010/14|49024 14|49038 14|49052 14|49066 14|49080 14|49094 14|49108 1449122 14

O 0= DOHA NA |

310 |49136/14|49150/14|49164 14|49178/14|49192 14|492006 14|49220 14|49234 14| 49248 14|49262 14
311 |49276/14|49290/14|49304 1449318 14|4933214|49346 14|49360 14| 493741449388 14149402 13
312 |4941514|49429 1449443 14|49457 14|49471 1449485 /14|49499 14|49513 14|495277 14|49541 13
313 [49554 14|49568 1449582 14|49596 14|49610|14|49624 14|49638 13|49651514|49665 14|496 79 14
314 |49693/14|49707 14|49721 13|49734 14|49748 14|49762 14| 49776 14|49790 13]49803 14|498177 14

315 498311449845 1449859 13|49872 1449886 14|49900/14|4991413|49927 14| 49941 |14149955 14
316 49969 1349982 1449996 1450010 14/50024 13|50037 14|50051 |14150065 114150079 13| 50092. 14
917 501061450120 13/50133 14/50147 14|50161 13|50174 14|5018814|50202 13150215 14|50229 14
318 50243 13/50256 14/50270 14/50284 13|50297 14|50311 1450325 13|50338 14150352 13150365 14
319 503791450393 13/50406 1450420 13|50433 14|50447 14|50461 13|50474 14| 50488 13150501 14

320 50515 14150529 13/50542 1450556 13|50569 14/50583 [1350596 14|50610/13|50623 1450637 14
321 50651|13|50664 14150678/13/50691 14150705 13150718 14|50732 13|50745 14150759 13150772 14
322 5078613150799 14150813 [1350826 14|50840 13|50853 13|50866 /14/50880 13150893 14150907 13
323 50920 1450934 13150947 1450961 1350974 1350987 14|5100113|51014 14151028 13151041 14
324 51055 13151068 13[51081|14/51095 13|51108 13|51121 114/51135 13|51148 14|51162 13/51175 13

|
eoo oue coe |

325 51188/14|51202 1351215 13/51228 14/51242 13|51255 13|51268 14|51282 13|51295 13|51308 14
326 5132213151335 13151348 14/51362|13/51375 13|51388 14|51402 13/51415 13151428 13151441 14
327 5145513/51468 13/51481/14|51495 13|51508 13|51521 13/51534 14|51548 13|51561 13151574 13
328 5158714|51601 13151614 13151627 13|51640 1451654 13|51667 13/51680 13151693 13151706 14 13
329 51720|13/51733 13/51746 13/51759 13|51772 1451786 13|51799 13|51812 13|51825 13151838 13

330 518511451865 13/51878 13/51891/13[51904 1351917 1351930 13|519434|51957 13151970 13
331 51983 13/51996 13/52009 13152022 13|52035 13/52048 1352061 14152075 13/52088 13/52101 13
332 52114 13152127 1352140 1352153 13|52166 13/52179 13|52192 13|52205 1315221813152231 13
333 52244 13152257 13/52270 14|52284 13|52297 13/52310 1352323 13|52336 1352349 13/52362 13
334 52375 13/52388 13152401 13|52414 13|52427 1352440 13|52453 13/52466 13/52479 13/52492 12

335 52504 13/52517 13/52530 1352543 [1315 255613152569 1352582 13|52595 13152608 13152621113
336 52634 13152647 [13152660 13/52673 13/52686 1352699 12/52711 13|52724 13152737 13152750 13 12
337 5276313152776 13152789) 13152802 13/52815 12/52827 1352840 13152853 1352866 13152879 13
338 52892 13152905 112152917 13/52930 13/52943 1352956 1352969 13|52982 12152994 13153007 all — ——
339 53020 13/53033 13153046 1253058 13|53071|13|53084 18153097 18153110 1253122113153135 13

Soo |

340 9314813/5316112/53173 13153186 13/53199 13/53212 12/53224 13/53237 13/53250 13153263 12
341 53275 13/53288 13/53301/13/53314 12/53326 13153339 13/53352 12/53364 13153377 13153300 13
342 53403 12/53415 13/53428 131/53441 12/53453 13/53466 13|53479 12/53491 18153504 13153517 12
343 93529 13153542 13153555 12153567 13/53580 13/53593 12153605 |13153618|13153631 12153643

344 53656 12/53668 13/53681 13/53694 12/53706 13/53719 13/53732 12153744 13/53757 12/53769 13

pal
N

345 53782 12153794 13153807 13/53820 12153832 13/53845 12153857 1353870 12153882 13/53895

346 53908 12153920 13153933 12153945 13153958 12153970 13/53983 12153995 13/54008 12134020 13
347 24033 [12154045 13154058 1254070 13|54083 1254095 13)54108 12154120 1315413312154145
348 84158 12/5417013/54183 12154195 13/54208 12154220 12|54233 12154245 13|54258 12554270
349 51288 12154295 112154307 13154320 12154332 1354345 19154357 13|54370 12|54382 12554394

c 0 N OD OH GU D |
HOMO NOS NA

m ka

350 54407 12154419 19154432 1254444 12054450 13154469 12/5481 13/54494 1254500 1254518
No. Ojal: 5d 25 di S55 qp dl 5&"d- Goal Zell 8 Gl) dl

1363

TABLE 32

Logarithms of Numbers
eee

3500-4000

No. | 0 d 1 d 2 d 3 ld] 4 laq 5 la] e Jal 7 Jal s Jal 9 Jal} Pro. parts

350 [5440712154419 13154432 12154444 12/54456 13|54469 12|54481 13154494 12154506 12154518|13
351 [5453111254543 12154555 1354568 1254580 1354593 12/54605|12154617|13154630|12/54642 12 13
352 [5465413154667 12154679 1254691 13|54704 12/54716 12/54728 13|54741 12] 54753 12154765 12l
353 [5477713154790 12154802 12/54814 13[54827 1254839 12| 54851 13|5486412|54876 12154888 12
354 |54900 13|54913 12154925 1254937 |12/54949 13|54962 12|54974 12]|54986 12] 54998 13|55011l12

|

355 [55023 12/55035 1255047 13155060 12/55072 12/55084 1255096 12155108 13[55121|12155133 12
356 |55145/12/55157 12/55169 13[55182/12|55194|12]55200 12]55218/12]5523012|55242/13|55255 12
357 [552671255279 12/55291 12155303 12|55315 1355328 12|55340 12|55352 1255364 12/553 76 12
358 |55388/12/55400 13|55413 12/55425 12|55437 12|55449|12|55461 12155473 12|55485 12155497 12
359 |55509/13|55522/12/55534 12/55546/12|55558 12|55570/12| 55582 |12|55594 12|55606 12155618 12

oo otc |
NOVIA

— jmd

360 155630112/55642112/55654/12155666/12/55678 13155691|12155703 12155715 /12155727/12155739 12
361 |55751|12/55763|12|55775|12/55787|12|55799|12|55811|12|55823|12|55835!12|55847|12)55859|12
362 155871 12/55883/12155895 12155907 12]55919/12]|55931]12]|5594312]|55955 12|55967/12|55979112
363 |55991|12/56003|12|56015|12|56027|11|56038|12|56050|12|56062|12|56074!12|56086|12|56098|12
364 |56110|1256122 12/56134|12)56146|12156158 12156170|12156182 12156194 11156205 12156217|12

=
D

365 |56229|12|56241|12]56253|12156265|12|56277|12|56289|12|56301|11|56312|12|56324|1256336|12
366 |56348/12/56360 12/56372/12/56384 1256396 11156407 1256419 1256431 1256443 12|56455 12
367 |56467 11156478|12156490 1256502 1256514 12156526 1256538 11156549 12/56561|1256573|12
368 156585 1256597 11156608 1256620 12156632 12156644|12/56656 11156667 1256679 12]56691 12
369 [5670311156714 12156726 12156738 | 12156750) 11|5676112/|56773 12156785 1256797 11156808|12

370 156820 12156832 12156844 11156855 12156867 1256879 12|56891 11|56902 12/56914|12/56926 11
371 [56937 12/56949/12156961 11156972 1256984 12156996 12/57008 11[57019/12/57031 12]|57043|u
372 |57054/12/57066 1257078 11157089 1257101 12]|57113|1]57124 1257136 12157148 11157159 12
373 |5717112/57183|1|57194(12]|57206 11|57217 1257229 12/57241 11|57252/12/57264 12157276 11
374 157287 1257299 1157310|12/57322|1257334 12157345 12/5735 7 11|5 7368 |12/57380 KE EH

OO DOHA GO D e |
oND N=

Ha j

375 |57403|1257415|11|57426|12|57438|11|57449|12|57461!12|57473|11|57484|12|57496|11|57507|12
376 [57519111157530/12/57542 111157553 11257565 11157576 1257588 12|57600|11[57611 12]57623 11
377 |57634|12|57646|11|57657|12/57669|11|57680|12|57692|11|57703|12/57715|11|57726|12|57738|11
378 |5774912]57761/11]57772 1257784 |1|57795 12/57807 11|57818 12157830 11157841 11157852 12
379 |57864/11]57875/12/57887 11|57898 12157910 11/57921 1257933 11|5794411|57955 12/57967 11

na
m=i

|
|

380 |57978|12|57990|11|58001|12|58013|11|58024|11|58035|12)58047|11|58058|12|58070|11|58081|11
381 [58092 12158104 11/58115|12/58127/11[58138 11158149 12/5816111/58172 1258184 11158195111
382 |58206/12|58218 11158229 11158240/12158252 111158263 11158274 12[58286|11158297 [1258309 11
383 [5832011158331 12/58343|11|58354 11158365 |12/58377/11158388|11158399/11158410 12/58422/11
384 158433 11158444 12158456 11158467 11158478 12/58490 11[58501 11|58512/12/5852411/58535 11

385 [58546 11158557|12/58569/11158580|111158591|11158602 12158614 11158625/11158636 11158647/12
386 [58659 11158670|11158681|11158692112158704 11158715 11158726 11158737/12158749 11158760|11
387 158771 111158782/12158794 11158805 |11158816|11158827 11158838 12/58850/1158861 1115887211 ROL PER:
388 [58883|1158894112/|58906/11/|58917/11/|58928 11158939 11158950 11|5896112|58973 11158984 11

389 158995 11159006|11159017|11159028|12159040 11159051/11159062 11159073/11[59084 1115909511

O 0 =D OA 0 nN-
© O o ND AUN

=

| 390 159106 12/59118111159129/11/59140/11/59151/11/59162/11/59173 11/59184 11/59195 12 59207 11
391 159218 11159229 11159240 11159251|11[59262 11159273 1115928411159295 11/59306 12 59318 11 10
392 |59329|11|59340|11|59351|11|59362|11|59373|11|59384|11159395|11|59406|11|59417|11 ae 11 —
393 159439/1159450|1|[59461 1159472159483 |11|59494 12/59506 11595177 11159528 11 E 11
394 |59550 11159561 11159572 11159583 11159594 (11159605 11/59616 11/59627 11/59638 11159649 11

395 |59660 11159671 11159682 11159693 11159704 11159715 11159726 11159737/11[59748 1115975911
396 59770 10159780 11159791 11159802 11/59813/11/59824 11159835 /11/59846|11/59857 11 59868 11
397 [59879 11159890 11159901 11159912 11159923 11159934|11[59945|11/59956 10159966 11 g 11
398 |59988 11159999 11160010 11160021 11160032 11[60043[11[60054|11/60065 11160076 10 os 11
399 |60097|11160108|11160119|1116013011160141 11160152 11[60163 10/60173/11/60184 1116019511

OO N D GT MN |
Koko ab DOHA NN

|

400 [60206|1:1160217/1:1160228 11160239 10]6024.9|11]60260| 116027 1 11160282 11160293 11160304 1

wal o kd ai da o kdl a ala A ds ad

1364

TABLE 32

Logarithms of Numbers

4000-4500

No. OR dit TN die 240 dl 15 di 49 IO CAGA IA Id s
400 [60206/11/60217/1160228/11160239/10|60249/11/60260/11|6027 1/11160282/11/60293
401 |60314|11160325111160336/11160347/11160358/11160369|10/60379/11160390|11160401
402 [60423 1060433 11160444. 11160455) 11160466) 1160477 1060487 1160498 11160509
403 [60531/10[60541/11|60552/11[60563/11[60574/10|60584/11[60595/11/60606/11160617
404 |60638|11160649|11160660|10/60670|11160681|11160692|11160703|10/60713|11160724

d Prop. parts

=

jm
m
m

405 |60746/10/60756|11160767|11160778|10/60788|11160799|11160810|11160821|10/60831
406 |60853|10/60863|11160874|11160885|10/60895|11160906|11160917|10/60927|11160938
407 |60959|11|60970|11|60981|10]60991!11]61002|11|61013|10]61023|11]61034!11|61045
408 |61066/11161077/1061087 11[61098/11/61109/10]61119/11161130/10/61140/11]61151
409 |61172|11|61183|11|61194|10]61204|11|61215!10]61225|11|61236|11|61247!1061257
410 |61278|11|61289|11|61300|10]61310!11|61321|10]61331|11|61342|10]61352|11|161363
411 [61384 11161395/10/61405/11]61416|1061426 11/61437|11161448/1061458 11161469
412 [61490 1961500 11/61511/10]61521/|11/61532 10]61542/11161553/1061563 11161574
413 [61595 11161606 10/61616|11161627|10/61637/11161648|10161658|11161669|10161679
414 [6170011161711 10161721 10/61731|11161742 1061752 11161763 10161773|11161784

=
2.

O 0 NOO OU WN H |

Qo 00-10»4Q2bt-—

pi

415 [61805|10/61815|11[61826|10/61836|11161847|10/61857|11161868|10/61878|10161888
416 [61909|11[61920|10/61930/11161941|10/61951|11161962/10/61972|10161982 11161993
417 |62014|1062024|10]62034|11|62045| 10162055} 11162066) 10162076 10/62086|11162097
418 |62118/10[62128/10/62138 11162149 10/62159|11162170|10/62180 10/62190|11162201
419 |62221|11J62232 10162242 1062252 11162263 10/6227 3} 11162284 10162294 10162304

62325|10/62335|11162346|10/62356 10/62366 11/62377/10162387 10/62397|11162408
421 [62428|11162439|10/62449|10/62459|10/62469|11162480|10/62490|10162500 11162511
422 [62531/11162542|10/62552 1062562 10/62572|11162583|10162593|10162603|10162613
423 [62634/1062644|11162655 10162665 1062675 10162685 |11162696 10162706| 10 62716
424 |62737|10/62747|10/62757|10/62767|11J62778 1062788 10] 627 98) 10162808 10162818

=

o
ke
©

425 |62839|10/62849|10/62859|11162870|10/62880|10/62890|10162900|10162910|11162921
426 162941) 10}6295 1) 10]62961)11]6297 2) 10]62982! 1062992 10163002 10163012|10163022
427 |63043/|10/63053/10/63063/10[63073/10/63083 11163094 10163104 10163114110163124
428 |63144/1163155/10/63165/10/63175/10/63185|10]63195 10163205 10163215 10163225
429 [63246|10/63256 10/63266 10/63276|10163286 10/63296/10163306|11 6331710163327

=
i=}

Kolo os Norādi MN |

O 0 N OD Oia MN

430 [63347 10163357 10/63367|10/63377 10/63387|10/63397|10163407|10l63417 11163428
431 |63448|10/63458|10/63468|10/63478 10163488 1063498 10163508 10163518 1063528
432 [63548 10/63558|10/63568 1163579 /10]63589 10163599 10/63609 10163619 1063629
433 [63649 10/63659|10/63669 10163679 1063689 10163699 |10163709 10163719 1063729
434 |63749/10/63759/10/63769|10/63779/1063789/1063799/1063809110163819 1063829

435 |63849/10/63859 10/63869|10/63879 1063889/1063899 1016390910 63919 1063929
436 163949) 10/63959|10/63969|10/63979| 9|63988|10163998|10164008 10 64018|10/64028
437 |64048|10/64058|10/64068|10/64078 10164088) 10164098 10164108 101641 18 1064128
438 [64147 1064157 10/64167 10/64177|10/64187 10164197 1016420710 6421710164227
439 [64246 10164256 10/64266 10164276 1064286 10164296 10164306 10164316 10164326

440 [64345|10/64355|10/64365|10/64375 1064385 10164395 9164404 10164414 10164424
441 [64444 10/64454/10/64464| 9/64473 10164483 10164493 10 64503 10/64513|10164523
442 [6454210164552 10164562 10164572 10164582 9645911064601 1064611/10/64621
443 |64640/10/64650/10/64660 10164670 10164680 916468910 64699 1064709 1064719
444 [64738 10164748 10/64758|10/64768| o/64777|10164787|10164797 10/64807| 9164816

=
2
©

|

445 164836 10164846) 10/64856| 9164865] 10164875] 10164885) 10 64895) 9164904 1064914
446 [64933 10/64943|10/64953 10164963 91649721 10164982 10 64992 10165002 9165011
447 165031) 9[65040|1065050 10165060 10165070| 96507910 65089 |10/65099| 9165108
448 |65128| 9165137/10/65147 10/65157 10165167 9165176 10 65186 10/65196| 9165205
449 165225) 9165234 10165244 10/65254 9165263 10165273 10165283} 9165292) 1065302

=
e

O MW IC O Ha GO DO em |

00 N O0» Cu PWN

450 [653211065331 10/65341| 96535010165360 9165369) 10/65379|10165389| 9165398
Now} 01d] Is ld). 2s idl: Salle dla tS lal eu IES

1365

TABLE 32

Logarithms of Numbers
—

4500-5000

dis 2 d 4 d|5 ld 6 d 7 a s Ia 9 lalf Prop. parts
10165341 10/65360| 965369 10165379/10/65389| 9165398/1016540810
1065437 9J65456 10165466 9/65475/10165485 10165495! 9165504110 10
10165533 9165552 10165562 9|65571|10]65581|10]65591! 9165600 10 —
10165629 9165648 1065658, 9|65667|10]65677| ol65686 10165696 10] 1 | 1
10165725 10165744] 9]65753 10/65763| 9165772 10165782 10165792| 9 3 E
9165820 9[65839 10[65849| 9|65858|10]65868| o]65877 10165887 ai 4 | 4
10165916 1065935 9]65944 10[65954 9[65963/10]65973| ol65982 10ll 5 | 5
1066011 1066030| 9]66039!10]66049| 9o[66058 10166068 | 9|66077|10| 6 | 6
1066106 9[66124/10[66134| 9[66143/10]66153| 9166162 10166172! all 7 Á
9166200 9166219 10/66229| 9166238] 0|66247|10166257| 9166266 10 s à
66276| 9[66285/10]66295 411066314 9|66323| 9663321066342! 9166351/10166361| 9
1066380, 966389 10166408} 9[66417 10/66427| 9[66436| 966445 /10166455| 9
1066474! 9166483 1066502| 9166511/10/66521| 966530! 966539110166549! 9
9166567 1066577 1066596| 9166605, 916661410[66624| 9166633) 916664210
9|66661|10166671 9166689}10166699| 9166708] 9[66717/10166727| 9166736] 9
9166764 10166783] 9|66792 9|66801|10]66811| o[66820| 916682910
9166857 9166876] 9[66885| 9|66894|1066904| o[66913| 966922 10
9166950 9166969] 9166978] 9|66987|10]66997| 9/67006! 967015 10
9167043 10167062! 9167071) 9167080| 9[67089 10[67099| 9167108] 9
9167136 9|67154|1067164| 9|67173| [67182 9/67191|10167201| 9
9167228 1067247 9167256] 9|67265| 9|67274|10]67284! 9167293] 9
10167321 9167339] 9167348] 9|67357|10|67367| 967376, 967385 9 9
10167413 9167431) 9167440) o[67449 10167459 9167468) 9167477] A | |
9167504 9|67523| 9167532) 9167541) o[6755010/67560| 9167569] ol] 1 | 1
9167596} $ 9|67614|1067624| 9167633] 9]67642| 9167651) 9167660] ol] 2 | 2
akts
9167688 7| 9167706] o|67715 9167724| 9167733] 9167742|10167752| all 4 | 4
9167779 967797] 9167806] 9|67815|10|67825| 9167834) 9167843] all 5 | 4
9167870 967888] 9|67897| 9]67906 10167916 9167925) 9167934] ol] 6 | 5
9167961 967979] 9167988] 9167997] 0|68006| 968015) 96802410] 7 | 6
968052 9|68070| 9|68079| 9168088] 9|68097| 9168106] 9168115] all g | 7
9| 8
9168142 9168160] 9168169] 9168178] 9168187] 9168196) 916820510
9168233 9168251) 9168260! 9168269] 9168278) 9|68287| 9168296] 9
968323] < 9168341) 9168350) 9168359] 9168368) 9[68377| 9168386] 9
9168413 9168431) 9[68440| 9168449] 9168458) 9|68467| 9168476] 9
8168502 968520] 9168529] 9168538] 9168547| 9168556) 9168565) 9
9168592 ol68610| 9168619] 9168628] 9168637) 9168646] 9|68655| 9
8168681 968699) 9168708) 968717! 9168726) 9168735] 9168744] 9
9168771 968789] sl68797 9168806] 9168815] 9168824) 9168833) 9
9168860 9168878| 8168886) 9168895] 9168904) 9[68913| 9168922) 9
9168949 38168966] 9168975 9168984] 9168993] 9169002) 9169011) 9
9169037 9169055! 9169064 9169073] 9169082) s[69090| 9169099] 9
9169126 ol69144| sl69152| 9169161! 9169170) 9[69179| 9[69188| 9 8
9169214 9169232! 9169241] 8169249] 9169258) 9169267) 969276 ai IT
8169302 9]69320| 2|69329| 2169338) 3169346) 9169355) 9|69364| of | | 1
9169390 969408| 9]69417| 3169425] 969434) 9169443] 9|69452| of 5 | 2
9169478 9|69496| 5169504 969513] 9[69522 9169531, 5|69539) 9 a E
9169566 9169583} 9|69592| 9169601] s[69609| [69618 9169627) oļ| 5 | 4
9169653 done? 1 8|69679| 9169688] 9]69697| s[69705 9169714 9| g | 5
38169740 9169758] 9[69767| 8|69775| 9169784) 9|69793| s|69801| 9| 7 | 6
3169827 169845] 9169854] 8|69862| 9|69871| 9|69880| 869888 dl g | e
3169914 9169932! 8169940) 9169949] 9169958] 8169966) 9169975) 9 iaa
al 2 d a 185 ale dar zal rali so dl 99 (d

1366

TABLE 32

Logarithms of Numbers

5000-5500

dj 1 di? 4 dl" 5% (alt Geile ASIA Sia die 19

69897) 9169906 969932 8169940} 9169949) 9169958) 8|69966| 969975
69984 3169992 8|70018| 970027) 9/70036| 8|70044| 9170053) 970062
70070) 9/70079 9|70105| 9[70114| 8[70122| 9170131) 9|70140| 8[70148
70157| 8|70165 8|70191| 9170200| 9[70209| 8|70217| 9|70226| 8|70234
70243| 9170252 9|70278| 8170286] 970295| 8|70303| 9170312) 970321

Prop. parts

70329| 9170338 9|70364| 8|70372| 9/70381| 8|70389| 9|70398| 8|70406
70415| 9170424 8|70449| 9170458) 9170467| 8|70475| 9|70484| 8|70492
70501| 8|70509 9|70535| 9170544| 8|70552| 9|70561| 8|70569| 9170578
70586| 9|70595 )12| 9/70621| 8|70629| 9170638) 8|70646| 9|70655| 9|70663
70672) 8|70680 9/70706| 8|70714| 9/70723| 8|70781| 9|70740| 9170749

œ o w o o | œ o owo | A

A o

70757| 9170766 8170791) 9170800} 8|70808| 9170817) 8170825) 9/70834
70842) 9/70851 8|70876| 9[70885| 8|70893| 9170902) 8|70910| 970919
70927| 870935 970961! 8|70969| 9|70978| 8|70986| 9|70995| 8|71008
71012| 8|71020 9|71046| 8|71054| 9/71063| 8|71071| 8[71079| 971088
71096, 971105 8|71130| 9[71139| s[71147 8|71155| 9|71164| 8|71172

«O 00 ei OO OO

71181) 3/71189 8171214) 9171223) 3171231) 9|71240| 8|71248| 9171257
71265} 8171273 9|71299| 8|71307| 8|71315| 9|71324| 8171332) 9171341
71349) 3171357 9171383) 8|71391| 8|71399| 9171408] s|71416| 9|71425
71433) 8|71441 8171466) 9171475) 8|71483| 9171492) 8[71500| 8|71508
71517) 8171525 8171550] 9171559) 8171567] 8|71575| 971584) 871592

Qo © 00 OO OO

71600) 9/71609 9171634 | 8|71642| 8171650] 9|71659| 8|71667| 8|71675
71684| 3171692 9| 871717, 3171725] 9171734) 8171742) 3171750) 9171759
71767) 871775 92) 8171800) 9171809 871817, 8[71825| 9|71834| 3171842
71850) 8|71858 871883, 9|71892| 871900) 8171908) 9171917} 8|71925
71933) 8|71941 8171966] 9171975) 8171983] 8|71991| 8|71999| 972008

o

72016 8172024 8172049] 8|72057| 9|72066| 8|72074| 8|72082| 8|72090
72099 8|72107 9172132 8|72140| 8|72148| 8|72156| 9|72165| 8|72173
72181) 8|72189 8|72214| 8|72222| 8|72230| 9172239) 8|72247| 8|72255
72263| 9172272 8|72296| 8|72304| 9172313] 3172321! 8|72329| 8|72337
72346| 8|72354 8|72378| 9/72387| 8|72395| 8|72403| s|72411| 8172419
72428) 8|72436 2| 8|72460| 9172469] 8|72477| 8|72485| 8|72493| 8|72501
72509| 9172518 8|72542| 8|72550| 8|72558! 9|72567| 8|72575| 8172583
72591) 8|72599 q 8|72624| 8172632) 8172640) 8172648] 8172656] 9|72665
72673) 872681 8172705! 8172713} 9172722) 8|72730| 8172738) 8|72746
72754| 8172762 8172787) 8172795] 8172803, 8|72811| s|72819| 8|'72827

«o «o oo co «o | oo o0 oo w o

NODOT eV DOD

Oo OO OO OO OO

72835| 8|72848 8|72868 8|72876, 8|72884| 8|72892 8/72900| 8172908
72916| 9172925 8|72949| 8172957| 8|72965| 8|72973| 8|'72981| 8|72989
72997| 9173006 8173030) 8|73038| 8173046, 8|73054| 8|73062! s|73070
73078| 8|73086 973111) 8173119) 8|73127| 8|73135| 8173143] 8|73151
73159| 8|73167 8|78191| 8|73199| 8|73207| 8|73215| 8|73223| 8|73231

OO OO OO 00 OO

73239] 3173247 973272) 8173280! 8|73288| 8173296] 8173304] s|73312
73320) 3173328 8173352) 8173360, 8173368! 8173376} 8173384] 8173392
73400) 8173408 4| 8173432, 8173440) 8173448) 8173456) 8173464) 3173472
73480) 8173488 8173512) 8173520) 8173528! 8173536) 8173544) 8173552
73560} 3173568 8173592) 873600) 8|73608| 8|73616| 8173624) s|73632

73640) 8/73648 8173672) 7|73679| 8|73687| 8|73695| 8|73703| 3173711
73719| 8|78727 8173751) 8|73759| 8|73767| 8|73775| 8|73783| 8|73791
73799 8173807 71173830| 8173838) 8173846, 8173854) 8173862) 8173870
73878) 8173886 8|78910| 8173918) 8173926) 7|73933| 8173941] 8173949
73957) 8173965 873989) 8173997] 8|74005| 8174013] 7174020) 8174028

74036} 8|74044 874068) 8174076) 8174084] 8|74092| 7174099) 8174107
Gh 2 : d 4 d| 5 jd 6ld| *7lal. 35 jal 9

|
|

OO OO OO OO OO

DO GI He GO DD

1367

TABLE 32

Logarithms of Numbers
ET nn

5500-6000

aj UP rele 26 di’ SP die ara? Brae eio qe vitia sitial bio Prop. parts

8174044] 8174052) 8174060} 8174068) 8174076) 8174084] 8|74092| 7|74099| 8174107
8174123] 8174131) 8|74139| 8|74147| 8174155) 7174162 3174170) 8|74178| 8174186
8|74202| 8174210} 8|74218| 7174225) 8174233) 8174241) 3174249] 8174257] 8174265
7|74280| 8|74288| 8174296) 8|74304| 8|74312| 8|74320| 7174327 38174335) 8174343
8[74359| 8|74367| 7|74374| 8|74382| 8|74390| 8174398) s[74406 8|74414| 7|74421

|

8|74437| 8|74445| 8174453) 8|74461| 7|74468| 8|74476| 8|74484| 3174492] 8|74500
8|74515| 8|74523| 8|74531| 8|74539| 8|74547| 7|74554| 8|74562| 8|74570| 8|74578
7|74593| 8|74601| 8|74609| 8|74617| 7|74624| 8|74632| 3174640) 8|74648| 8|74656
8|74671| 8|74679| 8|74687| 8|74695| 7|74702| s|74710| 8|74718| 8|74726| 7|74733
8|74749| 8|74757| 7|74764| 8|74772| s[74780| 8|74788| 8|74796| 7|74803| s|74811

8|74827| 7174834 8|74842| 8|74850| 8|74858| 7174865 8|74873| s|74881| 8|74889
8|74904| 8|74912| 8|74920| 7|74927| 8|74935| 8|74943| 7|74950| 8|74958| 8|74966
7|74981| 8174989) 8|74997| 8|75005| 7|75012| 8|75020| 8|75028| 7175035] 8|'75043
8|75059| 7175066 8|75074| 8|75082| 7|75089| 8|75097| 8|75105| 8|75113| 7|75120
8|75136| 7|75143| 8|75151| 8|75159| 775166! 8|75174| 8|75182| 7|75189| 8|75197

NOOOTPWNNrH

8175213) 7175220 8175228) 3175236) 7|75243| 3175251) 8175259] 7175266) 38175274
7175289) 8|75297| 8175305) 7|75312| 8175320) 8|75828| 7175335 8175343) 8|75351
8175366) 8|75374| 7|75381| 8175389] 8|75397| 775404 | 8175412) 8175420) 7175427
7175442) 8175450) 8175458) 7|75465| 8175473] 8|75481| 7175488 3175496) 8|75504
8175519) 7175526) 8175534) 8|75542| 7175549] 3175557) 8175565] 7|75572| 8/75580

8175595] 8|75603| 7|75610| 8|75618| 8|75626| 7|75633| 8|75641| 7|75648| 38175656
7|75671| 8|75679| 7|75686| 8|75694| 8|75702| 7|75709| 8|75717| 7|75724| 8|75732
7175747 8|75755| 7|75762| 8|75770| 8|75778| 7|75785| 8|75793| 7|75800| 8|75808
8|75823| 8|75831| 7|75838| 8|75846| 7|75853| 8|75861| 7|75868| 8|75876| 8|75884
8|75899| 7|75906| 8|75914| 7|75921| 8|75929| 8|75937| 7|75944| 8|75952| 7|75959

7|75974| 8|75982| 7|75989| 8|75997| 8|76005| 7|76012| 8|76020| 7|76027| 8|76035
8|76050| 7|76057| 8|76065| 7|76072| 8|76080| 7|76087| 8|76095| 8|76103| 7|76110
7|76125| 8|76133| 7|76140| 8|76148| 7|76155| 8|76163| 7|76170| 8|76178| 7176185
7176200 8|76208| 7|76215| 8|76223| 7|76230| 8|76238| 7|76245| 8|76253| 7|76260
7176275 8|76283| 7|76290| 8|76298| 7/76305 8|76313 7|76320| 8|76328| 7/76335

7|76350| 8|76358| 7|76365| 8|76373| 7|76380| 8|76388| 7|76395| 8|76403| 7|76410
7|'76425| 8|76433| 7|76440| 8|76448| 7|76455| 7|76462| 8|76470| 7|76477| 8|76485
8176500 7|76507| 8/76515| 7|76522| 8|76530| 7|76537| 8|76545| 7|76552| 7|76559
7|76574| 8|76582| 7|76589| 8|76597| 7|76604| 8|76612| 7/76619| 7|76626| 8|76634
8|76649| 7176656 8|76664| 7|76671| 7|76678| s|76686 7|76693| 8|76701| 7|76708

7|76723| 7|76730| 8|'76738| 7|76745| 8|76753| 7|76760| 8/76768| 7|76775| 7|76782
7176797 s|76805 7|76812| 7|76819| 8|76827| 7176834 8|76842| 7|76849| 7|76856
7|76871| 8|76879! 7|76886| 7|76893| 8|76901| 7|76908| 8|76916| 7|76923| 7|76930
7176945) 8|76953| 7|76960| 7176967| 8|76975| 7|76982| 7|76989| 8|76997| 7177004
7177019) 7|77026| 8|77034| 7|77041| 7|77048| 8|77056| 7|77063| 7|77070| 8|77078

877093, 7177100| 7177107) 8|77115| 7|77122| 7|77129| 8|77137| 7|77144| 7|77151
7177166 7|77173| 8|77181| 7177188 7|77195| 8|77203| 7|77210| 7|77217| 8|77225
8|77240| 7|77247| 7|77254| 8|77262| 7|77269| 7|77276| 7|77283| 8|77291| 777298
8|77313| 7|77320| 7|77327| 8177335 7|77342| 7177349) 8|77357| 7|77364| 7|77371
7177386 7|77393| 8|77401| 7177408 7|77415| 7|77422| 8|77430| 7|77437| 7|77444

7177459| 7177466) 8|77474| 7|77481| 7|77488| 7|77495| 8|77503| 7|77510| 7|77517
7|77532| 7177539) 7|77546| 8|77554! 7|77561| 7|77568| 8|77576| 7|77583| 7|77590
g|77605! 7177612| 7|77619| 8|77627| 7|77634| 7|77641| 7/77648| 8|77656| 7177668
7177677 8|77685| 7177692 7|77699| 7|77706| 8|77714| 7|77721| 7177728) 7|77785
7|77750| 7|77757| 7177764 8|77772| 7|77779| 7|77786| 7|77793| 8|77801| 7|77808

OQ» O0» Ov E S HR

7|77822| 8|77830| 7|77837| 7|77844| 7|77851| 8/77859| 7|77866| 7|77873| 7|77880

de RGB. GR al SK a alai" Al 6 (dal wd" s td] 9

1368

78104

d| 1

d 2

dj 3

TABLE 32

Logarithms of Numbers

6000-6500

dj 4

dj 5

dj 6

died

d 8

diy 9

d

7177822
8177895
7177967
7178039
7178111

8177830
7177902
7177974.
7178046
7178118

7177837
7177909
7177981
7178053
7178125

7177844
7177916
7177988
8178061
7178132

7177851
3177924
8177996
7178068
8178140

8177859
7177931
7178003
7178075
7178147

7177866
7177938
7178010
7178082
7178154

7177873
7177945
7178017
7178089
7178161

7177880
7177952
8178025
8178097
71/8168

7
8
7
7
8

78176
78247
78319
78390
78462

7178183
7178254
7178326
8178398
7178469

7178190
8178262
7178333
7178405
7178476

7178197
7178269
7178340
7178412
7178483

7178204
7178276
7178347
7178419
7178490

7178211
7178283
8178355
7178426
7178497

8178219
7178290
71718362
7178433
7178504

7178226
71718297
7178369
7178440
8|78512

7178233
8178305
7178376
7178447
7178519

7178240
7178312
7178383
3178455
7178526

78533
78604
78675
78746
78817

7178540
7178611
7178682
7178753
7178824

7178547
7178618
7178689
7178760
7178831

1178554
7178625
7178696
7178767
71718838

78561
78633
78704
78774
78845

8178569
7178640
7178711
7178781
7178852

7178583
7178654
7178725
7178796
7178866

7178590
7178661
778732
7178803
71178873

7178597
7178668
7178739
7178810
7|78880

78888
78958
79029
79099
79169

7178895
7178965
7179036
7179106
7179176

7178902
7178972
7179043
7179113
7179183

7178909
7178979
7179050
7179120
7179190

78916
78986
79057
79127
79197

7178923
7178993
7179064
7179134
7179204

78937
79007
79078
79148
79218

7178944
7179014
7179085
7179155
7179225

78951
79021
79092
79162
79232

79239
79309
79379
79449
79518

7179246
7179316
7179386
7179456
7179525

7179253
7179323
7179393
7179462
7179532

7179260
7179330
7179400
7179470
7179539

79267
79337
7179407
71119477
7179546

7179274
7179344
7179414
7179484
7179553

79288
79358
79428
79498
79567

7179295
7179365
7179435
7179505
7179574

79302
79372
79442
79511
79581

79588
79657
79727
79796
79865

7179595
7179664
71179734
7179803
7179872

7179602
71179671
7179741
7179810
7179879

7179609
7179678
7179748
7179817
7179886

7179616
7179685
6179754
7179824
7179893

79623
79692

79761) 7

79831
79900

6179906

19637
79706
79775
79844
79913

7179644
7179713
7179782
7179851
7179920

79650
79720
79789
79858
79927

79934
80003
80072
80140
80209

7179941
7180010
7180079
7180147
7180216

7179948
7180017
6180085
7180154
7180223

7179955
7180024
7180092
7180161
6180229

7179962
6/80030
7180099
7180168
7180236

7179969
1180037
7180106
7180175
71180243

6179975
7180044
7180113
7180182
7180250

79982
80051
7180120
6180188
71180257

7179989
7180058
7180127
7180195
7180264

7179996
7180065
7180134
7180202
718027 1

80277

) 180346

80414
80482
80550

7180284
7180353
7180421
7180489
7180557

7180291
6180359
7180428
7180496
7180564

7180298
7180366
6180434
6180502
6180570

7180305
7180373
7180441
7180509
7180577

7180312
7180380
7180448
7180516
71180584

6190318
7180387
7180455
7180523
7180591

7180325
6180393
7180462
7|80530
7|80598

7|80332
7180400
6180468
6180536
6[80604

7180339
7180407
7180475
7180543
7180611

80618
80686
80754
80821
80889

7180625
7180693
6180760
7180828
6180895

7180632
6180699
7180767
7180835
7180902

6180638
7180706
7180774
6180841
7180909

7180645
7180713
7180781
7180848
7180916

7180652
7180720
6180787
7180855
6180922

7180659
6180726
7180794
7180862
7180929

6180665
7180733
7180801
6180868
7180936

7180672
7180740
7130808
7180875
7180943

7180679
7180747
6180814
7180882
6180949

80956
81023
81090
81158
81224

7180963
7181030
7181097
6181164
7181231

61980969
7181037
7181104
781171
7181238

7180976
6181043
7181111
71181178
7181245

7180983
7181050
6181117

6181184)

6181251

7180990
7181057
7181124
7181191
7181258

6180996
7181064
7181131
7181198
7181265

7181003
681070
6181137
6181204
6181271

7181010
71181077
7181144
7181211
71181278

1181017
71181084
781151
71181218
71181285

81291

7181298

7181305

6181311

71181318

71181325

6181331

71181338

1181345

6181351

Prop.

00 NC OA GO DD |

OO RO G4 U9 DO — |

parts

NO O Gra VDO DO | 00

1

DO DNA LJ Šo An

NOA A GO DO DO A | D

dif i

dj 2

oi g

d| 4

dl 5

d| 6

d 7

d 8

d 9

inā

1369

TABLE 32

Logarithms of Numbers
Fr

6500-7000

de Us id" 25/d: 3). (dls A dls Sin ale 6 idly Tin ldle Siulalr 9 Prop. parts

d
81291 7181298 7181305 6/81311| 7|81318| 7|81325| 6|81331| 7[81338 7181345 6|81351| 7
81358 7181365 681371 7|81378| 7[81385| e[81391| 7|81398| 7181405 681411) 7|81418| 7
81425 6/81431| 7181438 7|81445| 6/81451| 7181458 7181465) 681471 7|81478| 7181485 6
81491| 7|81498| 7181505 6|81511| 7|81518| 7|81525| 6/81531) 7|81538| 6[81544| 7|81551| 7
81558| 6|81564| 7181571) 7|81578| 6|81584/ 7|81591| 7|81598| 6|81604| 7|81611| 6|81617| 7
81624) 781631! 6/81637| 7|81644| 7|81651| 681657! 7|81664| 7|81671| 681677! 7|81684
81690) 7|81697| 7|81704| 6|81710| 7|81717| 6|81723| 7|81730| 7|81737| 6[81743| 7|81750
81757 6|81763| 7|81770| 6|81776| 7|81783| 7|81790| 6|81796| 7|81803| 6|81809| 7|81816
81823| 6|81829| 7|81836| 6|81842| 7|81849| 7181856 6|81862| 7|81869| 6|81875| 7|81882
81889| 6|81895| 7|81902| 6|81908| 7|81915| 6|81921| 7|81928| 7181935 6|81941| 781948

omu ono |
BAe CAL ES]

81954 7181961) 7[81968| 6[81974| 7|81981| 6[81987| 7[81994| 682000) 7[82007| 782014
82020| 7|82027| 6|82033| 7|82040| 6|82046| 7|82053| 7182060) 6/82066| 7182073| e[82079
82086| 6|82092| 7[82099| 6|82105| 7|82112| 7|82119| 6|82125| 7|82132| 6|82138| 7|82145
82151 7|82158| 6|82164| 7|82171| 7|82178| 6|82184| 782191! 6|82197| 7|82204| 682210
82217| 682223 7|82230| 6|82236| 7|82243| 6|82249| 7|82256| 7|82263| 6|82269| 7182276

82282| 7|82289| 6|82295| 7|82302| 6|82308| 7|82315| 6|82321| 7|82328| 6|82334| 7|82341
82347| 7|82354| 6|82360| 7|82367| 6|82373| 7|82380| 7|82387| 6|82393| 7|82400| 6/82406
82413| 6|82419| 7182426| 6|82432| 7182439 6|82445| 7|82452| 6|82458| 7|82465| 682471
82478| 6|82484| 7|82491| 6|82497| 7|82504| 6|82510| 7/82517) 6|82523| 7|82530| 6|82586
82543| 6|82549| 7|82556| 6|82562| 7|82569| 6|82575| 7|82582| 682588 7|82595| 6]82601' 6

82607| 7|82614| 6|82620| 7|82627| 6|82633| 7|82640| 6|82646| 7|82653| 6|82659| 7182666
82672| 7|82679| 6182685) 7|82692| 6|82698| 7182705 6|82711| 7|82718| 6|82724, 6|82730
82737| 6|82743| 71182750 6|82756| 7|82763| 6|82769| 7|82776| 682782| 7|82789| 6|82795
82802| 6|82808| 682814! 7|82821| 6|82827| 7|82834| 6|82840| 7|82847| 6|82853| 7|82860
82866 6|82872| 7|82879| 6|82885| 7|82892| 6|82898| 7|82905| 6|82911| 7|82918| 682924

82930| 7|82937| 6|82943| 7|82950| 6|82956| 7|82963| 6|82969| 6|82975| 7|82982| 6|82988
82995 6|83001| 7|83008| 6|83014| 6|83020| 7|83027| 6|83033| 7|83040| 6|88046| 683052
83059 6|83065| 7|83072| 6|83078| 7|83085| 6|83091| 6|83097| 7|83104| 6|83110| 7|88117
83123) e[83129| 7|83136| 6|83142| 7|83149| 6|83155| 6|83161| 7|83168| 6|88174| 7|83181| 6
83187 6|83193| 7|83200| 6|83206| 7|83213| 6|83219| 6|83225| 7|83232| 6|83238| 7/83245

83251| 6|83257| 7|83264| 683270) 6|83276| 7|83283| 6|83289| 7|83296| 6|83302| 6|83308
83315| 6|83321| 6|83327| 7183334| 6|83340| 7|83347| 683353] 6|83359| 7|83366| 6|83372
83378 7183385 683391] 7|83398| 6|83404| 6|83410| 7|83417| 6|83423| 6|83429| 7|83436
83442) 6|83448| 7183455 6|83461| 6|83467| 7|83474| 6|83480| 7|83487| 6|88493| 683499
83506| 6|83512| 683518) 7|83525| 6|83531| 6|83537| 7|83544| 6|83550| 683556) 7|83563

83569| e|83575 7183582) 6|83588| 6|83594! 7|83601| 6|83607| 6|83613| 7|83620| 6|83626
83632| 7|83639| 6|83645| 6|83651! 7|83658| 6|83664| 6|83670| 7|83677| 6|83683| 6/83689
83696| 6|83702| 683708) 7|83715| 6|83721| 6|83727| 7|83734| 6|83740| 683746) 7183753
83759 6|83765| 6|83771| 7|83778| 6|83784! 6|83790| 7|83797| 6|83803| 6|83809| 7183816
83822 6|83828| 7|83835' 6|83841| 6|83847| 6|83853| 7|83860| 6|83866| 6|83872| 783879

83885| el83891 6|83897| 7|83904| 6|83910! 6|83916| 7|83923| 6|83929| 6|83935| 7|83942
83948 6183954 6|83960| 7|83967| 6|83973| 6|83979| 6|83985| 7|83992| 683998 6/84004
84011! 684017] 6|84023| 6|84029! 7184036] 6|84042| 6|84048| 7|84055| 6/84061 6/84067
84073 7184080) 684086] 6|84092| 6|84098| 7184105) 684111) 6|84117| 6/84123 7184130
84136 684142) 684148) 784155 6|84161! 6|84167| 684173) 7184180) 6184186 6/84192

e

|

84198| 7184205 684211! 6|84217| 684223) 7184230) 6|84236| 6184242) 6184248 71184255
84261 684267! 684273) 7184280) 684286] 6[84292 6|84298| 7184305| 6184311 Eo
84323 7184330 684336) 6|84342| 6|84348| 6|84354| 7|84361| 6184367 6/84373 de
84386 684392) 484398) 6|84404| 6|84410| 7184417) 6[84423 684429 6/84435 Lë
84448 684454) 684460) 6184466 7184473) 6|84479| 6|84485| 6/84491 6[84497| 718

«o Qo -1 C» GOD |
OOP GO DD H

84510! 084516 684522) 6]84528| 7184535 684541) 6|84547| 6184553 6184559] 7|84566
aima sai ssh 4, all 551 d 6) 1d qid 8 d 9

1370

TABLE 32
Logarithms of Numbers

No.| 0 dl? 2434: Seidl a alo emi dl 9 ¡dij Prop. parts
700 |84510 684522! els4528 7184535] 6|84541| 684547) 84553 7184566) 6
701 |84572 684584) 684590) 7184597 684603) 684609) 184615 84628 e] | 7
702 |84634 6184646) 6|84652| 6184658) 7134665 | c|84671| 684677 084689, 7—7
703 [84696 6184708) 684714) 6184720 6|84726| 7184733] 6|84739 c|84751| g] l| !
704 [84757 184770) 6|84776| 684782) 684788) 84794) «184800 s[s4813) d 2| 1
705 184819 e84831| 684837] 7184844) 84850) olg4856 e| 84862 SEH 4 | 3
706 [84880 6184893 6|84899| 684905] 84911) 84917] 7184924 demand 5| 4
707 |84942 684954| 684960] 7184967 484973) 6184979] 6|84985 c|84997| e] 8 | 4
708 |85003 185016} 685022 685028) 6|85034| 685040) 85046 6 qssoss Ai?
709 [85065 6|85077| 685083) 6|85089| 685095) 6[35101| el85107 685120 e] 8 | 6
710 |85126 85138) 685144) 6|85150| 685156! 7|85163| 6|85169 6|85181| 6
711 |85187 6|85199| 6|85205| 6|85211| 6|85217| 1185224 685230 6|85242| 6
712 |85248 6|85260| 6|85266| 6|85272| 6|85278| 1185285 685291 685303! 6
713 |85309 685321) 6|85327| 685333) 6|85339| «|85345| 7185352 685364! 6
714 |85370 6|85382| 685388) 685394) 685400) 6854061 6185412 2185425 6
715 185431 685443) 6|85449| 85455] 6|85461| 6|85467| 685473 685485] 6
716 |85491 6|85503| 685509] 2185516 6|85522| 6185528) 6|85534 685546 6
717 |85552 685564] 685570) 85576) 6|85582| 61855881 685594 685606, 6
718 |85612 7|85625| 6|85631| 6|85637| 6|85643| 6|85649| 85655 6185667] 6
719 |85673 6|85685| 6|85691| 6|85697| 6|85703| els5700| 6185715 6185727 6
720 |85733 6|85745| 6|85751| 6|85757| 6|85763| 6185769! 6185775 2185788 6
721 |85794 6|85806| 6|85812| 6|85818| 6858241 85830) 6185836 6[85848 6 6
722 |85854 6|85866| 6|85872| 6|85878| 6|85884| 6185890! 685896 6185908} e|| ——
723 |85914 6|85926| 6|85932| 6|85938| 6|85944| 6185950! 6185956 el85968 e] 1 | 1
724 |85974 6|85986| 6|85992| 6|85998| 6|86004| els6010| 6186016. 6 686028) e| 2! 1

setā A 3| 2
725 |86034 el86046] 6|86052| 6|86058| 6|86064| «1860701 6l86076 86088) e| 4 | 2
726 |86094 6|86106| 6|86112| 86118) 6|86124| 61861301 86136 6|86147! e] 5| 3
727 |86153 6|86165| 6|86171| 6|86177| 6|86183| els6180 686195 6|86207| e| 6 | 4
728 |86213 6|86225| 6|86231| 6|86237| 6|86243| 862491 6|86255 686267] e] 7 | 4
729 |86273 6|86285| 686291) 6|86297| 6|86303| 5|86308| 686314 686326] e| 8 | 5

9-5

730 l86332 6 6|86344| 686350) 686356) ols6362| 6|86368| 686374 86386] 6
731 |86392 6|86404| 686410) 186415) 86421] 86427] 636433 86445] 6
732 |86451 7| 186463] 86469] 6|86475! e|86481| 486487) 6186493 31865041 6
733 |86510 86522| 6|86528| 6|86534| 686540) 86546] 86552 865641 6
734 |86570 5|86581| 6|86587| 686593) 686599) 86605! el86611 7| 6|86623| 6
735 |86629 6186641) 3186646) 61866521 86658] 86664! 686670 866821 6
736 |86688 686700! 5|86705| 6|86711| 686717! 686723! 86729 6|86741! 6
737 |86747 686759! 5|86764| 6|86770| 686776! 867821 6186788 6186800] 6
738 |86806 5|86817! 6|86823| 6|86829| 686835] 686841! 86847 686859] 5
739 |86864 6|86876| 6|86882| 6|86888! 6|86894| 6869001 «86906 6|86917| 6
740 |86923 6|86935| 6|86941| 686947] 6|86953! 5|86958| 61869641 « 6186976 6
741 [86982 686994! s[86999| 687005] 687011 687017! 87093 6187035) 5 $
742 [87040 j| 187052] e]87058| 6|87064| 687070] 3187075! 687081 7| 87093) 6
743 [87099 6 0187111| 5|87116| 687122) 687128) e|87134| 6|87140 | 5|87151 e| 1| 0
744 187157 e/87169| 687175] 6|87181| 5|87186| 6871921 6187198 6|87210| e| 9 | 9
745 [87216 6|87227| 687233] 687239] 187245) 6872511 5187256 87268) e] 2| 2
746 |87274 6|87286| 5|87291| 6|87297| 6|87303| 6l87309| 87315 6|87326| «| 5 | 2
747 |87332| 6 ej87344 5|87349| 6|87355| 6|87361| 487367! 487373 s87384 e| ¿| 3
748 |87390 6|87402| 6|87408| 5|87413| 687419] 6|87425| 687431 7 5|87442| e| 7 | ú
749 |87448 6|87460| 687466! s|87471| 6|87477| 6|87483| 87489 s|87500| el g | 4
750 |87506 6|87518| 5|87523| c|87529| 87535) 875411 6187547 87558) di 9 | 4
No. 1% dd 2° lah 3 lala 6 r d 9 dl

>>

1371

TABLE 32

Logarithms of Numbers
FE

7500-8000

No.| 0 d 1 d| 2 [dl 3 |d 4 jd 5 Jal 6 d 7 ja s Jal 9 Jal} Prop. parts

750 [87506 6/87512| 687518 5|87523| 687529 687535) 6|87541! 687547 5187552) 6187558 | 6
751 [87564 6|87570| 6|87576| 5|87581| 6|87587| 687593) 6|87599| 5187604! 687610] 687616) 6
752 |87622| 6|87628| 587633 6|87639| 6|87645| 687651 5|87656| 6|87662| 687668) 687674 5
753 |87679| 6/87685 687691) 6[87697 687703 5|87708 687714 687720) 687726) 5187731) 6
754 |87737| 687743 | 687749 | 587754 687760 6|87766| 687772 5|87777| 6|87783| 687789 6

755 |87795| 5|87800| 6|87806| 6187812 6187818 5]87823| 687829 6|87835| 6|87841! 587846 6
756 |87852| 6|87858| 6|87864| 5/87869| 6|87875| 6|87881| 6|87887| 5|87892| 6|87898! 6|87904| 6
757 |87910| 5|87915| 687921 6|87927| 6|87933| 5|87938| 6|87944| 6|87950| 5|87955| 6|87961| 6
6
5

758 |87967| 6|87973) 5187978 6187984) 6/87990| 6|87996| 5|88001| 6|88007| 6|88013| 588018
759 [88024 688030 6|88036| 5|88041| 6|88047| 6|88053| 5|88058| 6|88064| e[88070| 688076
760 |88081| 6|88087| 6|88093| 5|88098| 6|88104| 6|88110| 6|88116| 5|88121| 6|88127| 6|88133
761 |88138| 6/88144 688150| 6|88156| 588161! 6|88167| 6|88173| 5|88178| 6|88184| 6|88190
762 |88195| 688201| 6|88207| 6[88213| 5|88218| 6/88224| 6|88230| 5|88235| 6|88241| 6|88247
763 |88252| 6/88258| 6|88264| 6|88270| 5|88275| 688281! 6|88287| 5|88292| 6|88298| 6|88304
764 |88309| 6|88315| 6|88321| 5|88326| 6|88332| 6|88338| 5|88343| 6|88349| 688355| 5|88360

«o 00-10» OUR Oo ND |
cet RUE RERS e

DO hn OY

765 [88366 688372| 5|88377| 6/88383| 6|88389| 6[88395| 5]88400| 6|88406| 6|88412| 5/88417
766 |88423| 688429| 5|88434| 6|88440| 6|88446| 5|88451| 6|88457| 6|88463| 5|88468| 6|88474
767 |88480| 5|88485| 6|88491| 6|88497| 5|88502| 6/88508| 5|88513| 6|88519| 6|88525| 5|88530
768 |88536| 6|88542| 5|88547| 6[88553| 6|88559| 5|88564| 6|88570| 6|88576| 5[88581| 6|88587
769 |88593| 5|88598| 688604| 6|88610| 5|88615| 6|88621| 6|88627| 5|88632| 6|88638| 5/88643

D> Q» Q» Q» a

770 |88649| 6|88655| 5|88660| 6|88666| 6|88672| 5|886 77, 6|88683| 6|88689| 5|88694| 6/88700
771 |88705| 6|88711| 6|88717| 5|88722| 6|88728| 6|88734| 5|88739| 6|88745| 5|88750| 6|88756
772 |88762| 5|88767| 688773 6|88779| 5|88784| 6|88790| 5|88795| 6[88801| 6|88807| 5|88812
773 |88818| 6|88824| 5|88829| 6|88835| 5|88840| 6|88846| 6|88852| 5|88857| 6|88863| 5|88868
774 |88874| 6|88880| 5|88885| 6|88891| 6|88897| 5[88902| 6/88908| 5|88913| 6|88919| 688925

go OQ» CO» Cv

775 |88930| 6|88936| 5|88941| 6|88947| 6|88953| 5|88958| 6|88964| 5|88969| 6|88975| 6|88981
776 |88986| 6|88992| 5[88997| 6|89003| 6|89009| 5|89014| 6|89020| 5|89025| 6|89031| 6|89037
777 |89042| 6|89048| 5|89053| 6|89059| 5|89064| 6|89070| 6|89076 5|89081| 6/89087] 5|89092
778 |89098| 6|89104| 589109 6|89115| 5|89120| 6/89126) 5|89131| 6|89137| 6|89148| 589148
779 |89154| 5|89159| 6|89165| 5|89170, 6|89176| 6|89182| 5|89187| 6|89193| 5|89198| 6/89204

En OQ» $ a O

780 |89209| 6|89215| 6|89221| 5|89226| 6|89232| 5|89237| 6|89243| 5]89248| 6[89254 689260
781 |89265| 689271 5|89276| 6|89282| 5|89287| 6|89293| 5|89298| 6|89304| 6|89310| 5|89315
782 |89321| 5|89326 6|89332| 5|89337| 6|89343| 5|89348| 6|89354| 6|89360| 5|89365| 689371
783 |89376| 6|89382 5189387) 6|89393| 5|89398| 6|89404| 5|89409| 6|89415| 6|89421| 589426
784 |89432| 5|89437| 6|89443| 5]89448| 6|89454| 5|89459| 6|89465| 5|89470| 6|89476| 589481

Q» OQ» C" OQ» Ov

785 |89487! 5189492) 6|89498| 689504) 5[89509| 6|89515| 5|89520| 689526) 5|89531| 689537
786 |89542| 6|89548| 5189553) 6|89559| 5|89564| 6189570 5|89575| 6|89581| 5|89586| 6[89592
787 |89597 6|89603| 6|89609| 5|89614| 6|89620| 5|89625 6|89631| 5|89636| 6|89642| 5|89647
788 |89653| 5|89658| 6|89664| 5|89669| 6|89675| 5|89680| 6|89686| 5|89691| 6|89697| 5|89702
789 |89708| 5|89713| 6|89719| 5|89724| 6|89730| 5|89735| 6|89741| 5|89746| 6|89752| 589757

oo omu

|
790 189763) 5|89768| 689774 5|89779| 6|89785| 589790 689796, 5189801) 6|89807| 5|89812
791 |89818! 5|89823| el89829 5189834) 6|89840| 5|89845 6|89851| 589856 6|89862| 5|89867
792 |89873| 5|89878| 5|89883| 6[89889 5|89894| 6|89900| 5|89905| 6|89911| 5/89916 689922
793 |89927| 689933 5|89938| 6|89944| 5|89949| 6|89955| 5|89960| 6|89966| 5|89971 689977
794 189982 689988 5|89993| 5|89998| 690004! 5|90009| 6|90015| 590020, 6|90026| 5|90031

DO ao c»

0037 5190042! 6|90048| 5[90053 6|90059| 590064 5]90069| 6|90075| 590080 6/90086] 5
706 90091 690097) 5|90102| 6|90108| 5|90113| 690119 5|90124| 5|90129| 6|90135| 5|90140| 6
797 |90146| 5|90151| 690157) 5|90162| 690168| 5|90173 6|90179| 5|90184 5/90189 eon. 5
798 190200] 6|90206! 5190211} 6|90217| 590222) 590227) 6190233 5/90238 6190244 5[90249 6
799 |90255| 5|90260| 6190266] 5|90271| 5[90276 690282, 5|90287, 690293 5190298} 690304. 5

O MO TO GEO DO |

|
800 190309) 5190314) 6|90320| 5|90325| 690331) 5|90336| 6190342 5190347) 5|90352| 690358 ai

No. tal al ual Salta lali 155 dl. Gs dl 7 d 8 d| 9 jd

1372

sl

TABLE 32

Logarithms of Numbers

8000-8500

Nowy om die tis die 2d x adv die (al 865 i | OR Ld D eer Jet ei Zait

d

800 |90309| 5|90314| 6|90320| 5|90325| e[90331| 5|90336| e6|90342| 5|90347| 5|90352| 6[90358| 5

801 |90363| e|90369| 5|903874| 6/90380| 5|90385| 5|90390| 6|90396| 5|90401| 6|90407| 5[90412| 5

802 |90417| e6[90423| 590428 6|90434| 5|90439| 6/90445| 5|90450| 5|90455| 6|90461| 5|90466| 6

803 |90472| 5|90477| 590482) 6/90488| 5|90493| e[90499| 5|90504| 5|90509| 6|90515| 5|90520| 6

804 |90526| 590531) 5|90536| 690542| 5|90547| 6190553) 590558) 5|90568| 6|90569| 5|90574| 6

805 |90580| 5|90585| 5|90590| 6|90596| 5|90601| 6[90607| 5|90612| 5|90617| 6[90623| 5|90628| 6
806 |90634| 5|90639| 5|90644| 6|90650| 5|90655| 5|90660| 6[90666| 5|90671| 690677! 5|90682| 5
807 |90687| 6|90693| 5|90698| 5|90703| 6|90709| 5|90714| 6|90720| 5|90725| 5[90730| 6|90736| 5
808 |90741| 6|90747| 5|90752| 5|90757| 690763) 5|90768| 5|90773| e[90779| 5|90784| 5|90789| 6
809 |90795| 5|90800| 6|90806| 5[90811, 5|90816| 6|90822| 5|90827| 5|90832| 690838) 5|90843| 6
5

6

5

5

6

C Ou £O DO H | e

810 |90849| 5|90854| 5|90859| e[90865| 5|90870| 5|90875| e[90881| 5[90886| 5|90891| 6|90897
811 |90902| 5|90907| 690913| 5|90918| 690924| 5|90929| 5[90934| 6|90940| 5|90945| 5|90950
812 |90956| 5|90961| 590966) 6/90972| 5|90977| 5|90982| 6|90988| 5[90993, 5|90998| 6|91004
813 |91009| 5|91014| 691020) 5|91025| 5|91030| 6|91036| 5|91041| 5|91046| 6|91052| 5|91057
814 |91062| 691068) 591073) 5|91078| 6|91084| 5|91089| 5|91094| 6|91100| 5|91105| 591110

815 |91116| 5|91121| 5|91126| 6/91132| 5|91137| 5|91142| 691148! 5|91153| 5|91158| 6|91164| 5
816 191169) 591174) 691180) 591185) 5|91190| 6|91196| 5|91201| 5|91206| 691212) 591217! 5
817 |91222| 691228) 5|91233| 5|91238| 5|91243| e[91249| 5|91254| 5|91259| 6|91265| 5|91270| 5
5
5

818 |91275| 691281) 5|91286| 5|91291| e|91297| 591302) 5[91307| 591312) 691318) 5/91323
819 |91328| e[91334| 5191339) 591344 691350] 5|91355| 591360) 591365) 691371) 5|91376

820 |91381| 691387 5191392) 591397 6|91403| 591408] 5191413] 5191418] 6|91424| 591429) 5
821 |91434| 691440) 5191445) 5191450] 5191455] 691461] 5191466) 5|91471! 691477) 591482] 5
822 191487) 591492) 6191498) 5191503] 5191508] 691514) 5191519) 5|91524! 5191529) 691535] 5
823 191540) 5191545] 6|9155:| 5191556] 5|91561| 5191566} 6|91572| 5191577] 5191582) 5191587
824 191593) 591598) 5|91603| 691609} 591614] 5|91619| 591624 691630] 391635] 5191640

6
5
825 191645) 6/91651/ 5|91656| 5|91661| 5/91666)| 6|91672| 5|91677| 5|91682| sl91687| 691693) 5
826 191698) 5|91703| 691709] 5|91714| 5191719] 5|91724| 691730! 5|91735| 5191740| 5|91745! 6
827 191751) 591756) 5|91761| 5|91766| 6|91772| 5|91777| 5|91782| 5|91787| 691793] 5|91798! 5
828 |91803| 5|91808| e|91814| 5|91819| 5|91824| 5|91829| 5|91834! 6|91840! 5|91845| 5191850! 5
829 |91855| 6|91861| 5|91866| 5|91871| 5|91876| 6|91882| 5|91887! 5|91892| 5|91897 6/91903| 5
830 |91908| 591913} s[91918| 6|91924| 5191929] 5|91934| 5191939] 5|91944| 691950 5191955
831 |91960| 5|91965| 691971) 5191976] 5|91981| 5|91986| 5191991] 691997) 5192002 592007
832 [92012 s[92018| 5192023) 5192028] 5|92033| 5|92038| 692044! 5|92049| sl92054 5192059
833 |92065| 5192070) 592075) 5192080) 5192085] 692091] 192096) sl92101| 3192106 592111
834 [92117] 5|92122| 5192127) 5|92132| 5|92137| 692143] 592148) 192153 5192158 592163
835 |92169| 5|92174| 5192179) 5192184] 5192189] 6|92195| 5192200) 5|92205 5|92210| 592215
836 |92221| 5|92226| 5|92231| 5192236] 5192241) 6|92247| 5192252! 5192257 5192262) 592267
837 |92273| 5192278) 5|92283| 5192288] 5192293] 5|92298| 692304 5192309) 5192314] 5192319
838 192324) 6192330) 5|92335| 5192340] 5192345] 5|92350| 192355! 692361 5192366] 592371
839 |92376| 5192381) 6/92387| 5192392] 5192397] 5|92402| 192407 5192412} 692418) 5192423

naman | c» o en cn

840 |92428| 5192433) 5|92438| 5192443] c|02449| 5|92454! 5192459 5(92464| 5|92469| 5|02474
841 [92480| 5192485 5192490] 5|92495| 5|92500| 5192505) 6|92511 5192516} 5192521) 592526
842 [92531 5192536) 692542] 5192547] 5192552) 5|92557| 5192562 5192567) 592572 6|92578
843 192583) 5192588) 5|92593| 5192598) 3192603) 692609] 5192614 5192619) 592624 592629
844 |92634| 5192639] 6192645] 5192650] 592655) sl92660| 5192665 5192670] 5/92675| 692681

845 |92686| 5192691] 5192696] 5|92701| 5|92706| 5192711 5192716) 6192722] 592727) 3192732
846 [92737 5192742) 5192747 5|92752| 692758] 5192763 5192768) 5|92773| 592778] 592783
847 192788) 5192793 692799] s[92804 5192809] 5192814 5192819] 592824! 5192829] 5192834
848 192840) 5|92845| 5[92850| 592855! 5|92860 5|92865| 5|92870| 5192875) 6|92881! 5|92886
849 |92891| 5|92896| 5|92901! 5|92906| 5|92911! 5|92916 5|92921| 692927 5|92932| 5192937

ná go

ao a a

mR GO DO DD O | ex

850 |92942| 5|92947| 502952! 5|92957! 5|92962 5|92967| 692973] 5|92978| 5|92983| 5|92988| 5

No. |r Quae ait 29) al A dð dA ds ONE d

np wc

1373

TABLE 32

Logarithms of Numbers
C

8500-9000

No. | 0 |dļ 1 jd 2 j|d 3 jad] 4 Jal 5 Jal e Jal v Jal s lal o [all Prop. parts

850 [92942 5192947 5192952) 5]92957 5192962) 5|92967| el92973| 5|92978| 5192983) 5192988
| 851 [92993 5192998) 5193003) 5|93008| 5193013} 5|93018| e[93024| 5193029) 5|93034| 3193039
852 [93044 5193049) 5193054) 5193059) 5193064! 5|93069| el93075 5193080) sl93085 5|93090
853 |93095| 5193100) 593105 593110 5193115} 5|93120| 593125 6|93131| 193136) 5|93141
854 |93146| 593151 593156 593161 593166] 5193171) 593176 5|93181| 593186) 693192

Ono Can Ov

o 1o oo ww |
COOP PO NN EK

855 193197) 5]93202| 593207 5|93212| 5|93217| s[93222 5193227| 5|93232| 5|93237| 5|93242
` 856 |93247| 5|93252| 693258 5|93263| 5|93268| 5|93273| 5|93278| 5|93283! 5|93288| 5193293
857 |93298| 5|93303| 5|93308| 5|93313| 5|93318| 5|93323| 5|93328! 6|93334'! 5|93339| 5193344
858 |93349| 5|93354| 5|93359| 5|93364| 5|93369| 5|93374| 5|93379| 5|93384| 5|93389| 5193394
859 |93399| 5|93404| 5|93409| 5|93414| 6|93420| 5|93425| 5|93430| 5|93435| 5|93440| 5|93445

Ü Cn or oo

860 |93450| 5|93455| 5|93460| 5193465) 5193470) 5|98475| 5193480) 5|93485| 5193490] 593495
861 |93500| 5|93505| 5|93510| 593515 5193520) 6|93526| 5|93531| 5|93536| 5193541] 5193546
862 |93551| 5|93556| 5|93561| 5|93566| 5|93571| 5|93576| 5|93581| 5|93586| 5|93591| 5|93596
863 |93601| 5|93606| 5|93611| 5|93616| 5|93621| 5|93626| 5|93631| 5|93636| 5|93641| 5|93646
864 |93651| 5|93656| 5|93661| 5|93666| 5|93671| 5[93676| 6|93682| 5|93687| 5|93692! 5|93697

o Cn Cn C

865 |93702| 5|93707| 5|93712| 5|93717| 5|98722| 5|93727| 5|93732| 593737 5|93742| 5|93747/ 5
866 |93752| 5|93757| 5|93762| 5|93767| 5|93772| 5|93777| 5|93782| 5|93787| 5|93792| 5|93797
867 |93802| 5|93807| 5|93812| 5|93817| 5|98822| 5|93827| 5|93832| 5|93837| 5|93842| 593847
868 |98852| 5|93857| 5|93862| 5|93867| 5|93872| 5|93877| 5|93882| 5|98887| 5|93892| 593897
869 |93902| 5|93907| 5|93912| 5|93917| 5|93922| 5|93927| 5|93932| 5|98987| 5|93942| 593947

QQ € C o

870 |93952| 5193957) 593962 5193967) [93972 5193977) 5193982) 5193987) 5|93992| 593997
871 |94002| 5|94007| 5|94012| 5194017) 5|94022| 5194027] 5194032) 5194037] 5194042) 5|94047
872 194052 5194057) 5|94062| 5194067) 5|94072| 5|94077| 5194082) 4194086) 5|94091| 5/94096
873 |94101| 5[94106| 5|94111| 5194116} 5|94121| 5|94126| 5|94131| 5[94136| 5194141) 5194146
874 |94151| 5194156) 5|94161, 5194166) 594171 5|04176| 594181] 5194186) 5|94191| 594196

Ku

or O N Cn Ov

875 |94201| 5|94206| 5|94211| 594216) 594221 5|94226| 5194231) 5194236) 494240. 5194245
876 |94250| 5194255) 5|94260| 5|94265| 5|94270| 5|94275| 594280) 5194285) 5|94290| 5194295
877 |94300| 5/94305| 5|94310| 5|94815| 5|94320| 5|94825| 5|94330| 594335 5|94340| 5|94345
878 |94349| 5|94354| 5|04359| 5|94364| 5|94369| 5|94374| 5|94379| 5|94384| 5194389] 5|94394
879 |94399| 5|94404| 5|94409| 5|94414| 5|94419| 5|94424| 5|94429| 4|04433| 5]94438| 5|94448

CON OOP WHF |
PPE PWNNNH OS

880 |94448| 5|04453| 594458) 5194463) 5|94468| 5194473) 5|94478| 5194483) 5|94488| 5194493
881 |94498| 5|94503| 4[04507| 594512) 594517 5|94522| 5|94527| 5194532) 5|94537| 5194542
882 |94547| 5|94552| 594557) 5|94562| 5194567) 494571) 594576) 594581) 5194586) 594591
883 |94596| 5|94601| 5]94606| 5|94611| 5|94616| 5|94621| 5194626) 4194630) 5194635) 5/94640
884 |94645| 5|94650| 5[94655| 5|94660| 5|94665| 5|94670| 5|94675| 5|94680| 5|94685| 4194689

GG Er er Gn | css ev es

885 |94694| 5|94699| 5|94704| 5|94709| 5|94714| 5|94719| 5|94724| 5|94729| 5|94734| 4/94738
886 194743 5]94748| 5|94753| 5|94758| 5|94763| 5|94768| 5|94773| 5194778) 5|94783| 4194787
887 |94792| 5|94797| 5|94802| 5|94807| 5|94812| 5|94817| 5|94822| 5|94827| 5|94832| 4194836
888 |94841| 5|94846| 5|94851| 5|94856| 5|94861| 5|94866| 5|94871| 5|94876| 4194880) 5|94885| :
889 |94890| 5|94895| 5|94900| 5194905] 5|94910| 5|94915| 4194919} 5|94924| 5|94929| 5|94934

OQ O QQ

890 194939) 5194944] 5|94949| 594954 | 5194959] 4194963) 5194968] 594973 | 5194978) 5|94983
891 |94988| 5194993) 594998 4195002! 5|95007| 5[95012 595017 595022) 5]95027| 595032
892 |95036| 5195041) 595046 5|95051| 5|95056| 5]95061| 595066 5195071) 495075 595080
893 |95085| 5195090) 595095 5195100} 4495105) 4|95109| 5|95114| 5|95119| 595124) 595129
894 195134) 5|95139| 4195143] 5195148) 5195153] 5195158) 595163) 5|95168| 5195173 495177

>

|

o Ore Ov

895 |95182| 5195187| 5195192! 595197) 595202) 5|95207| 4195211) 5|95216| 595221) 5|95226
896 195231) 5195236] 4195240) 595245] 5195250) 5|95255| 595260) 595265) 5|95270| 4195274
897 195279] 5195284] 5195289] 5195294) 595299) 4195303 5195308) 595313) 5|95318| 595323
898 195328] 4195332) 5|95337| 595342] 5|95347| 5|95352| 5|95357| 4195361] 5195366) 595371
899 195376) 5195381) 5|95386| 495390] 5195395] 5|95400| 5|95405| 5|95410| 595415) 495419

Cn CY OX CN Cn
OO NO GT GOOD |
HG GW DDD EO

900 lo5424 5|95429| 5|95434| s[05439| 5[95444 4|95448| 5|95453| 5]95458| 5|95468| 5|95468| 4

No. o la n al a dh als spas eb (dl: s 92d

1374

TABLE 32
Logarithms of Numbers

dj 8 ld] 9 dll Prom parts
Wet al gea Lad ða alo
900 | 3195434! s[05439| slo5444 4|95448| 5195453 595463. 5195468) 4 E
901 31954821 5|95487| 1954991 5|95497| 4195501 s95511 95516 dh | 5.
902 51955301 5|95535| 31955401 5195545 5195550 95559 «95564 de
903 495578 5|95583| 195588) 5|95593| 5195598 doot" 5]95612| a 1| 9
904 4195626) 5|95631| 3195636) 5|95641| 195646 195655 95660 | 2 | 1
905 4|95674| 5195679 3195684! 3195689) 5195694 195703 295708 4| 2| 2
906 495722, 595727 5|95732| 5195737 5195742 595751] 595750 | 5 | 2
907 4195770 5|95775| 5|95780| 5/95785 4195789 dp 195799 595804) | 6 | 3
908 5|95818| 5|95823| 5|95828| 4|95832| 195837) : ]95847| 5]95852| A 7 | 4
909 5|95866| 5|95871| 4195875 5|95880| 5195885 195805 495800 a| 8 | 4 |
910 195914! 495918) 1959231 195928) [05933 4195942) sl95947 5
911 4195961) 195966) 1959711 5|95976 4195980 5195990 5|95995| 4
912 5196009} 5|96014| 5|96019| 4196023) 5196028 5196038 4196042| 5
913 5|96057! 4|96061| 5|96066| 5196071 5196076 5|96085| 5|96090| 5
914 5196104} 5|96109| 5|96114! 4196118) 5|96123 5196133) 4|96137| 5
915 5|96152| 4|96156| slo6161 506166 sl96171 5196180) 5|96185| 5
916 5|96199| 5196204 3196209] 4196213 5|96218 4|96227| 5|96232. 5
917 4196246] 5|96251| 5|96256| 1962611 4|96265 5|96275| 5196280) 4
918 5196294! «96298 3196303! 196308) 5196313 5196322 196327) 5
919 5|96341| sl96346 41963501 5196355 5196360 ¿196369 196374) 5
920 41963881 s[06393| 196398) 406402. slo6407 596417 4|96421| 5
921 496435, 5|96440| 5|96445| sl96450 4196454 5|96464| 196468) 5
922 5|96483| 4|96487| 5|96492| 1964971 «196501 3196511) 4/96515| 5
923 5|96532| 406534. 196539) 5196544! 496548 5196558 4196562. 5
924 5196577] 4|96581| 3196586) 1965911 4196595 5196605 4|96609| 5
925 9| 5|96624| 4|96628| 196633) 5|96638| 196642 3196652) 4|96656| 5
926 4196670) s|96675| 5|96680| sl96685 4196689 5196699 4|96703| 5
927 al96717 5|96722| 196727) 4|96731 196736 4196745 5196750) 5
928 596764 5|96769| slo6774 ¿96778 5196783 4196792) 5|96797| 5
929 51968111 5|96816| 4196820 196823) 5196830 196839 5|96844| 4
930 5|96858| 4196862) 5|96867| 196872 «196876 5196886 4196890) 5
931 4196904| 5|96909! 5196914! ¿06918 5196923 4196932) 3196937] 5
932 5196951 5|96956| 4196960) 5196965 3196970 5196979 5196984 4
933 4196997] 5|97002| 5|97007| 4197011, 197016 4197025 | 5197030) 5
934 5|97044| 5197049] 4197053) 197058 197063 3197072) 5|97077| 4
935 4197090] 3197095! 197100) 407104. 5197109 4197118) 197123) 5
936 597137) 197142] 4197146] sl97151 4197155 5197165 4197169! 5
937 4|97183| s|97188 «97192 5|97197| 3197202 5197211) 597216 4
938 5197230) 4197234| 197239) 4|97243| 5197248 4197257] 51972621 5
939 5197276) 4197280] 8197285! slo7290 4197294 5197304 4197308 5
940 5197322) 5197327] 4|97331| slo7336 alo7340 197350) 4197354 5
941 4197368) 597373 41973771 5197382 5197387 3197396] 41974001 5 4
942 al97414 5|97419| slo7424 4|97428| 5197433 5[97442| 5|97447| 4
943 4197460) 5|97465! slo7470 4197474! 5197479 197488| |97493| 4| 1| 9
944 4197506) 597511] 197516) 4197520, 3197525 597534 5197539 4| 5 | 9
945 7548| 497552) 597557) 5|97562| 197566 5197571 197580 397585 4| % | 3
946 94 4197598] 5197603) 4197607) 197612) 5197617 197626| 197630| j| 5 | 2
947 4197644] 5197649| 4197653) 5197658 5197663 197672| 497676 5| 8 | 2
948 5|97690| 5/97695] 197699) 5197704. 4197708 497717, 3197722 dd © | 2
949 5197736 497740] slo7745 4197749 5197754 497763 3197768 4| £ | 3
950 s[07782 4|97786| 1977911 4197795 sl97800 197809 4|97813| || 2 | *
No. al 2 jd s dla lal 5 dal d. galai om al | a

yu

1375

TABLE 32

Logarithms of Numbers
T
9500-10000

dj 2 d 4 dl 8 Prop. parts

97772 5|97782 5|97791 ( 5/97809
97818 4197827 4197836 5/97855
97864 5/97873 5/97882 4197900
97909 : 4|97918 5/97928 5/97946
97955 5/97964 5/97973 " d 4197991
98000 4198009 5|98019 5|98037
98046 5|98055 5|98064 4198082
98091 4198100 4198109 4198127
98137| a] 598146 5|98155| A ¿[98173
98182 598191 5|98200 4198218

98227 4198236 4198245 4198263
98272 7| 498281 4198290) alt 4198308
98318 598327 5/98336 5/98354
98363 598372 598381 5/98399
98408 598417 5/98426 5/98444
98453 5/98462] At 5/98471 5/98489
98498 5/98507 5|98516 d 5198534
98543 598552 5/98561 ( 598579
98588 5/98597 4198605 4198623
98632 4198641 4198650 4198668
98677 4198686 4198695 4198713
98722 5198731 35| 5198740 598758
98767 598776 4198784 4198802
98811 4198820 4198829 4198847
98856 5/98865 5/98874 5/98892

o ie oue cow |
PE LWNNNHO | ex

98900 4198909 4198918 4198936
98945 i 5|98954 5|98963 i 5/98981
98989 4198998 4199007 || 4199025
99034 5199043 599052 Y 4199069
99078 4199087 4199096 5|99114
99123 4199131| 5]: 4199140 d 4| 4199158
99167 599176 5/99185 ( 4199202
99211) 5196 4199220 4| 5199229 5/99247
99255 4199264 4199273 t : 5|99291
984 |99300 4199308 4199317 5/99335

985 |99344 4199352 4199361 5199379
986 |99388 4199396 4199405 4199423
987 |99432| Ar 5|99441 4199449 5|t 4|99467
988 |99476 4199484 4199493 5/99511
989 199520 4199528 4199537 5199555

990 199564 4199572 4199581 At ( 5|99599
991 |99607 4199616 4199625 9| 5/9 4199642
992 |99651 4199660 5/99669 7 4199686
993 |99695 399| 5199704 4199712 997 726| 499730
994 [99739 4199747 4199756 j 5/99774

995 199782 4199791 ( 5|99800 ( ( 4199817
996 |99826 5|99835| At 4|99843 5| 5199861
997 199870 74| 4199878 4199887 4199904
998 |99913 5|99922| At 4199930 4| 4199948
999 199957 4199965 4199974 4199991

Sig >

1000 100000 5100009 4100017 5 5100035! 4
No. | 0 d| 2 d| 4 | d 8 |

1376

TABLE 33

Logarithms of Trigonometric Functions

Diff.

=
o
y

cot

. 00000
. 00000
. 00000
. 00000
. 00000

. 00000
. 00000
. 00000
„00000
. 00000

. 00000
. 00000
. 00000
. 00000
. 00000

. 00000
. 00000
209999
. 99999
1399999

„99999
800999
. 99999
299999
. 99999

99999
199999
299999
299999
. 99998

. 99998
. 99998
. 99998
. 99998
. 99998

. 99998
. 99998
599997
. 99997
. 99997

. 99997
. 99997
«990997
99997
„99996

9. 99996
- 99996
. 99996
. 99996
. 99996
. 99995
. 99995
- 99995
. 99995
. 99995
. 99904
. 99994
. 99994

eo
. 46373 13. 53627
. 76476 . 23524
. 94085 13. 05915
. 06579 12. 93421

. 16270 12. 83730
. 24188 . 75812
. 90882 . 69118
. 36682 . 63318
. 41797 . 58203

. 16373 . 03627
. 90512 . 49488
. 54291 . 45709
. 57767 . 42233
. 60986 „89014

„63982 „86018
„66785 „83215
„69418 . 30582
. 71900 . 28100
. 74248 . 25752

. 76476 . 28524
. 78595 . 21405 |
. 80615 . 19385
. 82546 . 17454
. 84394 . 15606

. 86167 . 13833
. 87871 . 12129
. 89510 9 | .10490
. 91089 . 08911
. 92613 : 07387
- 94086 - 05914
. 95510 . 04490
. 96889 . 03111
. 98225 . 01775
. 99522 . 00478
„00781 o |11. 99219
. 02004 . 97996
. 03194 . 96806
. 04353 . 95647
. 05481 . 94519
- 06581 . 93419
. 07653 . 92347
. 08700 . 91300
. 09722 . 90278
. 10720 . 89280
. 11696 . 88304
412651100 . 87349
. 13585 zla 56415
. 14500 . 85500
. 15395 | $229 | | 84605
. 16273 . 83727
817153 . 82867
. 17976 . 82024
. 18804 . 81196
. 19616 „80384
„20413 . 79587
A bye . 78805
221964 Le . 78036
. 22720 . 77280 99994
. 23462 . 76538 |. . 99994
. 24192 . 75808 |10. . 99993

CENTOS ui ooxtono^| €

DO ODO rmnOoOOOr-coococoo-eooooooweoocooooooeococooooooooooeoooooooooooocoooo

cot at tan

QD? |o- nora ards

t
00
o

TABLE 33

Logarithms of Trigonometric Functions

tan

. 24186
. 24903
. 25609
. 26304
. 26988

. 27661

. 28324
. 28977
. 29621
. 30255

. 75814
. 75097
. 74391
. 73696
. 73012

. 24192
. 24910
. 25616
. 26312
. 26996

. 30879
: 31495
. 32103
. 32702
. 33292

. 33875

. 94450
„85018
. 35578
. 36131

. 72339
. 71676
. 71023
. 70379
. 69745

. 27669
. 28332
. 28986
. 20629
. 30263

. 75808
. 75090
. 74384
. 73688
. 73004

. 00007
. 00007
. 00007
. 00007
. 00008

. 69121
. 68505
. 67897
. 67298
. 66708

. 30888
. 31505
. 32112
. 32711
. 33302

. 72331
. 71668
. 71014
. 70371
. 69737

. 00008
. 00008
. 00008
. 00008
. 00009

1377

cos «178°
y

. 99993
. 99993
. 99993
. 99993
199992

. 99992
. 99992
. 99992
. 99992
-99991

. 36678
. 37217
. 37750
. 38276
. 38796

. 39310

. 39818
. 40320
. 40816
. 41307

. 66125
. 65550
. 64082
. 64422
. 63869

. 33886
. 94461
. 35029
. 35590
. 36143

. 69112
. 68495
. 67888
. 67289
. 66698

. 00009
. 00009
. 00010
. 00010
. 00010

99901
. 99991
. 99990
. 99990
. 99990

. 63322
. 62783
. 62250
. 61724
. 61204

. 36689
. 37229
. 37762
. 38289
. 38809

. 66114
. 65539
. 64971
. 64410
. 63857

. 00010
. 00011
. 00011
. 00011
. 00011

. 99990
. 99989
. 99989
. 99989
199989

. 41792
. 42272
. 42746
. 43216
. 43680

. 60690
. 60182
. 59680
. 59184
. 58693

. 39323
. 39832
. 40334
. 40830
. 41321

. 63311
. 62771
. 62238
. 61711
. 61191

. 00012
. 00012
. 00012
. 00013
. 00013

. 99988
. 99988
. 99988
. 99987
. 99987

. 60677
. 60168
. 59666
. 59170
. 58679

. 00013
. 00014
. 00014
. 00014
. 00015

. 99987
. 99986
. 99986
. 99986
. 99985

. 44139
. 44504
. 45044
. 45489
. 45930

. 46366

. 46799
. 47226
. 47650
. 48069

. 58208
. 57728
„57254
„56784
. 56320

. 41807
. 42287
. 42762
. 43232
. 43696

. 55861

. 55406
. 54956
. 54511
. 54070

. 44156
. 44611
. 45061
. 45507
. 45948

. 58193
. 57713
. 57238
. 56768

. 00015
. 00015
. 00016
. 00016
. 00016

. 00017
. 00017
. 00017
. 00018
. 00018

. 99985
. 99985
. 99984
. 99984
. 99984

. 99983
. 99983
. 99983
. 99982
. 99982

. 48485
. 48896
. 49304
. 49708
. 50108

. 53634
. 53201
. 52774
. 52350
. 51931

. 46385
. 46817
. 47245
. 47669
. 48089

. 00018
. 00019
. 00019
. 00019
. 00020

. 99982
. 99981
. 99981
. 99981
. 99980

. 51515
. 51104
. 00696
. 50292
. 40892

. 48505
. 48917
. 49325
. 49729
. 50130

. 00020
. 00021
. 00021
. 00021
. 00022

. 99980
. 99979
. 99979
; QUITO
. 99978

. 50504
. 50897
. 51287
. 51673
. 52055

. 49496
. 49103
. 48713
. 48327
. 47045

. 50527
. 50920
. 51310
. 51696
. 92079

. 00022
. 00023
„00023
. 00023

. 99978
49991777
299977
. 99977
. 99976

. 02434
. 52810
. 53183
. 53552
. 53919
. 54282

. 47566
. 47190
. 46817
. 46448
. 46081
. 45718

. 52450
. 02835
. 53208
. 58578
. 53945
. 54308

oo oD DO OE DO O OO O ODO DO O O OO OO OH ODO EO O ODO OH ODO OO O ODO O O Oo CO

9. 99976
„99975
„99975
„99974
„99974
9. 99974

cos

sec

cot

BO? lor nwnaa-~1060

t
oo
o

1378

TABLE 33

Logarithms of Trigonometric Functions

00
Ū
o

2% sin = esc tan pd cot sec gend cos «177°
d 1 1 1 y
O | 8 54282 | 260 |11.45718 | 8 54308 | 26; |11. 45692 |10. 00026 | , | 9. 99974 | 60
1 54642 | 300 | | 45358] .54669 | 561 45331 | .00027 | ) | .99973 | 59
2 54999 | 227 | 45001 | .55027 | 328 44973 | .00027 | | | .99973 | 58
3 55354 | 351 | - 44646 55382 | 359 44618 | .00028 | 4 | .99972 | 57
55 44266 | . 00028 ` 99972 | 56
349
5 | 8.56054 | 346 HI. 43946 | 8. 56083 ed 11. 43917 |10. 00029 y 9. 99971 | 55
7 | Zen | 349. Lieser | mera 1344 inasai lec pongo [UE || VERD Ieee
8 57084 | 341 42916 | 57114 | 341 42886 | .00030 | 9 99970 | 52
9 57421 | 337 42579 | 57452 | 338 42548 | .00031 | ¿ | ¿990609 | 51
8. 57757 SC T1. 42243 | 8. 57788 396 e
"58089 | 332 | 41911 | “ester | 333 |" 41378 D 00082 nm 70088 49
58419 | 330 | "41581 | :58451 | 330 | :41549| :00032| 9 | ¡09068 | 4
58747 | 328 41253 | .58779 | 328 41221 | ¿00033 | 1 | :99967 h
59072 | 325 40928 | . 59105 | 326 40895 | .00033 | 9 | ¿99967 | 4
8.59395 | 229 |īī 40605 | 8 59428 | 323 Sa Ë
59715 | 320 | 40985 | 59749 | 321 | mn A ood Ð 00986 t
60033 | 318 39067 | . 60068 | 319 | ‘30939 | 00034 | 9 | 2 95066 | 43
60349 a 39651 | ` 60384 zy 39616 | .00035| | |. See 2
z 60973 311 | ae : A 211 39302 | . 00036 | ¿ | 99964 | 41
61282 | 309 38718 | 61319 | 310 Hl ee Be os? x € osos [DON
61589 | 307 38411 | . 61626 | 307 38874 | ¿00087 (CH | eones (eee
61894 | 305 38106 | ` 61931 ti 38069 | ` 00038 5 90982 37
:62795 | 298 | 37205 | .62834 | 299 | 37168 | 100039 | © | 99901 | 32
63091 | 296 | “36900 | | 63131 | 297 | :36869 | 00040 | l | (99960 | 33
63385 | 294 | “36615 | :63426 | 295 | :36574| 100040 | O | 90060 | 32
63678 SC ` 36322 | | 63718 29 36282 | . 00041 A ; 93050 F
8. 63968 h
"ES | am [TE poora ECan | aso Paga los | Pos
-64543 | 287 | 35457 | | 64585 | 287 | “35415 | .00042| 0 | ¡00088 | 28
-64827 | 284 | | 35173 | | 64870 | 285 | 35130 | 00043 | 1 | 09037 | 2
¿65110 | 289 | ¿34800 |: 65154 | 284 asas Moos | | 99b cen
8.65391 | 29! 1-349009 | & 6 RECTE A Eae
- 85301 | 279 [1.34909 | & 65435 | 289 [II 34565 |10. 00044 | , | 9.99956 | 25
65947 | 277 | :34053 | ‘65003 | 278 | :34007| 00048 | O | 99088 | 4
.66223 | 276 | 33777 | :66269 | 276 | : "00046 VEP 299952. KE
r E 274 [0833731 | 1000046 -99954 | 22
¿ME 66497 | 279 | -33503 | .66543 | 273 | | 33457 | 00046 9 | 90054 | 21
8. 66769 | 579 1133231 | 8. 66816 | TT 33184 |10. 00047 9.99953 | 20
41 | . 67039 .32961 | . 67087 32913 | . 000 i
42 | 67308 | 269 | 10 32602 | : 67356 | 269 | :32644| 00048 | 0 | 99954 | 18
43 | .67575 2 .32425 | .67624 | 268 | "32376 | 700049 | 1 |: ea uu
44 |. 67841 | ze | 32159 | :67890 264 | 32110 | .00049 | © | ‘99951 | 16
» r8 11. 3189
46 | 0763367 | 203 lares Deed T HØGAR 31846 |10. 00050 | , | 9.99950 | 15
47 . 68627 260 . 31373 s 68678 261 G 31399 . 00051 0 . 99949 14
48 .68886 | 259 Kan [14 [emrandas zeng tat «00051 | 4 : 99949 13
49 | ` 69144 SE .30856 | | 69196 ape .30804 | . 00065 SA thes e
50 ` Sha 1 2
50 | 8 69400 | 354 |11. 30600 | 8. 69453 | 5-. (TI. 30547 |10. 00053 9.99947 | 10
51 | 69654 253 | 30346 | .69708 | 22% | -30292 | .00054 e 99946 | 9
.30093 | ` 69962 30038 | .000
53 | .70159 | 292 | "29841 | 70214 | 252 | : -00054 | | | .99946| 8
S : 70409 250 | 20591 | ` 70465 E 208 get vs s 90941 à
S :
a 70658 Seet 29342 8. 70714 Sok LE 29286 10. 00056 | , | 9.999441 5
a san: tee ` 71453 ` 28547 | ` 00058 ` 99942 | 2
So | s 71880 | 242 |, 28362 | - T1607 243 | 28303 | 00059 | ! | 99941 | 1
: | i 8.71940 | ^55 |11. 28060 |10. 00060 9. 99940 0
90295 cos Diff. sec cot Diff. Diff. T
—— Ea ee eee

LARA

TABLE 33

Logarithms of Trigonometric Functions

27880 | .72181 | 239 | .27819 | .00060 | 9 99940 | 59
27641 | .72420 | 339 | .27580 | .00061 | 1 | :99939 | 58
27403 | .72659 | 237 | .27341 | .00062 | | | :99938 | 57
27166 | .72896 | 336 | .27104| .00062 | 9 | :99938 | 56
11. 26931 | 8.73132 | 234 |11.26868 [10.00063 | , | 9.99937 | 55
26697 | .73366 | 234 | .20634| .00064 | | | :99936 | 54
26465 | .73600 | 535 | .26400 | .00064 | Ü | :99936 | 53
26233 | .73832 | 537 | .26168 | .00065 | ! | :99935| 52
26003 | .74063 | ¿39 | .25937 | .00066 | | | :99934| 51
11. 25774 | 8. 74292 | 799 |11.25708 |10. 00066 | , | 9.99934 | 50
25546 | .74521| 597 | .25479 | .00067 | ! | . 99033 | 49
25320 | .74748 | 554 | .25252 | .00068 | | | :99932| 48
25094 | .74974 | 595 | .25026 | .00068 | 9 | :99932| 47
24870 | .75199 | 224 | .24801| .00069 | | | :99931| 46
11. 24647 | 8.75423 | 299 [11.24577 |10.00070 | , | 9.99930 | 45
24425 | .75645 | 555 | .24355 | .00071 | 4 | .99929 | 44
24205 | .75867 | 22e | .24133| .00071 | 9 | :99929 | 43
23985 | .76087 | 229 | .23913 | .00072 1 | :99928 | 42
23766 | .76306 | 219 | .23694| .00073 | | | :99927| 4i
11. 23549 | 8.76525 | 5,7 |11. 23475 |10.00074 | Q | 9.99926 | 40
23333 | .76742 | 21; | .23258 | .00074 | 9 | .99926 | 39
23117 | .76958 | 219 | .23042 | .00075 | 1 | :99925 | 38
22903 | .77173 | 313 | .22827 | .00076 | | | :99924| 37
22690 | . 77387 | 213 | .22613 | .00077 | ] | :99923 | 36
11. 22478 | 8. 77600 11. 22400 |10. 00077 9.99923 | 35
22267 | .77811 | 311 | .22189 | .00078 | | | .99922| 34
22057 | .78022 | 211 | .21978 | .00079 | | | :99921| 33
21848 | .78232 | 210 | .21768 | .00080 | ¿ | .99920 | 32
21640 | . 78441 | 202 | .21559 | .00080 | 9 | :99920| a
11. 21432 | 8. 78649 11. 21351 |10. 00081 9.99919 | 30
21226 | .78855 | 208 | .21145| .00082 | 1 | .99918| 29
21021 | .79061 | 209 | :20939 | .00083 | ) | .99917 | 28
20817 | .79266 | 204 | .20734 | .00083 | 9 | .99917 | 27
20614 | .79470 | 204 | . 20530 | .00084 | | | .99916 x
-20412 | 8. 79673 11. 20327 |10. 00085 9. 99915
ie | 202 | .20125 | .00086 | | | .99914| 24
20010 | .80076 | 201 | .19924 | .00087 | ¿ | .99913 | 23
19811 | .80277 | 201 | “19723 | .00087 | 9 | .99913 | 22
19612 | .80476 | 199 | -19524 | .00088 | | | . 99912 a
; 80674 11. 19326 |10. 00089 9. 99911
" ens 80872 | 198 | .19128 | .00090 1 | 99910 | 19
19022 | .81068 | 198 | :18932| .00091 | ) | .99909 | 18
18827 | | 81264 | 199 | :18736 | .00091 | ] | .99909 | 17
18633 | :81459 | 193 | 18541 | .00092 | } | .99908 E
1653 11. 18347 |10. 00093 9. 99907
it šā 193 | 18154 | .00094 | | | .99906 | 14
18056 | .82038 | 192 | 17962 | .00095 | | | .99905 | 13
17866 | 82230 | 19 .17770 | .00096 | ) | .99904| 12
17676 | .82420 | 190 | .17580 | .00096 | ] | .99904| 11
11. 17487 |8.82610 | ¡gg |11. 17390 |10. 00097 | , | 9. 99903 | 10
17299 | 82799 (17201 | .00098 | | | .99902
17112 | .82987 | 185 | :17013 | .00099 | ; | .99901 | 8
16925 | .83175 | 188 | '16825 | .00100 | | | .99900 | 7
16739 | 83361 | 186 | 16639 | .00101 | | | .99809| 6
11. 16554 | 8.83547 | jg; |11. 16453 |10. 00102 o | 9.99808) 5
16370 | .83732 | 135 | 16268 |. 00102 1 | 99898 | 4
16187 | .83916 | |84 | . 16084 1 | - 99897 | 3
16004 | : 84100 | ¡39 | .15900 | .00104| | | . 99896] 2
` 15823 | ` 84282 (15718 | .00105| | |.
11 15642 | 8. 84464 | 182 |11. 15536 |10. 00106 | ! | 9.99894 B
i Diff
sec cot Diff tan ese Ú sin +80?

1380

TABLE 33

Logarithms of Trigonometric Functions

4% sin oat csc tan de cot sec e cos «1759
ā y
0 | 8.84358 | ¡gy |11. 15642 | 8.84464 | ¡g9 |11. 15536 |10. 00106 | , | 9.99894 | 60
1 | .84539 | 379 | .15461 | . 84646 | 184 | .15354 | .00107 | | | .99893 | 59
3. |Í Zë) 19 Ces 55006 250. eeler
4 | :85075 | 178 | :14925 | .85185 | 172 | :14815 | .00109 | 9 | 99891 | 56
5 | 8 85252) |77 |11.14748 | 8 85363 | ¡my 11. 14637 |10. 00110 | , | 9.99890 | 55
7 | ¿85605 | 178 Vitess |177| ses Leer ISAS] ae
8 | ¿85780 | 179 | “14220 | ¿85893 | 178 | “14107 | ¿00113 | * | ¡90887 | 52
9 | :85955 | 175 | 14045 | 86069 176! | agost [000114 1 | 99886 | 51
10 [8.86128 | 173 11. 13872 | 8 86243 | 174 [11. 13757 |10. 00115 | | | 9.90885 | 50
12 || scara | 179. \oonageag ke acesi Lie KC len potty [OUS QNSE ODE
13 | .86645 | !7! | ' 13355 | 86763 | 172 | :13237 | .00118 | 1 | 00882 | 47
14 | .86816 | 17] | 13184 | 86935 | 172 | :13065 | :00119 | l | :99881| 46
15 [s 86987 169 |11. 13013 | & 87106 | van 11. 12894 |10. 00120 | , | 9.99880 | 45
: 87156 | 369 | . 12844] .87277 | |7) | .12723 | .00121 | ¿ | .99879 | 44
17 87325 169 | - 12675 | . 87447 | |49 | . 12553 | .00121 | 9 | ‘ 99879] 43
eee ee ee JE
20 8. um 166 |11. 12171 | 8.87953 | |g7 |11. 12047 |10. 00124 1 | 9. 99876 | 40
22 | 88161 | 166 | * E Caen TEE divi (ii i ee d R
23 | ` 88326 e ` 11674 | | 88453 SCH .11547 | .00127 | ! | :99873 37
` 884 ` 11510 | ` 88618 ` 11382 | ` 00128 99872 | 36
164 i ;
25 | 8. 88654 Ti. 11346 | 8. 88783 | 199 (1111217 |10.00129 | | (990871 | 35
26 | .88817 | 105 | .11183 | t 88048 | 165 | ” 11052 | . 00130 | ! | 9987
27 | seen | 163 | “11020 | :so111 | 193 | :10889 | :00131 | 1 | 99809 | 33
28 | . 89142 E ` 10858 | | 89274 i .10726 | .001322 | | |. das =
` 89304 ` 10696 | ` 89437 10563 | ` 00133 ` 99867
160 ia 161 D . 1 ` 86 Sut
30 |8.
A ANS IB ES qu AME dE
32 | :so784 159 | "10216 | 89920 | 190 | “10080 | 100136 | 1 | 99864 | 28
33 | | 39943 E . 10057 | .90080 | 160 | “09920 | ¿00137 ! | ` 35563 27
34 | .90102 | |5g | .09898 | .90240 | 199 | 09760 | ‘00138 | ! | ¡90862 | 26
35 | 8.90260 F .
Xp dis d IIS I E
37 | :90574 | 197 | ‘09496 | :o0715 | 158 | “09985 | ¡00141 | 1 | ¡00889 | 28
38 | aan | 156 | “09270 | 2. 90872 | 157 | :09128 | ¡00142 | 1 | 99888 | 22
39 | | 90885 tee 09115 | ` 91029 1 "08971 | | 00143 : ; s. 31
40 | 8 91040 ;
41 | “otros | 185 Vegan | 91340 | 196 VE a A
vk AE UL | Zosemid
43 | .91502 | 193 | '08498 | :91650 | 199 | :08350| | 00147 Wr C
44 | .91655 | 153 | :08345 | | 91803 153 | -08197 | 00148 | 1 | | WESS ð
45 | 8. 91807 | |5, 11. 08193 | 8. 91957 11. 08043 |10. 00149 | | | 3 99851 | 15
46 | .91959 08041 | .92110 | 153 07890 | .001 1
47 | :92110 | 151 | :07890 | :92262 | 152 | :07738 | ‘oois2| 2 | hl 18
48 | .92261 | |5) | .07739 | .92414 | 152 | “07586 | ¿00153 | 1 | .99847
49 | .92411 | 120 | l07589 | .92565 h "07435 | ¿00154 | 1 | “90846 i
50 | 8.92561 deem
AB NP "IR Sy ago ds dp m
52 | .92859 | 142 | sozial | :93016 | 150 | weil n ooien ! | 00843 | 3
53 | .93007 | 122 | .06993 | :93165 | 149 06835 | .00158 | 1 | ‘99
54 | .93154 | 147 | .06846 | | 93313 R . 06687 | .00159 | 1 | ` m ó
55 | 8 93301 11. 0669 i EI
56 | :e3448 | 147 ("06552 | 93600 | 147 |: 06538 |10. 00160) , | [5
57 | .93594 el .06406 | .93756 | 147 | “06244 | .00162 | ! | “o0838 | 3
55 | 93740 145 | .06260 | | 93903 n .06097 | .00163 | 1 | “90837 | 2
oo 1638885 | 145 | 00115 | EH | 00164 Ma ai
ls ` 05970 | 8 94195 11. 05805 |10. 00166 9. 99834 | 0
Diff.
| 942» cos 1” sec cot DR tan ese ion sin «850

TABLE 33

Logarithms of Trigonometric Functions

1381

59.5 sin pu ese tan pa 4 cot sec SH cos +174?
y y
O | 8.94030 | |44 |11.05970 | 8. 94195 | 145 |11.05805 |10. 00166 | , | 9.99834 | 60
1 | .94174 | 143 | .05826 | .94340 | 142 | .05660 | . 00167 | ! | 00833 | 59
2 | .94317 | 144 | .05683 | .94485 | |45 | .05515 | .00168 | ! | | 99832] 58
3 | -94461 | 142 | .05539 | .94630 | ¡33 | .05370 | .00169 | ! | :99831| 57
4 | .94608 | 143 | .05397 | .94773 | 144 | 05227 | .00170 | ! | :99830| 56
5 | 8.94746 | |41 |11. 05254 | 894917 | |43 |11.05083 |10.00171 | , | 9.99829 | 55
6 | .94887 | 149 | .05113 | .95060 | 143 | .04940 | 00172 | ! | :99828 | 54
7 | .95029 | ol .04971| .95202 | |42 | .04798 | 00173 | l | :99827 | 53
8 | .95170 | ¡49 | -04830 | .95344 | 145 | .04656 | .00175 | 2 | :99825 | 52
9 | .95310 | 149 | .04690 | .95486 | 122 | .04514 | :00176 | ! | :99824 | 51
10 | 8.95450 | ¡39 |11. 04550 | 8.95627 | |40 |11.04373 |10. 00177 | , | 9.99823 | 50
11 | .95589 | 339 | .04411 | .95767 | 449 | .04233 | .00178 | ! | .09822| 49
12 | .95728 | i39 | .04272 | .95908 | 155 | .04092 | .00179 | ! | 99821 | 48
13 | .95867 | |3g | .04133 | .96047 | 139 | -03953 | .00180 | ! | -99820 | 47
14 | .96005 | ¡3g | .03995 | .96187 | |38 | .03813 | .00181 | | | :99819 | 46
15 | 8.96143 | ¡37 |11.03857 | 8. 96325 von |11.03675 |10. 00183 | , | 9.99817 | 45
16 | .96280 | |37 | .03720 | .96464 | 132 | .03536 | . 00184 | l | “99816 | 44
17 | .96417 | 136 | .03583 | .96602 | [35 | .03398 | .00185 | ! | :99815 | 43
18 | .96553 | 136 | .03447 | .96739 | 138 | .03261 | .00186 | | | 99814 | 42
19 | «96689 | 156 | 03311 | .96877 | |56 | .03123 | .00187 | ] | (90813 | 41
20 | 8. 96825 | |35 |11. 03175 | 8.97013 | |25 |11. 02987 |10. 00188 | > | 9.99812 | 40
21 | .96960 | |35 | .03040 | .97150 | 137 | .02850 | .00190 | 2 | .99810 | 39
22 | .97095 | |34 | .02905 | .97285 | 123 | .02715 | .00191 | | | :99809 | 38
23 | .97229 | |34 | .02771 | .97421 | |36 | .02579 | .00192 | | | :99808 | 37
24 | .97363 | 133 | .02637 | .97556 | 122 | .02444 | .00193 | | | . 99807 | 36
25 | 8.97496 | |33 |11. 02504 | 8.97691 | ¡24 |11.02309 |10. 00194 | > | 9.99806 | 35
26 | .97629 | 133 | .02371 | .97825 | 134 | .02175 | .00196 | 7 | .99804 | 34
27 | .97762 | 133 | .02238 | .97959 | 13% | 02041 | :00197 | | | .99803 | 33
28 | .97894 | 132 | .02106 | .98092 | 133 | .01908 | :00198 | | | .99802 | 32
29 98026 | 131 | -01974 | .98225 | 133 | .01775 | .00199 | | | .99801 | 31
30 | 8.98157 | |3, |11. 01843 | 8.98358 | ,32 |11. 01642 |10. 00200 | > | 9.99800 | 30
31 | .98288 | 13, | .01712| .98490 | 122 | 01510 | .00202 | 1 | .99798 | 29
32 | :98419 | 139 | .01581 | .98622 | 122 | .01378 | .00203 | | | .99797 | 28
33 | 98549 | 13) | .01451 | .98753 | 1231 | .01247 | :00204 | , | .99796 | 27
34 | .98679 | 129 | .01321| .98884 | 131 | :o1116 | :00205 | 5 | .99795 | 26
35 | 8. 98808 | j59 |11. 01192 | 8 99015 | |2) |11. 00985 |10. 00207 | , | 9.99793 | 25
36 | .98937 | 129 | -01063 | .99145 | 130 | -00855 | .00208 | | | .90792 | 24
37 | .99066 | 122 | :00934| :99275 | 130 | .00725 | .00209 ; | .99791 | 23
38 | .99194 | |28 | 00806 | .99405 | j | -00595 | -00210 5 | .99790 | 22
39 | -99322 | 128 | -00678 | .99534 | 15$ | .00466 | .00212 7 | .99788 | 21
40 | 8.99450 | |97 |11.00550 | 8.99662 | ,59 |11. 00338 10. 00213 | , | 9.99787 | 20
41 | .99577 | joy | .00423 | .99791 | |28 | -00209 | .00214 | ; | . 99786] 19
42 | 99704 | jog | .00296 |s.99919 | |27 [1100081 | -00215 | 9 | -99785 | 18
43 | -99830 | |26 | -00170 | 9. 00046 | ¡28 |10. 99954 | .00217 | 7 | .99783 | 17
44 | 8.99956 | 126 |11. 00044 | :00174 | 122 | .99826 “00218 i R 4

99699 |10. 00217 997

48 | 200997 | 125 oros | «00427 | 126 | 99573 | 00220 Li .99780 | 14
47 | .00332 | 125 | :99668 | .00553 | 125 | .99447 | .00222 | 7 | .99778 | 13
48 | .00456 | 125 | .99544 | .00679 | 156 | 99321 | -00223 | | 99777 | 12
49 | .00581 | 125 | ‘99419 | .00805 | 195 | -99195 | .00224 |, | .9977
50 | 9. 00704 10. 99296 | 9. 00930 10. 99070 |10. 00225 | y | 9.99775 | 10

124 7 5 | 125 98945 | . 00227 .99773 | 9

51 | ` 00828 .99172 | .01055 | 129 | .98t j 7 77
52 | .00951 | 123 | “99049 | .01179 :98821 | .00228 1 | .99772| 8
: i 123 | ` 6 | 01303 | 124 98697 | . 00229 sor
53 | .01074 | 123 | 98926 | .01303 | 124 | .98697 | . 2 | xem | 2
54 | og | 122 | :o8804 | .01427 | 153 | .98573 E n MC

10. 98450 |10.

56 | orao | 122 |” 08560 | .o1673 | 123 |. 98327 | .00253 1 | .99767| 4
rote | 21820820 101501790 |25 ere geng |8f00235 [iq | 9599765 | 3
bs | eotes2 | 121 eegen 101918 |122 0598082 | 0500236 |., | -99764 | 2
59 | 01803 | 124 | 98197 | .02040 | 155 | .97960 | .00237 | 5 | 99763 | 1
60 | 9.01923 | 120 |10.98077 | 9. 02162 10. 97838 |10. 00239 9. 99761 `

l i Dit| <
959» cos 1 sec cot P tan esc 1 Sin A

t
Qo
o

1382

TABLE 33

Logarithms of Trigonometric Functions

. 99761
. 99760
. 99759
. 99757
. 99756

. 99755
. 99753
. 99752
. 99751
. 99749

. 99748
. 99747
. 99745
. 99744
. 99742

. 99741
. 99740
. 99738
. 99737
. 99736

. 99734
. 99733
. 99731
. 99730
. 99728

. 99727
. 99726
. 99724
. 99723
. 99721

. 99720
. 99718
199717
199716
. 99714

. 99713
99711
. 99710
. 99708
. 99707

. 99705
. 99704
. 99702
. 99701
. 99699

. 99698
. 99696
. 99695
. 99693
. 99692

. 99690
. 99689
. 99687
. 99686
. 99684

. 99683
. 99681
. 99680
. 99678
. 99677
. 99675

D one ko, en ao O

sin

ff.
oo
Q2

o

TABLE 33

Logarithms of Trigonometric Functions

1383

FE AAA as
79 sin En ese tan v cot sec Nä cos «172°
y y

O | 9.08589 | jog |10. 91411 | 9.08914 | wes /10. 91086 |10. 00325 | , | 9. 99675 | 60
1 08692 | 103 | .91308 | .09019 | 105 90981 | .00326 | 5 | .99674 | 59
2 08795 | 109 | .91205 | ma | 104 90877 | .00328 | 2 | .99672 | 58
3 08897 | 105 | .91103 | .09227 | 104 90773 | .00330 | Ý | ‘99670 | 57
4 08999 | 105 | .91001 | 09330 | 103 90070 | .00331 | 4 | :99669 | 56
5 | 9.09101 | o, |10.90899 | 9.09434 | |03 |10.90566 [10.00333 | | | 9.99667 | 55
6 09202 | 192 | .90798 | .09537 | 108 90163 | .00334 | 5 | .99666 | 54
7 09304 | ¡91 | -90696 | .09640 | 103 90360 | .00336 | | | ‘99664 | 53
8 09405 | 191 | .90595 | 09742 | 102 90258 | .00337 | 1 | :99663 | 52
9 09506 | |0) | .90494 | me | 103 90155 | .00339 | 2 | :99661 | 51
10 | 9.09606 | |0, 10. 90394 | 9.09947 | |02 |10.90053 |10. 00341 | | | 9.99659 | 50
11 09707 | |0) | - 90203 | .10049 | 102 89951 | . 00342 | 5 | .99658 | 49
12 09807 | |0) | .90193 | 10150 | 101 89850 | .00344 | ? | :99656 | 48
13 09907 | “gg | . 90093 | :10252 | 102 89748 | .00345 | 5 | :99655 | 47
14 10006 | 10) | -89994 | . 10353 | 101 89647 | .00347 | 2 | :99653 | 46
15 | 9.10106 | gg |10. 89894 | 9.10454 | |0; |10. 89546 |10. 00349 | | | 9.99651 | 45
16 10205 | 94 | .89795 | .10555 | 101 89445 | .00350 | 5 | .99650 | 44
17 10304 | 93 | . 89696 | .10656 | 191 89344 | .00352 | Ý | :99648 | 43
18 10402 | 99 | .89598 | .10756 | 100 89244 | .00353 | 5 | .99647 | 42
19 10501 | $2 | .89499 | .10856 | 100 89144 | . 00355 | 2 | :99645 | 41
20 | 9.10599 | gg |10.89401 | 9.10956 | jo |10.89044 |10.00357 | , | 9.99643 | 40
21 10897 | gs | .89303 | .11056 | 109 88044 | .00358 | 5 | .99642 | 39
22 10795 | 95 | .89205| .11155 | 90 88845 | .00360 | 2 | .99640 | 38
23 10893 | 95 | .89107| .11254| 3° 88746 | .00362 | ? | :99638 | 37
24 10990 | 97 | .89010 | . 11853 | 99 88647 | .00363 | 5 | .99637 | 36
25 |9.11087 | gy |10. 88913 | 9. 11452 | gy 10.88548 |10. 00365 | 5 | 9.99635 | 35
26 | .11184 2| presse |Osgasst | 2205 88449 | .00367 | Ý | .99633 | 34
27 | ¿11281 | 2 .88719 | . 11649 | 38 88351 | .00368 | á | :99632 | 33
28 | ` 11377 E. ¿68622 [19700747 | 1308 88253 | .00370 | Ý | 99630 | 32
29: | 11474 | Si | 98526 | .11845 | 28 88155 | .00371 | 5 | 99629 | 31
30 | 9. 11570 10. 88430 | 9. 11943 | yy |10.88057 |10. 00373 | „ | 9.99627 | 30
31 | .11666 | 99 | 88334 | .12040 us 87960 | .00375 | 1 | .99625 | 29
32 | .11761| 96 | .88239 | .12138 | 95 | .87862| .00376 | 5 | .99624 | 28
33 11857 | 99 | "88143 | | 12235 o 87765 | .00378 | 5 | .99622 | 27
34 11952 de . 88048 |. 12332 | 96 87668 | . 00380 | 5 | .99620 | 26
5 | 9. 12047 = |10. 87953 | 9. 12428 10. 87572 |10. 00382 9.99618 | 25
- fuso || 95. lewerssa MC0ū2s25 bech 87475 | .00383 | 3 | .99617 | 24
ar || 102236 | 24: pov87764 [4012621 | ee 87379 | .00385 | 5 | .99615 | 23
ac ëtt "| horereod 10812717 | cioe 87283 | .00387 | 1 | .99613 | 22
39 | ` 12425 $ 87575 | :12813 | 96 87187 | .00388 | , | .99612 | 21
40 | 9. 12519 10. 87481 | 9.12909 | gs |10. 87091 |10. 00390 | 5 | 9.99610 | 20
41 | .12612 | 93 | 87388 | .13004 | $2 | .86996 | .00392 1 | .99608 | 19
42 12706 | 94 | “87294 | .13099 ue 86901 | .00393 | 5 | .99607 | 18
43 12709 || 5021 But ptkfgī94 | es 86806 | .00395 | 5 | .99605 | 17
44 12892 2 .87108 | . 13289 | 95 86711 | .00397 | 5 | .99603 is

10. 87015 | 9. 13384 10. 86616 |10. 00399 9. 99601
7 y Tio 93 | ` 86922 | . 13478 ME 86522 | .00400 ; ` 99600 | 14
47 13171 | 93 | "86829 | | 13573 86427 | .00402 | $ | .99598 | 13
48 13263 | 92 | 86737 | .13607 | 9% | .86333 | .00404 | 7 | .99596 | 12
49 | 13355 | $2 | .86645 | .13761| $4 | .86239 | .00405 | (Ð | .99595 *
5 e 55 10. 86146 |10. 00407 9. 99593
` 1 ens 92 epe m IE 94 86052 | .00409 | 2 | .99591 | 9
52 13620 | 91 | 86370 | . 14041 2 85959 | .00411 | 1 | . 99589 8
53 invo | 197 Eege | gaos 85866 | .00412 | 5 | .99588| 7
94 ||| Krass 86187 35014297 | 2509 85773 | .00414 | 5 | .99586 | 6
55 | 9.13904 10. 86096 | 9.14320 | 5 |10.85680 |10. 00416 | 2 | 9.99584 | 5
56 13994 | 90 |*.86006 | . 14412 |- 92 85588 | .00418 | 1 | .99582 Ļ
57 14085 | 91 | “85915 | ¿14504 | ' 85496 | .00419 | 3 | .99581 | 3
58 14175 | 90 85825 | .14597 | 99 85403 | .00421 | 2 | .99579 | 2
59 14266 | 91 | 85734 | ` 14688 2 "85812 | .00423 | 3 | .99577 1
60 |9.14356 | 99 |10. 85644 | 9. 14780 10. 85220 |10. 00425 9. 99575 | l
: , ek ..
970» cos dE sec cot ra tan esc 1’ sin «820

1384

TABLE 33
Logarithms of Trigonometric Functions
o .
8 > sin Diff Di
5 1 ese tan Á cx eg Dif. cos «171°
Í Ta y
0 | 9. 14356 10. 85644 eg
A k . 1478 7
[mS Aar ie S
a SE 4 SOR RA E estan oeren ët M. Ai NE
. 6 | 15054 | 9! : 8 . 99572
a lana | Hg 84946 | . 00430 | 2 p:
.85286 | .151 91 - 00430 .99570 | 57
A 14803 RÀ 10. 85197 M 91 84855 | . 00432 7 : 99568 56
6 | -14891 | gg | . 89109 | . 15327 der P a I
.85020 | .15417 | 99 E 5 99565
EN 22 34931 | | 84583 | .0 EE 54
1 1 BIS 91 Ras . 00437 . 99
CM EST 88 | 184843 -18898 | 90 | -84402 |. 00441 2 99561 | 22
10 |9.15245| gg |10. 84755 | 9. 15688 RE FOSSE log dE ER
12 13421 gg | -84667 | .15777 do O. $4223 tdi 1 | 9.99557 | 50
: . 84579 | .158 0 : 995
B 15508 | $ 8 67 84133 2 | - 99556} 49
„84492 | . 1595 89 . 00446 . 9955
14 15596 | 88 8 6 84044 2 99554 | 48
. 84404 | .16046 | 20 . 00448 99552 | 47
15 15683 | Ëm 89 83954 | .00450 | 2 | ` e
84317 | 9. 161 . 004: . 99550
de s aa "iem umen: [Rome a
18 TRE 7.) EE, E e El EE |
91 e . 00455 :
A eer ross a 83599 5 | 2 | - 99545] 43
. 83970 . 16489 88 4 . 00457 9954 E
20 |9.16H6| 15 9| 88 | seul 00459 | 2 | ` 31,2
21 deso sud nae eee 10. 83423 |10. 00 Hae qc
e E ek epee ood MERC ss |10. 33423 |10. 00461 | 2 | 9. 99539 | 40
| . 8: . 00463
23 16374 | 85 83711 | . 16753 88 832: 2 | -99537 | 39
88 . 83247 | . 00465
E .83540 | . 16928 | 87 : 9 | .00467 9
25 |9.16545| * |i ` 83072 | .00 1 | -99583 | 37
é 0. 83455 88 00508 . 9953
26 16631 | 86 . 17016 10. 82984 |10 2 2| 36
27 16631 | g5 | -83369 | .17108 s; |10. 82984 |10. 00470 | > | 9. 99530 | 35
28 16716 | g5 | -83284 | . 17190 87 Ke eg [eitis eae o
29 I0 d 85! W35198 [Gere Bv. [252879 naa 102 | CEP NE
. 83114 17363 | 86 | ` (23 | .00476
30 [9.16970 | > [ER ` 82637 2 | :99524| 32
i0. 83030 87 . 00478 9
31 17055 | 89 „17450 10. 82550 2 | 90522 | 34
` 829. ; 10. 00480
32 dēt 2 82945 | . 17536 | 86 82464 2 | 9.99520 | 30
3e IIS | Bey SSC [gros e o [od a ieee
34 17307 | 84 .82777 | .17708 | 86 is . 00483 .99517 | 2
.82693 | 177 ge |.:82292 |. 100485 |3 8
35 17391 84 . 17794 . 82206 S I . 99515 27
: 10. 82609 86 . 00487
36 17474 | 83 - 17880 10. 82120 37 | 2 | .99513 | 26
37 17553 | 84 .82526 | .17965 | 39 . 82035 10. 00489 | 7 | 9.99511 | 25
38 17558 | gg | .82442 | .18051 E ee ` 99509
i E . 81949 | .00493 | 2 24
39 Ene. 82359 | . 18136 | 85 . 99507
E Raa DE e meee te 2 23
40 17807 | 59 : J . 81779 : 2 | .99505| 22
10. 82193 85 . 00497 -
4] 17890 | 33 5 . 18306 10. 81694 2 . 99503 | 21
2 |) 537590 | gad. E e tt Sr (ee lhe IES
43 renee |. 82) BE (ee 84, PAR D (go EE 1
. 815 o 5 . 00503 2 19
44 18137 | 82 81945 | .18560 | $ ` 99497
. 81863 | | 18 84 | -81440 | .00505 | 2 18
45 18220 | °° .18644 | 8 81356 1 | .99495| 17
46 53 Ho si780 |w 18728 | %* [10 81277 |i 00808 - 99
47 EUN ME EE ` 18812 Sh eee ties E 5 5799492 ic
48 18465 | 82 |: . 18896 i : 0 99490
49 so 131535 E 81104 | .00512 | 2 | | 14
50 ed 11 inp lios ` 19063 RE 430057 WË 4 90486 | 12
51 g1 |10. 81372 | 9. 191 . 00516 99
52 eg EN C ` 19229 a a is. ; 9 ee ið
53 18871 | $l : . 19312 "a . 00520 ` 99
č . 80688 2 | - 99480 9
54 18952 | 81 „81129 | .19395 | 83 „00522 994
Ë : ` 81048 95 | gg | .80605 | .00524 | 2 | : T8 |- i8
55 19033 81 . 19478 8 8052' 9 . 99476
: 7 3 | -80522 | .00526 | 2 7
56 19033 | go |10. 80967 | 9. 19561 i 9 | .99474
2 ` 80887 g2 |10. 80439 |10. 005 6
Sri | 8 4B DIE dE IHE IE
59 19273 | gq | -80727 | .19807 82 |0 . 00532 s 4
5 : . 80647 82 - 80193 | .00 2 . 99468 3
60 | 919433 | 80 |10. 80567 | o. 19971 | 82 e 80020 El
1 - SE 10. 80029 |10. 00538 | 2 . 99464 1
98% COS Diff à 9. 99462 0
im sec cot Diff t Diff
an
csc v > sin 4

Ek
00
jt

o

TABLE 33

Logarithms of Trigonometric Functions

. 80567
. 80487
. 80408
. 80328
. 80249

. 80170
. 80091
. 80012
. 79933
. 79855

. 80029
. 79947
. 79866
. 79784
. 79703

. 00538
. 00540
. 00542
. 00544
. 00546

MAD 04
. 79698
. 79620
. 79542
. 79465

. 79622
. 79541
. 79460
. 19379
. 79299

. 00548
. 00550
. 00552
. 00554
. 00556

. 79387
. 79309
. 79232
. 79155
. 79078

. 79218
. 79138
. 79058
. 78978
. 78898

. 00558
. 00560
. 00562
. 00564
. 00566

. 79001
. 78924
. 78847
„78771
„78694

. 78818
. 78739
. 78659
. 78580
. 78501

. 00568
. 00571
. 00573
. 00575
. 00577

. 78618
. 78542
. 78466
. 78390
. 78315

. 78422
. 78343
. 78264
. 78186
. 78107

. 00579
. 00581
. 00583
. 00585
. 00587

. 78239
. 78164
. 78088
. 78013
. 77938

. 78029
. 17951
. 77873
360095
CN

. 00589
. 00591
. 00593
. 00596
. 00598

. 77639
. 77562
. 77484
. 17407
. 17330

. 00600
. 00602
. 00604
. 00606
. 00608

. 77863
. 77789
77714
. 77639
. 71565

L 77253
MAS
224/099
. 77023
. 76946

. 00610
. 00612
. 00615
. 00617
. 00619

. 77491
. 47417
. 77343
. 17269
„77195

. 76870
. 76794
. 76717
. 76641
. 76565

. 00621
. 00623
. 00625
. 00628
. 00630

. 77122
. 77048
„76975
„76902
. 76829

. 76490
. 76414
. 76339
. 76263
. 76188

. 00632
. 00634
. 00636
. 00638
. 00641

. 99368
. 99366
. 99364
. 99362
. 99359

. 76756
. 76683
. 76610
. 76538
. 16465

. 76113
. 76038
. 15963
„75888
„75814

. 00643
. 00645
. 00647
. 00649
. 00652

. 99357
. 99355
. 99353
. 99351
. 99348

. 76393
. 76321
. 76248
. 76177
. 76105
. 76033

. 75739
. 75665
. 75590
. 75516
. 75442
. 75368

. 00654
. 00656
. 00658
. 00660
. 00663
„ 00665

| D O DO DO DO DO GO DO DO BO DO CO DO DO DO DO DO CO BO B2 BO DO DO GO DO DO DO DO BO DO DO DO GO TO BO NNNNN NNNNA NNNNN NNNNN DDD DO DO

9. 99346
„99344
. 99342
. 99340
. 99337
. 99335

sec

tan

csc

eS? |o odo o-10:«

T
QO
o

1386

TABLE 33

Logarithms of Trigonometric Functions

tan

cot

cos -169°
y

. 23967
. 24039
. 24110
. 24181
. 24253

. 24324

. 24395
. 24466
. 24536
. 24607

. 76033
„75961
„75890
„75819
. 75747

9. 24632
. 24706
. 24779
. 24853
. 24926

. 24677
. 24748
. 24818
. 24888
. 24958

. 25028
. 25098
. 25168
. 25237
. 25307

. 25376

. 25445
. 25514
. 25583
. 25652

. 75676
. 75605
. 75584
. 75464
. 15393
. 75323

. 75252
. 75182
. 75112
. 75042

. 25000
. 25073
. 25146
. 25219
. 25292
9. 25365
. 25437
. 25510
. 25582
. 25655

. 75368
. 75294
. 75221
. 75147
. 75074

. 00665
. 00667
. 00669
. 00672
. 00674

. 99335
. 99333
. 99331
. 99328
. 99326

. 75000
. 14027
. 14854
. 74781
. 74708

. 00676
. 00678
. 00681
. 00683
. 00685

. 99324
. 99322
. 99319
. 99317
. 99315

. 74972
. 74902
. 74832
. 74763
. 74693

9. 25727
. 25799
. 25871
. 25943
. 26015

. 74635
. 74563
. 74490
. 74418
. 74345

. 00687
. 00690
. 00692
. 00694
. 00696

. 99313
. 99310
. 99308
. 99306
. 99304

. 25721
. 25790
. 25858
. 25927
. 25995

. 74624
. 14555
. 74486
. 14417
. 74348

. 26086
. 26158
. 26229
. 26301
. 26372

. 74273
. 74201
. 74129
. 74057
. 13985

. 00699
. 00701
. 00703
. 00706
. 00708

. 99301
. 99209
2109207
. 99294
. 99292

. 26063
. 26131
. 26199
. 26267
. 26335

. 26403
. 26470
. 26538
. 26605
. 26672

. 74279
. 74210
. (4142
. 74073
. 74005

9. 26443
. 26514
. 26585
. 26655
. 26726

. 73914
. 73842
. 73771
. 73699
. 73628

. 00710
. 00712
. 00715
. 00717
. 00719

. 99290
. 99288
. 99285
. 99283
. 99281

. 73937
. 73869
. 13801
. 73733
. 73665

. 20797
. 26867
. 26937
. 27008
. 27078

. 73557
. 73486
. 73415
. 73345
. 13274

. 00722
. 00724
. 00726
. 00729
. 00731

. 99278
. 99276
. 99274
209271.
. 99269

. 26739
. 26806
. 26873
. 26940
. 27007

. 73597
. 73530
. 73462
. 13395
. 13328

. 27148
. 27218
. 27288
i 27357
. 27427

. 73203
. 73133
. 73063
. 72992
. 72922

„00733
„00736
„00738
. 00740
. 00743

. 99267
. 99264
. 99262
. 99260
. 99257

. 27073
. 27140
. 27206
. 27273
. 27339

. 73261
. 73194
„78127
„73060
. 72993

9. 27496
. 27566
. 27635
. 27704
. 27773

. 72852
. 72782
.72712
„72648
. 72573

. 00745
. 00748
. 00750
. 00752
. 00755

. 99255
. 99252
. 99250
. 99248
. 99245

9. 27405
„27471
. 27537
. 27602
. 27668

72927
. 72860
. 72794
2727
. 72661

. 27842
.127911
. 27980
. 28049
. 28117

. 72504
. 72434
.12365
. 72296
. 12227

. 00757
. 00759
. 00762
. 00764
. 00767

9. 27734
.27799
. 27864
. 27930
. 27995

9. 28060

. 72595
. 12529
. 72463
. 72398
. 12332

9. 28186
. 28254
. 28323
. 28301
. 28459

. 72158
. 72089
. 72020
. 71951
. 71883

. 00769
. 00771
. 00774
. 00776
. 00779

9. 99243
. 99241
. 99238
. 09236
. 99233

9. 99231
.. 99229
. 99226
. 99224
. 99221

. 72266
. 72201
„72136
. 72070
. 12005
. 71940

. 28527
. 28595
. 28662
. 28730
. 28798
. 28865

. 71814

. 71746
s TM COR
. 71609
. 71541

. 00781
. 00783
. 00786
. 00788
. 00791

. 71473
. 71405
„71338
„71270
71202
MTS

„00793
„00796
„00798
„00800
„00808
. 00805

9. 99219
3 Sed
. 99214
: 99212
. 99209

9. 99207
. 99204
..99202
. 99200
229907

9. 99195

cO» N O D

cos

sec

cot

tan

esc

O? |0 - nwa

4
“J
o

1387

TABLE 33
Logarithms of Trigonometric Functions
1 1-5 sin xd ese tan Ys À cot sec Ge cos «1682
y y
O | 9.28060 | ¿5 |10.71940 | 9.28865 | gg |10. 71185 |10. 00805 | „ | 9.99195 | 60
1 | -28125 | 65 | -71875 | . 28033 | 67 | .71067 | .00808 | 3 | .99192| 59
2 | -28190 | g4 | .7I810 | .29000 | G7 | .71000 | 00810 | 2 | :99190 | 58
3 | .28254 | 65 | -71746 | .29067 | 67 | .70933 | .00813 | 3 | mal 57
4 | .28319 | 65 | .71681 | .20134 | $7 | . 70866 | ‘00815 | 2 | ‘99185 | 56
| 5 |9.28384 64 |10. 71616 | 9. 29201 | we |10. 70799 |10. 00818 9 | 9.99182 | 55
6 | -28448 | 64 | .71552 | .29268 | 57 | .70732 | .00820 | 2 | .99180| 54
7 | 28512 - 71488 | .20335 | g; | .70665 | .00823 | 3 | 99177 | 53
8 | .28577 M . 71423 | .29402 | gg | .70598 | .00825 | 2 | :99175 | 52
9 | | 28641 és . 71359 | .29468 | g7 | .70532 | | 00828 | 3 | ‘99172 | a
10 | 9. 28705 10. 71295 | 9. 29535 10. 70465 |10. 00830 9. 99170 | 50
11 | .28769 FR ` 71231 | .29601 Së . 70399 | .00833 | 3 | .99167 | 49
12 | .28833 | g3 | .71167 | .29668 | 64 | .70332 | .00835 | 2 | :99165| 48
13 | .28896 | gj | -71104 | .29734 | 66 | .70266 | .00838 | 3 | 99162 | 47
14 | .28960 | g4 | .71040 | .29800 | Só | .70200 | .00840 | 2 a x
29024 10. 70976 | 9. 29866 10. 70134 |10. 00843 9. 9915
i po E -70913 | ` 29932 ae - 70068 | .00845 | 2 | .99155 | 44
17 | ¿29150 | € - 70850 | .29998 | § | :70002 | .00848 | 3 | `99152 | 43
18 | :29214 | 6% | “70786 | :30064 66 | -69936 | :00850| 2 | :99150 | 42
19 | .29277 HE .70723 | .30130 | 2 | .69870 | :00853 | 3 ct d
" ` 30195 10. 69805 |10. 00855 9.
2 pee 63 noða aoe! 05 | . 69739 | . 00858 3 | .99142 | 39
22 29466 | 93 | "70534 | 30326 -69674 | .00860 | 2 | .99140 | 38
23 | .29529 | 68 | “70471 ` 303901 4 - 69609 | .00863 | 5 | .99137 | 37
24 | .29591 | 02 | 70409 | .30457 | 66 | | 69543 E á E 2 1
30522 10. 69478 |10. 00
4 tat 62 MEES E 65 | '69413 | .00870 E 99130 | 34
27 | .29779 | 93 | “70221 | ¿30652 | 99 | “60348 | | 00873 3 | .99127 | 33
[i Sa hen 30717 | 99 | ` 69283 | .00876 :99124 | 32
28 | | 29841 "70159 | ` 4: S
29 | ` 29903 es . 70097 | .30782 | $3 | .69218 | .00878 | 2 | .99122 | 31
30 | 9. 29966 10. 70034 | 9.30846 | gs |10. 69154 |10. 00881 | 5 | 9.99119 | 30
31 30028 | 92 69972 | ` 30911 .69080 | .00883 | 3 | .99117 | 29
32 | ¿30090 | 9? | `69910 | :30975 | 94 | :69025 | | 00886 3 | ¿99114 | 28
61 ; 1040 | 65 | "68960 | .00888 99112 | 27
33 | 30151 ` 69849 | 3 41 4 27
34 | 30213 | 82 [2069787 | | 31104 04 | 68896 | .00891 | 3 | .99109
35 | 9.30275 10. 69725 | 9.31168 | gg |10.68832 |10. 00894 | 5 | 9. 99106 | 25
36 | .30336 Lo „69664 | . 31233 | 83 : 68767 - 00896 > - 99104 24
37 | ` 30398 1169602--00:31297 MOT. Jee SC 23
38 | .30459 | 91 | “60541 | | 31361 04 | .68639 | 00901 | 3 - 99099 22
39 | 30521 | 62 | 69479 | .81425 | 0% | -68575 | .00904 | 3 |. A err
a m
B E EE |
41 | .30643 ` 69: : oo men -00909 | 3 | 9 19
61 68384 | ` 00912 | 2 | | 99088
42 | | 30704 69296 | .31616 | 6% |: : 8 | 18
43 | 30765 | 91 .69235 | .31679 | 63 | .68321 | .00914| 3 - 99086 17
44 | | 30826 At 69174 | .31743 | 6% | .68257 | .00917 | 3 mons D.
45 | 9.30887 | ei 10. 69113 -31800 E: 10. 68194 10. 00920 2 | 9. 99080 | 15
46 | .30947 | 8° | .69053| . 63 | -68130 | .00922 3 | .99078 | 14
47 | 031008 .68992 | .81933 | 63 | .680 "00! 2 ES 13
48 | ` 31068 E .68932 | .31996 | 03 - 68004 : 00928 4 : 99072 12
49 | .31129 | 6) | 68871 | .32059 | 63 | . 67 OSU E E
BEE Eeer ma (ES?
O || 25 | Ok i 63 | -67815 | -00936 | 3 al
2 | ` 31310 - 68690 | .32248 | 63 | .67752 | .00: 3 | -99062 | 8
e :31370 | 90 | “68630 | . 32311 E . 67689 | .00941 | 3 - 99059 7
d 32373 ` 67627 | .00944 ` 99056.
O eee [S - 64 |10.00946! + | 9.99054 | 5
66 | lao 59 |” Geary | 32498 | 62 d 67502 | .00949 S | .9901| 4
dā Lēts $0 i ` 325€ 63 ` 67439 | . 00952 ` 99048 3
57 | 131609 | 60 | -68391 | .32561 | gz | -67439 | .00952 3 | .99048 | 3
58 | -31669 59 | .68331| . 32623) go | .67377 | .00954 | 3 | -99046 | 2
` 31728 ` 68272 | ` 32685 . 67: . 00€ cM deceret Mes
60 | 9.31788 | 60 |10.68212 | 9.32747 | 9? |10. 67253 |10. 00960 9. 990 8
; DEN o. a
1012» cos Diff sec cot FP tan ese E sin 78

1388

TABLE 33

Logarithms of Trigonometric Functions

12° sin Din:
3 1⁄ csc tan d
| 1 cot sec S cos -167°
o | 9.31788 1 |
q 59 |10. 68212 | 9. 327
1 | -31847 to ` 68153 : 32810 ES 67190 | 00962 | 2 | 99038 | 59
2 | 31907 . 32872 - 67128 |. 3 | :99035 | 38
1E | 58 | IE. 61 | -67 00965 | 3 | .99035 | 58
:67975 | 132005 | 92 | :67005 | 00970
ROB 62 | 67005 | :00970 | 2 ` 99030 | 56
5 [932084 | 54 |ī0. 67916 | 9. 33057 10. 66943 Ie oE
: sanas | D cem | © 38119 62 | UL . 99027 | 55
7 | «82202 | 59 | .67798 | .33180 | 62 | :60820 00978 | 2 | 199022 | 33
IB AENEIS | 82 | ` 00978 : 99022 | 5
-67739 | .33242 | g; | .66758 | .00981 : 2
EUR ET 3| go | 66697 | .00984 | 3 :99016 | 31
10 [9.32978 | 59 |10.67622 | 9. 33365 10. 6663 alarm.
NE AEN IE IE - 66635 |10. 00987 | > | 9.99013 | 50
12 | 32495 | 55 | .67505 | .38487 | Qi 166513 | 100992 | 3 | ‘90008 | 48
IB | 28 | I ANE 3| .00992 - 99008
- 67447 | .33548 | G] | .66452 | -00995 : 47
15 | 9.32670 | 25 1 g Sr os 2 | 2002 do
15 | 9.32670 | 5g [10.67330 | 9. 33670 10. 663 E Jr
IB IN I E - 66330 |10. 01000 | 3 | 9.99000 | 45
UB INN UB | Si - 66269 | .01003 | 3 | . 98007 | 44
UB | 38 | Coria | INE 08 | ` 01006 ` 98994
- 67156 og ` [9066147 |W01000 | ES 42
E -33913 | QV | .66087 2 | 98080 | 41
20 | 9.32960 | gg |10.67040 | 9. 33974 10. 66 01014 | Fees
Aag quU | > saosa | co ee 026 |10. 01014 . 98986
JE GENE IB JE - 65966 | . 01017 3 | 08083 | 39
Ap | 58 | IB INE 5905 | :01020 | 3 | :98950| 38
- 66867 60 | ` 65845 | :01022 | 2 | ‘oso7s| 37
RTT -34215 | 0 65785 3 | '98975 | 36
25 | 9.33248) 57 |10. 66752 | 9. 34276 5 bo na |9 us
AE MSN | > UE . 65724 |10. 01028 9897
z |: 57 | 0008 | - 34838 | eo | - 95064 |. 01031 3 | "98969 | 34
dE JAN 68a -34396 | Go | . 65604 | :01033| $ :08967 | 33
Er N or a IR šā ` 65484 | 101039 3 | `. 2
30 | 9.33534) 57 |10. 66466 | 9. 34576 10. 2| ? S 98955 |0
E a7 |10. 69486 |'9. 34575 | so |10. 65424 [10.01042
s2 | cocar | 36 | -e6333 - 84635 | go | -65365 | .01045 | 3 ` 98955 | 29
` . 34814 t 1053 |
Gba ID 60 | -65186 | 01053 | 3 ` 98947 | 26
AE MA IU 10. 65126 |10. 01056 9894
Am WM IM | 39 65067 | 01059 | 3 | . 98941 | 24
38 | :38987 | 56 | .66013| .35051 | (9 #5008 | God | 3 | Casas | 23
IE Eae DNE E IINE E
40 se |10. 65900 | 9. 351 : 70
ÄREM -35170 | 5g |10.64830 |10. 01070 o =
43 34212 | 56 | -65788 | . 35288 Se Ee LAE
4i [| 194209 | ge. [11565732 EE S "cl o | 3 | loses | 18
45 56 10. 65620 | 9. 35 ` 64536 1084 l
AN | 30 "iii -35464 59 10. 64536 |10. 01084 A ot
AB cA NN JB M. 64477 | .01087 | 3 | “98913 | 14
4 |, 995 NE 0 5r MELLE NĒ 9510 | 13
o wasser! 6 3105295 SEE 5s | 04300 | 101093 | 3 | Z98907 | 12
by [9.34698 | 55 310. 65342 | 9. 35757 D 960 | 01006 | $ | -98004 | ji
ECIAM I | 58 10. 64243 |10.01099 | * |5. 3
SC Stee E E D zi
Sak ee AAO eE E Gana? | Comos | 3 | oso! 8
54 | cause | 33 | count oo 38 - 64069 | -01107 | 3 teu] e >
$6 | 34084 | sg [10. 65066 | 9. 36047 58 (ton | comio | $ | 198890 | d
57 35044 | 99 „65011 | .36105 | 98 10. 63953 |10. 01113 3 [3
3o Lé | er Inadobo a Së | corto | 3 | INE
28 VS ās. E E E -63837 | connie | 3 men 3
55 grees a NES Gro | .or22 | 3 | Cosme | 2
a 10. 64791 | 9: 36336 | 57 |10. 63664 |10. 01125 3 wes 1
að hF 0. 63664 |10. 01128 | 3 9.98359 | 4
à = ET .98872 | 0
i di xx (biti t
1 sin +770

1389

TABLE 33
Logarithms of Trigonometric Functions
o> i
13 DIS. cos «1662
y
o 3 . 98872 60
P 2 . 98869 59
2 3 . 98867 58
^ 3 . 98864 57
3 . 98861 56
5 3 . 98858 55
d 3 . 98855 54
T 3 . 98852 53
3 3 . 98849 52
3 . 98846 51
3 . 98843 50
3 . 98840 49
3 . 98837 48
3 . 98834 47
3 . 98831 46
3 98828 45
3 98825 44
3 98822 43
3 98819 42
3 98816 41
3 98813 40
3 98810 39
3 98807 38
3 98804 37
3 98801 36
3 98798 35
3 98795 34
3 98792 33
3 98789 32
3 98786 31
3 98783 30
3 98780 29
3 98777 28
3 98774 27
3 98771 26
3 98768 25
3 98765 24
3 98762 23
3 98759 22
3 98756 21
3 98753 20
4 98750 19
3 98746 18
3 98743 a
3 98740 16
3 98737 15
3 98734 14
3 98731 13
3 98728 12
3 98725 11
3 98722 10
4 98719 9
3 98715 8
3 98712 7
3 98709 6
3 98706 5
3 98703 4
3 98700 3
3 98697 2
4 98694 1
98690 0
; 4
Diff.
y «76°

1390
TABLE 33
Logarithms of Trigonometric Functions
14°- sin S esc tan me F cot sec a cos -165°
y y
0 | 9. 38368 10. 61632 | 9. 39677 10. 60323 |10. 01310 9.98690 | 6
1 | .38418 | 20 | 61582 | .30731 | 54 | .60269 | . 01313 | 3 | 98687 59
2 | .38469 | 5) | .61531| 130785 | 23 | . 60215] .01316 | 3 | 208684 58
3 | 38519 | 51 | -61481 | . 30838 | 54 | . 60162} .01819 3 | :98681 | 57
Å e Es E Lu $3 | 60108 | .01322 | 3 | :98678 | 56
6 | 38670 | 50 | 61330 | 39999 | 94 |” 60001 | 01329 | 4 | 98671 | 34
7 | 138721 | 51 | 161279 | 140052 | 53 | 59948 | .01332 | 3 | :98608 | šā
8 | .38771 | 50 | .61229 | :40106 | 93 | :59894 ` 01335 E ` 08665 | 52
9 | .38821 ` 61179 | | 40159 59841 | `. 01338 ` 98662
2 .98662 | 51
10 | 9.38871 | go |10. 61120 | 9. 40212 e 10. 59788 |10. 01341 Å 9.98659 | 50
AE ENEE
13 | ¿39021 | 30 | “60979 | 40372 | 53 | 50628 | 501351 | 3 | osea9 | 47
14 | .89071 | 2) | 60929 | | 40425 | 23 | | 59575 ` 01354 - : 08646 1 Ze
15 [939127 | 4g [1060870 |9. 40478 | 55 |10.59522 10. 01357 | 3 | 9.98643 | 45
17 | 239220 | 50 | :&orso | :40584 | 5% | v29416 | velas | © US
18 | :39270 | 50 | :60730 | 40636 | 52 | :593e4 | 01367 | 3 | l9 S5 | 43
19 | .39319 | šo | :60681| :40689 | 23 | 50811 :01370 | 3 98630 |. 41
20 | 9. 39869 | 49 [10 60631 -40742 | gg |10. 59258 |10. 01373 : 9.98627 | 40
22. || 39467 | 9 |.:60533 | idoga El
22 | :39807 | 50 | - 60583) :40847 | 53 | .59153| .01380 | 3 | :98620 [í 38
24 | .39566 | 44 | 60434 | :40952 | 52 | :59048 toissa | 9 | Sesoni || 58
i ale.
25 [9.39015 | 49 10. 60385 | 9. 41005 | 55 10. 58095 |10.01390 | y | 9.98610 | 35
27 | aon | 49 | 360287 | 241109 | 92 | :os8o1| 01390 | 3 | veneer] šā
28 | ¿39762 | 19 | “60288 | aal 52 | 58839 | 01399 | 3 | Bt 33
29 | 39811 | 72 | .60189 | :41214 | 53 | 58786 701408 | £ | 198597 | 31
30 | 9.39800 | 49 10. 60140 | 9. 41266 | 5 0.58734 |10. 01406. : 9.98594 | 30
32 | 30008 | 49 | -60091 | -41318 | 52 | .58652| .01409 | 3 | : 08591 | 29
33 | .40006 | 48 | "59994 | ‘41422 | 92 ` 58578 solaio | < || bea Pa
34 | (40055 | 19 | ¿59045 Ee
€ g 52 . ` a .
2 Ponens 49 EE TEE 52 |10. 58474 |10. 01422 > 9. 98578 | 25
37 | 40200 | 48 | -59848 | . 41578 | 51 | .58422 | 01426 | $ | .98574 | 24
38 | ¿0200 | 49 | -59800 | .41620 | 52 | .58971| 01420 | 3 | ml 23
39 | .40297 19 | 59703 | | 41733 | 92 58267 | comas | 3 |. k.
40 |9. ET. 4 |e
10 [9.40946 | jg 10. 59654 | 9. 41784 | 59 [10.58216 |10. 01439 | 3 | 9. 98561 | 20
42 | 34032 | 48 | : 30606 | .41836 | gi | .58164| .01442 | 3 | 08558 | 19
43 ` 40490 | 48 "59510 | 41030 | 52 .98113 | .01445 4 . 98555 18
44 | .40538 | 48 | :59462 | 41900 | 9! 88010 | ^1 01452 |Ë `o8548 |Í 16
45 | 9. 40586 10. 59414 | 9.42041 % 10.57 ; 3 ss is
R 50414 | 9. 42041 | 59 |10. 57959 |10. 01455 | 4 | 9.98545 | 15
47 | 40082 | 48 | + 59866) -42093 | 51 | -57907 | .O1450 | $ | “08541 |Í. 14
48 | 240050 | 48 | 29818 | -42144| 51 | 57856 | .01462 | 3 | mea | 13
49 | .40778 | 48 | .59222 | 42046 | 91 kna o NR
50 | S dosis BT ATA. .01469 | 3 | .98531| 11 |
51 . 40873 48 i 59127 : 42348 51 10. 57703 |10. 01472 3 9. 98528 10
52 | .40921 | 48 | :59079 | | 42399 | 51 en E Le AO S
53 | .40968 | 42 | .59032| 42450 | 5! | 57 oras |8. A
54 | 141016 | 15 fui 58984 |Mkaosou | 19. kerora oras EE
55 9. 41 . 51 : : . 98515 6
36 | % 41063 | 4g |10.58937 | 9.42552 | 5, |10.57448 |10. 01489 * | 9.98511 | 5
47 | -58889 | . 42603 57397 | .01492 | 3
57 | .41158 . 58842 | .42653 | 50 | : 311 PEE [IS
583 OPTAT 51. [887347 [AR 01495 98505 | 3
e 47 | -58795 | .42704 . 57296 | .01499 | £
60 lo 1202 | 48 | 58748 | .42758 | $1 | 57245 | ¿01502 | 3 :98498 | 1
ls: E 10. 58700 | 9. 42805 10. 57195 |10. 01506 | * | 9.98494 | 0
905 cos vj Diff i 4
104 1 sec cot tan csc A s sin

T
J
a

o

TABLE 33

Logarithms of Trigonometric Functions

«OO ADORNO `

. 58700
. 58653
. 58606
. 58559
. 58512

. 58465
. 98418
. 58372
„58325
„58278

„57195
„57144
. 57094
. 57043
. 56993

„01506
„01509
„01512
„01516
„01519

. 58232
. 58185
. 58139
. 58092
. 58046

. 56943
. 56892
. 56842
. 56792
. 56742

. 01523
. 01526
. 01529
. 01533
. 01536

1391

cos -164°
y

. 08494
. 98401
. 98488
. 98484
. 98481

. 98477
. 98474
. 98471
. 98467
. 98464

. 57999
. 57953
. 57907
. 97860
. 97814

. 56692
. 56642
. 56592
. 56542
. 56492

„01540
„01543
„01547
„01550
„01553

. 98460
. 98457
. 98453
. 98450
. 98447

. 57768
. 57722
. 07676
. 07630
. 57584

. 56442
. 56393
. 56343
. 56293
. 56244

. 01557
. 01560
. 01564
. 01567
201571

. 98443
. 98440
. 98436
. 98433
. 98429

. 57539
. 57493
. 57447
. 57401
. 57356

. 56194
. 56145
. 56095
. 56046
. 55996

. 01574
. 01578
. 01581
. 01585

. 98426
. 98422
. 98419
. 98415
. 98412

. 55947
. 55898
. 55849
. 55799
. 55750

. 98409
. 98405
. 98402
. 98398
. 98395

. 57310
. 57265
. 57219
-57174
. 57128

. 55701
. 55652
. 55603
. 55554
. 55505

. 98391
. 98388
. 98384
. 98381
. 98377

. 57083
. 57038
. 56992
. 56947
. 56902

. 55456
. 55408
. 55359
. 55310
. 50262

. 98373
. 98370
. 98366
. 98363
. 98359

. 56857
. 56812
. 06767
. 56722
. 56677

. 55213
„55164
. 55116
. 55067
. 55019

. 98356
. 98352
. 98349
. 98345
. 98342

. 56633
. 56588
. 56543
. 56498
. 56454

. 54971
. 54922
. 04874
. 048526
. 54778

. 98338
. 98334
. 98331
. 98327
. 98324

. 56409
. 56365
. 56320.
. 56276
. 56231

. 54729
. 54681
. 54633
. 54585
. 54537

. 98320
. 98317
. 98313
. 98309
. 98306

. 56187
. 56143
. 56099
. 56054
. 56010
. 55966

. 54489
. 54441
. 54304
. 54346
. 54298
. 54250

. 98302
. 98299
. 98295
. 98291
. 98288
. 08284

D |o—= neko oc -100:

sec

tan

sin

1
J
=

o

1392

F
`

TABLE 33
Logarithms of Trigonometric Functions
sin eE csc tan Tü cot sec M cos -163°
y
9.44034 | 44 |10. 55966 | 9.45750 | 4y |10. 54250 |10. 01716 | „ | 9.98284 | 60
-44078 | 44 :55922 | . 45797 | 4% | .54208 | .01719 | 4 | .98281 | 59
di IB EB E-IME A
.44210 | 14 | .55790 | :45940 | 48 | :54060| .01730 | 3 | :98270 | 56
9.44253 | ** 3, : 4 l-5 98266 | 55
: 44 |10. 55747 | 9. 45987 | ¿g |10. 54013 |10. 01734 | 4 | 9.98266 | 55
-44297 | 44 55703 | .46035 | 47 | .53065 | .01738 | 3 | .98262 | 54
PIENE Hr | g] g
aaas || 43 55572 | . 46177 | 47 | .53823| .01749 | $ | 198251 | 51
9.44473 | 44 ies qd : 3 082
44 |10. 55528 | 9. 46224 | 4, |10. 53776 |10. 01752 | 4 | 9.98248 | 50
44516 | 43 55484 | .d6271 | 4g | .53729 | .01756 | 4 | .98244 | 49
44602 | 13 | :55398 | 46366 | 17 | 23034 | 201768 | 3 | 98287 | 47
44646 | 14 | 155354 aal 47 | :53587 | 01767 | £ | 98233 | 46
9. 44689 | 4° ; "A: i 4 lg :
44 |10.55311 | 9. 46460 | 47 |10.53540 |10. 01771 | y | 9.98229 | 45
-44733 | 4 55267 | .46507 | 47 | -53493 | .01774 | % | .98226 | 44
` 44819 | 43 SRI | ose ados eee 4 | danais || dd
` 44862 | 43 55138 | .46648 | * | :53352| .01785 | 3 toi a
97 44905 | ` 22 068005 muet | oco. lija Dia D deeg E
i 43 |10. i
- 44948 4j 55052 ` 46741 ae 53259 | . 01793 3 98207 | 39
„45035 | 43 54965 AED 47 XE ee AE viv
.45077 | 42 54923 | "46881 | 59 | 553119 | giao | 5 (Lógum | ge
se ds ae rex pad 4 | 98196 | 36
"45120 | 43 |10. 54880 | 9.46928 | ¿y D 53072 |10. 01808 | 3 | 9.98192 | 35
-45163 | 4 54837 | . 46975 | 4g | -53025 | .01811 | % | .98189 | 34
45202 | 13 | 154708 | :47114 | 46 | 52886 | 01823 | 4 | Zär) 91
PURO NM ue med. VAR i 3 |_-98177 | 31
453% | 43 [0 54666 | 47160 | D 52840 0.01826 | 4 | 998174 | 30
V ` 47207 52793 | . 01830 ` 98170 | 29
45419 54581 | ` 47253 | 49 52747 E
an ē 24081 | . 47253) 46 | . 52747 | .01834 | 1 | 98166 | 28
„45504 | 42 54496 | . 47346 | 47 | ` 52654 Kier BE E
o. 45647 E aaa la So PET i ees
45547" e [10 9.47392 | „g |10: 52608 |10. 01845 | 4 | 9.98155 | 25
; J 54411 | . 47488 | 4 52562 | . 01849 98151 | 24
` 45632 54368 | 47484 | 49 52516 4
: 45632 | 12 gases tr O - 01853 | 3 | .98147 | 23
ore | 42 24220 |. 47530 | 46 | .52470| .o1856 6
gat) 42 | bated | 46 |_- 52424 | . 01860 | $ | 98140 | 21
` 28801 | 43 |10 54242 | 9. 47022 | „g |10. 52378 [0.01864 | | | 9.98136 | 20
Å 25 99 | .47668 | 46 | .52332 | .01868 :98132 | 19
` 45843 54157 | | 47714 522 3
v E BIST | 4214 | 4e | 52286 | .oiēvī | % | :os1o9| 18
e ala | ad HE
5 : = 4 `
9. 45969 | 42 10. 54031 9. 47852 45 |10.52148 |10. 01883 | , | 9.98117 | 15
See EE SECHER | .or800 | 4 | :osrO| 18
_-46186 | 41 53864 | . 48035 | 46 (61968 | o1ses |4 98102 | 11
= X 1 L3
9. 46178 42 10. 53822 9. 48080 ds 10. 51920 10.01902 | , | 9.98098 | 10
Y 35700. [2242120 (as) ae .01906-| 4 | .98094 | 9
iÍ i 51829 | ` 01910 98090 | 8
e 53697 | .48217 | 19 | 51783 | .01913 | 39 | o8087| 7
SE 53655 | . 48262 | 45 | .51738 | 01917 4 | :98083| 6
SS 42 10. 53614 9. 48307 dd 10. 51693 10. 01921 | 4 [9.98079 | 5
46469 | A 153531 | lides9g 1125 E .01925 | 4 | .98075 | 4
: 3 .51557 | ` 01933 | 4
„46552 | 41 46 : . 98067 2
9.46594 | 742 (10 23406 |7g 45439 ag ger | zosi EE
; 9. 48534 | 10. 51466 |10. 01940 9. 98060 | 0
Diff. i S
SCH 1 sec cot p tan ese (Pif. gin 7

4
J
Q2

o

1393

TABLE 33
Logarithms of Trigonometric Functions
1795 sin "a csc tan i cot sec A cos «162°
y y
0 | 9. 46594 10. 53406 | 9. 48534 10. 51466 |10. 01940 „98060 | 60
41 45 4
1 | .46635 | 4| | .53365 | .48579 | 45 | .51421 | .01944 | f | .98056 | 59
2 46676 | 4; | .53324 | .48624 | 45 | .51376 | .01948 | % | .98052 | 58
3 46717 | 4, | .53283 | . 48669 | 12 | .51331 | .01952 | 4 | .98048 | 57
4 | .46758 | 49 | .53242 | .48714 | 45 | .51286 | .01956 | f | .98044 | 56
5 | 9.46800 | 4; |10.53200 | 9. 48759 | 45 |10.51241 |10.01960 | , | 9.98040 | 55
6 | .46841 | 41 | .53159 | .48804 | 42 | .51196 | .01964 | $ | .98036 | 54
7 46882 | 4; | .53118 | .48849 | 42 | .51151 | .01968 | $ | .98032 | 53
8 46923 | $! | .53077 | .48894 | 45 | .51106 | .01971 | 3 | .98029 | 52
9 46964 | 4; | .53036 | .48039 | 19 | 51061 | .01975 | $ | .98025 | 51
10 | 9.47005 | 4, |10.52995 | 9.48984 | 45 |10.51016 |10.01979 | , | 9.98021| 50
11 47045 | 10 | .52955 | . 49029 | 45 | .50971 | .01983 | f | .98017 | 49
12 47086 | 4! | .52914 | .49073 | 48 | .50927 | .01987 | 4 | .98013 | 48
13 47127 | 41 | .52873 | .49118 | 45 | .50882 | .01991 | 4 | .98009 | 47
14 47168 | fl | .52832 | .49163 | 49 | .50837 | . 01995 | 4 | .98005 | 46
15 | 9.47209 | 4) |10.52791 | 9. 49207 | 45 [10.50793 |10. 01999 | , | 9.98001 | 45
16 47249 | 40 | .52751 | .49252 | 44 | .50748 | .02003 | 4 | .97997 | 44
17 47290 | 4) | .52710 | :49296 | 45 | .50704 | .02007 | 4 | .97993 | 43
18 47330 | 19 | :52670 | .49341 | 44 | .50659 | .02011 | $ | .97989 | 42
19 47871 | 45 | .52629 | | 49885 | 45 | .50615 | .02014 | 4 | .97986 | 41
20 | 9.47411 | 4, |10.52589 | 9.49430 | 4, |10.50570 |10. 02018 | , | 9.97982 | 40
21 47452 | 41 | .52548 | .49474 | 45 | .50526 | .02022 | 4 | .97978 | 39
22 47492 | 40 | "52508 | . 49519 | 44 | .50481 | .02026 | 4 | .97974 | 38
23 47533 | 4) | .52467 | . 49563 | 44 | -50437 | .02030 | 4 | .97970 | 37
24 47573 | 40 | .52427 | .49607 | 45 | -50393 | .02034 | 4 | .97966 | 36
25 | 9.47613 | 4, |10.52387 | 9. 49652 | 4, |10.50348 |10.02038 | , | 9.97962 | 35
26 47654 | 44 | .52346 | .49696 | 44 | -50304 | .02042 | 4 | .97958 | 34
27 47694 .52306 | . 49740 | 14 | .50260 | .02046 | 4 | .97954 | 33
28 47734 | 10 | 52266 | .49784 | 44 | .50216 | .02050 | 4 | .97950 | 32
29 | :47774 | 10 | .52226 | . 49828 | 44 | .50172 | .02054 | 4 | . ee S
9. 47814 10. 52186 | 9. 49872 10. 50128 |10. 02058 9794
a .47854 | 40 | 52146] . 49916 | 44 | . 50084] . 02062 4 | 97938 | 29
32 47894 | 10 | ‘52106 | :49960 | 14 | .50040 | .02066 | 4 | -97934 | 28
33 47934 P. -52066 | .50004 | 44 | .49996 | .02070 | 4 | .97930 | 27
34 47974 | 49 | :52026 | .50048 | 44 | -49952 | .02074 | y | . EC žē
48014 10. 51986 | 9. 50092 10. 49908 |10. 02078
Se E 48054 | 10 | 51946 | . 50136 F . 49864 | . 02082 | 4 | -97918 | 24
37 48094 | 40 | :51906 | :50180 | 45 | . 49820] .02086 | 4 | -97914 | 23
38 48133 1 - 51867 | . 50223 | 44 | .49777 | .02090 | 4 | .97910 | 22
39 48173 | 10 | :51827 | .50267 | 44 | .49733 | .02094 | 4 | . dt A
213 10. 51787 | 9. 50311 10. 49689 |10. 02098 :
di i GE 39 "aal .50355 | 4% | :49645 | .02102 4 | 97898 | 19
42 48292 | 40 | ' 51708 | .50398 | 4% | .49602| .02106 | 4 | .97894 | 18
43 48332 | 10 | “51668 | .50442 | 43 | .49558 | .02110 | 4 | .97890 | 17
39 29 | | 50485 ` 49515 | . 02114 ` 97886 | 16
44 48871 | 28 | 0.51629 a 5 g
45 | 9.48411 10.51589 | 9. 50529 | 43 |10. 49471 |10. 02118 | 4 | 9.97882 | 15
46 48450 | 39 | :51550| .50572 | 443 | .49428 | .02122 | 4 | .97878
47 48490 | 40 | :51510| .50616 | 43 | .49384 | .02126 | 4 | .97874 | 13
39 50659 ` 49341 | .02130 ` 97870 | 12
48 48529 E5147 i [43 e i 12
49 48568 25 :51432 | :50703 | 43 |_. 49297 | .02134 | 5 | . 97866
50 | 9. 48607 10. 51393 | 9. 50746 | 43 |10. 49254 |10. 02139 | 4 | 9.97861 | 10
51 48647 | 40 | 51858 | .50789 | 44 | .49211 | .02143 | 4 | -97857| 9
52 48686 | 39 | :51314| 250833 | 43 | .49167 | .02147 | 4 | . 97853
39 50876 ` 49124 | | 02151 97849 | 7
53 48725 "51275 | . "E P T
54 48764 39 51236 | . 50919 | 43 | .49081 | .02155 | 4 | .97845
55 | 9. 48803 10. 51197 | 9.50962 | 43 |10. 49038 |10. 02159 | 4 | 9.97841 | 5
56 48842 28 .51158 | .51005 | 43 | . 48995 |. 02103 ae 97837 4
57 48881 51119 | .51048 | 44% | . 48952] . a 1?
39 48908 | ` 02171 97829 | 2
58 48920 | 39 | .51080 | .51092 | 43 |. 71 |4 97829 | 2
48959 ` 51041 | `. 51135 ` 48865 | .02175 | 4 |.
80 9 48998 | 39 10. 51002 | 9.51178 | 49 |10. 48822 |10. 02179 ` 07821 S
; DE e
107°" cos m sec cot Wet tan csc 1 sin «720

1394

. 51002
. 50963
. 50924
. 50885
. 50847

TABLE 33

Logarithms of Trigonometric Functions

tan

. 51178
. 51221
. 01264
. 51306
. 51349

. 00808
. 50769
. 50731
. 50692
. 50653

. 01392
. 51435
. 51478
. 51520
. 51563

. 50615
. 50576
. 50538
. 50500
. 50461

. 51606
. 01648
. 51691
. 51734
. 51776

cot

. 48822
. 48779
. 48736
. 48694
. 48651

cos -161?
Y

. 97821
197817
. 97812
. 97808
. 97804

. 48608
. 48565
. 48522
. 48480
. 48437

. 97800
. 97796
. 97792
. 97788
. 97784

. 50423
. 50385
. 00346
. 50308
. 50270

. 51819
. 51861
. 51903
. 51946
. 91988

. 50232
. 50194
. 50156
. 50118
. 50080

. 52031
. 52073
. 92115
. 52157
. 52200

. 50042
. 50004
. 49966
„49928
. 49890

„52242
. 52284
. 52326
. 52368
. 52410

. 49852
. 49815
240777
. 49739
.49702

. 52452
. 52494
. 02536
. 02578
. 52620

. 49664
. 49626
. 49589
. 49551
. 49514

. 52661
. 52708
. 02745
. 02787
. 02829

. 40477
. 49439
. 49402
. 49365
. 49327

. 52870
. 52912
. 52953
. 02995
. 53037

. 49290
. 49258
. 49216
. 49179
. 49142

. 53078
. 93120
. 53161
. 53202
. 93244

. 49104
. 49067
. 49030
. 48993
. 48957

. 53285
. 03327
. 53368
. 53409
. 93450

. 48920
. 48883
. 48846
. 48809
. 48773
. 48736

„53492
. 03533
. 53574
. 53615
. 03656
. 53697

. 48394
. 48352
. 48309
. 48266
. 48224

. 97779
. 97775
xot
. 97767
. 97763

. 48181
. 48139
. 48097
. 48054
. 48012

297759
. 97754
„97750
. 97746
. 97742

. 47969
. 47927
. 47885
. 47843
. 47800

. 97738
. 97734
. 97729
. 97725
OTT

. 47758
. 47716
. 47674
. 47632
. 47590

E Or
. 97713
. 97708
. 97704
. 97700

. 47548
. 47506
. 47464
. 47422
. 47380

. 97696
. 97691
. 97687
. 97683
. 97679

. 47339
.47297
. 47255
. 47213
. 47171

. 97674
. 97670
. 97666
- 97662
. 97657

. 47130
. 47088
. 47047
. 47005
. 46963

. 97653
. 97649
. 97645
. 97640
. 97636

. 46922
. 46880
. 46839
. 46798
. 46756

. 46715
. 46673
. 46632
. 46591
. 46550

. 97632
. 97628
- 97623
. 97619
. 97615

. 97610
. 97606
. 97602
. 97597
. 97593

. 46508
. 46467
. 46426
. 46385
. 46344
. 46303

. 97589
. 97584
. 97580
. 97576
. 97571
„97567

sec

cot

tan

sin

Alorwuwruajo 00

4
NI
=a

o

1395

TABLE 33

Logarithms of Trigonometric Functions
bam EE

ese iff. iff. cos -160°
y

y

. 51264 . 48736 | 9. 53697 . 46303

. 51301 . 48699 . 53738 .46262 | .02437
. 01338 . 48662 „53779 . 46221 . 02442
. 51374 . 48626 . 03820 . 46180 . 02446
. 51411 . 48589 . 53861 .46139 | .02450

. 51447 . 48553 | 9. 53902 . 46098 . 02455
. 51484 . 48516 . 53943 i . 46057 . 02459
. 51520 . 48480 . 53984 . 46016 . 02464
. 51557 . 48443 . 04025 . 45975 . 02468
. 51593 . 48407 . 54065 . 45935 . 02472

. 51629 . 48371 | 9. 54106 . 45894 . 02477
: 51666 . 48334 . 54147 . 45853 . 02481
. 51702 . 48298 . 54187 . 45813 . 02485
. 51738 . 48262 . 04228 . 45772 . 02490
. 91774 . 48226 . 54269 . 45731 . 02494

. 51811 . 48189 | 9. 54309 . 45691 . 02499
. 51847 . 48153 . 04350 . 45650 . 02503
. 51883 . 48117 . 54390 . 45610 . 02508
. 51919 . 48081 . 54431 : 45569 . 02512
. 51955 . 48045 . 04471 . 45529 . 02516

. 51991 . 48009 | 9. 54512 . 45488 . 02521
. 52027 . 47973 . 04552 . 45448 . 02525
. 52063 . 47937 „54593 „45407 „02530
„52099 . 47901 . 04633 . 45367 . 02534
„52135 . 47865 . 54673 . 45327 . 02539

. 52171 . 47829 | 9. 54714 . 45286 . 02543
- 52207 . 47793 . 94754 . 45246 . 02547
. 02242 . 47758 . 04794 . 45206 . 02552
. 52278 . 47722 „54835 „45165 „02556
. 52314 . 47686 . 54875 . 45125 . 02561

. 52350 . 47650 | 9. 54915 . 45085 . 02565
. 02385 . 47615 „54955 . 45045 . 02570
. 52421 . 47579 . 04995 . 45005 . 02574
. 52456 . 47544 . 55035 . 44965 . 02579
. 52492 . 47508 „55075 „44925 „02583

. 52527 . 47473 | 9. 55115 . 44885 „02588
. 02563 . 47437 . 95155 . 44845 . 02592
. 52598 . 47402 „55195 „44805 „02597
. 02634 . 47366 . 00235 . 44765 . 02601
. 52669 / „47331 . 55275 . 44725 . 02606

. 52705 „47295 | 9. 55315 . 44685 . 02610
. 52740 . 47260 „55355 7 . 44645 . 02615
. 52775 .47225 . 55395 . 44605 . 02619
. 92811 . 47189 „55434 . 44566 . 02624
. 52846 . 47154 . 00474 . 44526 . 02628
9. 52881 = |10. 47119 | 9. 55514 . 44486 . 02633
. 52916 . 47084 . 00004 . 44446 . 02637
. 92951 . 47049 . 55593 . 44407 . 02642
. 52986 . 47014 . 55633 . 44367 . 02647
. 53021 . 46979 . 55073 < . 44327 . 02651

. 53056 10. 46944 | 9. 55712 „44288 |10. 02656
. 53092 .46908 | .55752 | : . 44248 | . 02660
. 53126 .40874 | . 55791 . 44209 | .02665
TESCO E .46839 | . 55831 . 44169 | .02669
153196 |. : „46804 | . 55870 ..44130 | .02674.
9. 53231 „46769 | 9. 55910 „44090 |10. 02678
. 53266 „46734 | . 55949 „44051 | . 02683
. 53301 .46699 | . 55989 .44011 | .02688
. 53336 . 46664 | . 56028 .43972 | .02692 . 97308
. 53370 . 46630 | . 56067 „43933 | .02697 . 97303
9. 53405 10. 46595 | 9. 56107 10. 43893 |10. 02701 9. 97299

9. 97567
. 97563
. 97558
. 97554
. 97550

9. 97545
. 97541
. 97536
. 97532
. 97528

9. 97523
. 97519
. 97515
. 97510
: 97506

9. 97501
. 97497
. 97492
. 97488
. 97484

9. 97479
. 97475
. 97470
. 97466
. 97461

9. 97457
. 97453
. 97448
. 97444
. 97439

9. 97435
. 97430
. 97426
. 97421
. 97417

9. 97412
. 97408
. 97403
. 97399
. 97394

9. 97390
. 97385
. 97381
. 97376
29492

9. 97367
. 97363
. 97358
. 97353
. 97349

9. 97344
. 97340
. 97335
. 97331
. 97326

9. 97322
. 97317
. 97312

|

=
ononon Suen ` ee

CU OUR AARAA Va Ons Ons OP POE CV CV B OUR POP OP ROP

IS

Ke T GT GT A OA GT a OR OI a

sec cot j tan csc

1396

TABLE 33

Logarithms of Trigonometric Functions

e y Di
20 sin Ý esc tan Diff cot Diff
1 sec 1’ cos «159°
0 | 9.53405 10. 4 .
7 35 |10. 46595 | 9. 5610
JE JEN IE EIE dB IHE TE
2 | -asats | 33 | Joe - 43854 | _ 2 | .97294 | 59
4 | 153544 | 35 | :46450 | 50204 30 | Lina Eens |24 | cores Wome
| 188544. :40491 [7.56224 | Gq | :48176 | 02715 97 |
han 5 lo 39 | [0743736 |0730 |33 Nē 280 15
6 io . 46422 | 9. 56303 10. 43697 d |. PE IEA
m I au 11 241 Kee BR 39 |’: 43058 | 02729 | 9 | "97274 | dd
EEUU vem 39 | 4019 | 102734 | 5 | 97266 | Es
9 | :53v16 | 34 | :46284 | 86450 39 | 43580 | 102738 | 4 | 97268 | 52
"46284 | 56459 | 39 | 23001 | ūzrās |5
10 |9.53781| 5 [I0 3 .43541 | .0 5 | :97257 | &i
10 51 | 35 |10. 46249 | 9. 564 a | 43541 | .02743 ` 97257
J—AE NE E EE E E. ;
a WT ga] MEME OCC : 43424 | ` 6 1122
iy Men || KST S 29 | kana feet ad
| 153888. Tbe 3o |. 43885 | 702762 | 22 pi
las 34 ī . 56654 | 39 „43346 02 4 . 97238 | 47
15 [9.53922] 35 |10. 46078 | 9. 56693 10 43307 Od ica
ime U gesent [Sel e pee oon 89 Gras haioasa |85 | Coa
is canos k A 39. paisa brige cg | a4 97224 | 44
18 | . 54025 | 34 | . 45975 | .56810 ee DNE 0 . 97220
] EHE 30 | 43190 [2002785 | 5» j-
2n mi 34 . 56849 ` ` 43151 5 . 97215 42
20 9.54093 | 34 |10. 45907 | 9. 56887 S 43 a 4 | eto | A
cow orcos |] 341 SIAM 39 "43074 iso 9. 97206 | 4
Ara 30 | Košūšoas Kri? 5 | emor| 39
23 [poss 34 a E 39 | 43085 | .02804 | 4 | .971 58
e aa [42996 [0902808 | 12 || 0 25 [con
os | s sees 34 771 | .57042 ` 42958 ke E,
25 [95263] 34 [10.45787 | 0.57081 2 mue log | ARCOS
am leas Mh 241 104 PB C Ed EE 9. 97182
283 f L| aa. 145669 Loosst 38 | .42880| .02822 2 |. B
29 dees 34 . 45635 57197 39 ir 02827 | 29 ` 97173 2
3 sa g3 ] 20049007. aa 10. s 4 31
32 |§ 4 34 | 45534 | .57312 | 38 intel iy “9. 97159.
aes UL resins Se eran | 099 GE in es 5 | orisa | 29
33 | 254534 | 53 | .45466 | :57389 | 38 -42649 | 102851 | Í | ml 28
35 |9.54601| 28 .45433 | .57428 | 39 em .02855 | £ | .97145 >
A 2 iÐ. 45309 | 0 5460 38 e EE > | 197140 26
:546 2: Lee "e : : „0286
38: [1854703 || $451 (NS 208 corsa | (89 Ges Lez | 5 | "97130 | 24
205 (Lee | 99] Bi. SI 1 38 | -42457 | . 02874 | $ :97126 | 23
40 | 9.54769 34 „45265 | .57619 | 38 labās ` 02879 | 5 07121 35
41 | 4109 | ga |10- 45231 | 9. 57658 39 Le 42881 | .02884 | 5 | 97116 21
ay || 754302 || 34 |, 740108 [o bsreos | [Es 10. 42342 |10. 02889 | 4 [9.9 zi
at. W sacos 1039 TEOT js 38 | .42304 | .02893 | £ ` 97107 fa
r pode lek [Wero > 42366 | ¿02808 | 5 | :97102 | 18
45 | 9.54936 | 323 vasooz |". 87810 195) E ER noe 5 | 97097 | 17
46 | .54969 | 33 10. 45064 | 9.57849 | °° . 42190 | .02908 | $ | :97092 16
aa RH A E 10. 42151 [10.02913] 4 | 9. js
48” ewe A KT 9887026 38 | - 42113] .02917 | $ Toda
49 | 188098 | a | «44964 ënnen | 5 42075 | 102922 | 5 | "97078 | 18
45 [55069 | ga | 44031 | 58001 38 | 22037 | .02927 | 5 :97073 | 19
51 | 53194 | 34 |10. 44898 | 9. 58039 Be eL COP “97068 | 11
3» [ 288056 |. ga | educa. aer o 10. 21961 |r0. 02937 | * 5 7085 | 70
58 1] 755009 aio SS 38 | «41928 | euni 97059 | 9
$4 |) 522202. EE MEE 2 -41885 | :02048 | 5 | "97054 | 8
55 [vg 225. sg | 14765 | 58191 | g Ed mo (97049 | 7
56 | .55301 | 33 10. 44732 | 9. 58229 | °° DUBIUM ` 97044 é
m |1 259901 | a8) Ea 10. 21771 |10. 02961 | 5 Leet
58 || 955367 |, 28 „44666 | .58304 | 37 . 41733 | .02965 | 4 9. 97039 5
59 |Í iesdvo IT 38 | -41696 | . 02970 | 2 :97030 | 3
60 Lech | <33 | |17: 44600 58880 | 33 41658 | (02975 | 5 | "97025 | 2
: 10. 44567 | 9. 58418 | 38 0 dl |; : 97020 1
É = |! 10. 02985 | 5 |9. l
110 oe 1 sec cot Diff 5 edly 0
1 tan esc Diff. : t
il^ sin -69°

TABLE 33

Logarithms of Trigonometric Functions

1397

21% sin DS tan m cot sec C cos «1582
y y
O | 9.55433 aa |10. 44567 | 9. 58418 | 37 |10. 41582 |10. 02985 | „ | 9.97015 | 60
1 | .55466 | 33 | .44534 | .58455 | 38 | .41545 | .02990 | P | .97010 | 59
2 | .55499 | 33 | .44501 | .58493 | 38 | .41507 | .02095 | % | .97005 | 58
3 | .55532 | 32 | .44468 | .58531 | 38 | .41469 | . 02909 | 5 | .97001 | 57
4 | .55564 | 33 | .44436 | .58569 | 32 | .41431 | .03004 | 5 | .96996 | 56
5 |9.55597 | 33 |10. 44403 | 9.58606 | 3g |10.41394 |10.03009 | ; | 9.96991 | 55
6 | .55630 | 33 | .44370 | .58644 | 32 | .41356 | .03014 | 2 | .96086 | 54
7 | .55603 | 35 | .44337 | .58681 | 37 | .41319 | .03019 | 5 | .96981| 53
8 | .55695 | 33 | .44305 | .58719 | 38 | .41281 | .03024 | 5 | 196976 | 52
9 | .55728 | 33 | .44272 | .58757 | 35 | .41243 | .03029 | 5 | .96971 | 51
10 [9.55761 | 35 |10. 44239 | 9.58794 | ze |10. 41206 |10. 03034 | , | 9.96966 | 50
lī | 585703 | 32 | .44207 | .58832 | 37 [141168 | .03038 | 5 | 96962 | 49
12 | .55826 | $3 | .44174 | .58869 | 32 | .41131 | .03043 | 5 | 196957 | 48
13 | .55858 | 32 | .44142 | .58907 | $2 | .41093 | .03048 | 5 | .96952 | 47
14 | .55801 | 33 | .44109 | .58944 | 37 | .41056 | .03053 | 5 | .96947 | 46
15 | 9.55923 | 33 |10.44077 | 9.58981 ze |10.41019 |10. 03058 | ; | 9.96942 | 45
16 | .55956 | 33 | .44044 | .59019 | 35 | .40981| .03063 | p | .96987 | 44
17 | .55088 | 32 | .44012 | .59056 | 32 | .40944| .03068 | 5 | .96982 | 43
18 | .56021 | 33 | .43979 | .59094 | 35 | .40906 | .03073 | 5 | .96927 | 42
19 | .56053 | 32 | .43947 | .59181 | 37 | .40869 | .03078 | 5 | .96922 | 41
20 | 9.56085 | 33 |10. 43915 | 9.59168 | 3, |10. 40832 |10. 03083 | ; | 9.96917 | 40
21 | .56118 | 33 | .43882 | .59205 | 32 | .40795 | .03088 | 2 | .96912 | 39
22 | .56150 | 32 | .43850 | .59243 | 37 | .40757 | .03093 | ¿ | .96907 | 38
23 | .56182 | 32 | .43818 | .59280 | 37 | .40720 | .03097 | 5 | .96903 | 37
24 | :56215 | 33 | .43785 | .59317 | 37 | . 40683 | .03102 | 5 | .96898 | 36
25 |9.56247 | 45 |10.43753 | 9.59354 | 44 |10.40646 |10. 03107 | „ | 9.96893 | 35
26 | .56279 | 32 | .43721| .59391 | 3% | .40609 | .03112 | 2 | .96888 | 34
27 | .56311 | 32 | .43689 | 59429 | 32 | .40571| .08117 | 2 | .96883 | 33
28 | .56343 | 32 | .43657 | .59466 | 37 | .40534 | .03122 | 2 | .96878 | 32
29 | :56375 | 32 | .43625 | .59503 | 37 | .40497 | .03127 | 3 | .96873 | 31
30 | 9.56408 | 35 10.43592 | 9.59540 37 |10. 40460 |10. 03132 | ; | 9.96868 | 30
31 | .56440 | 32 | .43560 | .59577 | 37 | .40423 | .03137 | 5 | .96863 | 29
32 | (56472 | 32 | .43528 | .50614 | 37 | .40386 | .03142 | 5 | .96858 | 28
33 | 156504 | 32 | 143496 | :59651 | 37 | .40349 | .08147 | 5 | .96853 | 27
34 | :56536 | 32 | .43464 | -59688 | $y | -40312 | .03152 | 5 | .96848 | 26
35 | 9.56568 | 3, |10.43432 | 9.59725 | 37 |10. 40275 |10. 03157 | 5 | 9.96843 | 25
36 | .56599 | 31 | .43401 | .59762 | 37 | .40238 | .03162 | 5 | .96838 | 24
37 | :56631 | 32 | .43369 | .59799 | $6 | . 40201] .03167 | 5 | .96833 | 23
38 | :56663 | 32 | .43337 | .59835 | 3% | .40165 | .03172 | 5 | .96828 | 22
39 | 56605 | 32 | :43305 | :59872 | 37 | .40128 | .03177 | 5 | .96823 | 21
40 | 9.56727 | go |10.43273 | 9. 59909 | 3; |10.40091 |10. 03182 | ; | 9. 96818 | 20
41 | .56759 | 32 | .43241| .59946 | 37 | .40054| .03187 | 5 | .96813 | 19
42 | 56790 | 3) | .43210 | .59983 | 34 | .40017 | .03192 | 5 | .96808 | 18
43 | 56822 | 32 | :43178 | :60019 | $2 | .39981| .03197 | p | .96803 | 17
44 | .56854 | 32 | .43146 | .60056 | 37 | .39944 | .03202 | 5 | .90798 | 16
45 | 9.56886 | 3, |10. 43114 | 9.60093 | 5, |10. 39907 |10. 03207 | 5 | 9.90798 | 15
46 | .56917 | 31 | .43083 | .60130 | 35 | .39870 | .03212 | 5 | .90788 | 14
47 | .56949 | 32 | 243051 | .60166 | 37 | .39834| .03217 | 5 | .96783 | 13
as | .56080 | 31 | 143020 | 60203 | 37 | .39797 | .03222 | g | .96778| 12
49 | :57012 | 32 | .42088 | 60240) 3; | .39760 | .03228 | 5 E n
50 | 9.57044 10. 42956 | 9. 60276 10. 39724 |10. 03233 9. 9676:

51 | .57075 = ` 42925 | . 60313 7 .39687 | .03238 | 5 | . 96762 9
52 | .57107| 32 | ‘42803 | . 60349 | 37 | . 39651 | .03243 | 5 | „96757 | 8
53 | musl 31 | 42862 | .60386 | 34 | .39614 | .03248 | 5 | .96752 | 7
54 | 257169 | 31 | ‘42831 | .60422 | 37 | .39578 | . 03253 | ; mi :
55 | 9.57201 10. 42799 | 9. 60459 ` |10. 39541 |10. 03258 <
56 | .57232 > ` 42768 | . 60495 > .39505 | . 03263 ; 90737 | 4
57 | .57264 | 32 | .42736 | .60532 | 36 | -39468 | .03268 | 5 : 96732 3
58 | 57205 | 31 | 42705} .60568 | 37 | .39432 | .03273 | 5 | 59872 Å
59 | 157326 | 31 | ¿42674 | -60605 | 34 | -39395 | . 03278 | 5 | -96722 | 1
60 | 9.57358 10. 42642 | 9. 60641 10. 39359 |10. 03283 | ? | 9.96717

; : Diff. : T

11 15 cos Diff sec cot GC tan csc 1 sin -08°

1398

TABLE 33

Logarithms of Trigonometric Functions

22% sin ps ese tan js cot sec ud cos «1572
y
0 | 9.57358 | 3; [10.42642 | 9. 60641 | ze [10.39359 |10. 03283 | ¿ | 9.96717| 60
1 | .57389 | 3, | .42611 | .60677 | 39 | . 30323] . 03289 | 9 | .96711| 59
2 | -57420 | 5, -42580 | .60714 | 36 | -39286 | .03294 | Š | .96706 | 58
3 | 57451 ` 42549 | | 60750 ` 39250 | | 03299 96701 | 57
4 | .57482 | 32 | .42518 | | 60786 sd :39214 | | 03304 r 96696 | 56
5 | 9.57514 | 3] [10.42486 | 9. 60823 | „g |10. 39177 |10. 03309 | „ | 9. 96001 | 55
6 | .57545 | 31 | .42455 | .60859 | 3e | .39141| . 03314 | 2 | .96686 | 54
2 HN 1e 3 k a lð: oc
9 | .57638 a .42362 | . 60967 2c ` 39033 | .03330 E 96670 | 51
10 [9.57669 | a |10. 42331 | 9. 61004 | 36 |10. 38996 |10.03335 | ; | 9. 96665 | 50
12 [sem | 81 | Casson [celere 986. [5022299 [0903340 Ge || SES de
13 | .57762 | 3! | ¿422388 | ‘61112 | 36 | 38888 | “03350 | 5 96650 | 47
14 | ` 57793 p .42207 | | 61148 a ` 38852 | | 03355 ri 96645 | 46
15 9. 57824 31 10. 42176 | 9. 61184 | 26 [10.38816 |10. 03360 | g | 9.96640 | 45
de BERA IE IHE TE
19 | :5747| SI | ‘4905 | ‘61328 | 36 | 8607 | ossai] 5 | cba | di
20 9. 57978 30 |10- 42022 | 9.61364 | 3e |10.38636 |10. 03386 | g | 9.96614 | 40
22 | 58039 | 31 tu: ki. 86 eeh E 5 Les 33
23 - 58070 E ` 41930 | ` 61472 Së ` 38528 | ` 03402 d ` 96598 a
.41899 | ` 61508 ` 38492 | | 03407 96593 | 36
30 36 : CAR
25 | 9.58131
26 sel 31 E tarsas | 19:9 | 35 PU 38456 |10: 03412 | g | 9.96588 | 35
27 | .58192 | Sy | .41808 | ‘61615 | 36 | 38385 | ‘03423 | 5 | ¿06877 | 33
28 | .58223 | 35 | .41777 | 61651 | 36 | :38349| :03428 | 5 | 063 | 32
29 | .58253 Si 41747 | | 61687 z ` 38313 | | 03433 3 | 196567 31
30 | 9. 58284
31 | seul 30 |" 41686 | “eres | 36 1038278 [1003438 | g | 9 96562 | 30
32 | 258345.| SE! raros |s4ta1702 | 1301 Kësse gadās) |55 evl
33 | 158875. | 30 | 41625 | ‘61830 | 39 | 238170 to 5 oe 27
S4 [38406 | 39 | .41594 | . 61865 | 36 | 38135 | .03459 | 5 | ¿06541 | 26
35 9. 58436 a 10. 41564 9. 61901 | 35 |10. 38099 |10. 03465 | . | 9. 96535 | 25
37 | .58497 | 39 | * 41503 Sete 36 ie Md AR E-
38 | .58527 | 30 |.:41473 | :62008 | 39 | :37992 | 103480 | 9 | See || 23
39 | .58557 | 3° | | 41443 | | 62043 22 | .37957 | ¡03486 | 9 Mund Ji
W SC 30 |10. 41412 | 9. 62079 35 10. 37921 |10. 03491 å 9.96509 | 20
41 | -58613 | 30 : 41382 -62114 | 36 | -37886 | .03496 | $ | 296504 | 19
43 | .58678 | 30 | 141322 POLARS: 0 t e 5 Poe ep
de (58709 | 3g CT |20€2221. ESO. herra usara > | 96488 | 16
9. 58739 | ` TE E 5 ? hg 3774 TALE OO
45 | 9. 58739) 3o 10. 41261 9. 62256 E 10. 37744 10. 03517 | 4 | 9.96483 | 15
47 ` 58799 2 .41201 | | 62327 ae ` 31673 Eo 5 Meu i
49 | 8829 | 30 | 41171 | .62362 | 25 [197638 [03583 | "> | 96467] 12
2 imu 30 | 41141 | .62398 | 36 | :37602| :03539 ` .96461 | 11
9. 10. 4 cu
Br [9859 go posun 9. 62433 = 10. 37567 10. 03544 | 5 | 9. 96456 | 10
52 | .58949.| 30 | :41051| 62504 | 36 | 37306 08855 | 19. || See 8
93 | .58979 | 39 | .41021 | .62539 | 35 | “37461 | 03560 | 5 7
5s 59009 30 | 40991 | .62574 | 33 | "37426 | | 03565 x 6
9. 59039 10. 40961 | 9. 62609 ` xe P 7 j
56 | .59069 | 30 40521 264, | 228 "MIEL Oase |5 |* 4
57 | .59098 | 35 | .40902 | :62680 | 35 | 37320 | baser | 9 |: 3
58 | .59128 | 30 | 40872 | | 62715 35 | 237285 | ¿03587 | 6 |: 2
60 | 959128 | 30 [20842 | .62750 | 35 | 37250 | 03592 | 5 |: 1
: ET 10. 40812 | 9. 62785 | 10.37215 |10. 03597 | 9 |9 0
Diff : ;
, Diff 1
112 -> COS 1 sec cot T tan ese s eb 72

1399

TABLE 33

Logarithms of Trigonometric Functions

tan i cot

9. 59188 . . 62785
. 59218 . 62820
. 59247 . 62855
. 59277 . 62890

. 59307 . 62926

. 59336 j . 62961
„59366 i . 62996
. 59396 : . 63031
. 59425 À . 63066
. 59455 > . 63101

9. 59484 1 9. 63135
. 59514 : . 63170
„59543 : . 63205
. 59573 3 „63240
„59602

9. 59632
„59661
„59690
. 59720
. 59749

9. 59778
. 59808
„59837
. 99866
. 59895

9. 59924
. 59954
. 59983
. 60012
. 60041

9. 60070
. 60099
. 60128
. 60157
. 60186
. 60215
. 60244
. 60273
. 60302
. 60331

. 60359
. 60388
. 60417
. 60446
. 60474

. 60503

PloHrwmwbhalauM.

| +
e.
e

o

1400

TABLE 33

Lock :
garithms of Trigonometric Functions

ma a l SS

24°? sin Diff
y P coc tan Diff. ,
7 114 co sec Diff
0 | 9. 60931 NES d. M cos «155°
1 . 60960 29 10. 39069 | 9. 64858 A y
2 60988 | 28 39040 | . 64892 | 34 10. 35142 |10. 03927 7
4 | .61045 29 38984 | ` 64960 | 31 35074 mēri g | - 96067} 59
5 | 9.61073 | 7° 38955 | . 64994 | 34 35040 02011 EE eeh 0,
6 | .61101 | 28 10. 38927 | 9. 65028 | ** 35006 | .03950 | 9 . 96056 | 57
3 aos 1-29] Delos od QN 07 34 |10. 34972 |10. 03 5 296050 7389
8 61158 | 29 38871 65096 | 34 34938 mi g | 9. 96045 | 55 |
9 61186 | 28 38842 | ` 65130 | 34 34904 eee 5 . 96039 3
10 | 9. 61214 28 38814 | ` 65164 | 34 34870 | . SECH 6 .96034 | 53
ATA Pa) eae 53 |_-34836 | .03978 | $ ` 96028 | 52
12 | :61270 | 28 eel s VE I 5 | 90022] 51
13 61298 | 28 28781 |M85205. | 04 SC aa eae
= 61326 | 28 38702 ` 65299 34 34735 ` 03995 6 | - 96011 K
15 | 9. 61354 28 38674 | . 65333 | 3 34701 votes 5 .96005 | 48
15 [9 61854 | og! [10 38616 | 9. 6536 33 o ae Ae ae
Hm 61411 | 29 38618 : 65400 34 |10. 34634 10. B | g | .95994]| 46
18 61438 | 27 38589 tom 34 34600 . 04012 | g | 9. 95988
19 61466 | 28 38562 ` 65467 33 34566 pee 5 . 95982 ri
20 | 9.61494) 7° 38534 | . 65501 | 34 34533 tie g | «95977 3
21 61522 | 28 10. 38506 | 9. 6553 34 34499 HÐ g | - 95971 | 42
22 61550 | 28 38478 ` 65508 33 |10. 34465 10. 5 | -95965 | 41
23 61578 | 28 38450 | .65602 | 34 34465 |10. 04040 | g | 9. 95960
24 61606 | 28 38422 ` 65636 34 34398 . 04046 | g . 95954 =
25 eer 23 r TE 04052 | g | . 95948 a
26 61662 | 28 10. 38366 | 9. 6570 34 | 34331 : 04063 5 | - 95942 šo
27 61689 | 27 attie E EH 10. 3 | g | -95937 | 36
ES 61717 | 28 38311 | 165770 | 34 uo 9. 9593
= 61745 | 28 38283 | | 65803 | 33 3 gl (tt d ` 95925 | 34
30 | 9. 61773 28 38255 | 65837 | 34 34197 non 6 ` 95920 ae
31 61773 | 27 10. 38227 | 9. 6587 33 Sege 149. RÐ ae 5
33 61856 28 38172 acosa (ee IE ĪSU D Ge
34 | 61883 | 27 Soia Mitte 21 34096 | .04103 Ë ts +
3561917 29 u Ari loa | en Ehl ook
36 61939 28 10. 38089 | 9 6603 34 33996 } bo 6 . 95885 a
ES SEN A ae, j ue 33 |10. 33962 10. ia 6 . 95879 Ad
94 2 . 6610 33s [55533929] 93 9. 9587
39 62021 | 27 38006 : : „04132 | 9 3| 25
40 [9 $2049 28 37979 | ` 66171 33 Lët Pass 4 ad] d
41 62049 | 27 10. 37951 | 9. 662 33 | -33829 Sð. ` re
42 62104 | 28 Selen (hast eee . 04150 | § | .95850 =
43 | 62131 | 27 | :37869 e | aa ems (1 ier 9. 95 ^:
44 62159 | 28 37869 Geste 33 33729 04161 | 9 ' 05839 Ap
45 |o 62186. 27 37841 assi 33 33696 -04167 | Ë ' 95833 i
15 [962196 | „g 10. 37814 | 9. 663 7 | 33 | 133663 | 04179 6 | "05827 | 17
47 62241 | 27 . 97786 risp 33 |10. 33629 USEC! 106 ` 95821 i
18 mee A | les 66104 | 33 | 33506 | -04190 | 3 |”: 98810 js
29 . 37732 : : :
so bú 2 ie 88470 |33 3555 [1504198 | 76 85804 | 13
51 62823 | əy |10. 37677 | 9. 6653 34 epe Eege esos CS
AM JEU. ID 00537 | 32 TO 33163 [I oir| Ó (6. 95786 H
ES 62482 | 2 os eode 33 33430 | . 04220 g | 9 95786 | 10
55 27 ` 3756 „66636 | 33 397 | .04225 | 9 . 95780 9
9. 62459 | >, 68 | .66669 | 33 33364 g | -95775
E A E EE 702 a 10. 33298 |10. 4237 ` 9576 6
67 ESCONDE 6735 | * : 33298 |10. 04243 ? 201 o
59 62 97 e . 66768 33 < 3265 ` 0424 6 9. 95757 5
60 | 9. 62595 | 27 tid, Z UE 20424 ee | 93761 Vē
1 - 10. 37405 | 9. 9834 99 | .04261 | © : 95745 3
aos re. (| D 9.66867 | 99 |10 SE R 04267 E c 2
: e cor SDE : 9. 95728 | 0
det csc Diff. > 4
T^ sin <65°

1401

TABLE 33

Logarithms of Trigonometric Functions

cot

. 62595 | } . 33133 |10. 04272
. 62622 A : . 33100 | . 04278
. 62649 | 3 . 33067 . 04284
. 62676 i i . 33034 . 04290
. 62703 : i . 33001 „04296

„62730 } i . 32968 110. 04302
. 62757 : : . 32935 . 04308
. 62784 : 4 . 32902 . 04314
. 62811 : : . 32869 . 04320
. 62838 d A . 32837 . 04326

. 62865 i : . 32804 . 04332
: 62892 : d . 92771 . 04337
. 62918 1 : . 32738 . 04343
. 62945 s s . 32705 . 04349
. 62972 : i . 32673 . 04355

. 62999 , | . 32640 . 04361
. 63026 , d . 32607 . 04367
. 63052 S : . 32574 . 04373
. 63079 Ë : . 32542 . 04379
. 63106 m : . 32509 . 04385

. 63133 : i . 32476 . 04391
. 63159 : R „82444 „04397
„63186 , : . 92411 . 04408
. 63213 : Tue . 32378 . 04409
. 63239 : : . 32346 . 04415

. 63266 l LS „82313 . 04421
. 63292 2 : . 32281 . 04427
. 63319 : : . 32248 . 04433
. 63345 : : . 32215 . 04439
. 63372 d : . 32183 . 04445

. 63398 Ë : . 32150 . 04451
. 63425 A L . 32118 . 04457
. 63451 A ; . 32085 . 04463
. 63478 4 . „82053 „04469
„63504 4 Å . 32020 . 04475

. 63531 ! A „81988 „04481
„63557 3 E . 31956 . 04487
. 63583 : d . 31923 . 04493
. 63610 : A „81891 „04500
„63636 : : . 31858 . 04506

. 63662 ; ! . 31826 . 04512
. 63689 : : . 31794 . 04518
. 63715 j y . 31761 . 04524
. 63741 : 4 „81729 „04530
„63767 : : . 31697 . 04536

. 63794 Í 9. . 31664 110. 04542
. 63820 H 3 „81632 | . 04548
. 63846 V .31600 | . 04554
. 63872 h h „81568 | . 04560
. 63898 ; À . 31535 | . 04566
. 63924 Å 1 . 31503 |10. 04573
„63950 Í À „81471 | .04579
. 63976 ! „81439 | .04585
. 64002 e A „81407 | . 04591
. 64028 e „81374 | . 04597
. 64054 | | 9. . 31342 |10. 04603 . 95397
. 64080 ; y „81310 | . 04609 . 95391
. 31278 | . 04616 . 95384
„81246 | . 04622 . 95378
.31214 | . 04628 . 95372
. 31182 |10. 04634 9. 95366

N
c0) -100| 4o t-o07 Séi
y

o

P? lornwuraolo 3t

tan csc i sin

4
e
Ha

o

1402

26% sin
y
0 9. 64184
1 . 64210
2 . 64236
3 . 64262
4 . 64288
5 9. 64313
6 . 64339
7 . 64365
8 . 64391
9 . 64417
10 9. 64442
11 . 64468
E2 . 64404
13 . 64519
14 . 64545
15 9, 64571
16 . 64596
17. . 64622
18 . 64647
19 . 64673
20 9. 64698
21 . 64724
22 . 64749
25 . 64775
24 . 64800
25 9. 64826
26 . 64851
27 . 64877
28 . 64902
29 . 64927
30 9. 64953
31 . 64978
32 . 65003
33 . 65029
34 . 65054
35 9. 65079
36 . 65104
37 . 65130
38 205155
39 . 65180
40 9. 65205
41 . 65230
42 . 65255
43 . 65281
44 . 65306
45 9. 65331
46 . 65356
47 . 65381
48 . 65406
49 . 65431
50 9. 65456
51 . 65481
52 . 65506
53 . 65531
54 . 65556
55 | 9.65580
56 . 65605
54 . 65630
58 . 65655
59 . 65680
60 9. 65705
T
1 16?» cos

TABLE 33

Logarithms of Trigonometrie Functions

n csc tan T cot sec SS, cos -153*
10. 35816 | 9. 68818 10. 31182 |10. 04634 | , | 9.95366 | 60
26 | -35790 | .68850 | 32 | .31150 | .04640 e | .95360 | 59
26 | 35764 | :68882 | 92 | :31118 | :04640 g | .95354 | 58
26 | -35738 | .68914| 32 | :31086 | :04652 | 9 | 95348 | 57
24 | .35712 | :65046 | 32 | :31054| :04659 6 | 95341 | 56
26 |10. 35687 | 9. 68978 | 25 |10.31022 |10. 04665 | & | 9.95335 | 55
26 | - 35661} .69010 | 35 | .30990 | .04671 | 6 | .95329 | 54
26 | -35635 | .69042 | 32 | .30958 | .04677 | 6 | 95823 | 53
26 | - 35609 | .69074 | 35 | .30926 | :04683 | Ê | :95317 | 52
25 |_. 35583 | ‘69106 | 32 | “30894 | :04690 6 | 95810 | 51
26 |10. 35558 | 9. 69138 | 3 |10. 30862 |10. 04696 | g | 9.95304 | 50
26 | + 35582 | .69170 | 35 | .30830 | .04702| $ | .95298 | 49
25 | + 35506 | .69202 | 35 | . 30708] :04708 | Ë | :05292 | 48
26 | -35481 | .69234 | 35 | .30766 | .04714 | 9 | 95286 | 47
26 | 35455 | .69266 | 35 | .30734 | 104721 | 7 | .95279 | 46
25 |10. 35429 | 9.69298 | 3, |10.30702 |10. 04727 | ¿ | 9.95273 | 45
26 | -35404 | . 693209 | 32 | . 30671} . 04733 | $ | ¡95267 | 44
25 | - 358378 | .69361 | 35 | .80639 | .04739 | 9 | ‘95261 | 43
26 | - 35353 | .69393 | 35 | .30607 | :04746 | 7 | .95254| 42
25 | 35327 | .69425 | 35 | .30575 | .04752 | D | :95248 | 41
26 |10. 35302 | 9.69457 | 3; |10. 30543 |10.04758 | „ | 9.95242 | 40
25 | -35276 | .69488 | 35 | .30512| .04764| $ | .95236 | 39
26 | - 35251] .69520 | 35 | .30480 | .04771 | 7 | .98229 | 38
25 | 35225 | .69552 | 35 | .30448 | .04777 | ê | .95223 | 37
26 | .39200| .69584 | 37 | .30416 | :04783 | D | :95217 | 36
25 |10. 35174 | 9.69615 | 35 |10. 30385 |10. 04789 | > | 9. 95211 | 35
26 | -35149 | .69647 | 35 | .30353 | .04796 | Z | .95204| 34
25 | «35123 | .69679 37 | .30321| :04802| Ë | “95198 | 33
25 | 35098 | .69710 | 35 | .30290 | :04808 | ê | :95192| 32
26 |_ 85073 | .69742 | 35 | .30258 | :04815 | 7 | 95185 | 31
25 |10. 35047 | 9.69774 a [10.30226 |10. 04821 | | | 9.95179 | 30
25 | - 35022 | .69805 | 35 | .30195 | .04827 | ê | :95173 | 29
26 | -34997| .60837 | 37 | .30163 | :04833 | ê | :95167 | 28
25 | - 34971] . 69868 | 32 | .30132 | 104840 | Z | :95160| 27
25 | .34946 | .69900 | 35 | :30100 | :04846 | ê | :05154 | 26
25 |10. 34921 | 9.69932 | 3; |10. 30068 |10. 04852 | 7 | 9.95148 | 25
26 | - 34896 | .69963 | 35 | .30037 | .04859 | 7 | 95141 | 24
25 | -34870 | . 69995 | 37 | 30005 | .04865 | $ | 195135 | 23
25 | - 34845 | . 70026 | 35 | .29974| 04871 $ | 95129 | 22
25 | .94820 | 70058 | 37 | .29942 | 04878 | 7 | 95122 | 21
25 |10. 34795 |9. 70089 | Dn 29911 |10. 04884 | è | 9.95116 | 20
25 | :34770 | .70121 | 31 | .29879 | .04890 | $ | 05110 | 19
26 | + 34745 | .70152 | 32 | .29848 | :04897 | 7 | (95103 | 18
25 | -34719 |. 70184 | 37 | .29816 | :04903 | 9 | ‘95097 | 17
25 | 34694 | . 70215 | 32 | .29785 | ú 04910 | 7 | 05090 | 16
25 |10. 34669 | 9. 70247 | 2, |10.29753 |10. 04916 | ¿ | 9.95084 | 15
25 | -34644 | .70278 | 31 | :20722 |». 04922 | 9 | sora | 14
25 | -34619 | .70309 | 35 | .29691 | .04929 | 7 | ‘95071 | 13
25 | 94594 |... 70841 | 35. | o20659 | 02935 | Ces
25 | 34569 | .70372 | 35 | .20628 | .04941 | 5 | 95059 | 11
25 |10. 34544 | € 70404 au |10. 29596 [10.04948 |. ¢ | 9.95052 | 10
25 | :34519 | .70435 | 51 | .20565 | .04954 | Ü ¡95046 | 9
25 | - 34494] .70466 | 25 | 29584 | (04061 |7 | 95039 | 8
25 | -34469 | .70498 | 57 | .20502 | 04967 | 5 | :95033| 7
24 | 34444 | . 70529 | 2: | 129471 | ‘04973 | 9 | 95027 | 6
25 |10. 34420 | 9. 70560 | 39 |10. 29440 |10. 04980 | „ |9.05020| 5
25 | -34895 | .70592 | 57 | . 20408 | .04986 | 9 | “osos 3
25 | :34370 | .70623 a | .29377 | 04993 | 7 | Mazoor Ii 3
AR IEEE IE IHE IE
221 MS i . 29: - 0500 . 94995
410. 34203 |o 70717 | 3? |10: 20283 |10. eons | 7 9. 94988 | 0
et sec cot Difi tan esc Diff sin -63°

1403

EEE — —

TABLE 33

Logarithms of Trigonometric Funetions
—— £§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§£§—§—§£§£§£§£§£§£§£§£§£§—§—§—q§q——(———(q—(——Å—Å—ÅÅÅÅÅÅÅÅÅQQ—Å—Å——— §ÅwÅwÅT

o S i :
27 > sin 1 csc tan Ee cot sec me. cos «1520
y y
0 | 9.65705 | 5, |10.34295 | 9.70717 | 4, Im 29283 |10. 05012 | ¿ | 9.94988 | 60
a || veio | SF 34271 | . 70748 | 3! 29252 | .05018 | 2 | .94982 | 59
A li Geng | 25 34246 | .70779 | 31 29221 | .05025 | & | .94975 | 58
3 | cerro | 25 34221 | .70810 | 31 29190 | . 05031 | 5 | .94969 | 57
4 | .65804 | 25 34196 | .70841 | 3) 29159 | .05038 | 4 | .94962 | 56
5 | 9.65828 | 95 |10.34172 | 9. 70873 | 9, |10.29127 |10. 05044 | „ | 9.94956 | 55
6 | 5853 | 25 34147 | .70904 | 31 29096 | .05051 | ( | .94949 | 54
7 | weBsys | 25 34122 | :70935 | 31 29005 | .05057 | $ | .94943 | 53
8 | .65902 | 25 34098 | .70966 | 31 29034 | .05064 | Z | .94936 | 52
9 | .65927 | 25 34073 | .70997 | 31 29003 | .05070 | $ | : 94930 | 51
10 | 9.65952 | 5, |10. 34048 | 9. 71028 | „| |10.28972 |10. 05077 | & | 9.94923 | 50
M | &5076 | 2 34024 | .71059 | 31 28941 | .05083 | Ê | .94917 | 49
12 | .66001 | 25 33999 | .71090 | 31 28910 | .05089 | 5 | .94911 | 48
13 || acosozs | 35 38978 ptoma121 |)! 28879 | .05096 | Z | .94904 | 47
14 | .66050 | 25 33950 | .71153 | 37 28847 | .05102 | Ê | .94898 | 46
15 | 9.60075 | 5, |10. 33925 | 9.71184 | 3, |10.28816 |10. 05109 | ¿ | 9.948901 | 45
16 | .66099 | 22 33901 fo 71215 | 5] |<u28785 | .05115 | .2 | 94885 | 44
tī | caora | 25 33876 | .71246 | 31 | .28754 | .05122 | 7 | 194878 | 43
18 | .66148 | 3 33852 | . 71277 | 31 | .28723 | .05129 | ( | ¿94871 | 42
19 | 06173 | 25 33827 | .71308 | 31 | .28692| .05135| 7 | .94865 | 41
20 | 9.66197 | 5, |10. 33803 | 9.71339 | 3, |10.28661 |10. 05142 | g | 9.94858 | 40
ar | mae ZS 33779 | .71370 | 31 | .28630 | .05148 | 2 | .94852| 39
22 | .66246 | 25 33754 | .71401 | 35 | 28599 | .05155 | & | .94845 | 38
23 | .66270 | 5 33730 | .71431 | 39 | .28509| .05161 | 7 | .94839 | 37
24 | .66295 | 25 33705 | . 71462 | 3I | .28538| .05168 A | .94832 | 36
25 | 9.66319 | 5, |10.33681 | 9.71493 | „| |10.28507 |10. 05174 | „ | 9.94826 | 35
26 | .66343 | 25 | .33657 | .71524 91 | .28476 | .05181 | & | .94819 | 34
27 | 66368 | 35 | .33632 | .71555 | 31 | .28445| :05187 | 9 | .94813 | 33
28 | .66392 | 24 | .33608 | .71586 | 31 | .28414 | .05194 | 7 | .94806 | 32
29 | ouni 25 | .33584 | .71617 | 31 | .28383 | .05201| § | .94799| 31
30 | 9.66441 | 5, |10.33559 | 9. 71648 | 5, |10. 28352 |10.05207 | „ | 9.94793 | 30
31 | .66465 | 24 | .33535 | .71679 | 3) | .28321| .05214| g | .94786 | 29
32 | :66489 | 24 | .33511 | .71709 | 39 | .28291]| .05220 | 7 | .94780 | 28
33 | .6e5313 | 24 | .33487 | .71740 | 31 | 28260 | .05227| ¿ | .94773 | 27
a£ | ceoss7 | 2£ [omasess |Ok1771 |03! | je::28229 | 005233 |£ | 694767 | 28
35 | 9.66562 | 5, |10.33438 | 9. 71802 | „| |10.28198 |10.05240 | „ | 9.94760 | 25
36 | .66586 | 24 | .33414 | .71833| 3) | .28167 | .05247 | g | .94753 | 24
37 | .66610 | 24 | .33390| .71863 | 30 | -28137 | .05253 | 7 | .94747 | 23
38 | .66634| 2% | .33366 | .71894 | 31 | .28106 | .05260 | 4 | .94740 | 22
39 | .66658 | 24 | 33342 | .71925 | 3) | -28075 | .05266 | 7 | .94734 | 21
40 | 9.66682 | 5, |10.33318 | 9.71955 | 3, |10.28045 |10.05273 | , | 9.94727 | 20
41 | .66706 | 2% | .33294| .71986 | 3) | «28014 | .05280 | g | .94720| 19
42 | .66731 | 25 | :33269| .72017 | 3] | .27983 | .05286 | | .94714 | 18
48 | 266755 | 34 | .33245 | -72048 | $ | .27952 | . 05293 I) 94707 "
44 | 66779 | 2 233221 101032076 |985| ļaex2ro22 |i Ei j
45 | 9. 66803 5 10. 33197 | 9. 72109 | 3, 10. 27891 |10. 05306 7 | 9 94094 15
46 | 066827 | 2 33173 | . 72140 27860 | .05 yr
47 | . 66851 e ` 33149 | | 72170 4 ` 27830 | . 05320 d ` 94680 | 13
48 | (66875 | 24 | 33125 | 72201 | 3) | .27799 | .05326 | 7 | .94674 | 12
49 | :66899 | 24 | :33101| .72231 | 3) | .27769 | .05333 | 7 |_. 94667 | 11
50 | 9.66922 | 5, |10.33078 | 9. 72262 | 5, |10. 27738 |10. 05340 | g | 9. 94660 10
AE IEEE
53 | 66994 24 | 133006 | .72354 | 3) | .27646 | .05360 | g |. 94640 7
54 | 1267018 | 2 132082 | :72384 | 39 | .27616 | .05366 | 7 | . 46
55 | 9. 67042. x 10. 32958 | 9. 72415 | g |10. 27585 |10. 05373 | 7 | 9. ÁR A
poo ou jo E ease IER | odela | 18
Se | garais | 29 32887 | 72506 | 39 | .27494 | .05393 | 4 | .94607 2
59 | 267137 | 24 | 32868 | .72537 | 34 | 27468 | .05400 | 7 | .94600| 1
60 | 9.67161 | 2% |10, 32839 | 9. 72567 | 99 |10. 27433 |10. 05407 9.94593 | o
) l l Á
+ : i Diff. e
117?» cs 2 sec cot ci tan esc t sin -02°

1404

hv
o
+

TABLE 33

Logarithms of Trigonometric Functions

coJoauacwm en |} * GO

10. 32839
. 32815
. 82792
. 32768
. 32744

cos -151°
y

. 94593
. 94587
. 94580
. 94573
. 94567

. 32720
. 32697
. 32673
. 32650
. 32626

. 94560
. 94553
. 94546
. 94540
. 94533

. 32602
. 92579
. 32555
. 32532
. 32508

. 32485
. 32461
. 32438
. 32414
. 32391

. 94526
. 94519
. 94513
. 94506
. 94499

. 32367
. 32344
. 32320
. 32297
„82274

. 94492
„94485
. 94479
. 94472
. 94465

. 32250
. 32227
. 32204
. 32180
32157

. 94458
. 94451
. 94445
. 94438
. 94431

. 32134
. 32110
. 32087
. 32064
. 32041

. 94424
. 94417
. 94410
. 94404
. 94397

. 32018
. 31994
. 31971
. 31948
. 31925

. 94390
. 94383
. 94376
. 94369
. 94362

. 81902
. 31879
. 31856
. 91833

. 94355
. 94349
. 94342
. 94335
. 94328

. 94321
. 94814
. 94307
. 94300
. 94293

. 94286
. 04279
. 94273
. 94266
. 94259

. 94252
. 94245
. 94238
. 94231
. 94224

. 94217
„94210
„94203
„94196
„94189
. 94182

sec

O FINO HB OAO NOD

-61°

EP

1405

TABLE 33

Logarithms of Trigonometric Functions

= 4
=

. 25149
. 25120
. 25090
. 25061
. 25031
. 25002
. 24972
. 24942
. 24913

. 24888
. 24854
. 24824
. 24795
. 24765
. 24736
. 24706
. 24677
. 24647
. 24618

. 24589
. 24559
. 24530
. 24500
. 24471
. 24442
. 24412
. 24383
. 24353
. 24324

. 24295
. 24265
. 24236
. 24207
. 24178

. 24148
. 24119
. 24090
. 24061
. 24031
. 24002
. 23973
. 23944
. 23914
. 23885
. 23856

lor bä E, OT

D
"E SIO NAAT O -I-]-100-1 NNONN NNONN NNNON ES ES ES ES ES NONNN NNNNN NNONN NNNNN NNNNN

T
c
&

o

tan

1406

TABLE 33

Logarithms of Trigonometric Functions

y
-9
^B

. 93753
. 93746
. 93738
. 93731
. 93724

. 93717
. 93709
. 93702
. 93695
. 93687

. 93680
. 93673
. 93665
. 93658
. 93650

. 93643
. 93636
. 93628
. 93621
. 93614

. 93606
. 93599
. 93591
. 93584
. 93577

. 93569
. 93562
. 93554
. 93547
. 93539

. 93532
. 93525
. 93517
. 93510
. 93502

. 93495
. 93487
. 93480
. 93472
. 98465

. 93457
. 98450
. 98442
. 98435
. 98427
. 93420
. 93412
. 93405
. 93397
. 93390
. 93382
. 93375
. 93367
. 93360
. 93352

. 93344
. 93337
. 93329
. 93322
. 93314
. 93307

Y
«600-10 0 RON O ` =

sin

Z
"SES 7400 -100-1 0000-100 N O0 -100 -100 -100 100-1 00-100 -100 NICO NICO NT NONON O0-1-100-1 ON NON NONON NONNO == 00 SI

NS? [or vor DOO

t
SA
o

1407

TABLE 33

Logarithms of Trigonometric Functions

19

y

0 | 9. 71184 91 |10. 28816 | 9. 77877 29 10. 22123 |10. 06693 9. 93307 60
1 . 71205 21 . 28795 . 77906 29 . 22094 . 06701 93299 59
2 . 71226 21 . 28774 . 77935 28 . 22065 . 06709 93291 58
3 . 71247 21 . 28753 . 77963 29 .22037 | .06716 93284 57
4 . 71268 21 . 28732 . 77992 98 „22008 „06724 93276 56
5 |9.71289 21 |10. 28711 | 9. 78020 29 10. 21980 |10. 06731 9. 93269 55
6 „71310 91 . 28690 . 78049 28 . 21951 . 06739 93261 54
7 . 71331 21 . 28669 . 78077 29 . 21923 . 06747 93253 53
8 . 71352 21 . 28648 . 78106 29 . 21894 . 06754 93246 52
9 . 71373 20 .28627 | .78135 28 . 21865 . 06762 93238 51
10 | 9.71393 91 |10. 28607 | 9. 78163 29 10. 21837 |10. 06770 9. 93230 50
kl . 71414 21 . 28586 . 78192 28 . 21808 | .06777 93223 49
12 . 71435 21 . 28565 . 78220 29 . 21780 . 06785 93215 48
13 . 71456 21 . 28544 . 78249 28 . 21751 . 06793 93207 | 47
14 . 7147 21 . 28523 . 78277 29 . 21723 . 06800 93200 46
15 | 9. 71498 21 |10. 28502 9. 78306 28 10. 21694 [10. 06808 9.93192 | 45
16 . 71519 20 . 28481 . 78334 29 . 21666 . 06816 93184 | 44
17 . 71539 21 . 28461 . 78363 28 . 21637 . 06823 93177 | 43
18 . 71560 21 . 28440 . 78391 28 . 21609 . 06831 93169 42
19 . 71581 21 . 28419 . 78419 29 . 21581 . 06839 93161 41
20 | 9.71602 on |10. 28398 9. 78448 28 10. 21552 |10. 06846 9. 93154 40
21 . 71622 21 . 28378 . 78476 29 . 21524 . 06854 93146 39
22 . 71643 21 . 28357 . 78505 28 . 21495 . 06862 93138 38
23 . 71664 21 . 28336 . 78533 29 „21467 | . 06869 93131 37
24 . 71685 20 . 28315 . 78562 28 . 21438 . 06877 93123 36
25 | 9. 71705 21 10. 28295 | 9. 78590 28 10. 21410 |10. 06885 9. 93115 35
26 . 71726 21 . 28274 . 78618 29 „21382 | . 06892 93108 34
27 71747 20 . 28253 . 78647 28 . 21353 | . 06900 93100 33
28 O ZEGT 21 . 28233 . 78675 29 . 21325 | . 06908 93092 | 32
29 . 71788 21 . 28212 . 78704 28 . 21296 . 06916

e
eo
CA
e
-
-1
w
©

30 | 9.71809 20 10. 28191 | 9. 78732 28 10. 21268 |10. 06923
31 . 71829 . 28171 . 78760 29 . 21240 . 06931

00 00 00 00 =1 00 00 00 00 00 00 ~ 00 00 00 00 00 -100 00 00 -300 00 00 00 -100 00 OO. ~ 00 00 OO =I 00 OO NO OO -30000-100 CONTRO CONT 00 00 TOO NIO -100 00
Ke)
[v]
©
00
>
w
+

32 . 71850 2 . 28150 . 78789 28 121217 . 06939 93061 28
33 . 71870 21 . 28130 . 78817 28 . 21183 . 06947 93053 24.
34 . 71891 20 . 28109 . 78845 29 221155 . 06954 93046 26
35 9. 71911 21 10. 28089 | 9. 78874 28 10. 21126 |10. 06962 9. 93038 25
36 . 71932 20 . 28068 . 78902 28 . 21098 . 06970 93030 24
37 . 71952 21 . 28048 . 78930 29 . 21070 . 06978 93022 2
38 . 71973 21 . 28027 . 78959 28 . 21041 . 06986 93014 22
39 . 71994 20 . 28006 . 78987 28 . 21013 . 06993 93007 21
40 9. 72014 20 10. 27986 | 9. 79015 28 10. 20985 110. 07001 9. 92999 20
41 . 72034 21 . 27966 . 79043 29 . 20957 . 07009 92991 19
42 . 72055 20 . 27945 . 79072 28 . 20928 . 07017 92983 18
48 . 72075 21 .27925 . 79100 28 . 20900 . 07024 92976 17
44 . 72096 20 . 27904 . 79128 28 . 20872 . 07032 92968 16
45 9. 72116 21 10. 27884 | 9. 79156 29 10. 20844 |10. 07040 9. 92960 15
46 . 72137 20 . 27863 . 79185 28 . 20815 . 07048 92952 14
47 21721157 20 . 27843 . 79213 28 „20787 . 07056 92944 13
48 2721374 21 „27823 „79241 28 . 20759 . 07064 92936 12
49 . 72198 20 . 27802 . 79269 28 .20731 . 07071 92929 11
50 9. 72218 20 10. 27782 | 9. 79297 29 10. 20703 |10. 07079 9. 92921 10
51 „72238 21 . 27762 . 79326 28 . 20674 „07087 92913 9
52 „72259 20 „27741 . 79354 28 . 20646 . 07095 92905 8
53 . 72279 20 227421 . 79382 28 . 20618 . 07103 92897 7
54 „72299 21 224101 . 79410 28 . 20590 za 92889 6
55 9. 72320 20 10. 27680 | 9. 79438 28 10. 20562 10. 07119 9. 92881 5
56 . 72340 20 . 27660 . 79466 29 . 20534 . 07126 92874 4
57 . 72360 21 . 27640 . 79495 28 . 20505 . 07134 iezi 2
58 272981 20 . 27619 . 79523 28 . 20477 . 07142 2 7
59 . 72401 20 . 27599 2070551 28 . 20449 . 07150 . 92850
60 9. 72421 10. 27579 | 9. 79579 10. 20421 |10. 07158 9. 92842 O
: T
; : ff.
121 cos er sec cot pd tan ese E sin <58°

1408

TABLE 33

Logarithms of Trigonometric Functions

(——— ANSIA E O A ATT ASA A ARO S + __— A
32% sin 7 esc tan vo cot sec ne cos «147°
y y
O | 9.72421 | 2) |10.27579 | 9. 79579 | „g |10. 20421 |10.07158 | g | 9.92842 | 60
1 72441 | 5) | :27559 | .79607 | 28 | .20393 | .07166 | 8 | .92834 | 59
` 72461 21 | 27589 | .79635 | 23 | .20365 | .07174| 8 | .92826 | 58
4 | ‘72502 | 20 | 27408 | 79601 | 28 | 30300 | 07190 | S | :92810 | 36
5 [9 72522 20 |10. 27478 | 9.79719 | og |10. 20281 |10. 07197 | g | 9. 92803 | 55
7 || 22562 || 20 ee Keng) 529 | ooo ZZ | IS QURE DD
8 72582 ae 27418 £79804 | 28 | 20196 | ‘07221 S | ‘92779 | 52

` 27398 | ` 79832 20168 | . 07229 92771 |. 51
20 28
10 [9 72022 21 |10. 27378 | 9.79860 | 2g |10. 20140 |10. 07237 : 9.92763 | 50
JE- EIE dE: EE IE IHE JE
13 72683 e pu ` 79944 E ` 20056 | .07261 s .92739 | 47
.27297 | | 79972 ` 20028 | | 07269 92731 | 46
20 28
THE 12723 + 10. 27277 9.80000 | sg |10. 20000 |10. 07277 : 9.92723 | 45
17 72763 | 20 | | 27937 nee 28 MEE rēgu 8 e 5
18 72783 | 20 Lana (280084 | *28 Nec ago16 |»iozsai | 9 Uae Hee
la ener 25 | Kat [M2 50119 a ` 19888 | ` 07309 S 92691 E
20 | 9. 72823 10. 27177 | 9. 80140 10. 19860 |10
E i os Tm „07317 9. 92683 | 40
21 | ` 7284 8
22 10508 20 kā RE 27 USE CER 8 $e x
23 72883 | 20 | '27117 | ¿80223 | 28 | :19777| 07341 | 8 | 926 57
24 72902 P ` 27098 | | 80251 2: .19749 | | 07349 d ru de
25 9 12922 Er 10. 27078 9. 80279 os |10. 19721 |10. 07357 | g | 9.92643 | 35
27 72962 | 20 | | 27038 Bee 28 EE es mE E
28 72982 | 20 27018 | .80363 | 28 | :19637| '07381| 8 ee $0
29 73002 a „26998 | | 80391 E .19609 | :07389 E bees a
30 [9 73022 is 10. 26978 9. 80419 og |10. 19581 |10. 07397 | g | 9.92603 | 30
32 73061 | 20 | '56939 sb 27 ii ietīt 8 āzis ihe
33 78081 | 20 | “26919 | :80502| 28 | 10498 faci Ie oo
34 | | 73101 = ` 26899 | | 80530 38 ` 19470 tb 8 Pon J
35 9. 73121 2 10. 26879 9. 80558 og |10. 19442 |10. 07437 s 9. 92563 | 25
37 73160 | 29 | “26840 | :80614 | 28 "We VOD 94 2529. [IS
38 73180 | 20 |.126899 |11180642 | 29 | 19358 Eus SEXIES
39 | | 73200 í ` 26800 | ` 80669 A 19331 | 07470 | 8 KSE ^
40 9. 73219 2 10. 26781 9. 80697 og |10. 19303 |10. 07478 ` 9. 92522 | 20
42 78259 | 20 Laast Loveozsa | 528 | Kater | iS KE
43 | 73278 | zo vëlleg |4 o7ā02 | 9 | varde las
44 | 73298 m 26702 | | 80808 * ` 19192 PME 8 ARS R
45 | 9.7331 S 10. 19164 |10 8 ës
45 73318 Sé 10. 20682 9. 80836 28 |10.19164 |10.07518 | y | 9. 92482 | 15
47 73357 2 .26643 | . 80892 | 28 nis TOt 8 E s 13
48 73377 26623 | .80919 | 27 | : ; 8 | "dogs:
i ` 80919 ` 19081
E ās 20 | -26604 | | 80947 3 19058. | L 207561 e 92449 | 11
Ə Ë : T :
$0 | 9 73416 | jọ [10.26584 | 9.80975 | „g |10. 19025 |10. 07559 9.92441 | 10
5l 73435 3) : 26565 .81003 | 22 | .18997 | .07567 : 92433 | 9
: .26545 | 81030 „18970 | .0757
53 | .73474| 19 26526 | . 81058 | 28 : |6 db es
` 26: ` 18942
E Er 19 | .26506 | 81086 3: 18914 | 107992 3 :92408 | 6
2 . 81086. Å X
TA qno HE I
$ zaa | 19 | 26467) 81141 x | 107608 | $ | .92392| 4
e 73572 | 20 | ` 26448 | S1169 | 27 | -18831 | 107616 8 | loza84| 3
58 5 25 | d ` 81196 .18804 | | 07624 .92376 | 2
59 g 73591 2 10: 28409 ` 81224 Jā . 18776 | . 07633 å - 92367 1
) 9. 81252 _|10. 18748 |10. 07641 9.92359 | 0
Diff ; xen
o Diff i
122 > cos 1’ sec cot 1 tan ese E sin «570

TABLE 33

Logarithms of Trigonometric Functions

1409

339.5 sin en csc tan Pit cot sec Ux cos -146°
T y
o |9.73611 10. 26389 | 9. 81252 10. 18748 |10. 07641 9. 92359 | 60
1 73630 | 19 26370 | .81279 | 27 | 18721 | 07649 | 8 | “92351 | 59

50 | 20 26350 | . 81307 | 28 18693 | . 07657 | 8 92343 | 58
3 em mi 26331 | ` 81335 ES -18665 | .07665 | 8 |. 92335 57
: 9 73708 a 10 26202 1300 d 10. ad 10. 07652 4 9. vx 55
19 28 (10 . g e A
BE ee VE El (| 892570 || 54
4 ao 4 26234 | .81473 | 28 | .18527 | | 07707 E | 92293 52
9 Kauss | 7 26215 | .81500 | 22 | 18500 | .07715 | 8 | : |.
10 | 9.73805 | jg |10.26195 | 9.81528 | sg D 18472 |70. 07723 s | 9. 92277 50
i Eon 19 LE mt zi THE ` 07740 E ` 92260 | 48
13 73863 | 20 26137 | . 81611 . 18389 | .07748 | $ | .92252 | 47
2| 19 26118 | .81638 | 27 18362 | | 07756 ` 92244 | 46
i 9 73901 19 H0. 26099 | 9. 81666 ee 10. 18334 |10. 07765 E 9. 92235 | 45
16 73921 = 26079 | .81693 | 2% |. 18307 | - 07773 21 92227 44
E us “4 aer E A Kaosa | 07789 | 8 | .92211 | 42
1 ` 92202 | 41
19 wars || ` 26022 | .81776 | 28 | | 18224 -07798 A o EU
20 [OTa ay e qu ; es
21 74017 2 t : ES
a + .92177 | 38
2 | me IB ES 4
24 | 174074 | 19 | !25926 | | 81913 27 | 18087 | .07839 | B | 292161 | 36
a e
25 | 9.74093 z 10. 25907 | 9. 81941 | 57 |10. 18059 |10. 07848 | g | 9. 92152 | 35
26 paria || 20 25887 | .81968 So |. 18032 | -07856 | g | .92144 | 34
28 | riis | 19 | :23849 | 182028 | 27 | 17977 | orsa 2 | 92120 | 32
28 O || 15 25849 25 LS E E 92127 | 32
29 74170 | 19 25830 | . 82051 | 35 | 17049 | ¿07881 | $ |_| -
30 |9.74189 | |) [10. 25811 | 9.82078 | „g |10.17922 |10. 07880 | y | 9. 92111 30
25792 | .82106 17894] . 07898 ` 921
S E qe 82133 | 27 17867 | .07906 | $ | :92094| 28
= EE St 82161 | 28 | ¿17839 | ¿07914 | 9 | 92086 | 27
= e 19 WE 82188 = ` 17812 | ` 07923 E ` 92077 | 26
9
35 | 9. 74284 6 10. 25716 | 9. $2215 | gg 10 17785 |10. 07931 | y 9. 92069 25
36 74303 | 19 25697 a8 pe -07940 | g | . 92060 | 24
37 gaze || 19 25678. [0882270 | Aes | [0217730 8 | ` 92052 | 23
30 | 174300 | 19 | :25640 | 182325 | 27 | (17675 | 07005 | 2 | 92085 | 21
Nu er meses arse mers
4l 74398 256 271 hie as p
19 17593 | . 07990 ` 92010
42 74417 25583 [6582407 | Sioa po A 18
43 74436 | 19 25564 | 82435 | 35 | . 17565 | 07908 | $ |. 92002 | 17
44 74455 | 19 25545 | .82462 | 27 | . 17538 cc ME
a rns acum a mom aem |g emer m
46 74493 B5 oz. M1 d:
19 17456 | . 08032 ` 91968
47 74512 | 1? 25488 | 82544 | 27 |. 1745 08032 | 9 91968 | 13
48 74531 25469 | ` 82571 ` 17429 SÉ 12
49 74549 e 25451 82599 ta .17401 08049 | y : = 1
50 | 9. 74568 | jg 10. 25432 | 9.82626 | 27 10. 17374 |10. 08058 | g | 9 91942} 10
539: 2681 17319 | ` 08075
E cU e ae Enos 4 ` 17292 08083 are 91917 7
1 . 17265 ;
25356 | . 82735 E
= ee) 18 32762 A 10. 17238 |10. 08100 9. 91900 5
55 | 9.74662 | ¡9 [TO m a 28 17210 | 08109 d ` 91891 4
56 | .74681 | ¡9 |. 27 | “17183 | .08117 .91883 | 3
57 | ` 74700 #25300 | 82817 | 27 | 17183 |. S 83 | 3
58 | .74719 | 12 | 25281 | .82844| 27 |. 17156 | -08126 | $ |: mail?
59 | 74737 | jg | 25268 | 82871 | 3g 10, 17101 |10. 08143 | ? | o 91857 | 0
60 | 9. 74756 |10. 25244 | 9. 82899 SS í
4 Diff ‘ a . sin e o
123?» cos ue sec cot T tan ese 1 56

1410

TABLE 33
Logarithms of Trigonometric Functions
34^» sin ES 1 ese tan = 1 cot sec ice cos «1450
y
0 | 9.74756 | jg |10. 25244 | 9. 82899 10. 17101 |10. 08143 9.91857 | 60
1 | -74775 | jp |. 25225 | .82926 27 | 17074 | .08151 8 | .91849 | 59
3 | 74812| 18 v ide 27 Po Pape 8 E =
4 | .74831| 19 | .25169 | .83008 | 38 | :16992 | ‘08177 | 9 | 91823 56
5 9. 74850 18 |10. 25150 | 9.83035 | 5; |10. 16965 |10. 08185 | y 9. 91815 | 55
7 | | 74887 5 tid E d = vi we 8 vec K
8 | 274906 | 1$ | .25094| .83117 | 28 | .16888 | .08211 | 9 | 91789 | 52
9 | .74924 | 19 | .25076 | 83144 | 27 | 16856 | .08219 R :91781.| 51
10 9. 74943 = 10. 25057 9.83171 | oy |10.16829 |10. 08228 | y | 9.91772 | 50
7 || D d dE dE
13 | .74999 | 19 | 925001 | ¿83252 | 27 | :16748 | .08254 | 9 vede S
14 | 75017 X ` 24983 | | 83280 E ` 16720 | | 08262 : et F-
15 | 9. 75036 10. 24964 | 9. 83307 10. 16693 |10. 0827 7:
& 18 s O 27 4 d EA 9. 91729 45
16 - 75054 E 24046 - 83334 55 | . 16666 | `. 08280 Ë 91720 | 44
18 | .75091 | 18 | 24909 | 83388 | 27 dā Rr acl
19 | .75110 P ` 24890 | | 83415 E ` 16585 | ` 08305 A kus 2
9 ` 08305 T
20 9. 75128 19 |10.24872 | 9.83442 | g |10.16558 |10. 08314 | y | 9.91686 | 40
21 | -T5147 | 18 - 24853 - 83470 27 | -16530 | .08323 | 2 | .91677 | 39
23 -75184 | 19 | 24816 3524) 27 16470 | 208549 | © 91660 | 37
24 -75202 | 19 | .24798 | 88551 | 27 | 16449 | -08349 | 91651 | 36
25 9. 75221 18 |10. 24779 | 9.83578 | 37 |10. 16422 |10. 08357 | y | 9.91643 | 35
26 | . 75289 | 19 | . 24761 - $3605 27 | - 16895 | .08366 | 9 | 91634] 34
28 | .75276 | 18 | "24724 | 83659 | 27 | 163% AER |) aero tee
29 | | 75294 a „24706 | ` 83686 x .16314 | .08392 | 9 as =
| 6 7 | 16314 | .08392 | 9 |:
30 9. 75313 fa 10. 24687 9. 83713 o; |10.16287 |10. 08401 | g | 9.91599 | 30
32 | 175350 | 19 | :24650| 83768 | 28 Teen B Be,
33 | | 75368 r "24632 |:837058 | 227 Í |6205 108425 | V9 med 2
2 . 75386 | 19 | 24614 | | 83822 xi .16178 | | 08435 A 91365 | 26
35 9. 75405 in 10. 24595 9. 83849 o; |10. 16151 |10. 08444 | y | 9.91556 | 25
37 | 75941 | 18 | ‘24559 | 53903 | 27 | ¿16007 | 08462 | 9 | ions] S
38. | ¿m6as9 | 19. po 024541 [093930 | 527! hecacord asia 108 ls DES
39 | .75478 | 19 | .24522 | 83957 | 27 | “16043 08479 | 9 qa | A
40 | 9.7549 AST. A Vd
ar [deat | ae aras z Free) vm a
42 | ¿75533 | | 24467 | . 84038 | 27 | Ti ` 085 Bi L:
7 i : 15962 | 008505 | * 914
43 | 275551 | 18 |. 94449 | 84068 |) 27 9 Tk
= „75569 | 18 | 324431 | | 84092 A toL VERUS 24 d Y
9. 75587 KIT =
15 - T5587 18 10. 24413 9. 84179 E 10. 15881 10, 08531 9 | 9.91469 | 15
EN (<. .24395 | .84146 | $2 | .15854 | .08540 91460 | 14
AE IER IE 7 EE
x -75660 | 18 | | 24340 | . 84227 E. Ger ta 9 < "S
50 | 9.75678 | |. 243: A o ES 8 La:
Dou 18 10. 24322 9. 84254 b 10. 15746 10. 08575 9 | 9.91425 | 10
52 | .75714 | 18 | .24286 | .84307 | 27 | 15693 Dd 9 e i
53 | .75733 : .24267 | .84334 | 27 1 08602 | 9 | 9130s >
5 75733 | 18 E E .15666 | | 08602 ` 91398
- 75751 | 1$ |_. 24249 | :84361| 27 15639 | 08611 | 2 91389 | 6
E 9. 75769 ^ 10.24: í ara va 8 =
57 - 75805 ig | «24195 | . 84442 | 27 | 15558 ve 9 rs 3
! E .24177 | 84469 | 27 15531 | 08 2 tā
rep 24177 | 84489 | 27 | ` 08646 91354 | 2
: 7 .24159 | .84496 | 27 | 15504 | 08655 | 9
60 |9.75859 | 18 2 0 . 08655 . 91345 1
A = 10. 24141 | 9.84523 | ^' un 15477 |10. 08664 | 9 | 9, 91336 | 0
03 COS Mii Diff. j 4
124 1 sec cot T tan ese Diff. sin 550
a

1411

TABLE
Logarithms of Tri 33
35° | I gonometric Fi
J> sin, |P ge
y Y ese tan Diff
ki e cot Di
0 9. 7585 sec iff.
- 59 4
` 75877 | 18 10. 24141 | 9. 84523 i piik t
2 || ¿75895 18 | .24123 | .84550 | 27 10. 15477 |1 m 4
4 :75913 | 18 | 24105 | .84576 | 28 . 15450 d 9. 91 ;
E 1175931 18 | -24087 | . 84603 27 | 118424) +. 08672 | S 114 e. 60
s-|s-ss4s | 19 lcd Lašiem 27 | - 15397 08681 | 9| :o1319 | 58
` 759687 | 18 10. 24051 9. 84657 27 -15370 | X GH E F et 58
8 175985 | 18 | - 24033 ` 84684 27 10. 15343 porwr) ge e A
EO ids (EH E 27 cy] voee 3 56
Em. [1276021 | 1? D Boetii .15316 | .08717 | $ .91292 | 5
10 Jesse | 18 22074 .84738 | 27 . 15289 E ol - 91283 54
. 76039 | am . 84 2 :152 ;
11 | -76057 (as [923901 |9 Ser 27 | 15236 | 008743 9 91266 | 32
AKA ` 723925 am! 27 1015209 i wess | Ý eet 51
o: 93 | " 5 N K . 15 : 9
i 76111 | 18 | 123889 - 84845 | 37 - 13182 | -08761 | g ea bc
am Bae e uS $5 : JE
"76146 | 17 | . 23871 91.28 |! i i
" pease? || err so id 10. ae -08788 | 9 dā E
ad be + d 84979 | 27 "15048 | 08806 | 9| 91194 =
19 1 1-096200 | [28818 | 85006 | 27 -15021 |. .9 1
20 | 9. 762 18 |_-23800 | . zech E" 08815 | 9| 91185 | 43
5 e m | 18 [O 23782 | 9. oe | us ; 14967 4 tt 4 Å 91176 a
z ct enu -85059 | 27 |10. 14941 - 08833 | y | .91167 e
24 | 76280 | 18 : 23729 "Bells | 27 | 14887 ASSUM T D
. 76289 g | -23729 5 .1
25 sā 18 | 23711 | 85166 26 - 14887 | - 08899 | g ar los
26 “76324 | 17 110. 23693 | 9. 851 27 | 14834 ` Kat 9 . 91132 a4
27 | `76342 | 18 | 23008 "85198 | 27 (TO. 14807 |10. 08877 | y | -91123 a
. 76360 g | -28658 8 Gry . 1478 k 9 5
29 763 2 . 85247 | ol .08895 | 9| ` 91114 | 35
; 7 18 . 23640 - | SH 5 + 5
EI ar] pease 55273 | 26 | 14727 | 08913 9 | 191096 | 38
31 ee ds. panos | 27 ees ee ee i eee 2
33 Eo 17 : 23569 ` 85354 | 27 10. 14673 IO 08931 ý [nese 31
. 76448 geg . 85 e261 LČ 14646 |. 9. 91
34 7646 1 ` 2355 5380 | . 08940 9 069 30
d 6 | 8 552 5 | HOT
eet E sn 27 | 114598 ee d 0504123
36 | .76501| !7 10. 23516 0725460 | 26 (EEN :08967 | o | -91042 Es
38 | | 76337 18 ` 23481 GE 1327: PS 10. 08977 | 0 . 91033 | 26
. 76537 AD ` 85514 | 27 | .14513 | . 9. 9102
39 dee 1 ` 23 5514 | ` 08986 | Y SCH 25
. 76554 7 463 | . 85540 | . 144 i
40 TES ig | 23446 | - 82067 7 j TERES 1 cod 4 i DIOE 2
13 | 76625 | 18 ` 23393 dd ineo] (ease ee | 9 | |
5 | . 2339: 56 T ; :
JE ANE IB AE LIE AME IE
45 76660 | 18 . 23358 | _. 85700 | 26 | - 14326 tēti 9 | -90960 E
46 ` 76677 | 17 10. 23340 | 9. 85727 | 5927 ieks 14300 | . od g | -90951 e
47 76605 | 18 . 23323 85754 | 27 |10. 14273 |10 58 al -90942 | 16
48 | 76712) Y ` 23305 pees |261 Lë 14246 Seu 9. 90933 | 15
Er 0 1275270 o SET ERIT Eo 9 | - 90924 5
50 | 9.76747 | +4 Di 23270 | .85834| 27 |: E Mei |49 Here e
51 | . 76765 ig |10. 23253 | 9. 85860 ZA cdi Geer | 10 | -90906 | 12
52 | .76782 17 . 23235 85887 | 27 10. 14140 |10. 09113 g |- 90896 | 11
58 ` 76800 | 18 .23218 | . 85 87 | 296 | -14113 s | | 9.90887 | 10 _
54 | T6817 | ji Es aereis 19271 Re "09131 9 | - 90878 9
55 | 976835 | 17 193183 | :85967 | 27 | I Pettey 142 |) bose) ||. 5
56 . 76852 wf 10. 23165 | 9. 85993 26 | _. 14033 . 09149 | Out e 90860 7
57 | . 76870 18 . 23148 86020 | 27 110. 14007 |10. 09 SB TG uS 6
58 | .76887 | 17 23130 | .86 0| 26 | - 13980 . 09158 | o | 9. 90842 5
id beed d Dios Se |927| | eed Larai | 9 |. 90832 4
60 | 9.76922 18 10. 23096 | 186100 | 27 | : 13927 |. ve vi Zz, 3
1 _ 2 |10. 23078 | 9. 86126 e |, ~ 13900 "00105 | 9| | 90814 2
125?» cos Diff. 86126 | ^ |10. 13874 [10. 0 9 | 90805
| WA 9204 | l
1’ sec CN DU 09204 | "|9.90796 | 0
XR Bag e [p EN
1’ sin «540

1412

TABLE 33
Logarithms of Trigonometric Functions
36% sin A csc cot sec ie cos -143°
4 4
0 | 9.76922 | ,, |10. 23078 . 13874 |10. 09204 | „ | 9.90796 | 60
1 | .76939 | |4 | 23061 - 18847 | .09213 | ,2 | .90787 | 59
2 | .76957 | 13 | .23043 -13821 | .09223 | 19 | 90777 | 58
3 | .76974 | 17 | .23026 - 18794 | .09232 | 5 | .90768 | 57
4 | .76991 | 17 | . 23009 -13768 | .09241 | 9 | .90759 | 56
5 | 9.77009 | |, |ī0. 22991 „18741 |10. 09250 | , | 9.90750 | 55
6 | .77026 | |4 | .22974 -13715 | .09259 | g | -90741 | 54
7 || zods. || 44 | 00822957 . 13688 | .09269 | 19 | .90731 | 53
8 | .77061 | 18 | :22939 .13662| .09278 | $ | .90722| 52
9: |) 257078 || SAAI 22022 .13635 | .09287 | $ | .90713| 51
10 |9.77095 | |, |10.22905 . 13608 |10. 09296 | | 9. 90704 | 50
i» || 072112 |] 27 | pmogsss .13582 | .09306 | 19 | .90694 | 49
12. || 077180 || 45 ūts22870 -13555 | .09315 | 9 | .90685| 48
13 | .77147| |7 | .22853 . 13529 | .09324 | ) | .90676 | 47
14 | .77164 | 17 | :22836 -13502 | . 09333 | ,)| .90667 | 46
15 | 9.77181 | ig |10.22819 . 13476 |10. 09343 | o | 9.90657 | 45
16. || .77199 | 18. [0222801 - 13449 | .09852 | $ | .90648 | 44
i Lavoro || 17 | ļelezērsā . 13423 | . 09361 | 9| .90639 | 43
18, || avasas || 47 [MT . 13397 | .09370 | 9 | -90630 | 42
Jo. | 77250 || 47 Eng .13370 | .09380 | 1) | < 90620 | 41
20 [9.77268 | |, |10. 22732 . 13344 |10. 09389 | , | 9.90611 | 40
2r || 077285 | 47 | [22715 .18317 | .09398 | |) | .90602 | 39
22 | .77302 17 | :22608 . 13291 | .09408 | 19 | .90592 | 38
23 | 277819 17 | 22681 . 13264 | .09417 | $ | .90583 | 37
z E 17 | :22604 . 13238 | .09426 | 3 | .90574| 36
. 7735 10. 22647 . 13211 |10. 09435 9.90565 | 3
e 5
26 | .77870 | |7 | -22630 13185 | . 09445 E .90555 | 34
27 477387 |Í 212.1 22613 .18158 | .09454 | ¿| .90546 | 33
28 | .77405 | 17 | -22595 - 13132 | .09463 | ,3 | .90537 | 32
2 e TAE PUE . 13106 | .09473 | 10 | :90527 | 31
10. 22561 .13079 |10. 09482 9. 90
ad i - 90518 | 30
31 77456 | 12 | . 22544 .13053 | . 09491 n . 90509 | 29
32 pu EE . 13026 | .09501 | 19 | ‘90499 | 28
33 - 77490 17 geed - 18000 | .09510 | ,9 | 90490 | 27
| iy | 10622493 . 12973 | .09520 | 19 | 90480 | 26
35 9. 77524 iz |10. 22476 . 12947 |10. 09529 | y | 9.90471 | 25
36 | 77541 | |7 | .22450 .12921 | .09538 | 0 | .90462 | 24
37 | 77858 | 17 | 22442 -12894 | .09548 | 19 | 90452 | 23
38 | 77575 | 17 | 22425 - 12868 | .09557 | 9 | .90443 | 22
E EE . 12842 | .09566 A1 .90434 | 21
10 9. 77609 17 |10. 22391 . 12815 |10. 09576 | y | 9.90424 | 20
ál | .77626 | 17 : 22374 . 12789 | .09585 | (0| .90415 | 19
42 | 77643 | |7 | 22357 . 12762 | .09595 | 19 | .90405 | 18
43 | -77660 | 17 | -22340 .12736 | .09604 | ,) | .90396 | 17
E ay [629393 . 12710 | .09614 | 19 | :90386 | 16
45 9. 77694 3 10. 22306 12683 |10. 09628 | „ | 9.90377 | 15
2 eus ta oem .12657 | .09632 | 0 | .90368 | 14
2. | ios Mna . 12631 | .09642 | 19 | 90358 | 13
Ai [Ens Lig! ees . 12604 | .09651 | 9 | :90349 | 12
AEL 15] pof 9 .12578 | .09661 | 19 | :90339 | 11
50 Ku me 10. 22222 . 12552 |10. 09670 | , | 9.90330 | 10
51 | 77795 | 17 - 22205 . 12525 | .09680 | 19 | .90320| 9
"MP GHI . 12499 | .09689 | 9 | :90311 8
54 | .77846 i ` 22154 WEE E o EM
i . 2| .90292| 6
1
Ji El qe
57 | .77896 | 17 | :92104 «12387 O A e ME
Ji gēli | -09737 |9| .90268| 3
38 | .77 121 (22087 12841 | | 09746 .90254| 2
. 71930 ` 22070 1231 10
60. | 9252020 wie) ci 5| .09756 | 19 | < 90244 1
219 i . 12289 |10. 09765 | 9 | 990235 | 0
Diff. i
126?» cos 1” sec tan ese p sin «530

1413

TABLE 33
Logarithms of Trigonometric Functions
37% sin em ese tan ii cot sec TR i cos «142 ?
M $
O | 9.77946 | ,7 |10. 22054 | 9.87711 | o; |10. 12289 |10. 09765 | ;„ | 9.90235 | 60
E || 277963 || 17 22037 | .87738 | 54 | .12262 | .09775 | 10 | .90225 | 59
Z || 227980 | 17 22020 | .87764 | 56 | .12236 | .09784 | |0| .90216 | 58
B. | 27997 | 32 22003 | .87790 | 57 | .12210| .09794 | 19 | 190206 | 57
As || 678018 || GĒ 21987 | .87817 | 55 | -12183 | .09803 | ,| .90197 | 56
5 |9.78030 | ¡7 |10.21970 | 9.87843 | sẹ |10.12157 |10.09813 | a | 9. 90187 | 55
6 | .78047 | 17 21953 | .87869 | Se | .12131 | .09822 | ,2 | .90178 | 54
7 | .78068 | 12 21937 | .87895 | 29 | .12105 | .09832 | 19 | :o0168 | 53
8 | .78080| |? 21920 | .87922 | 54 | .12078 | .09841 | ,9 | .90159 | 52
9 | .78097 | 17 21903 | .87948 | 58 | .12052 | .09851 | 19 |_. 90149 | 51
10 |9.78113 | ¡7 |10. 21887 | 9.87974 | „g |10.12026 |10. 09861 | o | 9.90139 | 50
Me |Í 4.78180. | | T7 21870 | .88000 | 35 | .12000 | .09870 | ,9 | .90130 | 49
E. nsus 3 21853 | .88027 | 24 | .11973 | .09880 | 19 | .90120 | 48
13 | .78163 | 18 21837 | .88053 | 55 | .11947 | .09889 ¡9 | .90111 | 47
14 |}; 78180 || 37 21820 | .88079 | 26 | . 11921 | .09899 | 10 | 90101 | 46
15 | 9.78197 | | |10. 21803 | 9. 88105 | sẹ |10. 11895 |10. 09909 | , | 9. 90091 | 45
a || 228213 | SE 21787 | .88131 | 59 | .11869 | .09918 | 9 | .90082 | 44
KA || 278280 | 17 21770 | .88158 | 26 | .11842 | .09928 | |9| .90072 | 43
18 | 278246 | |5 21754 | .88184 | 26 | .11816 | .09937 | ,)| .90063 | 42
19 | :78263 | 17 21737 | .88210 | 20 | .11790 | .09947 | || .90053 | 41
20 | 9.78280 | jẹ |10.21720 | 9.88236 | ze |10.11704 |10. 09957 | y | 9.90043 | 40
21 | .78296 | 19 | .21704 | .88262 | 29 | .11738 | .09966 | 0 | . 90034] 39
32; || egesta | Tí 21687 | .88289 | 26 | .11711 | .09976 | 1) | .90024 | 38
24: || 78820 | 39 21671 | .88315 | 26 | .11685 | .09986 | |9| 190014 | 37
24 | .78346 | |4 21654 | .88341 | 26 | .11659 | .09995 | ¡9 | .90005 | 36
25 | 9.78362 | |; |10.21638 | 9.88367 | ze |10. 11633 |10. 10005 | 5, | 9.89995 | 35
26 | .78379 | |? 21621 | .88393 | 3% | .11607 | .10015 | |9| 189985 | 34
27 | 78305 | 19 21605 | .88420 | 26 | .11580 | .10024 | ,9 | .89976 | 33
28 | 78412 | 1% 21588 | .88446 | 26 | .11554 | .10034| I0 | .89966 | 32
29 | 78428 ai 21572 | .88472 | 26 | ¿11528 | . 10044 | 25 | .89956 | 31
30 | 9. 78445 | |; |10. 21555 | 9.88498 | sẹ 10. 11502 |10. 10053 | jo | 9.89947 | 30
O | 35 21539 | .88524 | 20 | .11476 | . 10063 | |) | .89937 | 29
32 | .78478 21522 | .88550 | 29 | 11450 | .10073 | ' | .89927 | 28
33 | 78494 | 16 21506 | .88577 | 26 | .11428 | .10082 | ,p | .89918 | 27
34 | .78510 E 21490 | .88603 | 26 | .11397 | . 10092 | |) | .89908 | 26
35 | 9.78527 | |; |10. 21473 | 9. 88629 | „g |10.11371 |10. 10102 | ,) | 9.89808 | 25
36 | .78543 | | 21457 | . 88655 | 26 | .11345 | .10112 | 'y | -89888 | 24
37 | 78560 | 17 21440 | .88681 | 526 | .11319 | .10121 | ¡9 | .89879 | 23
38 | .78576 | 16 21424 | .88707 | 26 | .11293 | .10131| | .89869 | 22
29 | .78592 e 21408 | .88733 | 26 | .11267 | .10141 | ¡9 |_. 89859 | 21
40 |9. 78609 10. 21391 | 9.88759 | 5; |10. 11241 |10. 10151 | „ | 9. 89849 | 20
41 | .78625 | 16 21375 | .88786 | 2% | .11214 | .10160 | ¡9 | .89840 | 19
a2 |lūrrgo42 || 2 21358 | .88812 | 5g | -11188 | .10170 | ip | -89830 | 18
43 | .78658 | 19 21342 | .88838 | 26 | .11162 | .10180 | || .89820 | 17
44 | .78674 d 21326 | .88864 | 26 | .11136 | .10190 | 75 | .89810 | 16
4 . 78691 10. 21309 | 9. 88890 | 5, |10. 11110 |10. 10199 89801 | 15
k pe 16 21293 | . 88916 SS 11084 | .10209 | 10 | .89791 | 14
47 | <78723 | 19 21277 | .88942 | 26 | . 11058 | .10219 | |) | -89781 | 13
4s | :78739 | 16 | "21261 | .88968 | 26 | .11032 | .10229 | ¡q | .89771 | 12
49 | | 78756 is 21244 | :88994 | 26 | .11006| .10239 | `g |_. 89761 x
78772 21228 | 9. 89020 10. 10980 |10. 10248 89752 | 1
$1 | 78788 | 19 | "21212 | 89046 26 | 10954 | :10258 | 10 | 89742 | 9
52 | .78805 | 17 | :21195 | :89073 | 54 | -10927 | .10268 | |0| .89732| 8
3 78821 | 16 | “21179 | .89099 ` 10901 | . 10278 .89722 | 7
: : 16 26 7 288 | 10 | 89712| €
54 | .78837 | 16 | ‘21163 | .89125 ze | .10875 | .10288 | jo |_. 897 ;
55 | 9. 78853 10. 21147 | 9. 89151 | ze |10. 10849 |10. 10298 | g | 9.89702 | 5
56 18869 Y AO) ūezi1si |9989177 | 10823 | .10307 | 49 | . 89693
57 | .78886 | 17 21114 | 89203 | 29 | :10797 | .10317 | |0| .89683 | 3
58 | :78902 | 19 | :21098| .89229 | 29 | .10771| .10327 309 | .89673 | 2
| : 89255 | 26 745 7 663 | 1
59 | .78918 | 16 | 21082 | .89255 | 26 | -10745 | .10337 | jo | 89663 | 1
60 | 9.78934 | 16 [1021066 | 9. 89281 | 10. 10719 |10. 10347 | ` 89653 :
^ : i | Diff. | :
1279» cos Dit sec cot Li tan csc | 1; sin «52°
II si dium. AAA

1414

TABLE 33
Logarithms of Trigonometric Functions
38% sin n. csc tan ipe cot sec ae cos -141°
y É
0 | 9.78934 | jg |10. 21066 | 9. 89281 | „g |10. 10719 |10. 10347 | , | 9.89653 | 60
J - 78950 17 | 21050 | .89307 3° | .10693 | .10357 | 10 | 89643 | 59
3 | 78983 | 19 Futari |. 080359 | 226 loruosaa bovaosrg | 19 | vestes || e
4 | .78999 | je | .21001| 80385 | 26 | .10615| 10386 | 10 | 89614 56
5 | 9.79015 |1; |10. 20985 | 9.89411 | ze |10.10589 |10. 10396 | jọ | 9. 89604 | 55
6 | .790831 | ig | .20969 | .89437| 26 | 10563 | . 10406 ` 89594 | 54
7 | .79047 | yg | .20953 | .sos63 | 26 | 10587 | .10416 | 10 | :89584 | 53
8 | .79063 | jẹ | .20937 | .89489 | 26 | ` 10511 | .10426 | 10 | 89574 | 52
9 | -79079 | Je | -20921 | .89515| 26 | :10485 | :10436 D 89564 | 51
10 | 9.79095 | ¡6 |10. 20905 | 9.89541 | 5, |10. 10459 |10. 10446 | jọ | 9. 80554 | 50
11 | . 79111 | 12 | . 20889] .89567 26 | 10433 | . 10456 89544 | 49
12 | .79128 | 1% | 20872 | | 89593 10407 | 10466 | 10 | “80534 | 48
13 | .79144 | 36 | .20856 | .89619 29 | ¿10381 | 10476 | 19) ¿89524 | 47
14 | .79160 | |g | -20840 | .89645 | 26 | | 10355 | 10486 M 89514 | 46
15 | 9.79176 10. 20824 | 9. 89671 10. 10329 |10. 1
16 | .79192 de "20808 | 89697 | 29 |. 10303 osos 9 ee d
17 | 379208 | 46 [--20792 |+:89723- 1:26 be ia0277 |: iwos1a | 10 || ($9485 JAS
18 | .79224 | |6 | .20776 | .89749 R 10251 | . 10525 m .89475 | 42
2 cog e E .89775 | 26 | -10225| .10535 10 | 89465 | 41
720744 | 9. 89801 10. 101 :
21 | 70272 | 18 [20728 | .89827 | 26 eis OORA 10 ietvi: 39
22 | .79288 | 36 | .20712 | .89853| 29 | ¿10147 | ¿10565 | 10| 89435 | 38
23 | | 79304 : 20696 | . 89879 | 26 ` "10575 | 10] :
Ü 26 | ¿10121 | | 10575 ` 89425 | 37
z . 79319 | jẹ | 20681 | 89905 | 26 | :10095 | 10585 im ` 89415 | 36
5 | 9.79335 . 110. 20665 | 9. 89931 1
26 | -79351 | 16 | .20649| 89957 | 29 nsa EE 10 Ee a
27 | . 79367) |g | .20633 | . 89983 | 29 | “10017 | 10615 | 19| 89385 | 33
28 | | 79383 .20617 | 90009 | 29 10 |] g
K 26 | -09991 | | 10625 ` 89375 | 32
29 | .79399 | 10 | 20601 | | 90035 .09965 | ` 10636 | 11 89364 | 31
30 | 9. 79415 10. 20585 | 9.90061 | 7° dee
| MET. Å o5 |10. 09939 |10. 10646 9. 89354 | 30
31 | .79431| 16 | 20569 | ` 90086 09914 | . 10656 | 10 | `` 89344 | 29
32 | .79447 | ¡5 | .20553 | .90112 | 2% | 09888 | | 10666 | 10 | 89834 | 28
33 | | 79463 | 1 .20537 | . 90138 | 26 09862 | < 10676 | 19 | ` 7
33 S oa ` 1067 ` 89324 | 27
-79478 | i$ | .20522 | .90164| 26 | “09836 | ` 10686 B ` 89314 | 26
35 | 9.79494 ig 10. 20506 | 9. 90190 | sẹ |10. 09810 |10. 10696 9. 89304 | 25
36 | .79510 18 | :20490| .90216 09784 | .10706 | 19 | ` 89294
37 | .79526 | ¡6 | .20474 | .90242 | 29 | “09758 | .10716 | 19 | ' 89984 5
38 | .79542 | ig | .20458 | .90268 | 29 |. :09732| :10726 | 10 | 89974 2
39 | .79558 | 1$ | .20442 | :90294 o ` 09706 | | 10736 I ` 89264 a
: : 86
40 | 9.79573 ue |10.20427 | 9.90320 | 54 |10.09680 |10. 10746 9. 89254 | 20
al : 79589 T8 20411 . 90346 | 35 | .09654 | . 10756 de 89244 | 19
} „20395 | . 90371 767 |
c 9 1 09629 | | 10767 .89233 | 1
43 | -79021 | |5 | -20379 | :90397 26 | 09603 | :10777 | 10 | 89223 p
79686 | yg | .20364 | .90423 | 28 | .09577| .10787 | 19 “s9213 | 16
45 | 9.79652 10. 20348 | 9. 90449 10. 09 797 | ire
46 | 79668 | 18 | 20332 | “90475 | 29 |" 09525 | logos | 10 | * 89703 | 18
47 | 79684 .20316 | .90501 | 29 | “o "neu |0 Le sores Pas
7 . E .09499 | ` 1081 891
48 | .79699 | !5 | '20301 | | 90527 | 26 Adae coe
2 .79715 | 19 | "20285 | :90553 n ` 09447 | 10838 | 1 (89162 | 11
50 9. 79731 i 10. 20269 9. 90578 D 10. 09422 10. 10848 Ea 9. 89152 | 10
52 "| Xerovo2 | T6) dusceno2as (61290630 | 14264 las: Moses E
79762 | 28) haw ` 90630 09370 | | 10868 ` 89132
33 | .79778 | i5 | .20222| .90656 | 26 | :09344| ‘10878 | 10 89122 | 7
.79793 | 16 | .20207 | .90682 | 29 | "09318 | 10888 10 | "oos
55 | 9. 79809 : |10.20191 | 9.90708 | 2° | E >
BB |78 | 16 20191 | 9. 90708 | 26 10. 09292 10. 10899 | 5, | 9.89101 | 5
5; | 0e | 15 | 20175 | 00734 | 25 | «092 .10909 | I0 | .89091 | 4
5s | iono | 16 | -20160 | -90759 | $5 | 00241} .10919 | lO | ¿89081 | 3
59 | :79872 | 19 | :20128 | “eos, | 26 | -09215 | .10929 | 7 | .89071| 2
E: = 0. 20113 | 9. 90837 10. 09163 |10. 10950 | ! | 9 89050 | 0
ee iff Diff. i
128 1 sec cot 1 tan ese SEH sin -51 o

1415

TABLE 33
Logarithms of Trigonometric Functions
39%, sin um esc tan nate cot sec ml cos -140°

y y
0 9. 79887 16 10. 20113 | 9. 90837 oe |10. 09163 |10. 10950 10 | 9. 89050 60
1 79903 15 . 20097 . 90863 26 . 09137 . 10960 10 . 89040 59
2 79918 16 . 20082 . 90889 25 . 09111 . 10970 10 | . 89030 58
3 79934 16 . 20066 . 90914 26 . 09086 . 10980 11 . 89020 SÉ
4 79950 15 . 20050 . 90940 26 . 09060 . 10991 10 . 89009 56
5 9. 79965 16 10. 20035 | 9. 90966 og |10. 09034 |10. 11001 10 | 9. 88999 55
6 79981 15 . 20019 . 90992 26 .09008 | .11011 11 . 88989 54
fi 79996 16 . 20004 . 91018 25 . 08982 . 11022 10 . 88978 53
8 80012 15 . 19988 . 91043 26 . 08957 . 11032 10 . 88968 52
9 80027 _ 16 . 19973 . 91069 26 „08931 | . 11042 10 „88958 51
10 9. 80043 15 10. 19957 | 9. 91095 og |10. 08905 |10. 11052 11 | 9 88948 50
11 80058 16 . 19942 . 91121 26 . 08879 . 11063 10 . 88937 49
12 80074 15 . 19926 . 91147 25 . 08853 . 11073 10 . 88927 48
13 80089 16 . 19911 . 91172 26 „08828 | . 11083 11 „88917 47
14 „80105 15 „19895 „91198 26 „08802 | . 11094 10 . 88906 46
15 9. 80120 16 10. 19880 | 9. 91224 oe |10. 08776 |10. 11104 10 9. 88896 45
16 80136 15 „19864 | . 91250 26 .08750 | .11114 11 . 88886 44
17 80151 15 . 19849 . 91276 25 .08724 | .11125 10 . 88875 43
18 80166 16 . 19834 | . 91301 26 .08699 | .11135 10 . 88865 42
19 . 80182 15 . 19818 . 91327 26 . 08673 „11145 | 11 . 88855 41
20 9. 80197 16 10. 19803 | 9. 91353 oe |10. 08647 |10. 11156 10 | 9. 88844 40
21 . 80213 15 . 19787 . 91379 25 . 08621 . 11166 10 . 88834 39
22 80228 16 : 110772 . 91404 26 .08596 | . 11176 | 13 . 88824 38
23 80244 15 | . 19756 . 91430 | 26 HOSS TO} ARTS 10 . 88813 on
24 80259 15 . 19741 . 91456 26 „08544 | . 11197 10 . 88803 36
25 9. 80274 16 10. 19726 | 9. 91482 | 25 |10. 08518 |10. 11207 | ,, 9. 88793 30)
26 . 80290 15 . 19710 . 91507 | 26 . 08493 218 10 . 88782 34
27 . 80305 15 . 19695 . 91533 26 . 08467 .11228 | |] . 88772 33
28 . 80320 16 . 19680 . 91559 26 . 08441 .11239 | 19 . 88761 32
29 . 80336 15 . 19664 . 91585 25 . 08415 . 11249 10 . 88751 31
30 9. 80351 15 10. 19649 | 9. 91610 26 10. 08390 |10. 11259 | i, | 9. 88741 30
31 80366 16 | : 19634 „91636 | 26 „08364 „11270 10 „88730 29
32 80382 15 . 19618 . 91662 | 26 . 08338 | . 11280 | qi „88720 28
83 80397 15 | . 19603 . 91688 25 . 08312 . 11291 | 19 . 88709 27
34 . 80412 16 | . 19588 . 91713 26 .08287 | .11301 | |, . 88699 26
35 9. 80428 15 |10. 19572 9. 91739 oe 10. 08261 10. 11312 | 1g 9. 88688 25
36 80443 15 ` . 19557 . 91765 26 . 08235 . 11322 | 19 . 88678 24
37 80458 15 . 19542 . 91791 25 . 08209 „11832 | 11 . 88668 28
38 80473 16 . 19527 . 91816 26 . 08184 | .11343 | 1g . 88657 E
39 80489 we 19511 . 91842 | 26 . 08158 211853 11 : 88647
40 9. 80504 15 10. 19496 | 9. 91868 | os 10. 08132 |10. 11364 | 19 9. 88636 20
41 80519 15 . 19481 . 91893 26 „08107 „11374 | 11 . 88626 19
42 80534 16 „ 19466 „91919 26 „08081 . 11385 | 19 . 88615 18
43 80550 15 . 19450 . 91945 26 . 08055 .11395 | |, . 88605 M
44 80565 15 . 19435 . 91971 | 925 . 08029 . 11406 10 . 88594
45 9. 80580 15 110. 19420 | 9. 91996 | 96 10. 08004 |10. 11416 11 9. 88584 15
46 80595 15 . 19405 . 92022 26 . 07978 «11427 | 10 . 88573 14
47 80610 15 . 19390 . 92048 25 E 07952 . 11437 11 ; 88563 13
48 80625 | 16 . 19375 .92073 | 56 . 07927 -11448 | 10 asā x
49 . 80641 15 . 19359 .92099 | 56 . 07901 „11458 | |1 Å
50 9. 80656 15 110. 19344 | 9. 92125 | 25 10. 07875 10. 11469 | 10 9. 88531 ri
51 80671 15 . 19329 . 92150 26 . 07850 . 11479 | tiu t 88521 S
52 80686 15 | „19314 „92176 26 . 07824 -11490 | 11 . 88510 :
53 . 80701 15 „19299 . 92202 25 . 07798 . 11501 10 si i
54 . 80716 15 „19284 | .92227 | 24 „07773 „11511 | 11 4
55 9. 80731 15 |10. 19269 | 9. 92253 | 26 10. 07747 10. 11522 10 9. SS 2
56 80746 | i6 .19254 | .92279 | 25 .07721 | .11532 | 1] | . 88468 E
57 80762 | 15 | .19238 | .92304 | 2g | .07696 | .11543 |10 | 1788457 | 3
58 80777 15 08110223 . 92330 26 | . 07670 „11553 | |] : :
59 | :80792 | 35 .19208 | .92356 | 35 | .07644 | .11564 | 31 | > 1
60 | 9.80807 | 10. 19193 | 9. 92381 " |10. 07619 |10. 11575 | | 9. 88425

| | 3 P: +

| - | | 1 | Diff :

129°- cos | Dif | see cot | Ap tan eset [qr sin — e5(o

1416

TABLE 33

Logarithms of Trigonometric Functions

tan 1 cot

Va,
o
y

CoONAAARAMHOT HS

. 80807 r . 92381 . 07619
"Suen : . 92407 . 07593
. 80837 h . 92433 . 07567
. 80852 y . 92458 . 07542
. 80867 A „92484 „07516

9. 80882 l . 92510 . 07490
. 80897 : . 92535 . 07465
. 80912 ! . 92561 . 07439
. 80927 ! . 92587 . 07413
. 80942 i „92612 „07388

9. 80957 ` . 92638 . 07362
. 80972 ! . 92663 . 07337
. 80987 : . 92689 „07311
„81002 : 192715 . 07285
. 81017 : . 92740 . 07260

9. 81032 : . 92766 . 07234
. 81047 . 18953 . 92792 . 07208
. 81061 . 18939 . 92817 . 07183
. 81076 . 18924 . 92843 „07157
„81091 . 18909 „92868 „07132

9. 81106 . 18894 . 02894 . 07106
. 81121 . 18879 . 02920 . 07080
. 81136 . 18864 . 92945 . 07055
. 81151 . 18849 . 92971 . 07029
. 81166 i . 18834 . 92996 . 07004

9. 81180 . 18820 . 93022 . 06978
. 81195 . 18805 . 93048 . 06952
. 81210 . 18790 . 93073 . 06927
. 81225 . 18775 . 93099 . 06901
. 81240 . 18760 . 93124 > . 06876

9. 81254 . 18746 . 93150 . 06850
. 81269 . 18731 . 93175 „06825
„81284 „18716 „93201 „06799
„81299 „18701 . 93227 . 06773
. 81314 . 18686 . 93252 . 06748

9. 81328 . 18672 | 9. 93278 . 06722
. 81343 .18657 | .93303 . 06697
. 81358 .18642 | .93329 . 06671
. 81372 . 18628 | .93354 . 06646
. 81387 .18613 | .93380 | 29 | .06620

9. 81402 . 18598 | 9. 93406 „06594
. 81417 .18583 | .93431 | | .06569
. 81431 . 18569 | .93457 . 06543
. 81446 .18554 | . 93482 . 06518

. 81461 .18539 | .93508 . 06492

9. 81475 .18525 | 9.93533 | „4 |10. 06467
. 81490 . 18510 | .93559 „06441
. 81505 .18495 | .98584 | 29 | 106416
. 81519 . 18481 | .93610 . 06390
. 81534 . 18466 | .93636 . 06364

9. 81549 . 18451 | 9. 93661 . 06339 |
. 81563 .18437 | .93687 . 06313
. 81578 . 18422 | .93712 | 2? | | 06288
. 81592 . 18408 | . 93738 . 06262

81607. . 18393 | . 93763 . 06237

9. 81622 . 18378 | 9. 93789 . 06211
. 81636 .18364| .93814 | 2? | .06186
. 81651 | | .18349 | .93840 . 06160
. 81665 . 18335 | . 93865 . 06135
. 81680 | 1% | .18320 | | 93891 . 06109

60 | 9. 81694 .18306 | 9.93916 | 7? |10. 06084

î^ : Ë
130?» cos i sec cot 1 tan

P? | or Nw 400 1000

4
R
Næ)

r

TABLE 33

Logarithms of Trigonometric Functions

1417

41% sin 1/ esc tan P cot sec BC cos «1380
X y
O | 9.81694 | |5 |10.18306 | 9.93916 | og |10.06084 |10. 12222 | ,, | 9. 87778 | 60
AE IE. 18291 | .93942 | 25 | .06058 | . 12233 | |! | .87767 | 59
2 || 281723 | 35 18277 | .93967 | 26 | .06033 | .12244 | |! | :87756 | 58
3 Hf ams |, de 18262 | .93993 | 25 | .06007 | .12255 | ll | .87745 | 57
ESA | de 18248 | .94018 | 52 | .05982 | .12266 | 1] | .87734 | 56
5 |9.81767 | |, |10. 18233 | 9.94044 | o5 |10. 05956 |10. 12277 | ,, | 9.87723 | 55
6 | .81781 | 1$ 18219 | .94069 | 22 | .05931| .12288 | 11 | .87712 | 54
5 jeans |Í e 18204 | .94095 | 55 | .05905 | .12299 | 11 | .87701 | 53
8 | .81810 | 1$ 18190 | .94120 | 52 | .05880| .12310 1l | .87690 | 52
6 | aereas | 15 18175 | .94146 | 29 | .05854 | .12321 | 1} | .87679 | 51
10 | 9.81839 | |5 |10. 18161 | 9.94171 ze |10. 05829 |10. 12332 | 4, | 9. 87668 | 50
TE AE 18146 | . 94197 | 28 | .05803 | .12343 | 1} | .87657 | 49
da || "1868 || 2 18132 | .94222 | 29 | .05778 | .12354 ll | .87646 | 48
13 | .81882 | |5 18118 | .94248 | 26 | .05752 | .12365 | || | .87685 | 47
14 | 81897 | |5 18103 | .94278 | 26 | .05727 | . 12376 | || | .87624 | 46
15 | 9.81911 | ¡5 |10.18089 | 9.94299 | „5 |10.05701 |10. 12387 | 5, | 9.87613 | 45
16 || «81926 | 15 18074 | .94324 | 25 | .05676 | .12399 | 1? | .87601 | 44
17 | .s1940 | |5 18060 | .94350 | 3° | .05650 | .12410 | |1 | .87590 | 43
18 | :s1955 | 19 18045 | .94375 | 25 | .05625 | .12421 ll | .87579 | 42
19 | ang) 1% 18031 | .94401 | 28 | .05599| .12432 ll | .87568 | 41
20 | 9.81983 | |5 |10.18017 | 9.94426 | „g |10. 05574 |10. 12443 | ,, | 9. 87557 | 40
21 || 3.281998 | 19 18002 | .94452 | 28 | .05548 | .12454 | || | .87546 | 39
28 | 292012 | 4 17988 | .94477 | 28 | .05523 | .12465 | |1 | .87535 | 38
BE Rio ne 17974 | .94503 | 28 | .05497 | .12476 | || | .87524 | 37
EE | 15 17959 | .94528 | 22 | .05472 | .12487 | |) | .87513 | 36
25 | 9.82055 | |4 |10.17945 | 9.94554 | „5 10. 05446 |10. 12499 | |, | 9.87501 | 35
26 | .82069 | |5 17931 | .94579 | 22 | .05421 | .12510 | H | .87490 | 34
27 | .82084 | 15 17916 | .94604 | 29 | .05396 | .12521 | || | .87479 | 33
28 | .82098 | M 17902 | .94630 | 25 | .05370| .12532 | || | .87468 | 32
29 if 8902 | a 17888 | .94655 | 25 | .05345 | .12543 | || | .87457 | 31
30 | 9.82126 | |5 |10.17874 | 9.94681 | 25 |10.05319 |10. 12554 | ¡2 | 9. 87446 | 30
Bi | sesorai | o 17859 | . 94706 | 26 | .05294 | . 12566 | |] | .87434 | 29
82 j| 018155 | a 17845 | 94732 | 25 | .05268 | .12577 | |] | .87423 | 28
ds || 82760 Gs 17831 | .94757 | 23 | .05243 | .12588 | || | .87412 | 27
34 | .82184 | 15 17816 | .94783 | 29 | .05217 | . 12599 | |] | .87401| 26
35 | 9.82198 | ,, |10. 17802 | 9.94808 | 5, |10. 05192 |10. 12610 | |2 | 9. 87390 | 25
36 [A2212] ór 17788 | .94834 | 29 | .05166 | .12622 17 | .87378 | 24
Z9 E c 17774 | .94859 | 29 | .05141 | .12633 | |, | .87367 | 23
38 | .82240 | 1$ 17760 | .94884 | 29 | .05116 | .12644 | ij | .87356 | 22
39 | :82255 | 1? 17745 | .94910 | 2$ | .05090 | .12655 |j | .87345 | 21
40 | 9.82269 | |, |10.17731 | 9.94935 | ze |10.05065 |10. 12666 | ,5 | 9.87334 | 20
VT j| 0482283 | Ta 17717 | .94961 | 26 | 05039 | .12678 | |] | .87322 | 19
12 Eege | e 17703 | .94986 | 29 | .05014 | .12689 | ul .87311 | 18
43 || EISE | rs 17689 | .95012 | 29 | .04988 | . 12700 | |2 | -87300 | 17
44 | 82326 | 12 17674 | .95037 | 29 | .04963 | .12712 | ¡7 | .87288 | 16
45 | 9.82340 | |4 |10. 17660 | 9.95062 | sẹ |10. 04938 |10. 12723 | 1; | 9.87277 | 15
46 | .82354 | 14 17646 | .95088 | 25 | .04912 .12734 | |, | -87266 | 14
47 | .82368| 14 17632 | .95118 | 26 | -04887 | .12745 | 12 | .87255 | 13
48 | .82882 | 14 17618 | .95189 | 25 | .04861 | -12757 | 1] | -87243 | 12
49 || 2489306 | yy 17604 | .95164 | 23 | .04836 | .12768 | 1; E E
50 | 9. 82410 10. 17590 | 9. 95190 10. 04810 |10. 12779 | 1» | 9.

51 | .82424 E 17576 | . 95215 7 104788 |) 12791 er 87209 9
52 | .82439 | 72 17561 | .95240 | 32 | .04760 | .12802 | 1; 87 98 | 8
53 | .82453 | |4 17547 | .95266 | 25 | .04734 | .12813 | jp | -S7187 | 7

54 | .82467 | |4 17533 | .95291 | 28 | .04709 | .12825 | jj | -87175 |
55 | 9.82481 | |4 |10. 17519 | 9.95317 | 25 |10. 04683 10. 12836 e 9. 87164 5

56 | .82495 17505 | . 95342 04658 | .12 E

57 | .82509 | 1 17491 | .95368 | 26 | :04632 | .12859 1 | .87141| 3
Sa | 82523 | + 17477 | . 95393 04607 | .12870 | |, | .87130| 2
v 25 4582 | . 12881 87119 | 1
59 || nég25a7 | ¿15 [10517463 | 95418 | 5g |: -0 i: 5 119 | 1

60 | 9. 82551 10. 17449 | 9. 95444 10. 04556 |10. 12893 9. 87 :
4

Á i Diff C
1319» cos Diff. sec cot E tan csc 1’ sin -48?

1418

TABLE 33
Logarithms of Trigonometric Functions
4295 sin d csc tan ES cot sec ae cos -137° |
y y
O | 9.82551 | |, |10.17449 | 9. 95444 | „5 |10. 04556 |10.12893 | ,, | 9.87107 | 60
1 | .82565 | |4 | .17435 | .95469 | 29 | .04531| .12904 | 1! | 87096 | 59
2 : 82579 14 | +17421| .95495 | 29 | .04505 | .12015 | 1? | .87085 | 58
Ad IES IB HE JE
j4, JE : 26 | : 12 Ë £
a ea te
; ; ; i í -87039 | 54
7 - $2049 S : 17351 ` 95622 oe „04378 | .12972 | 19 | 387028 | 53
9. geet Eë ` 17323 | ` 95672 E ` 04328 ` 12995 a :87005 | 31
10 9. 82691 ^ 10. 17309 9. 95698 d 10. 04302 10. 13007 | 4, | 9. 86993 | 50
IET 20) Der .13018 | 11 | . 86982} 49
12 à > q
AE | ú | AE JE IHE JE
14 | .82747 | |4 | .17253 | | 95799 a „04201 | ` 13053 E ` 86947 2
15 | 9. 82761 10. 17239 | 9. 95825 10. 04175 |10. 13064 931
x os VN Sp 9. 86936 | 45
16 | .82 12
17. |) pares | UB. [6212 le (Eer Ll EM
18 | .82802 | 1% |. 17198 | .95901 | 29. |- 01000 | 13008 |11 pod Ü
19 | ` 82816 ës .17184 | | 95926 X „04074 | .13110 = theo a
20 9. 82830 x 10. 17170 9. 95952 295 |10.04048 |10. 13121 | |, | 9.86879 | 40
22 | .82858 | 1% | “17142 20 25 URNA EET e E
28. || 282872 | 14 Kuss |/.96028 |0626! Kessler KEE TE
24 | | 32885 n .17115 | :96053 * .03947 | . 18168 | 12 I z
25 9. 82899 Y 10. 17101 9. 96078 26 |10. 03922 |10. 13179 z 9. 86821 | 35
27 | .82927 | 1% | ` 17073 VUES 25 GS "RS 11: E
28 | «82941 | 14 | 17059 |.:.96155 | "26 |. seas E Puse, r
29 | | 32955 Ys .17045 | | 96180 oe „03820 | . 13225 | !! Me 2
30 | 9.8296 0.03795 |10. 13237 | 12 |9
30 F9 82968 y, 10. 17032 9. 96205 5 10. 03795 10. 13237 | |, | 9.86763 | 30
32 | 582996 | 14 [17004 |4c96256 | 1253 ek | S
33 | .83010| 42 | :16990| | 96281 | 25 | : 93719 bu beer 2
34 | .83023 | 1% | :16977 | | 96307 2 ` 03693 E 11 ri zd
= d Æt : LLC ES
35 9. 83037 v 10. 16963 9. 96332 25 |10. 03668 |10. 13295 | |, | 9. 86705 | 25
37 | .83065 | li | “16035 | “96383 | 26 03617 ass Deeds
38 | :83078 i: .16922 | .96408 | 29 | ' 03592 S 12 GA i
2 -83092 | |4 | -16908 | .o6433 | 23 | 03567 | | 13341 B ` 86659 | 21
at MEC 14 Orie AER 95 |10. 03541 |10. 13353 19 | 9. 86647 £ Ð
42 | .s3133 r. | 26 M ee =.
48 | „88147 | 1% | 16853 |: ..96535 1 025. Bass SEGA jor ee eee
44 | .83161 | |3 | :16839 | | 96560 50 03440 | 213400 | 12 86600 | 16
45 | 9.83174) |, 10. 16826 | 9.96586 | 5. |10.08414 |10. 13411 | |! |-9. 86589 | 15
46 | 83188 .16812 | .96611 | 29 03389 | .1 12
47 |. 83202 13 | .16798 | | 96636 Sad gm 4 5134259 (12) o 13
` 83215 .16785 | .96662 | 26 |: sacos Vel N E
1 . 83229 | 13 | .16771 | . 96687 x ` 03313 a140 HA e
9. 8324: kaka : a ve
50 x 14 |10. 16758 | 9.96712 | 510. 03288 |10. 13470 a 9. 86530 | 10
52 BA 14 | .- 16744 | 96738 | 55 | .08262 138221 "$6518 | | 19
; . 16730 | . 96763 | 2 03237 | 1 EH :
58 | .83283 | 12 | .16717 | 96788 | 25 | osa | :13808 | 12 || adas | oe
54 | .83297| 14 | “16703 | "e 26 | -08212 | .13505 | 12 | .86495| 7
5 13 AREIS: .96814 | : .03186 | | 1351 2
55 | 9.83310 10. 16690 | 9.96839 | 2 fT p O e NE
56 83324 14 B 25 0. 03161 |10. 13528 9. 86472 5
56 |. 14. | 16676 | „96864 | 22 1.203136 |..13540 1 12 | 486460 |. La
58 | 85592 | 13 | -16662 | .96890 | 95 | .08110 | 13552 | 12 | :86448| 3
50 | sosa | 14 | - 16649] . 96015 | 25 | "03085 | 13564 | 12| .86436| 2
60 | o Soana | 18 |, 16635 | 96940 | 38 | 03060 | -18575| Hi | 86425 1
i j 0.16622 | 9. 96966 | ^? |10. 03034 |10. 13587 | 12 | g. 86413 | 0
Diff iff. | pig |
132°> cos ] sec cot Diff t Diff ; n
1 1 an ese EU sin -47°

1419

TABLE 33

Logarithms of Trigonometric Functions
————— ms

cos -136°
y

um

| € EA
o

Y

9. 83378 S f ; $ y
| 83392 | ! | | ` 86401
. 83405 : : d . 86389
. 83419 s 4 : . 86377
. 83432 A ; A . 86366

9. 83446 ) b c . 86354
. 88459 : A : . 86342
. 83473 s 4 : . 86330
. 88486 : : à . 86318
. 88500 m À : . 86306

. 83513 À ! j . 86295
. 83527 < E é . 86283
. 83540 A : R „86271
„83554 ; 8 . . 86259
. 83567 i S : . 86247

JAS ; i j . 86235
. 83594 i . 86223
. 83608 | i „86211
. 83621 l . 86200
. 83634 | i . 86188
. 83648 i : . 86176
. 83661 , . 86164
. 83674 . 97 k . . 86152
. 83688 . 97 : . 86140
. 83701 . 86128

. 88715 : f y . 86116
. 83728 3 : E . 86104
. 83741 i : À . 86092
. 88755 Ķ i t . 86080
. 83768 : M : . 86068

. 83781 : ; Å . 86056
. 83795 : > : . 86044
. 83808 : $ 1 . 86032
. 83821 : e : . 86020
. 83834 : A : . 86008
. 83848 Å h E . 85996
. 83861 i : : . 85984
. 83874 : : : . 85972
. 88887 A 4 : . 85960
. 83901 d : : . 85948
. 88914 9. : i „85936
„83927 3 : 4 . 85924
. 83940 : d : . 85912
. 88954 ; : y . 85900
. 88967 ; i : . 85888

. 83980 k ; ! . 85876
. 88993 A f > . 85864
. 84006 : ; > . 85851
. 84020 d i À . 85839
. 84033 : d S . 85827

. 84046 : : i „85815
. 84059 : 4 4 . 85803
. 84072 ; : : . 85791
. 84085 : : 1 . 85779
. 84098 Ë : 4 „85766
„84112 ` B y . 85754

. 84125 ; , A : . 85742
. 84138 A : À . 85730

. 84151 ; ! + . 85718
. 84164 : 4 : . 85706

. 84177 D ; i „85693

OO NO CI] DO

Lied EES

t
B
o

cos

1420

TABLE 33
Logarithms of Trigonometric Functions
440 sin e esc tan SE cot sec xus E cos «1350
y y
o |9 84177 13 |10.15823 | 9.98484 | „5 |10. 01516 |10. 14307 | ,, | 9. 85693 | 60
15810 | . 98509 ` 01491 | . 14319 85681 | 59
2 84203 e “15797 | ` 98534 Ge ` 01466 | ` 14331 i .85669 | 58
3 84216 | 13 | .15784 | .98560 | 26 | 101440 |= 14343 12 | .85657 | 57
84229 | 33 | .15771 | .98585 | 52 | .01415 | .14355 | 13 | .85645 | 56
5 |9 84242 13 |10.15758 | 9. 98610 | 5, |10.01390 |10. 14368 | ,, | 9.85632 | 55
Ide d 2:
8 | 284282 13 | .15718 | .98686 | 25 | ”o1314| :14404 | 12 | :85596 | 52
9 84295 i ` 15705 | ` 98711 ds .01289 | ` 14417 Ts .85583 | 51
10 9. 84308 13 |10. 15692 | 9.98737 | s5 |10. 01263 |10. 14429 | ,, | 9. 85571 | 50
12 | .84334| 13 THE Hec 25 dist Er 12 uec 48
13 || 284347 | 19 | 15653 | 9.98812 | -29 butorss | :44466 | 18 | «8553421 PD
14 | .84360 | 13 | :15640| :98838 S „01162 | :14478 |12| 85522 | 46
13 9. 84373 » 10. 15627 9. 98863 25 |10. 01137 |10. 14490 | |3 | 9. 85510 | 45
i Te 25 | -01112| .14503 | 13 | 85497 | 44
17 | .84398 .15602 | ` 98913 01087 | . 14515 85485 | 43
13 26 9 eds 1b
1 `
AE NIE IE IER IB AER IE
20 9. 84437 13 10. 15563 | 9. 98989 ze |10.01011 |10. 14552 | |2 | 9. 85448 | 40
22 | 84463 | 13 SET See 25 Zoe Tu 13 d 38
23 | .84476 | 13 | 15524 | 99065 | 25 | “00085 | 145890 | 12 | 385411 Ss
24 | ` 84489 R 15511 | | 99090 7 .00910 | | 14601 E ` 85399 30
25 9. 84502 is 10. 15498 9.99116 | 5: |10. 00884 |10. 14614 | ,) | 9. 85386 | 35
26 | .84515| 1 - 15485 "99141 | 25 | .00859 | .14626 | 12 | 85374 | 34
15 | ee ` 99166 ` 00834 | | 14639 .85361 | 33
28 | .84540 15460 | .99191 | 29 00809 | .14651 | 12
29 | .84553 19 | “15447 | .99217 | 26 “00783 | 14663 | 12 85307 31
30 |9. 84566 10. 15434 5 e
30 84566 | jg |10. 15434 9. 99242 25 |10. 00758 |10. 14676 | |, | 9. 85324 | 30
32 | .84592 | 13 | “15408 Se 26 ee TES Eee ae
33 | .84605 | 19 | :15395| 199818 | 25 | 1060682] 10713 | 12 pesa] eo
34 | .84618 | 19 | :15382| :99343 m 00657 | ` 14726 | 13 on 2
35 9. 84630 e 10. 15370 9. 90368 26 |10. 00632 |10. 14738 ys 9. 85262 | 25
37 | .84656 | 13 | “15344 PATE 25 di tr 13 | "gš287 | 28
38 | 34660 | 19 T5231 | 109444 1525 1 100556 |0 dārzs Ee
39 | .84682 | 13 | “15318 | | 99469 ae ` 00531 TER 13 E. 2
i ilg
40 9. 84694 D 10. 15306 9. 99495 25 |10. 00505 |10. 14800 | |3 |9.85200 | 20
42 | .84720 | 13 | ' 15280 | ‘90545 | 25 SES TR 121 rss TE.
13 .84733 | |3 | 15267 | ` 99570 B. .00430 | ` 14838 | 13 yeu 17
- Cams 13 |_- 15255 | .99596 | 29 | :00404 | :14850 e .85150 | 16
4 "84758 | i$ |10.15242 | 9.99621 | 5. |10.00379 |10. 14863 9.85137 | 15
6 | ` 84771 15229 | `. 99646 | 25 00354 | . 14875 | 12
47 | .84784 | 13 | '15216 | ¿09672 | 29 | ' 00328 kas 13 im a
48 | .84796 | 13 | . 15204] .99697 | 29 | | 00303} | 14900 | 12 | 85100 12
x 284809 | iig | 15191 |". 99722 L io 1650874 En
9. 84822 10. 19.9 7 :
51 284835 | 18 "15108 | 00774 | 26 | 9.00258 [9-314926 | jo Ee [110
52 | .84847 .15153 | .99798 | 29 | “00202 | 14051 | 13 vae E
53 | .84860 D „15140 | .99823 | 25 | ` 00177 mt 12 d use 7
5% | 84878 | |2 | 18127 | ‘90848 | 25 | 00152] 14976 |13 | 185024 | 6
55 9. 84885 13 |10. 15115 | 9. 99874 10. 00126 |10. 14988 js 9. 85012
SH - 84898 | 2 EH ¡“90899 | 25" [orar nor DEO S100. 2
57 - 849111 A A M00076 | s011 |) ERO ROT DURS
58 84923 Ë - 15077 ` 99949 3 .00051 | | 15026 ds . 84974 2
. 84936 9. 99975 ` 00025 1 ,
SEL cm 13 5 3 - 15039 ` 84961 1
A 84949 10. 15051 [10. 00000 | 7? |10.00000 |10. 15051 | 12 | o; 84949 | 0
Diff "
£ ! Diff.
134 > cos 1 sec cot Ð tan csc vent sin 450

1421

TABLE 34
Haversines
0° 1° 2° 3° 4°
H Log Hav "Nat Hav| Log Hav | Nat. Hav] Log Hav | Nat. Hav Log Hav | Nat. Hav| Log Hav | Nat. Hav] /
0 | Inf. Neg. 0. 00000|5. 88168 0. 00008ļ|6. 48371 0. 00030|6. 83584 0. 0006917. 085640. 00122] 60
1 | 2.32539| . 00000} . 89604 . 00008} . 49092 . 00031] . 84065) . 00069] . 08925) . 00123] 59
2 | 2. 92745| . 000001 . 91016| . 00008] . 49807, . 00031] . 84543 . 00070] . 09284! . 00124] 58
3 | 3. 27963) . 000001 . 92406, . 00008| . 50516) . 00032) . 85019] . 00071] . 09642! . 00125] 57
4 . 52951| . 00000| . 93774) . 000091 . 512191 . 000331 . 85492| . 00072} . 09999] . 00126} 56
5 | 3. 72333|0. 00000|5. 95121/0. 00009|6. 51916/0. 00033|6. 85963|0. 0007217. 1035410. 00127] 55
6 | 3. 881691 . 000001 . 96447| . 000091 . 52608, . 00034| . 86431! . 00073] . 10708! . 00128| 54
7 | 4. 01559 . 00000] . 97753, . 00009] . 53295| . 00034| . 86897| . 00074] . 11060| . 00129| 53
8 . 13157, . 00000ļ5. 99040, . 000101 . 53976, . 00035| . 87360| . 00075| . 11411] . 00130] 52
9 . 23388| . 0000046. 00308, . 000101 . 54652| . 00035| . 87821| . 000761 . 11760| . 00131) 51
10 | 4. 32539|0. 00000[6. 01557|0. 00010]6. 55323|0. 000366. 88279/0. 00076|7. 12108|0. 00132| 50
bl . 408181 . 000001 . 02789) . 000111 . 55988) . 00036} . 88735} . 000771 . 12455] . 00133] 49
12 . 48375, . 00000} . 04004) . 000111 . 56649} . 00037] . 89188) . 00078] . 12800] . 00134] 48
13 . 55328) . 00000| . 05202) . 000111 . 57304] . 00037] . 89639 . 00079] . 13144] . 00135] 47
14 . 61765} . 000001 . 06384) . 00012) . 57955) . 00038) . 90088} . 000801 . 13486) . 00136] 46
15 | 4. 67757|0. 00000[6. 075500. 00012|6. 58600/0. 00039|6. 90535|0. 00080|7. 13827/0. 00137} 45
16 . 733631 . 00001| . 08700) . 00012] . 59241} . 00039| . 90979| . 00081] . 14167] . 00139| 44
17 . 78629| . 000011 . 09836) . 00013] . 59878} . 00040} . 91421] . 00082] . 14506) . 00140} 43
18 . 83594} . 000011 . 10956] . 000131 . 60509) . 000401 . 91860} . 000831 . 14843, . 00141} 42
19 . 88290} . 000011 . 12063) . 000131 . 611386) . 000411 . 92298} . 00084] . 15179] . 00142) 41
20 | 4. 92745/0. 000016. 131550. 000146. 61759|0. 0004116. 92733|0. 00085|7. 1551310. 00143] 40
21 | 4. 96983] . 000011 . 14234| . 00014] . 62377) . 00042] . 93166] . 00085] . 15846) . 00144] 39
22 | 5.01024] . 000011 . 15300, . 00014} . 62991) . 000431 . 93597. . 000861 . 16178) . 00145) 38
23 . 04885) . 000011 . 16353) . 00015} . 63600} . 000431 . 94026} . 000871 . 16509) . 00146} 37
24 . 08581} . 000011 . 17398) . 00015} . 64205) . 00044) . 94453] . 00088] . 16839} . 00147) 36
25 | 5. 12127|0. 00001|6. 18421|0. 000156. 64806/0. 00044]6. 94877|0. 00089|7. 17167/0. 00148} 35
26 . 15534| . 000011 . 19437| .00016| . 65403| . 00045] . 95300} . 00090] . 17494| . 00150| 34
25 . 18812} . 00002] . 20441| . 00016} . 65996| . 00046} . 95720) . 000911 . 17820| . 00151| 33
28 . 21971| . 00002] . 21433] . 00016] . 66585| . 00046} . 96139| . 000911 . 18144) . 00152) 32
29 . 250191 . 00002} . 22415) .00017| . 67170| . 00047| . 96555. . 00092] . 18468; . 00153| 31
30 | 5. 27963|0. 00002|6. 23385,0. 0001716. 67751/0. 00048|6. 96970,0. 00093|7. 18790|0. 00154| 30
31 . 30811} . 00002| . 24345| . 00018| . 68328] . 00048] . 97382| . 000941 . 19111| . 00155] 29
32 . 335691 . 000021 . 25294] . 00018} . 68901| . 00049} . 97793) . 000951 . 194301 . 00156] 28
33 . 362421 . 000021] . 262331 . 00018] . 69470) . 00050] . 98201) . 00096} . 197491 . 00158] 27
34 . 38835} . 00002| . 27162) . 00019} . 70036| . 00050| . 98608] . 00097| . 20066) . 00159) 26
35 | 5. 4135210. 00003]6. 28081!0. 00019]6. 70598/0. 00051|6. 99013|0. 00098|7. 20383|0. 00160} 25
36 . 43799] . 000031 . 289911 . 00019} . 71157! . 00051] . 99416) . 000991 . 20698) . 00161] 24
37 . 461791 . 00003] . 29891} . 000201 . 71712] . 00052]6. 99817) . 00100} . 21012) . 00162] 23
38 . 48496] . 00003] . 30781| . 00020] . 72263] . 00053|7. 00216] . 00100) . 21325) . 00163) 22
39 . 50752| . 00003} . 31663| . 00021) . 72811} . 00053) . 00613) . 00101 . 21636] . 00165} 21
40 | 5. 52951/0. 00003|6. 32536/0. 00021]6. 73355,0. 0005417. 01009|0. 00102|7. 21947|0. 00166] 20
41 . 55095| . 00004| . 33400) . 00022| . 73896] . 00055] . 01403| . 00103] . 22256] . 00167] 19
42 . 571891 . 00004] . 34256) . 00022) . 74434! . 00056] . 01795] . 00104] . 22565) . 00168) 18
43 . 59232] . 00004) . 35103) . 00022) . 74969] . 00056] . 02185) . 00105] . 22872) . 00169] 17
44 . 61229} . 00004] . 35943) . 00023) . 75500) . 00057 . 02573] . 00106 . 23178 . 00171) 16
45 | 5. 63181/0. 00004l6. 367740. 00023|6. 76028|0. 0005817. 029600. 00107|7. 23483/0. 00172] 15
46 „65090! . 00004] .37597| . 00024| . 76552) . 00058] . 03345) . 00108| . 23787] . 00173) 14
47 . 66958] . 00005| . 38412] . 00024) . 77074] . 00059} . 03729] . 00109) . 24090; . 00174 13
48 . 68787] . 00005) . 39220! . 00025} . 77592] . 000601 . 04110) . 001101 . 24392) . 00175} 12
49 . 70578, . 00005} . 40021! . 00025} . 78108) . 00060} . 04490) . 00111| . 24693 . 00177] 11
50 | 5. 7233210. 00005|6. 40814/0. 00026|6. 78620 0. 00061|7. 048690. 00112|7. 24993|0. 00178] 10
oil . 14052. . 00006] . 41600! . 00026] . 79129) . 00062] . 05245) . 00113] . 25292) . 00179} 9
52 .75739| . 00006} . 42379) . 00027] . 79636, . 00063] . 05620) . 00114] . 25590} . 00180} 8
53 . 11394| . 00006] . 43151! . 00027] . 80139] . 00063] . 05994] . 00115] . 25886, . 00181 7
54 | . 79017] . 00006] . 43916 . 00027] . 80640) . 00064] . 06366, . 00116] . 26182 . 00183) 6
55 5. 8061110. 00006l6. 4467510. 00028]6. 81137 0. 00065|7. 067360. 00117[7. 26477/0. 00184 5
56 ” 82176 ` 000071 . 45427| . 00028] . 81632| . 00066] . 07105| . 00118] . 26771) . 00185] 4
57 . 83713! . 00007] . 46172) . 00029) . 8212-4] . 00066] . 07472) . 00119) . 27064 . 00186 B
58 . 85224| . 00007] . 46911| . 00029| . 82614 . 00067] . 07837) . 00120 .27355| . 00188] 2
59 . 86709! . 00007] . 47644! . 00030] . 83100) . 00068] . 08201, . 00121 . 27646 : 00189 1
60 5. 88168 0. 00008|6. 48371/0. 00030|6. 83584 0. 00069|7. 08564 0. 00122|7. 27936 0. 00190 0
359° 358° 357° 356° 355°

1422

TABLE 34

Haversines

5° 6° k 8° 9°

Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav} Log Hav | Nat. Hav] Log Hav | Nat. Hav] /

7. 27936|0. 00190|7. 43760/0. 002747. 57135|0. 00373|7. 68717/0. 00487|7. 78929 0. 00616] 60
. 28225) . 00192] . 44001 . 00275| . 57341| . 00374| . 68897, . 00489] . 79089| . 00618| 59
-28513| . 00193| . 44241) . 00277| . 57547| . 00376| . 69077) . 00491| . 79249| . 00620| 58
. 28800, . 00194| . 44480) . 00278] . 57752| . 00378| . 69257| . 00493| . 79409! . 00622| 57
. 29086, . 00195| . 44719| . 00280| . 57957| . 00380| . 69437| . 00495| . 79568] . 00625| 56

. 29371/0. 00197|7. 44957/0. 00282|7. 58162|0. 00382|7. 69616/0. 00497|7. 79728/0. 00627| 55
. 29655| . 00198| . 45194| . 00283| . 58366 . 00383| . 69794| . 00499] . 79886, . 00629) 54
. 29938) . 00199| . 45431| . 00285] . 58569| . 00385| . 69972| . 00501] . 80045) . 00632) 53
. 30220) . 002011 . 45667, . 00286] . 58772, . 00387| . 70150| . 00503| . 80203, . 00634} 52
. 30502 . 00202) . 45903| . 00288| . 58974| .00389| . 70328| . 00505| . 80361| . 00636| 51

10 | 7. 30782 0. 00203|7. 46138/0. 00289|7. 59176/0. 00391|7. 70505/0. 00507|7. 805190. 00639] 50
11 . 31062. . 00204| . 46372 . 00291| . 59378 . 00392] . 70682| . 00509| . 80677| . 00641| 49
12 | .31340 . 00206] . 46605 . 00292| . 59579| . 00394] . 70858| . 00511| . 80834| . 00643| 48
13 | . 31618) .00207| . 46838) . 00294] . 59779| . 00396] . 71034| . 00513] . 80991| . 00646| 47
14 | .31895 . 00208| . 47071] . 00296| . 59979| . 00398] . 71210| . 00515| . 81147! . 00648| 46

15 | 7. 32171/0. 00210|7. 47302|0. 00297|7. 60179|0. 00400|7. 713850. 00517|7. 81303/0. 00650| 45
16 | . 32446) . 00211| . 47533| . 00299| . 60378| . 00402] . 71560| . 00520| . 81459 . 00653| 44
17 | .32720 . 00212) . 47764, . 00300| . 60577| . 00403| . 71735| . 00522] . 81615| . 00655 48
18 | .32994| . 00214] . 47994) . 00302] . 60775| . 00405| . 71909 . 00524| . 81771) . 00657] 42
19 | .38266| . 00215| . 48223) . 00304| . 60973 . 00407] . 72083] . 00526| . 81926| . 00660] 41

- 33538 0. 00216|7. 4845210. 00305|7. 61170/0. 00409|7. 7225710. 00528|7. 82081/0. 00662] 40
21 . 33809, . 00218| . 48680| . 00307| . 61367 . 00411| . 72430| . 00530] . 82235! . 00664 39
22 | .34079| .00219| . 48907| . 00308| . 61564| . 00413] . 72603| . 00532] . 82390| . 00667] 38
23 | .34348| . 00221| . 49134| . 00310| . 61760 . 00415] . 72775! . 00534] . 82544| . 00669] 37
24 . 94616, . 00222| . 49360) . 00312| . 61955| . 00416] . 72948| . 00536| . 82698| ` 00671| 36

25 | 7. 348840. 00223|7. 49586/0. 00313|7. 62151|0. 00418|7. 73119 0. 0053917. 82851/0. 00674| 35
26 | .35150| .00225| . 49811 . 00315| . 62345) . 00420] . 73291) . 005411 . 83004| . 00676] 34
27 | .35416| . 00226| . 50036, . 00316| . 62540 . 00422| ` 73462 . 00543} . 83157| . 00679] 33
28 | .35681| . 00227| . 50259 . 00318| . 62733| . 00424] ` 73633) ` 00545| . 83310| . 00681| 32
29 | .35945| . 00229] . 50483| . 00320| . 62927 . 00426] . 73803) ` 00547| . 83463| . 00683] 31

30 | 7. 36209/0. 00230|7. 507060. 00321|7. 631200. 00428|7. 73974 0. 00549|7. 83615/0. 00686| 30
3l . 36471) . 00232| . 50928) . 00323| . 63312| . 00430| . 74143| . 00551| . 83767| . 00688| 29
32 | .36733| . 00233| . 51149| . 00325| . 63504| . 00432] | 74313| . 00554| . 83918, . 00691| 28
33 . 36994) . 00234| . 51370| . 00326| . 63696| . 00433| . 74482| . 00556 . 84070) . 00693| 27
34 . 37254 . 00236| . 51591| . 00328| . 63887| . 00435| . 74651) ` 00558| . 84221| . 00695| 26

35 | 7. 375140. 00237|7. 51811/0. 0033017. 640780. 00437 7. 74819/0. 00560|7. 84372/0. 00698| 25
36 | .37773| . 00239| . 52030| . 00331) . 64269| . 00439 . 74988| . 00562] . 84522| . 00700] 24
37 | .38030| .00240| . 52249 . 00333] . 64458 . 00441 . 75155 . 00564| . 84672| . 007031 23
38 | .38288| . 00241] . 52467| . 00335| . 64648| . 00443 . 75323| . 00567] . 84822| . 00705| 22
39 . 98544| . 00243] . 52685| . 00336| . 64837| . 00445] ` 75490| . 00569| . 84972| . 00707] 21

40 | 7. 388000. 00244|7. 529020. 00338|7. 65026 0. 00447|7. 75657|0. 00571|7. 85122/0. 00710] 20
41 . 39054 . 00246| . 53119 . 00340] . 65214| . 00449] . 75824 . 00573| . 85271| . 00712| 19
42 | .39309| . 00247| . 53335| . 00341| . 65402! ` 00451| . 75990, . 00575| . 85420| . 00715] 18
48 - 39562 . 002491 . 53550| . 00343] . 65590) . 00453] . 76156| . 00578| . 85569| . 00717] 17
44 . 89815) . 00250] . 53766| . 00345] . 65777) . 00455] . 76321| . 00580| . 85717) . 00720] 16

45 | 7. 40067/0. 0025217. 53980|0. 0034717. 65964 0. 00457|7. 76487/0. 00582|7. 85866/0. 00722] 15
46 . 40318) . 00253| . 54194| . 00348] . 66150| . 00459] ` 76652 . 00584] . 86014 . 00725] 14
47 . 40568) . 00255| . 54407] . 00350} . 66336| . 00461] ` 76816| . 00586] . 86161! . 00727| 13
48 „40818| . 00256| . 54620| . 00352] . 66521| . 00463] ` 76981) . 00589| . 86309| . 00730| 12
m9 . 41067, . 00257] . 54833) . 00353| . 66706! . 00465 . 77145, . 005911 . 86456| . 00732] 11

90 | 7. 41315/0. 00259|7. 55045|0. 00355|7. 66891 0. 00467|7. 77308|0. 00593|7. 86603|0. 00735| 10
ol . 41563) . 00260} . 55256] . 00357] . 67075! . 00469 . 17472. . 00595) . 86750| . 00737
52 . 41810 . 00262) . 55467! . 00359] . 67259| . 00471 . 77635 . 00598| . 86896) . 00740
58 . 42056 . 00263| . 55677| . 00360] . 67443| . 00473 . 77798) . 00600} . 87042| . 00742
54 . 42301| . 00265| . 55887| . 003621 . 67626! . 00475 . 77960, . 00602| . 87188| . 00745

. 425460. 00266|7. 56096 0. 00364|7. 67809 0. 00477|7. 78122/0. 00604|7. 87334 0. 00747
56 . 42790 . 00268| . 56305 . 00366] . 67991 . 00479| . 78284| . 00607| . 87480| . 00750
57 . 43034 . 00269] . 56513] . 00367] . 68173) ` 00481) . 78446) . 00609} . 87625! . 00752
58 . 43277) . 00271| . 56721| . 00369] . 68355) ` 00483| . 78607| . 00611| . 87770] . 00755
59 . 43519) . 00272] . 56928| . 00371| . 68536|. 00485| . 78768| . 00613| . 87915| . 00757
60 | 7. 43760|0. 00274|7. 57135/0. 00373|7. 68717/0. 00487|7. 78929|0. 00616|7. 8805910. 00760

OO ADORNO
-I

D
o
-I

a
or
-I

CQ rb WHE CI DO TOO

354? 353? 352? 351? 350?

1423

TABLE 34
Haversines
sss
10° 11° 12° 13° 14°

^ Log Hav |Nat. Hav} Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav | Nat. Hav| Log Hav | Nat. Hav] '
0 7. 880590. 00760|7. 96315/0. 00919|8. 03847|0. 01093|8. 10772/0. 01281|8. 17179/0. 01485| 60
1 . 88203| . 00762| . 96446) . 009211 . 03967| . 01096] . 10883| . 01285| . 17282| . 01489| 59
2 . 88348| . 007651 . 96577) . 00924] . 04087, . 010991 . 10993) . 01288| . 17384| . 01492] 58
3 . 88491) . 007671 . 96707| . 00927| . 04207, . 01102] . 11104) . 01291] . 17487| . 01496| 57
4 . 88635| . 007701 . 96838 . 00930] . 04326| . 01105] . 11214| . 01295| . 17590| . 01499] 56
5 | 7. 88778/0. 00772|7. 96968/0. 00933|8. 04446/0. 01108|8. 11324/0. 01298|8. 17692/0. 01503] 55
6 . 88921, . 00775| . 97098) . 009351 . 04565| . O1111| . 11435| . 01301] . 17794! . 01506] 54
7 . 89064) . 00777) .97228| . 00938] . 04684 . 01114] . 11544) . 01305) . 17896) . 015101 53
8 .89207| . 00780) . 97358, . 009411 . 04803] . 011171 . 11654| . 01308] . 17998) . 015131 52
9 ..89349| . 007831 . 97487) . 00944] . 04922) . 01120] . 11764) . 013111 . 18100) . 01517] 51
10 | 7. 89491/0. 00785|7. 97617|0. 0094718. 05041/0. 0112318. 11873|0. 0131418. 18202/0. 01521| 50
11 „89633| . 00788] .97746| . 009491 . 05159) . 011261 . 11983| . 01318] . 18303) . 01524] 49
12 . 89775| . 007901 .97875| . 009521 . 05277, . 01129] . 12092) . 013211 . 18405) . 01528] 48
13 . 89916) . 00793] . 98003) . 00955} . 05395) . 01132] . 12201) . 01324) . 18506) . 01531) 47
14 . 90057) . 00795} . 98132) . 00958} . 05513, . 01135} . 12310) . 01328] . 18607, . 01535} 46
15 | 7. 90198/0. 00798|7. 98260/0. 00961|8. 05631/0. 01138|8. 124190. 01331]8. 187090. 01538] 45
16 . 90339| . 008011 . 98389| . 00964) . 05749| . 01142] . 12528) . 01334] . 18810| . 01542] 44
17 . 90480) . 008031 . 98517| . 00966| .05866| . 01145] . 12636 . 013381 . 18910) . 01546] 43
18 . 90620) . 00806] . 98644) . 00969] . 05984! . 01148] . 12745) . 01341] . 19011 . 01549] 42
19 . 90760} . 008081 . 98772) . 00972] . 06101) . 01151] . 12853) . 01344] . 19112) . 01553] 41
20 | 7. 90900 0. 0081117. 98899/0. 0097518. 06218/0. 01154]8. 12961/0. 01348|8. 19212/0. 01556] 40
21 . 91039| .00814| . 99027| . 00978| . 06335! . 01157] . 13069| . 01351) . 19313) . 01560] 39
22 . 91179) . 00816} . 99154! . 009811 . 06451) . 01160] . 13177) . 01354) . 19413} . 01564] 38
23 . 91318] . 00819] . 99281) . 00984] . 06568) . 01163] . 13285) . 01358] . 19513} . 01567] 37
24 . 91457| . 008211 . 99407! . 00986] . 06684! . 01166] . 13392) . 01361) . 19613) . 01571] 36
25 | 7. 915960. 0082417. 99534/0. 00989|8. 06800/0. 01170|8. 13500/0. 01365|8. 197130. 01574) 35
26 . 91734] . 00827] . 99660 . 00992] . 06917) . 01173] . 13607) . 01368] . 19813, . 01578) 34
27 . 91872| . 008291 . 99786| . 00995| . 07032) . 01176] . 13714, . 01371| . 19913| . 01582] 33
28 . 92010| . 00832|7. 99912 . 00998] . 07148| . 01179] . 13822) . 01375| . 20012, . 01585| 32
29 . 92148| . 00835|8. 00038| . 01001] . 07264| . 01182] . 13928 . 01378| . 20112| . 01589] 31
30 | 7. 92286/0. 00837|8. 00163/0. 01004|8. 07379/0. 01185|8. 14035|0. 01382|8. 20211|0. 01593| 30
o . 92423| . 00840] . 00289! . 01007] . 07494| . 01188] . 14142) . 01385] . 20310) . 01596) 29
32 . 92560| . 00843| . 00414! . 01010| . 07610) . 01192] . 14248| . 01388] . 20410) . 01600| 28
33 . 92697) . 00845] . 00539 . 01012] . 07725) . 01195] . 14355) . 01392] . 20509) . 01604) 27
34 . 92834! . 00848] . 00664! . 01015] . 07839) . 01198] . 14461] . 01395] . 20608) . 01607] 26
35 | 7. 929700. 00851|8. 00788 0. 010188. 07954 0. 01201|8. 14567 0. 01399|8. 20706/0. 01611] 25
36 93107 .00853| . 00913| . 01021] . 08069) . 01204] . 14673] . 01402] . 20805) . 01615] 24
ot . 93243] . 00856} . 01037) . 01024] . 08183! . 01207] . 14779] . 01405] . 20904) . 01618) 23
38 . 93379| . 00859] . 01161! . 01027] . 08297] . 01211) . 14885) . 01409] . 21002) . 01622] 22
39 . 93514| . 00861] . 01285) . 01030] . 08411) . 01214] . 14991) . 01412] . 21100} . 01626} 21
40 7. 93650/0. 00864|8. 01409|0. 01033|8. 08525 0. 012178. 15096/0. 01416|8. 21199|0. 01629 20
41 „93785! . 008671 . 01532! . 01036] . 08639) . 01220] . 15201) . 01419} . 21297 . 01633 19
42 93920 . 00869] . 01656) . 01039] . 08752 . 01223| . 15307| . 01423] . 21395) . 01637] 18
43 . 94055! . 00872] . 01779| . 01042) . 08866) . 01226 . 15412 . 01426] . 21493) . 01640) 17
44 .94189 . 00875} . 01902) . 01045] . 08979) . 01230] . 15517) . 01429) . 21590) . 01644 ie
45 | 7. 943240. 00877|8. 02025|0' 01048|8. 09092/0. 01233|8. 15622 0. 01433|8. 21688|0. 01648 1
46 94458) .00880| . 02148] . 01051] . 09205) . 01236] . 15726] . 01436) . 21785) . 01651 14
47 -94592| . 00883] . 02270) . 01054] . 09318! . 01239] . 15831) . 01440) . 21883) . 01655 13
48 . 94726] . 00886| . 02392) . 01057] . 09431] . 01243] . 15935 . 01443 . 21980 . 01659) 12
49 . 94859] . 00888] . 02515) . 01060] . 09543, . 01246] . 16040 . 01447] . 22077 - 01665 R
0 94992 0. 0089118. 026370. 010638. 09656/0. 01249|8. 16144/0. 01450|8. 22175|0. 01666

Su 10 05126 . 008941 . 02758| . 01066] .09768| . 01252] . 16248 . 01454 . 22272 . 01670 A
52 .95259| . 00897| . 02880| . 01069] . 09880| . 01255] . 16352| . 01457 . 22368 . 01674 ;
53 . 95391) . 008991 . 03001) . 01072] . 09992) . 01259] . 16456) . 01461 . 22465| . 01677 i
54 . 95524| . 00902) . 03123| . 01075] . 10104) . 01262] . 16559| . 01464 „22562| . 01681

55 7. 95656|0. 00905|8. 03244|0. 01078|8. 10216 0. 012658. 16663 0. 01468[8. 22658 O. 01685 Å
56 . 95788| . 00908} . 03365| . 01081] . 10327| . 01268 . 16766 . 01471 122159 tek S
57 . 95920] . 00910} . 03486! . 01084] . 10439) . 01272 . 16870 . 01475 jd ios 2
58 96052 . 00913] . 03606| . 01087| . 10550| . 01275| . 16973 . 01478 . 22947 . 01696

59 | :96183| . 00916] . 03727| . 01090] . 10661| .01278| . 17076, . 01482] . 23044) . 01700) J
60 7. 9631510. 00919Í8. 03847 0. 01093|8. 10772/0. 01281]8. 17179|0. 01485|8. 23140 0. 01704

349? 348? 347? 346? 345?

1424

TABLE 34
Haversines
15° 16° 172 18° 19°
k Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav| Log Hav | Nat. Hav d
0 | 8. 23140/0. 01704]8. 28711|0. 01937|8. 33940 0. 02185|8. 3886710. 02447|8. 4352210. 02724] 60
1 | .23235| . 01707| . 28801, . 01941| . 34025] . 02189] . 38946) . 02452] . 43597| . 02729| 59
2 | .23331| . 01711] . 28891| . 01945] . 34109! . 02193| . 39026| . 02456] . 43673| . 02734| 58
3 | .23427| . 01715] . 28980) . 01949] . 34194| . 02198] . 39105| . 02461| . 43748| . 02738| 57
4 | .23523| .01719| . 29070| . 01953] . 34278 . 02202] . 39185| . 02465| . 43823| . 02743| 56
5 | 8. 23618/0. 01723|8. 29159|0. 01957|8. 34362|0. 02206|8. 3926410. 02470|8. 4389910. 02748| 55
6| .23713| . 01726| .29249| . 01961] . 34446] . 02210] . 39344| . 02474] . 43974| . 02753| 54
7| .23809| .01730| . 29338) . 01965] . 34530! . 02215] . 39423| . 02479| . 44049| . 02757] 53
8 | .23904 . 01734] . 29427) . 01969] . 34614| . 02219] . 39502| . 02483] . 44124| . 02762] 52
9 | .23999| . 01738) . 29516) . 01973] . 34698 . 02223] . 39581| . 02488] . 44199| . 02767| 51
10 | 8. 24094|0. 01742|8. 29605|0. 01977|8. 347820. 02227|8. 396600. 0249218. 442730. 02772| 50
11 | .24189| . 01745| . 29694| . 01981] . 34865| . 02232] . 39739| . 02497| . 44348| . 02776| 49
12 | .24283| . 01749] . 29783) . 01985| . 34949| . 02236] . 39818| . 02501| . 44423| . 02781] 48
13 | . 24378) . 01753| . 29872, . 01989] . 35032, . 02240| . 39897| . 02506| . 44498 . 02786| 47
14 | .24473| . 01757] . 29960, . 01993] . 35116 . 02245| . 39976 . 02510] . 44572| . 02791| 46
15 | 8. 24567/0. 01761|8. 30049/0. 01998|8. 35199/0. 02249|8. 40055/0. 02515|8. 446470. 02796| 45
16 | .24661| .01764| . 30137 . 02002| . 35282| . 02253| . 40133| . 02520| . 44721! . 02800] 44
17 | .24755 . 01768) . 30226. . 02006] . 35365, . 02258] . 40212| . 02524| . 44796 . 02805| 43
18 | .24850| . 01772] . 30314| . 02010] . 35449| . 02262| . 40290| . 02529| . 44870! . 02810| 42
19 | .24944| . 01776] . 30402| . 02014] . 35532, . 02266] . 40369| . 02533] . 44944| . 02815| 41
20 | 8. 25037/0. 01780|8. 30490|0. 02018|8. 35614/0. 02271|8. 4044710. 02538|8. 45018/0. 028201 40
21 | .25131| . 01784| . 30578) . 02022] . 35697] . 02275] . 40525| . 02542| . 45093| . 028241 39
22 | .25225| . 01788| . 30666| . 02026| . 35780, . 02279] . 40603] . 02547] . 45167 . 02829] 38
23 | .25319| . 017911 . 30754| . 02030| . 35863] . 02284] . 40681| . 02552] . 45241| . 02834| 37
24 | .25412| . 01795| . 30842, . 02034| . 35945] . 02288] . 40760| . 02556] . 45315 . 02839| 36
25 | 8. 255050. 01799|8. 30929/0. 02038|8. 36028/0. 0229218. 40837|0. 02561|8. 45388 0. 02844| 35
26 | .25599 .01803| . 31017) . 02043| . 36110| . 02297] . 40915| . 02565| . 45462 . 02849| 34
27 | .25692| .01807| . 31104| . 02047] . 36193| . 02301] . 40993 . 02570] . 45536 02853| 33
28 | . 25785) .01811| . 31192) . 02051] . 36275] . 02305| . 41071] . 02575| . 45610! _ 02858] 32
. 29 | .25878| . 01815) . 31279) . 02055| . 36357| . 02310| . 41149| . 02579| . 45683 . 02863| 31
30 8. 259710. 01818|8. 31366/0. 02059|8. 36439/0. 02314|8. 41226/0. 02584|8. 4575710. 02
31 | .26064 .01822| . 31453] . 02063| . 36521| . 02319] . 41304 . 02588| . 45830 “13873 dd
32 | .26156 . 01826) . 31540! . 02067] . 36603| . 02323] . 41381| . 02593] 45904 . 02878| 28
33 | . 26249) . 01830) . 31627, . 02071| . 36685, . 02327] . 41459| . 02598| . 45977 . 02883| 27
a ..: 26341 . 01834) . 31714 . 02076| . 36767| . 02332| . 41536| . 02602] . 46050| . 02887| 26
5 | 8. 26434/0. 01838|8. 31800|0. 02080|8. 36849|0. 0233618. 4161310. 02607 12 5
36 | .26526| . 01842| . 31887| . 02084| . 36930 . 02340] . 41690 Bits iet sie o 21
37 | .26618 .01846| . 31974| . 02088] . 37012| . 02345| . 41767 02616 . 46270| . 02902] 23
38 | .26710| . 01850] . 32060| . 02092] . 37093| . 02349| . 41845| 02621 . 46343| . 02907] 22
a . 26802) . 01854] . 32147) . 02096] . 37175| . 02354] . 41921! . 02626] . 46416 . 02912| 21
8. 26894 0. 01858|8. 32233/0. 02101]8. 37256/0. 02358|8. 419980. 02630
41 | . 26986] . 01861] . 32319] . 02105] . 37337 . 02363| 42075 Hiren deed n tā
42 | .27078| . 01865) . 32405| . 02109| . 37419| . 02367| ` 42152| | 02639 . 46634 . 02926| 18
43 | .27169| .01869| . 32491 . 02113] . 37500| . 02371] . 42229| | 02644 46707 . 02931| 17
44 | .27261| .01873| . 32577 5 Å - 46780) .
a a LE M 2971) . 02117] . 37581) . 02376] . 42305 .02649| . 46780| . 02936) 16
i . 273520. 0187718. 32663|0. 02121]8. 37662|0. 02380|8. 42382 0. 02653]: |
46 | .27443| . 01881] . 32749| . 02126| . 37742, . 02385] . 42458 RE ler mace tu
47 | . 27534) .01885| . 32834| . 02130] . 37823| . 02389| 42535 . 026631 . 46998| . 02951| 13
48 | .27626 . 01889) . 32920| . 02134] . 37904| . 02394] ` 42611| 02668| ` 47070 . 02956| 12
2 SE . 01893} . 33006) . 02138] . 37985) . 02398| . 42687) -02672| ` 47142 ` 02961] 11
5 : 2/8070. 0189718. 33091 0. 0214218. 38065 0. 02402|8. 427640. 0267718. 47215
51 | .27898 .01901| .33176| . 02147] . 38146 . 02407 saa i, Su
52 | .27989| .01905| . 33262| . 02151] . 38226| | 02411] . 42916 . 02686] . 47359| . 029761 8
53 | .28080 . 01909| . 33347, . 02155| . 38306| . 02416] . 42992 | 02691 . 47431 . 02981] 7
54 ZEND . 01913) . 33432 . 02159] . 38387| . 024201 . 43068| ` 02696 . 47503 . 02986| 6
55 | 8. 28260/0. 01917|8. 33517/0. 02164|8. 384670. 02425|8. 4 JE | d
56 | .28351| . 01921] . 33602 . 02168} . 38547| 02429 S T 4
57 . 28441 . 019251 . 33686 . 02172| . 38627| . 02434| . 43295 . 02710 .47719| .03000| 3
98 | .28531| . 01929| . 33771| .02176| . 38707| . 02438 . 43371| .02715| . 47791| .03005| 2
59 | .28621| . 61933] . 33856) . 02181] . 38787| . 02443 . 43446| .02719| . 47862| . 030101 1
60 8. 287110. 0193755. 33940/0. 02185|8. 388670. 02447|8. 4352210. 02724|8. 4793410. 03015 0
344° 343° 342° 341° 340° Í

1425

TABLE 34
Haversines
20° 21° 22° 23° 24°

D Log Hav | Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav] Log Hav | Nat. Hav Log Hav | Nat. Hav! '
0 | 8. 479340. 03015|8. 52127/0. 03321|8. 56120/0. 0364118. 59931/0. 03975|8. 63576/0. 04323| 60
1 . 48006, . 030201 . 52195) . 03326] . 56185) . 03646] . 59993| . 039801 . 63635! . 04329| 59
2 . 48077, . 03025| . 52263) . 03331] . 56250) . 03652] . 60055| . 03986| . 63695! . 04335| 58
3 . 48149| . 03030] . 52331) . 033371 . 56315| . 036571 . 60117| . 03992| . 63754! . 043401 57
4 . 48220| . 03035| . 52399 . 033421 . 56379) . 036631 . 60179! . 03998] . 63813| . 04346] 56
5 | 8. 48292 0. 03040|8. 524670. 03347|8. 56444|0. 03668]8. 60241/0. 04003|8. 6387210. 04352| 55
6 . 48363, . 03045] . 52535| . 03352] . 56509) . 03674] . 60303! . 04009] . 63932| . 04358| 54
7 . 48434| . 03050] . 52602| . 033581 . 56574) . 03679| . 60365 . 040151 . 63991| . 04364| 53
8 . 48505, . 03055] . 52670) . 03363] . 56638| . 03685] . 60426| . 040201] . 64050] . 04370] 52
9 . 48576, . 03060] . 52738) . 03368| . 56703| . 03690] . 60488| .04026| . 64109| . 04376] 51
10 | 8. 48648 0. 03065|8. 52806 0. 03373|8. 56767 0. 03695|8. 60550 0. 04032|8. 64168|0. 04382] 50
11 . 48719 . 03070| . 52873) . 033791 . 56832| . 03701] . 60611) . 04038| . 64227| . 0438S| 49
12 . 48789| . 03075| . 52941| . 03384] . 56896) . 03706] . 60673| . 04043] . 64286] . 04394] 48
13 . 48860) . 030801 . 53008) . 03389] . 56960. . 03712] . 60734| . 04049] . 64345! . 04400] 47
14 . 48931) . 030851 . 53076 . 033941 . 57025 . 03717| . 60796) . 04055) . 64404| . 04406| 46
15 | 8. 49002 0. 03090|8. 53143 0. 03400]8. 57089/0. 03723|8. 60857|0. 04060|8. 64463|0. 04412| 45
16 . 49073| . 03095] . 53210| . 03405] . 57153) . 03728] . 60919| . 04066] . 64521| . 04418| 44
17 . 49143] . 031011 . 53277) . 034101 . 57217) . 03734] . 509801 . 04072] . 64580! . 04424] 43
18 . 49214, . 03106] . 53345) . 03415] . 57282) . 037401 . 51041| . 04078] . 64639] . 04430] 42
19 . 49284, . 03111} . 53412) . 034211 . 57346, . 03745] . 61103, . 04083] . 64697) . 04436] 41
20 | 8. 49355/0. 03116|8. 53479/0. 03426|8. 57410/0. 03751]|8. 61164 0. 04089]8. 64756/0. 04442] 40
21 . 49425) . 03121] . 53546| . 03431} . 57474| . 037561 . 61225) . 040951 . 64815| . 04448] 39
22 . 49496) . 03126] . 53613) . 03437] . 57538, . 03762] . 61286, . 041011 . 64873] . 04454] 38
23 . 49566) . 03131] . 53680) . 034421 . 57601. . 03767] . 61347, . 04106] . 64932) . 04460] 37
24 . 49636) . 03136] . 53747| . 03447] . 57665) . 03773] . 61408) . 04112] . 64990} . 04466) 36
25 | 8. 4970610. 03141|8. 53814 0. 03453|8. 57729|0. 03778|8. 614690. 04118|8. 650490. 04472] 35
26 . 49777, . 03146] . 53880) . 03458] . 57793) . 03784] . 61530) . 04124] . 65107| . 04478] 34
27 . 49847| . 03151) . 53947| . 034631 . 57856| . 037891 . 61591| . 04130| . 65165) . 04484] 33
28 . 49917, . 03156] . 54014| . 03468] . 57920| . 03795] . 61652| . 04135] . 65224|.. 04490] 32
29 . 49987; . 03161] . 54080) . 03474] . 57984| . 03800 . 61713) . 04141 . 65282) . 044961 31
30 | 8. 5005610. 03166|8. 54147|0. 03479|8. 58047 0. 03806|8. 61773 0. 04147|8. 65340/0. 04502) 30
31 . 50126 . 03171] . 54214| . 03484] . 58111| . 03812] . 61834) . 04153] . 65398) . 04508] 29
32 . 50196) . 03177] . 54280) . 034901 . 58174! . 03817] . 61895) . 04159] . 65456) . 04514] 28
39 . 50266) . 03182] . 54346) . 03495] . 58238) . 03823] . 61955) . 04164 . 65514 . 04520] 27
34 . 50335) . 03187] . 54413) . 03500] . 58301! . 03828] . 62016! . 04170] . 65572) . 04526] 26
95 8. 50405|0. 03192|8. 54479 0. 03506|8. 58364 0. 03834|8. 62077 0. 04176|8. 656300. 04532 25
36 . 50475| . 031971 . 54545| . 03511] . 58427|.. 03839] . 62137| . 04182] . 65688) . 04538] 24
ad. „50544! . 03202] . 54612 . 03517| . 58491| . 03845| . 62197| . 04188| . 65746| . 04544] 23
38 . 50614! . 032071 . 54678) . 035221 . 58554| . 03851] . 62258| . 04194) . 65804| . 04550] 22
39 A 50683 | 20321217 54744 . 035271 . 58617) . 03856] . 62318) . 041991 . 65862| . 04556) 21
40 | 8. 50752/0. 0321818. 54810/0. 03533|8. 58680/0. 03862|8. 62379|0. 04205]|8. 65920/0. 04562 20
41 . 50821) . 03223] . 54876) . 03538] . 58743) . 03867] . 62439| . 04211] . 65978) . 04569 19
42 . 50891] . 03228] . 54942! . 03543] . 58806 . 03873] . 62499 . 04217] . 66035) . 04575 18
43 . 50960} . 03233] . 55008) . 03549] . 58869] . 03879] . 62559 . 04223] . 66093) . 04581 17
44 . 51029) . 03238] . 55073) . 03554] . 58932) . 03884) . 62619) . 04229] . 66151) . 04587] 16
45 | 8. 510980. 03243|8. 55139|0. 03560418. 58994 0. 03890|8. 62680|0. 04234]8. 66208 0. 04593] 15
46 . 51167) . 03248] . 55205 . 03565] . 59057) . 03896] . 62740) . 04240] . 66266 . 04599 14
47 „51236! . 03254) . 55271) . 03570] . 59120) . 03901} . 62800| . 04246) . 66323) . 04605] 13
48 . 51305) . 03259) . 55336] . 03576] . 59183] . 03907] . 62860, . 04252 . 66381 . 04611 12
49 . 51374! . 03264] . 55402) . 03581] . 59245| . 03912] . 62919! . 04258] . 66438| . 04617 11
50 | 8. 514420. 03269|8. 55467 0. 03587|8. 59308/0. 03918|8. 62979|0. 04264]8. 664960. 04623| 10
51 „51511! . 03274] . 55533) . 03592] . 59370| . 03924] . 63039 . 04270 . 66553 . 04629 9
52 „51580! . 032791 . 55598) . 03597] . 59433| . 03929] . 63099| . 04276) . 66610. . 04636| 8
53 . 51648| . 03285] . 55664| . 03603] . 59495, . 03935] . 63159) . 04281 : 66668 . 04642] 7
54 . 51717) . 03290] . 55729) . 03608] . 59558) . 03941] . 63218) . 04287] . 66725 . 04648 :
55 | 8. 51785 0. 0329518. 55794 0. 03614|8. 59620 0. 03946|8. 63278 0. 04293|8. 66782 /0. 04654

56 . 51854! . 033001 . 55859| . 03619| . 59682| . 03952] . 63338, . 04299] . 66839) . 04660 4
57 . 51922| . 03305| . 55925| . 03624] . 59745) . 03958] . 63397 . 04305| . 66896 . 04666 :
58 . 51990) . 03311] . 55990) . 03630] . 59807, . 03963] . 63457 . 04311 . 66953| . 04672 4
59 . 52058) . 03316] . 56055) . 03635] . 59869 . 03969] . 63516 . 04317 . 67010 . 04678 i
60 8. 5212710. 0332118. 56120/0. 03641|8. 599310. 03975|8. 63576|0. 04323|8. 67067|0. 04685

339° 338° 3304 336° 330%

1426

25°

TABLE 34

Haversines

Log Hav

px 60

0 | 8.67067 . 0626
i 2 . 76786| . 05859] . 79769) . 06276| 59
2 67181 ` 04697 ` 10527 í . 76836) . 05866] . 79818 . 06283] 58
3 | .67238| .04703| . 70582 . . 76887) .05873| . 79866) . 06290| 57
4 | .67295| .04709| . 70636) . . 76938| . 05880] . 79915 d z

. 70691 0. . 76988 0. 05887|8. 79964 0.
6 * 67409. 04728|*. T0548 . 77039) . 05894] . 80013| . 06311| 54
7 | .67465 . 047281 . 70800) . . 77089 . 05901] . 80061| . 06318] 53
8 | .67522| .04734| . 70854. . . 77139 . 05907| . 80110) . 06326] 52
9 | .67579 .04740| . 70909 . . 77190 .05914| .80158 . 06333] 51
. 70963 0. . 77240 0. 05921|8. 80207 0. 06340| 50
11 TID } . 77291 . 05928| . 80256) . 06347| 49
12 | . 67748] .04759| . 71072] . . 77341, . 05935] . 80304| . 06354| 48
13 | .67805| .04765| . 71126| . . 77391| . 05942) .80353| . 06361| 47
14 | .67861 .04771| . 71180| . . 77441 . 05949| . 80401) . 06368] 46
l . 04777|8. 712340. . 77492 0. 05955|8. 80449 0. 06375| 45
16 167974 04783 . 71289| . . 77542. . 05962| . 80498) . 06382| 44
17 | .68030| . 04790] . 71343, . . 77592 .05969| . 80546) . 06389] 43
18 | .68087| . 04796] . 71397| . . 77642) . 05976| . 80595 . 06397] 42
19 | .68143| . 04802] . 71451 . 77692 . 05983| . 80643) . 06404] 41
2 . 68199/0. 04808|8. 715050. . 77742/0. 05990|8. 80691 0. 06411| 40
21 ` 68256 . 04815] . 71559] . . 77792| . 05997] . 80739) . 06418] 39
22 | . 68312} . 04821] . 71613] . . 77842) . 06004] . 80788) . 06425] 38
23 | . 68368) . 04827] . 71667] . . 77892) . 06011] . 80836) . 06432] 37
24 | . 68424} . 04833] . 71721 . 77942 . 06018] . 80884) . 06439] 36
25 | 8. 68480/0. 04839|8. 71774 0. . 77992 0. 06024|8. 80932 0. 06446] 35
26 | . 68536] . 04846] . 71828. . . 78042, . 06031] . 80980) . 06454] 34
27 | . 68592] . 048521 . 71882 . . 78092) . 06038] . 81028 . 06461] 33
28 | . 68648] . 04858] . 71936) . . 78142 . 06045] . 81076 . 06468] 32
29 | . 68704] . 04864] . 71989) . . 78191| . 06052| . 81124| . 06475| 31
30 | 8. 687600. 04871|8. 72043 0. . 75201/0. 05649|8. 78241/0. 06059|8. 81172 0. 06482| 30
31 | .68815| . 04877| . 72097| . . 75252) . 05656| . 78291) .06066| . 81220) . 06489] 29
32 | .68871| .04883| . 72150) . . 75304| . 05663] . 78341| . 06073| . 81268) . 06497] 28
33 | .68927| . 04890] . 72204 . . 75355| . 05670| . 78390| . 06080] . 81316) . 06504| 27
34 | .68983| . 04896] . 72257 . 75407| . 05676] . 78440| . 06087 . 81364 . 06511} 26
35 | 8. 69038/0. 04902|8. 72311 0. . 754580. 05683|8. 78490 0. 06094|8. 81412 0. 06518| 25
36 | .69094| . 04908] . 72364| . - 75510, . 05690| . 78539| . 06101] . 81460! . 06525| 24
37 | .69149| . 04915| . 72418 . 75561] . 05697| . 78589| . 06108] . 81508 . 06532] 23
38 | .69205 .04921| . 72471| . - 75613} . 05703| . 78638, . 06115| . 81555| . 06540] 22
39 | .69260| . 04927] . 72525| . . 75664! . 05710] . 78688} . 06122] . 81603 . 06547| 21
40 | 8. 69316/0. 04934|8. 72578 0. - 797150. 05717|8. 78737 0. 06129|8. 8165110. 06554| 20
41 | .69371| . 04940] . 72631| . - 79767) . 05724] . 78787| .06136| . 81699) . 06561] 19
42 | .69427| .04946| . 72684. . - 75818| . 05730] . 78836) . 06143| . 81746| . 06568| 18
43 | .69482| .04952| . 72738 . | - 75869) . 05737| . 78885| . 06150| . 81794 . 06576] 17
44 | .69537| . 04959] . 72791 . 75920) . 05744| . 78935| . 06157] . 81841| . 065831 16
45 | 8. 69593 0. 04965|8. 72844 0. - 759720. 05751|8. 789840. 06164|8. 8188910. 06590] 15
46 | . 69648] . 04971| . 72897|. - 76023) . 05757| . 79033| . 06171] . 81937] . 06597) 14
47 | . 69703] . 04978] . 72950] . - 76074) . 05764] . 79082] . 06178} . 81984) . 066051 13
48 | . 69758] . 04984] . 73003) . - 76125) . 05771] . 79132) . 06185} . 82032) . 06612] 12
49 | . 69814] . 04990] . 73056) . - 76176) . 05778) . 79181} .06192| . 82079 . 06619] 11
50 | 8. 69869/0. 04997|8. 7310910. - 76227/0. 05785|8. 79230 0. 06199|8. 82126 0. 06626| 10
51 | .69924 . 05003] . 73162| . . 76278) . 05791] . 79279) .06206| . 82174| . 06633] 9
52 | . 69979] . 05009] . 73215] . . 76329 . 05798) . 79328) . 06213] . 82221) 06641| 8
53 | . 70034) . 05016] . 73268 . - 76380) . 05805] . 79377) . 06220] . 82269] ` 06648] 7
54 | .70089 . 05022] . 73321 - 76431) . 05812] . 79426) . 06227] . 82316] . 066551 6
55 | 8. 701440. 05028|8. 73374 0. - 76481/0. 05819|8. 79475 0. 06234|8. 82363/0. 06662| 5
56 | .70198| . 05035| . 73426) . - 76532| . 05825| . 79524| . 06241| . 82410) . 06670| 4
57 | . 70253] . 05041] . 73479| . - 76583) . 05832] . 79573) .06248| . 82458| _ 066771 3
58 | . 70308] .05048| . 73532| . - 76634) . 05839] . 79622| . 06255| . 82505 | 06684] 2
59 | .70363 .05054| . 73584 . - 76684) . 05846] .79671 . 06262| . 82552 | 066911 1
60 | 8. 7041810. 05060|s. 73637 0. - 76735 0. 05853|8. 79720 0. 06269|8. 82599 0. 0
334° 332° 331°

1427

TABLE 34
Haversines
30° 31° 32° 33° 34°

3 Log Hav |Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav

0 | 8. 82599/0. 06699|8. 85380/0. 07142|8. 880680. 07598|8. 90668/0. 08066|8. 93187/0. 08548| 60
1 . 82646) . 06706] . 85425| . 07149) . 88112, . 07605] . 90711| . 08074) . 93228) . 08556} 59
2 . 82694) . 06713) . 85471) . 07157| . 88156| . 07613] . 90754) . 08082] . 93270, . 08564] 58
3 . 82741| . 06721) . 85516) . 07164] . 88200) . 07621] . 90796| . 08090] . 93311| . 08573| 57
4 .82788| . 06728| . 85562| . 07172| . 88244) . 07628| . 90839| . 08098] . 93352) . 08581| 56
5 | 8. 82835|0. 06735|8. 85607/0. 07179|8. 88288|0. 07636|8. 90881/0. 081068. 93393/0. 08589| 55
6 „82882| . 06742) . 85653) . 07187] . 88332| . 07644] . 90924| . 08114] . 93435| . 08597| 54
7 „82929| . 06750| . 85698) . 07194) . 88375] . 07652) . 90966| . 08122| . 93476| . 08605| 53
8 .82976| . 06757| . 85743| . 07202| . 88419| . 07659] . 91009| . 08130| . 93517| . 08613| 52
9 . 83023) . 06764| . 85789| . 07209| . 88463| . 07667] . 91051, . 08138) . 93558| . 08621| 51
10 | 8. 83069|0. 06772|8. 85834 0. 07217|8. 88507|0. 07675|8. 91094|0. 081468. 93599|0. 086301 50
11 „88116| . 06779| . 85879| . 07224) . 88551! . 07683| . 91136| . 08154| . 93640| . 08638) 49
12 . 83163| . 06786] . 85925| . 07232) . 88595| . 07690| . 91179| . 08162] . 93681) . 08646| 48
13 „83210| . 06794] . 85970| . 07239] . 88638| . 07698| . 91221| . 081701 . 93722| . 08654| 47
14 „83257| . 068011 . 86015) . 07247| . 88682| . 07706| . 91263) . 08178| . 93764! . 08662| 46
15 | 8, 83303/0. 06808|8. 86060/0. 07254|8. 88726|0. 07714|8. 91306/0. 08186|8. 93805 0. 08671| 45
16 . 83350| . 06816| . 86105| . 07262] . 88769) . 077211 . 91348| . 08194] . 93846) . 08679| 44
17 . 83397| . 06823] . 86151) . 07270} . 88813, . 07729] . 91390. . 08202) . 93886, . 08687) 43
18 . 83444! . 06830] . 86196) . 07277] . 88857| . 07737] . 91432 . 08210) . 93927, . 08695) 42
19 . 83490} . 06838] . 86241) . 07285} . 88900) . 07745) . 91475, . 08218) . 93968) . 08703) 41
20 | 8. 8353710. 06845|8. 86286|0. 07292|8. 88944|0. 07752|8. 91517|0. 08226|8. 94009|0. 08711) 40
21 . 83583| . 06852] . 86331| . 07300] . 88988! . 07760} . 91559| . 08234] . 94050| . 08720) 39
22 .83630| . 06860} . 86376| . 07307| . 89031| . 07768| . 91601, . 08242] . 94091| . 08728) 38
23 . 83676! .06867| . 86421| . 07315] . 89075 . 07776| . 91643 . 08250] . 94132| . 08736] 37
24 . 83723) . 06874] . 86466) . 07322] . 89118) . 07784] . 91685] . 08258] . 94173) . 08744] 36
25 | 8. 8376910. 0688218. 86511|0. 07330|8. 89162/0. 0779118. 917280. 08266|8. 942130. 08753] 35
26 . 83816] . 06889] . 86556] . 07338] . 89205] . 07799] . 91770) . 08274] . 94254 . 08761] 34
27 . 83862| . 06896] . 86600) . 07345] . 89248! . 07807] . 91812) . 08282] . 94295] . 08769} 33
28 . 83909] . 06904) . 86645] . 07353] . 89292 . 07815] . 91854 . 08290] . 94336] . 08777) 32
29 . 83955) . 069111 . 86690) . 07360] . 89335| . 07823] . 91896 . 08298] . 94376] . 08785) 31
30 | 8. 840020. 0691918. 86735|0. 0736818. 89379 0. 07830|8. 919380. 08306|8. 94417/0. 08794] 30
31 . 84048| . 06926] . 86780 . 07376] . 89422) . 07838] . 91980| . 08314] . 94458| . 08802| 29
32 „84094! . 06933| . 86825| . 07383] . 89465| . 07846] . 92022) . 08322] . 94498| . 08810) 28
33 „84140| . 06941| . 86869) . 07391] . 89509 . 07854] . 92064 . 08330) . 94539) . 08818 27
34 ` 84187) . 06948] . 86914! . 07398] . 89552 . 07862] . 92105| . 08338| . 94580, . 08827] 26
35 | 8. 84233/0. 06955|8. 86959 0. 0740618. 895950. 07870|8. 92147/0. 08346|8. 94620|0. 08835) 25
36 ` 84279] . 06963] . 87003 . 07414] . 89638] . 07877] . 92189 . 08354] . 94661| . 08843 24
37 -84325| . 06970] . 87048) . 07421] . 89681] . 07885] . 92231| . 08362) . 94701, . 08851 23
38 . 84371| .06978| . 87093) . 07429] . 89725| . 07893] . 92273| . 08370] . 94742 . 08860] 22
39 "84417! . 06985| . 87137 . 07437| . 89768 . 07901] . 92315, . 08378| . 94782) . 08868 21
40 8, 84464/0. 06993|8. 87182/0. 07444|8. 89811/0. 07909|8. 92356 0. 08386|8. 948230. 08876 20
41 -84510| . 07000] . 87226| . 07452] . 89854 . 07917] . 92398 . 08394] . 94863 . 088851 19
42 ` 84556| . 07007| . 87271! . 07459| . 89897| . 07924] . 92440. . 08402] . 94904 . 08893} 18
43 "84602! . 07015] . 87315! . 07467] . 89940! . 07932] . 92482. . 08410] . 94944 . 089011 17
44 ` 84648] . 07022] . 87360) . 07475] . 89983) . 07940} . 92523| . 08418) . 94985 . 08909} 16 `
45 8. 84694 0. 0703018, 874040. 0748218. 900260. 0794818. 92565|0. 08427|8. 95025|0. 08918 15
46 . 84740| . 070371 . 87448] . 07490} . 90069} . 07956] . 92607) . 08435 . 95065) . 08926) 14
47 ` 84785| . 07045| . 87493, . 07498] . 90112 . 07964] . 92648| . 08443 . 95106) . 08934) 13
48 ` 84831] . 07052] . 87537! . 07505} . 90155} . 07972) . 92690) . 08451 . 95146] . 08943] 12
49 ` 84877) . 07059] . 87582, . 07513} . 90198 . 07980] . 92731) . 08459 . 95186) . 08951] 11
50 8. 8492310. 07067|8. 87626 0. 07521|8. 90241/0. 07987|8. 927730. 084678. 95227 0. 08959 10
51 ` 84969| . 07074| . 87670| . 07528) . 90284| . 07995| . 92814 .08475| .95267, . 08967| 9
52 ` 85015| . 07082| . 87714| . 07536] . 90326| . 08003| . 92856 . 08483] . 95307| . 08976) 8
53 ` 850601 . 07089] . 87759] . 07544] . 90369} . 08011] . 92897 .08491| . 95347} . 08984] 7
54 ` 85106| . 07097) . 87803) . 07551] . 90412 . 08019) . 92939 . 08499} . 95388 . 08992] 6
55 8 851520. 071048. 87847 0. 07559|8. 90455|0. 08027|8. 92980|0. 08507|8. 954280. 09001 5
56 ` 85197, .07112| . 87891! .07567| . 90498) . 08035| . 93022 .08516| . 95468} . 09009] 4
57 ` 85243| .07119| .87935 .07574| . 90540, . 08043} . 93063 .08524| . 95508] . 09017) 3
58 ` 85289| . 07127| . 87980, . 07582] . 90583 . 08051] . 93104 -08532| . 95548] . 09026) 2
59 ` 85334| . 07134] . 88024) . 07590) . 90626, . 08059 . 93146| . 08540| . 95588, . 09034| 1
60 8 85380|0. 07142|8. 880680. 07598|8. 90668|0. 08066|8. 931870. 08548|8. 95628 0. 09042 0

329°

328°

327°

326°

325°

1428

TABLE 34

Haversines

35° 37° 39

Log Hav |Nat. Hav Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav| ’

0. 10068|9. 02528|0. 10599|9. 04699|0. 11143] 60
„02565| . 10608| . 04735| . 11152| 59
. 02602) . 10617| . 04770| . 11161] 58
„02638| . 10626| . 04806| . 11170] 57
„02675| . 10635| . 04842| . 11179| 56

. 02712/0. 10644|9. 04877|0. 11189] 55

8. 95628
- 95668, . 09051] .
. 95709. . 09059] .€
. 95749| . 09067] . :
. 95789 . 09076| . 98152| .

. 95828/0. 0908418. 98191|0

DONO deo. c
o

. 95868 . 090931 . 98229) . . 02748| . 10653] . 04913) . 11198] 54
. 95908 . 091011 . 98268) . . 02785] . 10662] . 04948) . 11207] 53
. 95948) . 09109} . 98307] . . 02821) . 10671] . 04984) . 11216] 52
. 95988, . 09118| . 98346 . . 02858) . 10680| . 05019| . 11225) 51

10 | 8. 96028/0. 09126|8. 983840. . 02894 0. 10689|9. 05055/0. 11234] 50

11 . 96068) . 09134] . 98423) . . 02931) . 10698] . 05090) . 11244] 49
12 . 96108) . 09143] . 98462) . . 02967) . 10707] . 05126) . 11253] 48
13 . 96148) . 09151} . 98500) . . 03004) . 10716] . 05161) . 11262] 47
14 . 96187) . 091601 . 98539) . . 03040) . 10725} . 05197| . 11271] 46

KS
a
00

. 962270. 09168|8. 985780. . 03077/0. 10734|9. 052320. 11280] 45

16 . 96267 . 09176| . 98616) . . 03113 . 10743] . 05268) . 11290] 44
17 . 96307) . 09185} . 98655) . . 03150) . 10752} . 05303) . 11299] 43
18 . 96346 . 09193] . 98693] . . 03186) . 10761] . 05339] . 11308} 42
19 . 96386) . 09202] . 98732) . . 03222) . 107701 . 05374} . 11317] 41

20 | 8. 96426/0. 09210|8. 98770)0. . 03259/0. 10779]9. 05409|0. 11326| 40

21 . 96465) . 09218| . 98809) . . 03295) . 10788| . 05445) . 11336| 39
22 . 96505) . 09227] . 98847| . . 03331) . 10797] . 05480) . 11345| 38
23 . 96545) . 092351 . 98886| . . 03368) . 10806} . 05515) . 11354| 37
24 . 96584| . 09244) . 98924| . . 03404| . 10815| . 05551) . 11363| 36

25 | 8. 96624/0. 09252|8. 98963 0. . 03440/0. 108249. 05586/0. 11373| 35

26 . 96663, . 09260] . 99001) . . 03476 . 10833] . 05621| . 11382| 34
27 . 96703) . 09269] . 99039| . . 03513) . 10842] . 05656, . 11391| 33
28 . 96742) . 09277| . 39078| . . 03549, . 108511 . 05692, . 11400| 32
29 . 96782, . 092861 . 99116) . . 03585| . 10861| . 05727| . 11410} 31

w
©
00

. 96821/0. 09294|8. 991540. . 03621/0. 10870|9. 05762|0. 11419| 30

31 . 96861) . 09303] . 99193) . . 03657) . 10879] . 05797| . 11428] 29
32 . 96900) . 09311] . 99231) . . 03694 . 10888} . 05832, . 11437] 28 `
33 . 96940) . 09320] . 99269) . . 03730) . 10897] .05867| . 11447] 27
34 . 96979} . 09328] . 99307] . . 03766) . 10906] . 05903) . 11456] 26

35 | 8. 97018/0. 0933618. 99346 0. . 03802/0. 10915|9. 05938|0. 11465| 25

36 . 97058) . 09345| . 99384) , . 03838) . 10924] .05973| . 11474] 24
37 . 97097| . 09353| . 99422) . . 03874! . 10933] . 06008 . 11484] 23
38 . 97136, . 09362] . 99460| . . 03910) . 10942} . 06043] . 11493] 22
39 . 97176} . 09370] . 99498) . . 03946) . 10951] . 06078) . 11502} 21

Ha
e
00

. 972150. 09379|8. 99536 0. . 039820. 10960|9. 06113 0. 11511] 20

41 . 97254 . 09387| . 99575) . . 04018) . 10969] . 06148) . 11521] 19
42 . 97294) . 09396] . 99613. . 04054 . 10978] .06183| . 11530] 18
43 . 97333) . 09404] . 99651 . 04090) . 10988| . 06218) . 11539] 17
44 . 97372| . 09413] . 99689 . 04126) . 10997| . 06253) . 11549] 16

45 | 8. 97411/0. 0942118, 99727 0. . 04162/0. 11006|9. 06288|0. 11558] 15

46 . 97450) . 09430| . 99765| . . 04198) . 11015| . 06323| . 11567] 14
47 : 97489 . 094381 . 99803 . 04234 . 11024| . 06358| . 11577] 13
48 . 97529) . 094471 . 99841| . . 04270) . 11033] . 06393 . 11586] 12
49 | .97568| . 09455] . 99879) . . 04306, . 11042] . 06428) . 11595] 11

50 | 8. 97607 0. 09464|8. 99917 0.
51 | .97646 . 09472] . 99955
52 | . 97685) . 09481|8. 99993 `
53 | .97724 .09489|9. 00031) `
54 | .97763 . 09498] . 00068 `
55 | 8. 97802 0. 09506|9. 00106 0.
56 | .97841| . 09515] . 00144 | .
57 | .97880 .09524| . 00182 |
58 | .97919 .09532| . 00220 `
59 | .97958 .09541| . 00258) `
60 | 8. 979970. 09549|9. 00295 0.

9. 04341|0. 11051|9. 064620. 11604| 10

. 04377 . 11060] . 06497! . 11614
. 04413) . 11070] . 06532) . 11623
. 04449| . 11079] . 06567! . 11632
. 04485| . 11088| . 06602) . 11642
. 04520 0. 11097]9. 0663710. 11651
. 04556) . 11106] . 06671 . 11660
. 04592) . 11115] . 06706] . 11670
. 04628] . 11124] . 06741| . 11679
. 04663| . 11134] . 06776] . 11688
. 04699/0. 11143|9. 06810/0. 11698

Qm rt0545 GO OO

324? 323?

321? 320?

40°

Log Hav

TABLE 34

Haversines

42° 43°

Nat. Hav | Log Hav

Nat. Hav | Log Hav

Nat. Hav| Log Hav | Nat. Hav

ee ee

9. 06810

. 06845) .
. 06880) .
. 06914) .

. 06949

. 069840.
. 07018) .
. 07053| .
. 07088) .

0. 11698[9. 08865

. 08899] .
. 08933) .
. 08966) .
. 09000} .

0. 12265|9. 10866
. 10899
. 10932
. 10965
. 10997

. 12852| . 12847
.12862| . 12879
. 12872] . 12911
. 12882] . 12943

. 18442
. 13452
. 13462
. 13472

1429

44?

Log Hav

Nat. Hav

0. 12843|9. 12815|0. 13432]9. 147150.
. 14746) .
. 14778) .
. 14809) .
. 14840) .

. 09101

. 0903410.
. 09068) .

` 09135| .
` 09169| .

. 11030
. 11063
. 11096
. 11129
. 11161

. 12891|9. 12975
. 129011 . 13007
. 12911| . 13039
. 129211 . 13071
. 12930] . 13103

. 13482]9.
. 13492
. 13502
. 13512
. 13522

14871

..14902| .
14934).
. 14965) .
. 14996) .

. 09202)0.
. 09236| .
. 09269) .
. 09303) .
. 09337| .

. 11194
. 11227
. 11260
. 11292
. 11325

. 12940|9. 13135
. 12950) . 13167
. 12960} . 13199
. 12970| . 13231
. 12979| . 13263

. 13532]9.
. 13542
. 13552
. 13562
. 13571

150270.

. 15058| .
. 15089} .
520]:
. 15152) .

. 09471

. 093700.
. 09404| .
. 09437] .

. 09504) .

. 11358
. 11391
. 11423
. 11456
. 11489

. 12989|9. 13295
. 12999| . 13326
. 130091 . 13358
. 18018] . 13390
. 13028| . 13422

. 1358119.
. 13591
. 13601
. 13611
. 13621

1518310.
. 16214) .
. 15245) .
. 15276) +.
. 15307] .

. 09571

. 09538) 0.

` 09605 .
` 09638 .
` 09672, .

. 11521
. 11554
. 11586
. 11619
. 11652

. 130389. 13454
. 13048] . 13486
. 18058) . 13517
. 130671 . 13549
. 130771 . 13581

. 1363119.
. 13641
. 13651
. 13661
. 13671

153380.

. 15369) .
. 15400) .
. 15431) .
. 15462) .

. 09705)0.
. 09739) .
. 09772) .
. 09805) .
. 09839) .

. 11684
SEA
. 11749
. 11782
. 11814

„13087]9. 13613
. 13097] . 13644
. 131071 . 13676
. 13116] . 13708
. 13126) . 13739

„13681]9.
„13691
„13701
led!
. 13721

154930.

. 15524) .
. 15555) .
. 15585) .
. 15616).

. 098720.
. 09905) .
. 09939) .
. 09972) .
. 10005) .

. 11847
11879
. 11912
. 11944
211977

. 13136/9. 13771

. 138146) . 13803
. 13156) . 13834
. 13166| . 13866
. 13175| . 13898

. 137319.
. 13741
. 13751
. 13761
. 13771

15647|0.

„15678|.
.15709|.
„15740|.
„15771

„100390.
„10072|.
„10105|.
. 10138) .
. 10172) .

. 12009
. 12041
. 12074
. 12106
. 12139

. 13185|9. 13929
. 131951 . 13961
. 13205) . 13992
. 18215] . 14024
. 13225] . 14056

. 13781]|9.
. 13791
. 13801
. 13811
. 13822

158020.

. 15832) .
. 15863) .
. 15894 .
. 15925) .

. 10271

. 10205)0.
. 10238) .

"10304 .
103370

El2171
. 12203
. 12236
. 12268
. 12300

. 13235|9. 14087
. 13244| . 14119
. 13254| . 14150
. 13264] . 14182
. 13274| . 14213

. 13832]9.
. 13842
. 13852
. 13862
. 13872

15955|0.
„15986|.
SEA
. 16048) . |
. 16078) .

. 10371

. 10404) .
. 10437 .
. 10470) .
. 10503} .

9. 12332

. 12365

7| .12397
. 12429

. 12461

. 13284|9. 14245
. 13294| . 14276
. 13304| . 14307
. 13314| . 14339
. 13323] . 14370

. 1388219.
. 13892
. 13902
. 13912
. 13922

161090.

. 16140| .
SEI AE
. 16201) .
. 16232) .

. 10569
. 10602

. 10536 0.

.10635 .
10668 .

9. 12494
. 12526
. 12558
. 12590
. 12622

. 18333|9. 14402
. 13343| . 14433
. 13353| . 14465
. 13363] . 14496
. 13373] . 14527

. 13932|9.
. 13942
. 13952
. 13962
. 13972

16262/0.

. 16293) .
. 16324) .
. 16354| .
. 16385| .

. 10701

10833
10866

` 10734, .
` 10767] .
` 10800) .

. 12655
. 12687
2719
. 12751
12783
12815

. 13383]9. 14559
. 13393] . 14590
. 13403] . 14621
. 13412] . 14653
. 18422) . 14684
0. 13432]9. 14715/0.

. 13983]9.
. 13993
. 14003
. 14013
. 14023

14033|9.

164150.
. 16446| .
. 16476) .
. 16507) .
. 16537] .

16568

ORNNWNROI

0.

318? 31

7? 316°

31

5°

1430

TABLE 34

Haversines

45°

47° 49°

Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav Log Hav | Nat. Hav z

9. 16568|0. 14645|9. 183760. 152679. 20140/0. 15900|9. 21863 0. 16543|9. 235450. 17197| 60
. 16598 . 14655) . 18405) . 15278) . 20169| . 15911] . 21891| . 16554] . 23573| . 17208| 59
. 16629| . 14665] . 18435) . 15288] . 20198, . 15921] . 21919] . 16565] . 23601| . 17219] 58
. 16659 . 14676] . 18465) . 15298] .20227| . 15932] . 21948] . 16576] . 23629] . 17230] 57
. 16690) . 14686] . 18495) . 15309] . 20256] . 15943] . 21976] . 16587] . 23656] . 17241] 56

9. 16720/0. 14696|9. 18524/0. 15319|9. 20285/0. 15953|9. 22004|0. 1659819. 236840. 17252] 55
. 16751) . 14706] . 18554| . 15330] . 20314| . 15964] . 22033] . 16608] . 23712! . 17263] 54
. 16781] . 14717] . 18584) . 15340} . 20343) . 15975] . 22061| . 16619] . 23739] . 17274] 53
. 16812) . 14727] . 18613) . 15351] . 20372] . 15985] . 22089] . 16630] . 23767] . 17285] 52
. 16842) . 14737] . 18643) . 15361] . 20401! . 15996] . 22118) . 16641] . 23794] . 17296] 51

9. 168720. 14748|9. 186730. 153729. 20430|0. 160079. 22146/0. 16652|9. 2382210. 17307] 50
. 16903) . 14758| . 18702) . 15382] . 20459| . 16017| . 22174| . 16663] . 23850! . 17318] 49
. 16933) . 14768| . 18732| . 15393] . 20488) . 16028] . 22202| . 16673] . 23877| . 17329| 48
. 16963| . 14779| . 18762 . 15403] . 20517| . 16039] . 22231! . 16684| . 23905) . 17340| 47
. 16994| . 14789] . 18791) . 15414] . 20546] . 16049] . 22259] . 16695| . 23932] . 17351] 46

9. 170240. 1479919. 18821/0. 15424]9. 20574|0. 16060]9. 22287 0. 16706|9. 2396010. 17362 45
. 17054| . 14810] . 18850) . 15435} . 20603| . 16071] . 22315| . 16717] . 23988| ` 17373| 44
. 17085| . 148201 . 18880. . 15445| . 20632| . 16081] . 22343| . 16728] . 24015 |. 17384] 43
. 17115) . 14830] . 18909| . 15456| . 20661| . 16092] . 22372| . 16738] . 24043| ` 17395| 42
. 17145) . 14841] . 18939 . 15466] . 20690 . 16103] . 22400| . 16749] . 24070) ` 17406} 41

9. 171750. 14851|9. 18968)/0. 15477|9. 20719|0. 16113|9. 224280. 16760)9. 24098/0. 17417| 40
. 17206) . 14861] . 18998| . 15487] . 20748| . 16124] . 22456| . 16771] . 24125| . 17428] 39
. 17236| . 14872} . 19027] . 15498] . 20776| . 16135] . 22484! . 16782] ` 24153| . 17439] 38
. 17266| . 14882| . 19057| . 15508| . 20805| . 16145| . 22512! . 16793 . 24180} . 17450] 37
. 17296| . 14892] . 19086| . 15519] . 20834! . 16156| . 22540| . 16804 . 24208] . 17461] 36

9. 17327/0. 14903|9. 19116/0. 1553019. 20863 0. 1616719. 22569 0. 16815|9. 2423510. 17472] 35
. 17357| . 14913] . 19145] . 15540] . 20891] . 16178] . 22597! . 16825 . 24263] . 17483] 34
. 17387 . 14923| . 19175| . 15551] . 20920] . 16188| . 22625] ` 16836] . 24290| . 17494] 33
. 17417| . 14934| . 79204] . 15561] . 20949] . 16199] ` 22653 . 16847| . 24317| . 17505| 32
. 17447! . 14944| . 19234) . 15572] . 20978] . 16210] . 226811 ` 16858| . 24345| . 17517] 31

9. 17477/0. 14955|9. 19263 0. 15582|9. 21006/0. 1622019. 22709/0. 16869|9. 24372|0. 17528] 30
. 17507] . 14965] . 19292. . 15593] . 21035! . 16231] . 22737| . 16880] . 24400] . 17539] 29
. 17538. . 14975] . 19322) . 15603] . 21064! . 16242] ` 22765 . 16891] . 24427] . 17550] 28
. 17568) . 14986] . 19351) . 15614] . 21092] . 16253] ` 22793) . 16902] . 24454] . 17561| 27
. 17598) . 14996] . 19381] . 15624] . 21121) . 16263] ` 22821! . 16913] . 24482| . 17572| 26

9. 176280. 15006|9. 19410/0. 15635|9. 211500. 16274 9. 228490. 16923]9. 24509|0. 17583] 25
. 17658) . 15017] . 19439| . 15646] . 21178| . 16285| . 22877| . 16934] . 24536| . 17594] 24
. 17688) . 15027] . 19469| . 15656| . 21207] ` 16296] . 22905| . 16945| . 24564| . 17605] 23
. 17718) . 15038] . 19498] . 15667] . 21236) . 16306| . 22933| . 16956| . 24591| . 17616] 22
. 17748| . 15048] . 19527| . 15677| . 21264| ` 16317| . 22961| . 16967] . 24618| . 17627] 21

9. 177780. 15058|9. 19557|0. 1568819. 21293 0. 16328 9. 2298910. 16978|9. 246460. 17638| 20
. 17808| . 15069] . 19586| . 15698| . 21322| ` 16339] . 23017| . 16989] . 24673] . 17649] 19
. 17838| . 15079] . 19615|. 15709] . 21350] . 16349| . 23045, . 17000] . 24700| . 17661| 18
. 17868} . 15090] . 19644| . 15720| . 21379| ` 16360| . 23073, . 17011] . 24728] . 17672| 17
. 17898| . 15100| . 19674| . 15730] . 21407 ` 16371] . 23100| . 17022] . 24755 . 17683| 16

9. 179280. 1511019. 19703|0. 1574119. 214360. 16382|9. 23128/0. 17033]9. 24782/0. 17694] 15
. 17958 . 15121| . 19732| . 15751| . 21464 . 16392] . 23156| . 17044| . 24809| . 17705| 14
. 17988) . 15131] . 19761| . 15762] .21493| ` 164031 . 23184| . 17055| . 24837, . 17716! 13
. 18018) . 15142] . 19790| . 15773] . 21521) ` 16414| . 23212| . 17066] . 24864| . 17727| 12

. . 18048) . 15152] . 19820| . 15783] . 21550! ` 16425| . 23240|.17076|'. 24891| . 177381 11

9. 18077 0. 15163|9. 19849/0. 15794|9. 21578 0. 16436|9. 23268 0. 17087|9. 249180. 17749] 10
. 18107] . 15173] . 19878] . 15804] . 21607] . 16446] . 23295 . 17098] . 24945] . 17760
. 18137 . 15183] . 19907) . 15815] . 21635! ` 16457] . 23323] . 17109| . 24973| . 17772
. 18167) . 15194] . 19936| . 15826] . 21664! ` 16468| . 23351| . 17120] . 25000| . 17783

.. 18197] . 15204] . 19965] . 15836] . 21692| . 16479| . 23379) . 17131| . 25027| . 17794

9. 182270. 15215|9. 19995/0. 15847|9. 21721 0. 16489|9. 234070. 1714219. 25054 0. 17805
. 18256| . 15225| . 20024| . 15858| . 21749| . 16500| . 23434 . 17153| . 25081 . 17816

. 18286; . 15236| . 20053| . 15868| . 21778 . 165111 . 23462| . 17164| . 25108! ` 17827

. 18316) . 15246} . 20082 . 15879| . 21806 . 16522) . 23490] . 17175

. 25135| . 17838
. 18346| . 15257| . 20111| . 15889] . 21834 . 16533] . 23518| . 17186] . 25163| . 17849
9. 18876|0. 15267|9. 201400. 15900]9. 21863/0. 16543|9. 235450. 17197|9. 25190 0. 17861

OO RO Cīļ Ke D O

C m N 024 O1 O NO DO

314? 313?

312° 311° 310°

50°

51°

TABLE 34

Haversines

1431

309°

308°

307°

306°

305°

4 Log Hav |Nat. Hav| Log Hav $
0 | 9. 25190/0. 1786119. 26797 9. 31409 ) 60
1 .25217| . 17872) . 26823) . 18545 . 31434] . 20623] 59
2 . 25244| . 178831 . 26850| . 18557] . . 31459| . 20634| 58
3 . 25271| . 17894| . 26876| . 18568] . . 31484) . 20646| 57
4 . 25298, . 17905| . 26903| . 18579 . 31508) . 20658| 56
5 | 9. 25325|0. 17916]9. 26929/0. 18591]9. 9. 30032/0. 1996719. 3153310. 20670} 55
6 .25352| . 17928] . 26956} . 18602 . 30057) . 19979] . 31558| . 20681| 54
fi .25379| . 17939] . 26982; . 18613 .30083| . 19991| . 31583| . 20693] 53
8 . 25406, . 17950] . 27008| . 18624 : . 30108] . 200021 . 31607| . 20705} 52
9 25433 179611 . 27035) . 18636 9; „80133| . 200141 . 31632) . 20717) 51
10 | 9. 254600. 17972|9. 27061|0. 18647]9. . 19; . 30158/0. 20026|9. 31657/0. 20729] 50
101 . 25487| . 17983] . 27088| . 18658| . 28653, . 19343| . 30184| . 20037] . 31682| . 20740| 49
12 .25514| . 179951 . 27114! . 186701 . 28679| . 193551 . 30209] . 200491 . 31706| . 20752| 48
13 . 25541) . 18006] . 27140} . 18681] . 28704| . 193661 . 30234) . 20060] . 31731) . 20764| 47
14 . 25568| . 18017] . 27167| . 18692] . 28730| . 193781 . 302591 . 20072] . 31756) . 20776| 46
15 | 9. 25595/0. 18028|9. 27193/0. 18704[9. 28756|0. 19389|9. 30285/0. 20084]9. 31780|0. 20788| 45
16 . 25622| . 18039] . 27219| . 18715| . 28782) . 19401} . 30310| . 20095| . 31805| . 20799| 44
17 . 25649| . 180501 . 27246| . 18727| . 28807) . 194121 . 30335. . 201071 . 31830) . 208111 43
18 .25676| . 18062] . 27272) . 18738| . 28833| . 19424] . 30360, . 201191 . 31854) . 20823| 42
| (19 . 25703| . 18073] . 27298| . 18749] . 28859; . 194351 . 30385} . 20130] . 31879| . 20835| 41
20 | 9. 25729/0. 18084|9. 27325|0. 18761]9. 28885 0. 19447|9. 30410/0. 2014219. 31903|0. 20847| 40
21 „25756| .18095| . 27351| . 18772| . 28910, . 19458] . 30436| . 20154| . 31928) . 208581 39
22 . 25783] . 18106] . 27377| . 18783| . 28936] . 19470] . 30461) . 20165| . 31953| . 208701 38
23 . 25810| . 18118] . 27403| . 18795| . 28962| . 19481| . 30486| . 20177) . 31977| . 20882| 37
24 . 25837| .18129| . 27430| . 18806| . 28987) . 19493| . 30511| . 201891 . 32002, . 20894| 36
25 | 9. 25864/0. 18140|9. 27456/0. 18817|9. 29013|0. 19504]9. 30536|0. 20200|9. 32026|0. 20906| 35
26 . 95891| . 18151] . 27482| . 18829] . 29039| . 19516] . 30561, . 20212] . 32051| . 20918| 34
27 .25917| . 18162] . 27508] . 188401 . 29064! . 19527] . 30586, . 20224] . 32076) . 209291 33
28 . 25944! . 18174] . 27535] . 18852] . 29090| . 19539] . 30611, . 20235] . 32100) . 20941] 32
29 . 25971 18185| . 27561 18863] . 29116| . 19550) . 30636) . 20247] . 32125) . 20953] 31
30 | 9. 25998|0. 18196]9. 27587|0. 18874]9. 29141/0. 1956219. 30662/0. 20259|9. 32149|0. 20965 30
31 | ` 26025] . 18207] . 27613} . 18886] . 29167| . 19573] . 30687, . 20271] . 32174] . 20977] 29
32 | . 26051| . 18219] . 27639] . 18897] . 29192] . 19585] . 30712] . 20282] . 32198] . 20989] 28
33 . 26078] . 18230] . 27666] . 18908] . 29218) . 19597] . 30737) . 20294] . 32223) . 21000) 27
34 . 26105 18241] . 27692} . 189201 . 29244 196081 . 30762| . 20306] . 32247 21012] 26
35 | 9. 26132 0. 18252ļ9. 27718/0. 18931|9. 29269 0. 19620|9. 30787|0. 20317|9. 32272|0. 21024| 25
36 | .26158| . 18263] . 27744] . 18943| . 29295| . 19631] . 30812| . 20329| . 32296| . 21036| 24
37 | .26185| . 18275] . 27770] . 18954] . 29320| . 19643] . 30837, . 20341| . 32321) . 21048| 23
38 . 26212| . 18286| . 27796| . 18965| . 29346 19654] . 30862! . 20352] . 32345, . 21060| 22
39 . 96238| . 18297] . 27822| . 18977| . 29371| . 19666] . 30887| . 20364| . 32370) . 21072) 21
40 9. 2626510. 18308|9. 27848|0. 18988|9. 29397|0. 19677|9. 30912|0. 20376|9. 32394|0. 21083 20
41 -26292| . 18320) . 27875| . 19000] . 29422} . 19689] . 30937| . 20388] . 32418) . 21095 19
42 -26319| . 183311 . 27901| . 19011] . 29448] . 19701] . 30962) . 20399] . 32443) . 21107 18
43 . 26345] . 18342] . 27927] . 19022] . 29473) . 19712) . 30987) . 20411 132467 . 21119} 17
44 . 26372) . 18353] . 27953 19034] . 29499 19724] . 31012] . 20423] . 32492) . 21131} 16
45 | 9. 263980. 18365|9. 2797910. 19045|9. 295240. 19735)9. 3103610. 20435|9. 32516/0. 21143) 15
46 . 26425| . 18376| . 28005| . 19057] . 29550} . 197471 . 31061, . 20446 132541 08921:155| H4
47 . 26452! . 183871 . 28031 190681 . 29575| . 19758] . 31086| . 20458] . 32565 21167| 13
48 .26478| . 18399] . 28057 9080| . 29601) . 19770] . 31111 20470| .32589| . 21178] 12
49 . 26505 18410} . 28083 19091] . 29626) . 19782] . 31136) . 20481] . 32614| . 21190} 11
50 | 9. 2653210. 18421|9. 28109/0. 19102]9. 2965210. 1979319. 31161/0. 20493|9. 32638|0. 21202 10
51 . 26558 184321 . 28135| . 19114] . 29677 19805] . 31186} . 20505] . 32662 2200204] 89
52 . 26585 18444] . 28161! . 19125| . 29703) . 19816; . 31211| .20517| . 32687 21226 8
53 . 26611 18455| . 28187| . 19137] . 29728| . 19828| . 31236| . 20528| . 32711 21238 (
54 . 26638] . 18466] . 28213 19148] . 29753] . 19840] . 31260) . 20540) . 32735) . 21250 EUN]
55 | 9. 266640. 18477|9. 28239|0. 19160|9. 29779 0. 1985119. 31285|0. 20552]9. 32760/0. 21262 5
56 .26691| . 18489] . 28265 9171] . 29804| . 19863} . 31310) . 20564) . 32784] . 21274) 4
57 . 26717| . 18500} . 28291 19183| . 29829] . 19874] . 31335| . 20575] . 32808] . 21285] 3
58 . 26744| . 185111 . 28317 9194) . 29855 19886] . 31360) . 20587] . 32833 21297 2
59 . 26770) . 18523] . 28342) . 19205] . 29880) . 19898] . 31385] . 20599] . 32857 21309 1
60 | 9. 26797|0. 18534|9. 28368|0. 19217]9. 29906|0. 19909[9. 31409/0. 20611|9. 32881 0.21321] 0

1432

TABLE 34

Haversines

55° 56° 57° 58° 59°
1 Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav | Nat. Hav] '
0 | 9. 32881 0. 21321|9. 34322 0. 22040|9. 357330. 22768|9. 37114 0. 23504|9. 38468 0. 24248| 60
1 | .32905| . 21333] . 34346| . 22052] . 35756| . 22780| . 37137 . 23516| . 38490, . 24261| 59
2 | . 32930) . 21345] . 34369| . 22064] . 35779| . 22792] . 37160 . 23529| . 38512! . 24273] 58
3 | .32954 . 21357| . 34393| . 22077] . 35802| . 22805| . 37183| . 23541| . 38535| . 24286| 57
4 | .32978 . 21369] . 34417| . 22089| . 35826| . 22817] . 37205| . 23553| . 38557| . 24298| 56
5 | 9. 33002 0. 21381]9. 34441|0. 22101|9. 358490. 22829|9. 372280. 23566|9. 385790. 24310| 55
6 | .33027 . 21393] . 34464 . 22113] . 35872| . 22841| . 37251! . 23578| . 38602| . 24323| 54
7 | . 83051) . 21405] . 34488| . 22125| . 35895 . 22853] . 37274| . 23590| . 38624 . 24335| 53
8 | .33075| . 21417] . 34512 . 22137] . 35918) . 22866| . 37296| . 23603] . 38646| . 24348| 52
9 |_. 33099) . 21429] . 34535 . 22149| . 35942| . 22878| . 37319 . 23615] . 38668| . 24360| 51
10 | 9. 33123 0. 21440|9. 34559 0. 221619. 359650. 22890|9. 37342 0. 23627|9. 38691 0. 24373| 50
11 | .33148| . 21452) . 34583) . 22173| . 35988| . 22902] . 37364| . 23640] . 38713| . 243851 49
12 | .33172 . 21464] . 34606 . 22185| . 36011| . 22915] . 37387] . 23652] . 38735| . 24398| 48
13 | .33196| . 21476] . 34630| . 22197| . 36034| . 22927] . 37410| . 23665| . 38757 . 24410] 47
14 | .33220 . 21488] . 34654 .22209| . 36058) . 22939| . 37433| . 23677| . 38780| . 24423| 46
15 | 9. 33244 0. 21500|9. 34677 0. 22221|9. 36081 0. 2295119. 37455|0. 23689|9. 388020. 24435| 45
16 | .33268| .21512| .34701 . 22234| . 36104| . 22964] . 37478| . 23702] . 38824| . 24448] 44
17 | .33292 . 21524} . 34725) . 22246| . 36127, . 22976| . 37501| . 23714] . 38846 . 244601 43
18 | .33317 . 21536} . 34748) . 22258| . 36150 . 22988] . 37523| . 23726| . 38868| 24473| 42
19 | .33341 . 21548] . 34772| . 22270| . 36173| . 23000] . 37546 . 23739] . 38891| 244851 41
20 | 9. 33365 0. 21560|9. 34795/0. 22282|9. 361960. 2301219. 375690. 23751|9. 389130. 24498| 40
21 | .33389 . 21572) . 34819) . 22294] . 36219| . 23025| . 37591, . 23764| . 38935| . 24510| 39
22 | .33413 . 21584] . 34843| . 22306] . 36243] . 23037] . 37614| . 23776| . 38957] . 245231 38
23 | .33437| . 21596] . 34866| . 22318| . 36266) . 23049| . 37636 . 23788] 38979! | 24535| 37
24 | .33461 . 21608) . 34890| . 22330] . 36289| . 23061] . 37659| . 23801| . 39002| ` 245481 36
25 | 9. 33485 0. 21620|9. 34913 0. 22343|9. 36312/0. 23074|9. 376820. 2381319. 39024 0. 245601 3
26 | . 33509) . 21632] . 34937] . 22355] . 36335 .23086| . 37704| . 23825| . 39046| 24573 34
27 | - 33533) . 21644) . 34960) . 22367] . 36358} . 23098| . 37727] . 23838] . 39068| . 245851 33
28 | -33557| . 21656) . 34984) . 22379] . 36381) . 23110] . 37749 . 23850] . 39090| . 24598] 32
x . 33581 . 21668) . 35007, . 22391| . 36404 . 23123] | 37772 . 23863] . 39112 24611] 31
0 | 9. 33605/0. 21680|9. 35031/0. 2240319. 364270. 23135|9. 377940. 2387519. 391340. 24
31 | . 33629) . 21692} .35054| . 22415| . 36450! . 23147] . 37817] . 23887| . 39156 ee ^
32 | .33653 .21704|.35078| . 22427] . 36473 . 23160| . 37840 . 23900| . 39178| 24648| 28
33 | -33677| . 21716] .35101 . 22440| . 36496| . 23172] . 37862| | 23919| | 39201 . 24661] 27
x m 21728| . 35125| . 22452| . 36519| . 23184] . 37885| . 23925| . 39223| | 246731 26
- 98725 0. 21740|9. 35148 0. 22464|9. 36542|0. 23196|9. 3790710. 23937: 3 [ 5
36 | .33749| .21752| . 35172, . 22476| . 36565 . 23209| . 37930 eee fate Āā
37 | -33778| . 21764) . 35195| . 22488] . 36588 . 23221| | 37952| | 23962| 39289] 24711 23
38 | .33797|.21776| . 35219) . 22500] . 36611] | 23233| . 37975| 23974| ` 39311 24723| 22
39 | .33821 .21788| . 35242| . 22512] . 36634) | 23246| . 37997| 23987| ` 39333 . 24736| 21
40 9. 33845 0. 21800|9. 35266 0. 22525|9. 366570. 23258|9. 38020 0. 2399919. 3935510, 24749 20
11 | - 33869 .21812|.35289|.22537| . 36680| . 23270| . 38042| . 24012] . 39377 24761| 19
42 | 33893 .21824|.35312 .22549| . 36703 . 23282| ` 38065| | 24024| | 39399 . 24774] 18
43 | - 33917) .21836|.35330| .22561| . 30720, . 23295| . 38087| | 240361 | 39121 ` 24786] 17
= SE 21848) . 35359| . 22573| . 36749] . 23307] . 38110) . 24049] . 39443| ` 247991 16
5 | 9. 5/0. 21860|9. 35383 0. 22585|9. 367720. 2331919. 3813210 1 (
46 | . 33988 . 21872] . 35406] . 22598] . 36794] .23332| . 38154 Sat Soto”, 24811] 15
47 | . 34012) . 21884] . 35429) . 22610] . 36817| . 23344] . 38177| ` 24086 . 39509) . 248361 13
48 | . 34036) . 21896) . 35453 . 22622] . 36840 . 23356] . 38199] ` 24099 39531| . 24849| 12
Lis 5 4000. .21908| 35476) . 22634 . 36863) . 23368| . 38222 =. 24111| . 39553| | 24862] 11
50 | 9. 0. 2192019. 35500 0. 2264619. 36886 0. 23381|9. 38244 0 119. 3c
51 | . 34108) . 21932) . 35523) . 22658| . 36909| . 23393 : 38267) - 24136] 39601]. 24887 K)
92 | :34132 . 21944) . 35546] . 22671] . 36932| . 23405| | 38289! ` 24148 .39619| . 24899] 8
93 | .34155| . 21956) . 35570 . 22683] . 36955 | 23418| 38311) 24161 .39641 . 24919] 7
91 | 34179 . 21968] . 35593 . 22695] . 36977| . 23430| . 38334 | 241731 . 39668 240841 A
55 | 9 34203 0. 21980]9. 35616 0. 22707|9. 37000 0. 23442|9. 38356 0. 2418619 39685/0. 24937| 5
56 - 34227 - 21992 - 35639 -22719 . 37023, .23455| . 38378 .24198| . 39706 . 249501 4
5 e -2 . 35663) . 22731| .37046 . 23467] 3 7
58 34974 . 22016 - 35686 - 22744 . 37069 . 23479 SEU d ES "es CS 2
; ,2 - 35709) .22756| .37091 .23492| . 38445] . 24236| . 39772| 24987] 1
60 9, 943220, 220409. 35733 0. 22768)9. 371140. 23504/9. 38468 0; 2424819, 39794 0. 25000 0
304 3032 3022 3002

301°

602

TABLE 34

Haversines

63°

1433

: Log Hav `
0 | 9. 39794 ; 60
1 . 39816 25013) 04011 51) 25772 . 486388) . 27313] . 44862) . 28095] 59
2 . 39838, . 25025]. 41137) . 25785 . 438658) . 27326] . 44882) . 28108] 58
3 . 39860, . 25038] . 41158) . 25798 . 48679) . 27339] . 44903] . 28121] 57
4 . 89881) . 25050] . 41180] . 25810 . 436991 . 273521 . 44923) . 28134] 56
5 9. 39903|0. 25063|9. 41201/0. 25823|9 43720|0. 273659. 44943|0. 28147] 55
6 „89925| . 25076| . 41222) . 25836 „43741| . 27378] . 44963) . 28160] 54
7 .39947| . 25088] . 41244! . 25849 . 43761) . 27391| . 44983| . 281731 53
8 . 399691 . 251011 . 41265| . 25861 . 43782) . 27404] . 45003, . 28186] 52
9 . 39991) . 25113] . 41287| . 25874 . 43802, . 274171 . 45024) . 28199] 51
10 | 9. 40012/0. 25126|9. 413080. 2588719 „43823|0. 2743019. 45044|0. 28212] 50
11 . 40034) . 25139] . 41329| . 25900 . 43843| . 27443| . 45064| . 28225| 49
12 . 40056| . 25151| . 41351! . 25912 . 43864| . 27456] . 45084| . 282381 48
13 . 40078| . 25164| . 41372) . 25925 . 43884| . 27469| . 45104| . 28252| 47
14 . 40100) . 251771 . 41393] . 25938 . 43905| . 27482| . 45124| . 282651 46
15 | 9. 401210. 25189|9. 41415/0. 2595119 „43926|0. 27495|9. 45144/0. 28278| 45
16 . 40143| . 252021 . 41436] . 25963 .43946| . 27508] . 45165| . 28291] 44
17 . 40165) . 25214] . 41457, . 25976 . 43967| . 27521| . 45185) . 28304] 43
18 . 40187, . 252271 . 41479, . 25989 .43987| . 27534] . 45205) . 28317| 42
19 . 40208, . 252401 . 41500, . 26002 . 44008| . 27547| . 45225| . 28330] 41
20 | 9. 40230)0. 25252|9. 41521|0. 26014ļ9 . 44028/0. 27560|9. 45245|0. 28343] 40
21 . 40252) . 25265] . 41543| . 26027 . 44048] . 27573] . 45265, . 28356| 39
22 . 40274| . 25278| . 41564| . 26040 . 44069} . 27586| . 45285, . 28369] 38
23 . 40295, . 25290| . 41585| . 26053 . 44089| . 275991 . 45305| . 28383] 37
24 . 40317, . 25303] . 41606| . 26065 . 44110| . 27612] . 45325) . 28396] 36
25 | 9. 40339/0. 25316]9. 41628/0. 26078|9 . 44130/0. 27625|9. 453450. 28409| 35
26 . 403601 . 25328] . 41649| . 26091 „44151| . 27638] . 45365 . 28422] 34
27 .40382| . 25341] . 41670) . 26104 .44171| . 27651] . 45385) . 28435] 33
28 . 40404) . 25354] . 41692) . 26117 . 44192) . 27664] . 45405) . 28448] 32
29 . 40425) . 25366] . 41713) . 26129 . 44212) . 276771 . 45426) . 28461] 31
30 | 9. 40447/0. 2537919. 417340. 26142]9 . 4423210. 2769019. 454460. 28474] 30
31 .40469| . 25391] . 41755| . 26155 .44253| . 27703] . 45466| . 28488] 29
92 . 40490, . 25404] . 41776| . 26168 . 44273] . 27716] . 45486. . 28501] 28
33 . 40512| . 25417] . 41798) . 26180 . 44294] . 27729] . 45506} . 28514] 27
34 . 40534) . 25429] . 41819] . 26193 .44314| . 27742] . 45526) . 28527] 26
35 | 9. 40555/0. 2544219. 418400. 26206|9 . 44334/0. 27755|9. 45546/0. 28540) 25
36 . 40577| . 25455] , 41861| . 26219 .44355| . 27768] . 45566, . 28553] 24
37 . 40599| . 25467] . 41882) . 26232 . 44375] . 27781] . 45586} . 28566] 23
38 . 40620] . 25480] . 41904| . 26244 . 44396) . 27794] . 45606) . 28580] 22
39 . 40642| . 25493] . 41925) . 26257 . 44416] . 27807] . 45625, . 28593] 21
40 | 9. 40663/0. 25506]9. 419460. 26270]9 . 44436/0. 27820]9. 45645|0. 28606] 20
41 „40685| . 25518] . 41967| . 26283 .44457| . 27833] . 45665) . 28619] 19
42 . 40707| . 25531] . 41988) . 26296 „44477| . 27846] . 45685) . 28632] 18
43 . 40728) . 25544] . 42009] . 26308 . 44497) . 27859] . 45705) . 28645] 17
44 . 40750) . 25556] . 42031) . 26321 . 44518] . 27873] . 45725) . 28658] 16
45 | 9. 40771/0. 25569|9. 42052/0. 263349 . 44538/0. 27886|9. 45745|0. 28672| 15
46 . 40793| . 25582] . 42073| . 26347 . 44558) . 27899| . 45765| . 28685| 14
47 . 40814| . 25594] . 42094) . 26360 „44579| . 27912] . 45785) . 28698] 13
48 . 40836] . 256071 . 42115) . 26372 . 44599| . 27925] . 45805) . 28711] 12
49 . 40858) . 25620] . 42136) . 26385 . 44619] . 27938] . 45825) . 28724] 11
50 | 9. 4087910. 25632]9. 42157|0. 26398|9 9. 4463910. 2795119. 45845|0. 28737] 10
51 . 40900, . 25645] . 42178) . 26411 . 44660] . 27964] . 45865] . 28751] 9
52 . 40922) . 25658] . 42199) . 26424 7| . 44680] . 27977] . 45884 . 28764 8
53 . 40943| . 25671] . 42221) . 26437 . 447001 . 279901 . 45904| . 28777 7
54 . 40965! . 25683] . 42242) . 26449 . 44721| . 28003] . 45924) . 28790] 6
55 | 9. 409860. 25696]9. 42263|0. 26462|9 . 44741/0. 28016]9. 4594410. 28803| 5
56 „41008! . 25709] . 42284| . 26475 . 44701. . 28029] . 45964 . 28816 4
an . 41029] . 25721| . 42305) . 26488 .44781| . 28042| . 45984| . 28830| 3
58 . 41051| . 25734] . 42326) . 26501 . 44801! . 28055} . 46004| . 28843| 2
59 . 41072! . 25747| . 42347) . 26514] . ( i „44822! . 28068] . 46023| . 28856| 1
60 . 4109440. 3019. 42368/0. 26526|9. 43617/0. 27300 . 4484210. 28081|9. 46043/0, 28869 0

299?

298?

297?

296?

295?

1434

TABLE 34

Haversines

65°

67°

69°

105 PPR A ege. [Xm

: Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav | Nat. Hav | Nat. Hav| Log Hav | Nat. Hav Y
0 | 9. 46043 0. 28869]9. 47222 0. 29663|9. 48378 0. 31270|9. 50626 0. 32082| 60
1| . 46063) . 28882] . 47241! . 29676| . 48397. . 30477 .50644| . 32095| 59
2 | .46083| . 28895] . 47261| . 29690] . 48416| . 30490 . 50662, . 32109| 58
3 | .46103 . 28909] . 47280) . 29703] . 48435 . 30504] . ` 50681| . 32122] 57
4 | .46123| . 28922| . 47300) . 29716] . 48454| . 30517] . 49587| . 31324| . 50699| . 32136| 56
5 | 9. 46142 0. 28935|9. 47319 0. 29730|9. 48473 0. 3053019. 49606 0. 31337|9. 50717 0. 32150| 55
6 | .46162 .28948| . 47338, . 29743| . 48492| . 30544| . 49625 . 31351| . 50736 . 32163| 54
7 | .46182|.28961| . 47358 . 29756| . 48511 . 30557| . 49643| . 31364] . 50754 . 32177| 53
8 | . 46202) . 28975] . 47377| . 29770| . 48530| . 30571] . 49662 . 31378| . 50772 . 32190] 52
9 | .46222| . 28988] . 47397 . 29783| . 48549 . 30584| . 49681| . 31391] . 50791| . 32204| 51
10 | 9. 46241 0. 29001|9. 47416 0. 297969. 48568 0. 30597|9. 49699 0. 31405|9. 50809 0. 32217| 50
11 | . 46261) . 29014] . 47435| . 29809| . 48587| . 30611] . 49718 . 31418] . 50827 . 32231| 49
12 | .46281| . 29027] . 47455| . 29823] . 48607| . 30624| . 49737 . 31432] . 50846! . 32245| 48
13 | .46301| . 29041] . 47474| . 29836] . 48626| . 30638] . 49755| . 31445| . 50864| . 32258] 47
14 | .46320 . 29054] . 47493| . 29849| . 48645| . 30651] . 49774 . 31459| . 50882 . 32272] 46
15 | 9. 46340 0. 29067|9. 47513 0. 29863|9. 48664 0. 30664|9. 49793 0. 3147219. 50901 0. 32285| 45
16 | . 46360) . 29080] . 47532 . 29876] . 48683, . 30678| . 49811 . 31486] . 50919 . 32299| 44
17 | .46380 .29093| .47552 .29889| . 48702. . 30691| . 49830, . 31499] . 50937 . 32313| 43
18 | .46399| . 29107] . 47571| . 29903| . 48720| . 30705| . 49849 . 31513] . 50956| . 32326] 42
19 | .46419 . 29120] . 47590, . 29916] . 48739) . 30718] . 49867) . 31526| 50974! . 32340] 41
20 | 9. 46439 0. 29133]9. 47610 0. 29929|9. 48758 0. 3073219. 4988610. 3154019. 509920. 32353] 40
21 | .46458 . 29146] . 47629| . 29943| . 48777) . 30745| . 49904 . 31553] . 51010! . 32367] 39
22 | .46478 . 29160] . 47648) . 29956| . 48796 . 30758| . 49923! . 31567| . 51029 . 32381| 38
23 | .46498 . 29173] . 47668| . 29969| . 48815| . 30772| . 49942 . 31580| . 51047| . 32394| 37
24 | .46517 .29186| . 47687| . 29983| . 48834| . 30785| . 49960 . 31594] . 51065. . 32408| 36
25 | 9. 465370. 29199|9. 47706 0. 29996|9. 48853 0. 30799|9. 49979 0. 31607|9. 51083 0. 324221 3
26 | . 46557) . 29212) . 47725) . 30009| . 48872 . 30812] . 49997| . 316211 . 51102| 32435 Së
27 | .46576| . 29226| . 47745| . 30023] . 48891 . 30826] . 50016) . 31634] . 51120| . 32449] 33
28 | .46596| . 29239] . 47764| . 30036] . 48910 . 30839] . 50034 . 31648] . 51138! . 32462] 32
2 . 46616| . 29252| . 47783| . 30049| . 48929) . 30852| . 50053| . 31661] . 51156. . 32476| 31
9. 46635 0. 29265|9. 47803 0. 30063|9. 48948 0. 30866|9. 50072 0. 3167519. 51174 0. 32
31 | .46655|.29279| . 47822| . 30076| . 48967| . 30879| . 50090 . 31688| . 51193 TAG a
32 | . 46675) . 29292] . 47841 . 30089] . 48986 . 30893] . 50109 . 31702] . 51211. 32517] 28
33 | .46694 . 29305] . 47860) . 30103| . 49004) . 30906| . 50127| . 31716] . 51229| 32531| 27
; . 46714 . 29318] . 47880 . 30116] . 49023| . 30920] . 50146 . 31729] ` 51247) . 32544] 26
9. 46733 0. 29332|9. 47899/0. 30129|9. 490420. 3093319, 50164 0. 3174319. 51265
36 | . 46753] . 29345] . 47918] . 30143] . 49061] . 30946] . 50183 VM Aron e E
37 | .46773| .29358| . 47937| . 30156| . 49080| . 30960] . 50201| . 317701 ` 51302) . 32585| 23
38 | . 46792) . 29371) . 47957] . 30169| . 49099| . 30973| ` 50220| . 31783| ` 51320| | 32590| 22
7 . 46812| . 29385] . 47976| . 30183] . 49118| . 30987] . 50238! . 31797| ` 51338 32612| 21
9. 46831/0. 2939819. 47995/0. 30196|9. 491370. 31000|9. 50257 0. 3181 5
41 | .46851 .29411| . 48014! . 30209] . 49155 . 31014] ` 50275 ed Ti
42 | . 46871) . 29424) . 48033} . 30223] . 49174| . 31027] . 50294 . 31837| 51303 32653| 18
43 | .46890| . 29438) . 48053| . 30236| . 49193| . 31041| . 50312 . 31851] . 51411. 32667] 17
: 46910] . 29451 . 48072) . 30249| . 49212| . 31054] . 50331 . 31865] . 51429) . 326811 16
5929 0, 2 3026319. 192310 310
15 9- 16020 0. 2046419. 48091 0. 30263/9. 49231 0. 31068|9. 50349 0. 31878)9. 51447 0. 32694 15
)| . 2t . 48110 . 30276| . 49250| . 31081| . 50368 . 31892] ` 51465 . 32708| 14
47 | .46968 . 29491) . 48129) . 30290] . 49268 . 31094| . 50386! . 31905] . 51483 . 327211 13
48 | .46988 .29504|.48148| . 30303| . 49287) . 31108] . 50405 . 31919] 51501 _ 327351 12
49 | .47007, .29517| . 48168 . 30316] . 49306 . 31121| . 50423. . 31932] 51519 . 307491 11
90 | 9. 47027 0. 295309. 48187 0. 30330|9. 49325 0. 31135|9. 50442 0. 31946|9. 51538 0. 32762| 10
51 | . 47046 . 29544] . 48206 .30343| . 49344 . 31148] . 50460| . 31959| . 51556 . 327761 9
92 | - 47066 _. 29557] . 48225 . 30356| . 49362 . 31162] . 50478. 31973] | 51574 . 327901 8
53 | .47085 . 29570] . 48244 . 30370] . 49381 . 31175] . 50497 . 31987] 51 :
M E 2 497 . 31987] . 51592) . 32803| 7
zap. a7 105 120083 (R03 0888 . 49400) . 31189] . 50515) . 32000] . 51610 . 32817] 6
99 | 9. 47124 0. 2959719. 48282 0. 3039719. 49419 0. 31202|9. 50534 0. £ c 0. 3:
56 ` 47144] 29610 - 48302) . 30410 . 49437| . 31216 Neri erties Mca gp cc 4
Ë : | . 29623] . 48321 . 30423] . 49456 . 31229] 50570 32 Ros
58 - 17183) . 20637 18840 . 30437 . 49475 . 31243] . 50589 E E eme E
$9. loot 2|. 29650} . 48359 . 30450| . 49494. . 31256| . 50607! . 32068| . 51700 . 32885
€ O. € a [E E S | . H D 1
60 9. 47222 0. 29663)9. 48378 0. 30463|9. 49512 0. 31270]9. 50626 0. 320829. 51718 0. 32899 0

294°

293°

292°

291°

290°

1435

TABLE 34
Haversines
70° 71° T2 73° 74°

+ Log Hav | Nat. Hav} Log Hav | Nat. Hav | Log Hav | Nat. Hav| Log Hav | Nat. Hav] Log Hav | Nat. Hav} '
O | 9. 517180. 32899|9. 527910. 33722|9. 53844 0. 34549|9. 54878 0. 3538119. 55893|0. 36218] 60
1 | .51736| .32913| . 52809| . 33735] . 53861. . 34563] . 54895) . 35395| . 55909| . 36232] 59
2 | .51754| . 32926] . 52826| . 33749] . 53879| . 34577] . 54912| . 35409] . 55926| . 36246] 58
3 | .51772| . 32940] . 52844| . 33763] . 53896| . 34591] . 54929| . 35423] . 55943| . 36260) 57
4 | . 51790) . 32954] . 52862) . 33777] . 53913, . 34604] . 54946] . 35437] . 55960, . 36274] 56
5 | 9. 51808/0. 32967]9. 52879/0. 33790|9. 53931 0. 3461819. 54963/0. 3545119. 5597610. 36288] 55
6 | . 51826) . 32981] . 52897) . 33804] . 53948 . 34632] . 54980. . 35465] . 55993] . 36302) 54
7 | .51844| . 32995] . 52915| . 33818] . 53966) . 34646] . 54997 . 35479] . 56010] . 36316} 53
8 | . 51862) . 33008] . 52932) . 33832] . 53983) . 34660] . 55014 . 35493] . 56027] . 36330) 52
9 | . 51880) . 33022) . 52950) . 33845] . 54000) . 34674] . 55031) . 35507) . 56043) . 36344) 51
10 | 9. 51898 0. 33036|9. 52968 0. 33859|9. 54017/0. 34688]9. 55048|0. 3552119. 56060/0. 36358] 50
11 | . 51916) . 33049] . 52985! . 33873] . 54035| . 34701] . 55065) . 35534] . 56077| . 36372] 49
12 | . 51934! . 33063] . 53003 . 33887] . 54052] . 34715] . 55082) . 35548] . 56093] . 36386] 48
13 | . 51952) . 330771 . 53021| . 33900] . 54069! . 34729] . 55099] . 35562] . 56110) . 36400] 47
14 | . 51970) . 33090} . 53038) . 33914] . 54087 . 34743] . 55116 . 35576] . 56127 . 36414] 46
15 | 9. 51988 0. 33104|9. 53056 0. 33928]9. 5410410. 34757|9. 55133|0. 35590|9. 56144|0. 36428] 45
16 | .52006| . 33118] . 53073) . 33942] . 54121| . 34771] . 55150| . 35604] . 56160] . 36442] 44
17 | . 52024) . 33132] . 53091) . 33956] . 54139) . 34784] . 55167] . 35618] . 56177, . 36456] 43
18 | . 52042) . 33145] . 53109) . 33969] . 54156! . 34798] . 55184! . 35632] . 56194) . 36470] 42
19 | . 52060) . 33159] . 53126) . 33983] . 54173! . 34812] . 55201| . 35646] . 56210) . 36484] 41
20 | 9. 52078 0. 33173|9. 53144/0. 33997|9. 541900. 34826|9. 55218 0. 3566019. 562270. 364981 40
21 | .52096| . 33186] . 53162| . 340111 . 54208| . 34840] . 55235) . 35074| . 56244| . 36512] 39
22 | .52114| . 332001 . 53179| . 34024| . 54225| . 34854| . 55252| . 35688] . 56260] . 36526| 38
23 | . 52132) . 33214] . 53197) . 34038| . 54242) . 34868| . 55269| . 35702| . 56277, . 365401 37
24 | .52150| . 33227] . 53214! . 34052| . 54260| . 34882] . 55286] . 35716] . 56294| . 36554] 36
25 | 9. 521680. 33241|9. 53232 0. 34066|9. 54277 0. 34895|9. 55303 0. 35730|9. 56310 0. 36568| 35
26 | .52185| . 33255] . 53249| . 34080] . 54294| . 34909] . 55320! . 35743| . 56327) . 36582| 34
27 | .52203| . 33269] . 53267| . 34093] . 54311| . 34923] . 55337, . 35757| . 56343) . 36596| 33
28 | .52221| . 33282] . 53285| . 34107| . 54329 . 34937| . 55354| . 35771) . 56360, . 36610) 32
29 | .52239| . 33296] . 53302) . 34121| . 54346| . 34951| . 55370) . 35785| . 56377, . 36624| 31
30 | 9. 52257 0. 33310|9. 53320 0. 34135|9. 54363/0. 34965|9. 55387 0. 35799|9. 56393 0. 36638| 30
31 | .52275| . 33323] . 53337| . 34149| . 54380. . 34979] . 55404| . 35813] . 56410) . 36652| 29
32 | .52293| . 33337] . 53355 . 34162| . 54397| . 34992| . 55421 . 35827| . 56426) . 36666) 28
33 | .52311| . 33351) . 53372| . 34176| . 54415| . 35006] . 55438, . 35841] . 56443) . 36680] 27
34 | .52328 .33365| . 53390) . 34190| . 54432) . 35020| . 55455| . 35855| . 56460, . 36694| 26
35 | 9. 52346 0. 33378|9. 53407 0. 34204]9. 54449 0. 35034|9. 55472 0. 35869|9. 56476 0. 36708| 25
36 | .52364| . 33392] . 53425| . 34218| . 54466 . 35048| . 55489 . 35883| . 56493 . 36722) 24
37 | .52382 . 33406] . 53442 . 34231] . 54483| . 35062| . 55506 . 35897] . 56509 . 36736| 23
38 | .52400 . 33419] . 53460 . 34245| . 54501| . 35076| . 55523 . 359111 . 56526) . 36750| 22
39 | .52418 . 33433] . 53477) . 34259| . 54518| . 35090| . 55539) . 35925| . 56543 . 36764| 21
40 | 9. 52436 0. 33447|9. 53495 0. 34273|9. 54535 0. 35103|9. 55556 0. 35939|9. 56559 0. 36778| 20
41 | .52453 ` 33461 . 53512, .34287| . 54552) . 35117| . 55573 . 35953| . 56576) . 36792| 19
42 | .52471| . 33474| . 53530| . 34300| . 54569| . 35131| . 55590| . 35967] . 56592, . 36806| 18
43 | .52489| . 33488] . 53547| . 34314| . 54587| . 35145| . 55607| . 35981] . 56609 . 36820| 17
44 | .52507 .33502| . 53565 . 34328| . 54604 . 35159| . 55624 . 35995 . 56625) . 36834] 16
45 | 9. 52525 0. 33515|9. 535820. 343429. 54621 0. 35173|9. 55641/0. 36009|9. 56642 0. 36848] 15
46 | .52542| . 33529] . 53600} . 34356] . 54638) . 35187| . 55657, . 36023| . 56658 . 36862| 14
47 | .52560| . 33543] . 53617 . 34369] . 54655| . 35201| . 55674 . 36036] . 56675 . 36877) 13
48 | . 52578 . 33557] . 53635 . 34383| . 54672) . 35215| . 55691, . 360501 . 56692) . 36891) 12
49 | .52596 .33570| . 53652, . 34397| . 51689 . 35228) . 55708 . 36064 . 56708) . 36905] 11
5261310. 33584|9. 536700. 34411|9. 54707 0. 3524219. 55725 0. 36078|9. 56725 0. 36919) 10

E ae ` 33598] . 53687| . 34425| . 54724| . 35256] . 55742). 36092) . 56741) . 36933) 9
52 | .52649| . 336121 . 53704| . 34439] . 54741| . 35270] . 55758) . 36106) . 56758) . 36947) 8
53 | .52667| . 33625] . 53722| . 34452) . 54758) . 35284] . 55775 . 36120) . 56774) . 36961] 7
54 | 52684 . 33639] . 53739| . 34466] . 54775! . 35298] . 55792 . 36134] . 56791) . 36975] 6
SSES : ADIN 9E91« 1 I 96148 ERRNTIO : 9 5

9. 52702 0. 33653|9. 53757 0. 34480|9. 547920. 35312|9. 55809 0. 36148|9. 56807 0. 3698:
5 ` 52720 ` 33667] . 53774) . 34494] . 54809| . 35326] . 55826 . 36162) . 56824 . 37003] 4
57 | ` 52738| . 33680] . 53792| . 34508] . 54826| . 35340] . 55842 . 36176} . 56840) . 37017 3
58 | . 52755| . 33694] . 53809| . 34521] . 54843| . 35354| . 55859| . 36190 . 56856 . 37031 2
59 | .52773| . 33708] . 53826| . 34535] . 54860| . 35368] . 55876 . 36204 . 56873 . 37045 1
60 9. 527910. 337229. 53844 0. 34549|9. 54878/0. 35381|9. 55893 0. 36218|9. 56889 0. 37059 0
289° 288° 287° 286° 285°

x
sE. |

1436
TABLE 34
Haversines
75° 76° e 78? 79*
$ Log Hav | Nat. Hav| Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav Log Hav | Nat. Hav| '
0 | 9. 568890. 37059|9. 57868|0. 379049. 58830/0. 38752|9. 597740. 39604]9. 6070210. 40460] 60
1 .56906| . .57885| . .58846| . 38767| . 59790| . 39619] .60717| . 40474] 59
2 .66922| . . 57901) . . 58862] . 38781] . 59806) . 39633] . 60733] . 40488| 58
3 . 56939] . Tórð .58878| . 387951 . 598211 . 396471 . 60748| . 40502 57
4 . 56955) . . 57933 . 58893] . 38809] . 59837| . 39661] . 60763! . 40517] 56
5 | 9. 56972|0. 37129/9. 5794910. . 58909/0. 38823|9. 59852/0. 39676|9. 60779/0. 40531] 55
6 .56988| . . 57965) . . 68925) . 38837] . 59868) . 39690] . 60794! . 40545) 54
T . 57005 . 57981) . . 589411 . 38852] . 59883) . 39704] . 60809! . 40560] 53
8 . 57021) . . 57998} . . 58957] . 38866] . 59899) . 39718] . 60825! . 40574] 52
9 - 54037, . . 58014 . . 58973) . 38880} . 59915) . 39732] . 60840} . 40588] 51
10 | 9. 57054/0. 37 „580300. 9. 58989|0. 38894|9. 59930|0. 39747|9. 60855|0. 40602] 50
11 . 57070) .: . 58046} . . 59004] . 389081 . 59946| . 39761] . 60870] . 40617] 49
12 . 57087] . . 58062] . . 9020| . 38923] . 59961] . 39775] . 60886] . 40631] 48
13 . 57103) . . 58078) . . 59036) . 38937] . 59977] . 39789] . 60901! . 40645] 47
14 . 57119} . . 68094) . . 59052 . 38951] . 599921 . 39804) . 60916] . 40660] 46
15 | 9. 57136)0. . 581100. . 59068/0. 38965|9. 60008/0. 39818|9. 60931/0. 40674] 45
16 71521. 158126). . 59083) . 38979] . 60023| . 39832] . 60947| . 40688] 44
17 . 57169) . . 58143] . . 59099} . 38994] . 60039} . 39846] . 60962) . 40702] 43
18 . 57185 . 58159} . . 59115] . 39008| . 60054! . 39861] . 60977] . 40717] 42
19 . 57201 . 68175). . . 59131] . 39022] . 60070] . 39875] . 60992! . 40731) 41
20 | 9. 57218|0. . 5819140. . 591470. 39036|9. 60085/0. 39889|9. 61008/0. 40745| 40
EA STEE .58207| . . 59162| . 390501 . 60101} . 39903] . 61023| . 40760| 39
22 .57250|. . 58223) . . 59178) . 39064] . 60116} . 39918] . 61038] . 40774] 38
23 . 97267] . . 58239] .: . 59194) . 39079] . 60132] . 39932] . 61053] . 40788] 37
24 . 57283 . 58255)! . 59210} . 39093] . 60147] . 39946] . 61069 . 40802} 36
25 | 9. 572990. - 58271/0. . 59225/0. 39107|9. 60163|0. 39960|9. 61084|0. 40817| 35
26 TOLI LO .58287| . . 59241| . 39121] . 60178] . 39975] . 61099] . 40831] 34
27 325/292 . 68303) . § . 59257) . 39135] . 60194] . 39989] . 61114] . 40845 33
28 . 57348) . . 58319} . . 59273) . 391501 . 60209] . 40003] . 61129] . 40860 32
29 . 57365} . 2908999| 9€ . 59289) . 39164] . 60225| . 400171 . 61145| . 40874 al
30 | 9. 5738110. 9. 5835110. . 593040. 39178|9. 60240/0. 40032]9. 6116010. 40888 30
31 2508973 . 68367) . . 59320) . 39192] . 60256] . 40046] . 61175! . 40903 29
82 .507414|.: . 58383 . 59336] . 39206] . 60271| . 40060] . 61190 . 40917] 28
33 . 97430) . .58399| .: . 59351] . 392211 . 60287| . 40074) . 61205 . 40931] 27
34 . 57446) .: . 58415) .: . 59367] . 39235] . 60302] . 400891 . 61221 . 40945} 26
29 9. 57463|0. 37 . 5843110. : . 593830. 3924919. 60318/0. 40103|9. 61236/|0. 40960 25
36 .94479| . < . 58447) .: -59399| . 39263] . 60333| . 401171 . 61251 . 40974] 24
SWA . 97495 sË . 58463) . . 59414) . 39277] . 60348] . 401311 . 61266 . 40988} 23
38 . 57511 . 58479) . < . 59430) . 39292] . 60364] . 401461 . 61281 . 41003] 22
39 57528) .: . 58495) .: . 59446} . 39306} . 60379] . 40160 . 61296] . 41017] 21
40 | 9. 5754410. : 9. 5851110. < 9. 59461/0. 39320]|9. 603950. 40174|9. 61312/0. 41031 20
41 - 97560 M . 58527 -59477| . 39334] . 60410| . 40188 . 61327| . 41046] 19
42 57577 97 „68543|.: . 59493) . 39348] . 60426| . 40203 . 61342) . 41060] 18
43 : 97593 - 3/664) . 58559) .: -59508| . 39363] . 60441| . 40217 . 61357| . 41074| 17
44 .57609| .: .98575| .: . 59524 39377| . 60456| . 402311 . 61372 . 410891 16
45 | 9. 576250. 9. 5859110. < . 5954010. 3939119. 60472/0. 40245|9. 6138710. 41103 15
46 - 97642 A . 08607| .: . 59556} . 39405] . 60487| . 40260 . 61402| . 41117] 14
41 - 97658 377 . 58623 . 99571} . 394201 . 60502| . 40274 . 61417} . 41131] 13
48 . 97674 En .58639| . < . 59587| . 39434| . 60518] . 40288 . 61433) . 41146| 12
49 191690 oe . 58655] .: . 59602} . 39448] . 60533} . 40303 . 61448} . 41160] 11
50 | 9. 57706 0. 37763|9. 58671|0. : . 596180. 394629. 60549 /0. 4031719. 61463|0. 41174] 10
51 - 57723 R . 58687 . 59634| . 39476] . 60564! . 40331 . 61478) . 41189] 9
92 - 57739 - 58703 : . 59649 394911 . 60579] . 40345) . 61493 . 41203] 8
53 : 97755 See . 98719 Gë . 59665) : 395051 . 60595! . 40360 261508 41217 7
54 SU - 58735 Sí . 59681] . 39519] . 60610 40374] . 61523| . 41232] 6
p 9. 57787 0. 37833|9. 58750/0. : 9. 59696 0. 39533|9. 60625 0. 40388|9. 615380. 41246| 5
56 | .57804| .37847| . 58766) . - 59712 .39548| .60641| . 40402] . 61553 ` 41260] 4
CH ERE d - 98782 d . 59728 . 39562 . 60656} . 40417] . 61568) . 41275 3
4 EEN -37 - 58798 -i : 59743 39576| . 60671) . 40431 . 61583| . 41289] 2
ae 5 H . 98814 E . 59759 . 39590 .60687| . 40445} . 61598 .41303| 1
9. 5786810. : . 5883010. : - 597740. 39604|9. 607020. 4046019. 616140. 41318 0
284? 283? 282? 281?

280?

STREIT

80°

TABLE 34

Haversines

81°

82°

83°

Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav Log Hav

84?

Nat. Hav| Log Hav | Nat. Hav

1437

0 | 9. 61614 0. 41318|9. 625090. 42178|9. 63389 0. 43041]9. 64253/0. 43907|9. 65102/0. 44774] 60

1 . 61629} . 41332] . 62524| . 42193] . 63403] . 43056] . 64267| . 439211 . 65116| . 44788] 59
2 . 61644) . 41346] . 62538| . 42207| . 63418| . 43070] . 64281| . 43935] . 65130| . 44803] 58

3 . 61659| . 41361] . 62553| . 42221] . 63432| . 43085| . 64296| . 43950| . 65144| . 44817| 57
4 . 61674| . 41375| . 62568| . 42236] . 63447] . 43099] . 64310] . 43964] . 65158| . 44831| 56

5 | 9. 61689/0. 41389|9. 62583|0. 42250|9. 63461/0. 43113|9. 64324|0. 43979|9. 65172/0. 44846] 55

6 . 61704, . 41404| . 62598) . 42264] . 63476| . 43128] . 64339| . 43993] . 65186] . 44860] 54

7 . 61719) . 41418| . 62612) . 42279] . 63490| . 43142] . 64353| . 44008] . 65200! . 44875| 53

8 . 61734) . 414321 . 62627| . 42293| . 63505) . 43157| . 64367| . 44022| . 65214| . 44889| 52

9 . 61749| . 41447] . 62642| . 42308] . 63519 . 43171] . 64381| . 44036| . 65228| . 44904| 51
10 | 9. 617640. 41461|9. 62657/0. 42322|9. 63534/0. 43185|9. 64396|0. 44051|9. 65242|0. 44918| 50
11 . 61779| . 41475| . 62671| . 42336] . 63548 . 432001 . 64410| . 44065| . 65256| . 44933] 49
12 . 61794| . 41490] . 62686) . 42351] . 63563, . 43214| . 64424| . 44080] . 65270| . 44947| 48
13 . 61809| . 41504| . 62701| . 42365) . 63577, . 43229| . 64438| . 44094] . 65284| . 44962| 47
14 . 61824| . 41518] . 62716| . 42379) . 63592) . 43243| . 64452| . 44109] . 65298| . 44976] 46
15 | 9. 618390. 41533|9. 62730|0. 42394|9. 63606 0. 43257|9. 64467|0. 44123|9. 65312/0. 44991] 45
16 . 61854| . 41547| . 62745| . 424081 . 63621) . 43272| . 64481| . 44138] . 65326] . 45005] 44
17 . 61869| . 415611 . 62760) . 42423| . 63635| . 43286| . 64495| . 44152] . 65340| . 45020| 43
18 . 61884| . 41576| . 62774| . 42437| . 63649| . 43301] . 64509| . 44166| . 65354| . 45034| 42
19 . 61899) . 41590| . 62789| . 424511 . 63664| . 43315| . 64523| . 44181] . 65368 . 45048| 41
20 | 9. 61914/0. 41604|9. 62804 0. 42466]9. 63678/0. 43330]9. 64538|0. 44195|9. 65382|0. 45063| 40
21 . 61929| . 41619] . 62819| . 42480| . 63693) . 43344| . 64552) . 44210] . 653906, . 45077| 39
22 . 61944| . 416331 . 62833| . 42494) . 63707| . 43358] . 64566| . 442241 . 65410] . 45092| 38
23 . 61959] . 416471 . 62848| . 425091 . 63722| . 43373] . 64580) . 44239| . 65424| . 45106| 37
24 . 61974, . 41662] . 62863) . 42523] . 63736, . 43387] . 64594) . 44253] . 65438] . 451211 36
25 | 9. 619890. 41676|9. 62877/0. 42538|9. 63751|0. 43402]9. 646090. 44268|9. 65452|0. 45135| 35
26 . 62003| . 41690] . 62892| . 425521 . 63765| . 43416] . 64623) . 44282] . 65466| . 45150| 34
27 . 62018] . 41705| . 62907) . 42566| . 63779) . 43430| . 64637| . 44296| . 65480] . 45164| 33
28 . 62033, . 41719| . 62921, . 42581] . 63794| . 43445| . 64651| . 443111 . 65493) . 45179| 32
29 . 62048) . 41733] . 62936, . 42595] . 63808| . 43459] . 64665| . 44325| . 65507, . 45193) 31
30 | 9. 62063|0. £1748|9. 62951|0. 42610|9. 638230. 43474|9. 646790. 44340|9. 65521|0. 45208] 30
31 . 62078, . 41762| . 62965 . 42624] . 63837| . 43488| . 64694| . 44354] . 65535) . 45222| 29
32 . 62093| . 41776| . 62980| . 42638| . 63851| . 43503] . 64708| . 44369| . 65549| . 45237] 28
33 . 62108| . 417911 . 62995| . 42653] . 63866| . 43517] . 64722| . 44383| . 65563| . 45251] 27
34 . 62123| . 41805| . 63009| . 42667] . 63880) . 435311 . 64736) . 44398| . 65577, . 45266| 26
35 | 9. 621380. 41819|9. 6302410. 42681|9. 638950. 43546|9. 64750|0. 44412|9. 65591/0. 45280| 25
36 . 62153| . 41834] . 63039| . 42696| . 63909) . 43560| . 64764) . 44427| . 65605) . 45295] 24
37 . 62168] . 41848] . 63053| . 42710| . 63923| . 43575| . 64778, . 44441| . 65619) . 45309) 23
38 . 62182] . 41862] . 63068, . 42725| . 63938| . 43589] . 64793, . 44455| . 65632| . 45324| 22
39 . 62197, . 41877] . 63082, . 42739| . 63952| . 43603] . 64807, . 44470] . 65646| . 45338| 21
40 | 9. 62212/0. 41891|9. 630970. 42753|9. 63966/0. 43618]9. 64821|0. 44484|9. 65660/0. 45353| 20
41 . 62227| . 41905| . 63112 . 42768] . 63981| . 43632] . 64835| . 444991 . 65674 . 45367| 19
42 . 62242| . 419201 . 63126, . 42782] . 63995| . 43647| . 64849| . 44513| . 65688| . 45381] 18
43 . 62257| . 41934] . 63141. 42797] . 64010] . 43661] . 64863] . 44528] . 65702 . 45396| 17
44 . 62272| . 41949] . 63156, . 42811] . 64024! . 43676] . 64877) . 44542] . 65716] . 45410) 16
45 | 9. 62287/0. 41963|9. 63170/0. 42825|9. 64038|0. 43690|9. 648910. 44557|9. 65729|0. 45425) 15
46 . 62301| . 41977] . 63185| . 42840] . 64058| . 43704] . 64905| . 44571| . 65743) . 45439) 14
47 . 62316) . 41992] . 63199| . 42854] . 64067) . 43719] . 64919| . 44586| . 65757, . 45454] 13
48 . 62331] . 42006] . 63214| . 42869] . 64081| . 43733] . 64934| . 44600] . 65771, . 45468| 12
49 . 62346| . 42020] . 63228) . 42883] . 64096| . 43748| . 64948| . 44614] . 65785| . 45483) 11
50 | 9. 62361|0. 42035|9. 63243|0. 42897|9. 64110|0. 43762|9. 64962|0. 44629|9. 65799|0. 45497 10
51 . 62376| . 42049| . 63258| . 42912] . 64124| . 43777| . 64976) . 44643| . 65812|. 45512 9
52 „62390| . 42063] . 63272| . 42926] . 64139| . 43791] . 64990| . 44658] . 65826| . 45526| 8
53 . 62405| . 42078| . 63287, . 42941] . 64153| . 43805| . 65004| . 44672| . 65840|. 45541 7
54 . 62420| . 42092] . 63301) . 42955| . 64167] . 43820} . 65018| . 44687] . 65854 . 45555] 6
55 | 9. 624350. 4210619. 63316|0. 42969|9. 64181/0. 43834|9. 650320. 4470119. 658680. 45570| 5
56 . 62450| . 421211 . 63330 . 42984] . 64196| . 438491 . 65046) . 44716) . 65881) . 45584] 4
57 . 62464| . 42135] . 63345 . 42998} . 64210] . 438631 . 65060) . 44730] . 65895) . 45599 3
58 .62479 . 421501 . 63360) . 43013] . 64224] . 43878] . 65074) . 44745] . 65909| . 45613) 2
59 . 62494) . 42164] . 63374! . 43027] . 64239) . 43892] . 65088) . 44759) . 65923) . 45628 1
60 | 9.625090. 42178|9. 63389|0. 43041|9. 64253/0. 43907|9. 65102/0. 44774|9. 65937|0. 45642) 0

279° 2119 276? 275°

278°

1438

TABLE 34

Haversines

85° 89°

4 Log Hav Nat. Hav| Log Hav | Nat. Hav] /
0 | 9. 6593710. 0. 48255|9. 6913210. 49127] 60
1 | . 65950) . 66770, . 46527] . . 68367| . 48270] . 69145 . 49142] 59
2| .65964|. . 66784| . 46541] . . 68380| . 48284| . 69158| . 49156| 58
3| .65978 . . 66797| . 46556] . . 68393 . 48299| . 69171! . 49171| 57
4 | .65992|. . 66811| . 46570) . . 68407) . 48313] . 69184 . 49186] 56
5 | 9. 66006/0. „ 66824 0. 46585|9. 0. . 68420/0. 48328|9. 69197/0. 492001 55
6 | . 66019] . . 66838) . 46599] . . 68433] . 48342] . 69209! . 49215] 54
7 | . 66033) . . 66851| . 46614] ` . 68446| . 48357| . 69222| . 49229| 53
8 | .66047 . . 66865| . 46628] . . 68459| . 48371] . 69235| . 49244| 52
9 | gene . 66878! . 46643] . . 68472 . 48386| . 69248| . 49258| 51
10 | 9. 66074 0. . 66892 0. 4665719, „68485|0. 48400|9. 69261/0. 49273| 50 _
11 | . 66088 . . 66905 . 46672) . . 68498 . 48415| . 69274 . 49287| 49
12 | 66102 | . 66919 ` 46686| . . 68511| . 48429| . 69286| . 49302] 48
13 |:.:66116|.. . 66932| . 46701| . . 68524| . 48444! . 69299| | 49316| 47
14 | .66129|. . 66946| . 46715] . i . 68537| . 48459| . 69312| . 49331| 46
15 | 9. 661430. . 66959 0. 4673019, y . 685500. 48473|9. 69325/0. 49346| 45
16 | . 66157] . . 66973 . 46744] . . 68563| . 48488| . 69338| . 49360| 44
17 | . 66170) . . 66986 . 46759] ` . 68576| . 48502] . 69350| . 49375| 43
18 | .66184| . . 67000. . 46773] ` . 68589| . 48517| . 69363| . 49389| 42
18 - 66198 . . 67013| . 46788] ` . 68602| . 48531| . 69376 . 49404| 41
9. 66212 0. . 67027 0. 4680219, i 5/0. „69:
adi et 562040]. 46817]. eege ees ieee
22 | . 66239 | . 67054| ` 46831] ` . 68641| . 48575| . 69414| . 49447| 38
23 . 66253 . . 67067| . 46846] . . 68654 . 48589| . 69427| . 49462] 37
24 M |.67081| . 46860] . . 68667| . 48604| . 69440 . 49476| 36
i . 670940. 4687519,
26 | `. 66294) . . 67108 : 46890" ` no mms o e Pe
27 | . 66307] . . 67121) . 46904] ` . 68706| . 48648] . 69478 . 495201 33
28 | .66321| ` . 67134 . 46919] . 68719 . 48662| . 69491! . 49535| 32
2 ua . 67148| . 46933] ` . 68732| . 48677| . 69504| . 49549] 31
; ; 9. 67161 0. 46948|9. ,
31 | .66362| . . 67175 SØKIR je em, at a a Se
32 | . 66376) . . 67188| . 46977] ` . 68771| . 48720| . 69542 . 49593| 28
33 | .66389 ` . 67202) . 46991] ` . 68784| . 48735| . 69555| . 49607] 27
tā SIE ua . 47006] . . 68797| . 48749| . 69567 . 49622| 26
| . 67228 0. i
NEE
37 | 266444) ` . 67255| . 47049] ` . 68836| . 48793| ` 69605| . 49665] 2
38 | . 66458) . . 67269 . 47064 . 68849] . 48807| . 69618 ` SE
39 | . 66471 ` . 67282) . 47078] ` . 68862| . 48822 tt ex 2
40 | 9. 6648510. . 67295 0.
41 | `. 66499) . ie E onore EHE T D n
42 55266512»: . 67322| . 47122 . 68900) . 48866| . 69669! ` doti pre
43 | .66526 ` . 67336 . 47136] ` . 68913 . 48880 ES nude
44 | .66539| ` . 67349| . 47151] ` . 68926| . 48895 Guns E lā
45 9. 66553 0. . 67362 0. 47165|9. . 4803719. 68939 0. 48909|9. 6970710. 49782| 15
. 66567| . . 67376| . 47180| . 68952| . 48924| ` 69
47 | .66580| ` . 67389| . 47194 ` 68965 48938| ` 6 keen 19
48 | .66594|.. . 67402 . 47209] ` . 68978) . 48953] ` MET eir ee
49 | .66607|. . 67416) . 47223] ` :68991|- 48907 100758 irem Er
E eee Q " - . 69758 . 49840| 11
E 10. 0. 9. | . 69004 0. 48982|9. 6977010. 49855| 10
„66635|. . 67443| . 47252
öl ` ; . 69017) . 48997] . 69783| . 498691 9
. 66648) ` . 67456| . 47267 69029 . 490
53 | .66662| ` . 67469| . 47282] ` . 69042 “49026 : 60808 it de
n tiri . 67483 . 47296] . - 69055 . 49040] . 69821 tads 6
ra EC - 6749600. 473119. - 69068 0. 4905519. 698340. 49927] 5
E eer 70210 : 67509) . 47325) . . 69081| . 49069] . 69846] . 499421 4
ee ic 67522) . 47340} . . 69094 . 49084] . 69859 ` 499561 3
ANCUS UTERE. . 69107 . 49098| . 69872| . 499711 2
ko opidum 87549) . 47369] - . 69120 .49113| . 69884 . 49985| 1
i | . 68354 0. 48255|9. 691320. 4912719. 6989710. 500001 0

274°

273°

271° 270°

TABLE 34

Haversines

1439

90° 91° 92° 93° 94°

i Log Hav | Nat. Hav} Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav Log Hav Nat Hav] ^"
0 | 9. 69897 0. 50000[9. 70648 0. 5087319. 713870. 5174519. 72112|0. 52617|9. 7282510. 53488 60
1 . 69910| . 50015| . 70661) . 50887| . 71399| . 51760| . 72124) . 52631| . 72837! . 53502| 59
2 „69922| . 500291 . 70678| . 509021 . 71411 . 51774| . 72136! . 52646] . 72849! . 535171 58
8 „69985| . 50044| . 70686| . 50916] . 71423) . 51789] . 72148| . 52660] . 72861! . 53531| 57
4 . 69948) . 50058| . 70698| . 50931] . 71436| . 51803] . 72160| . 52675| . 72873| . 535461 56
5 | 9. 69960/0. 50073|9. 707100. 50945|9. 71448 0. 51818|9. 72172/0. 5268919. 72884|0. 53560! 55
6 . 69973| . 500871 . 70723| . 50960] . 71460| . 51832] . 72184) . 52704| . 72896] . 53575| 54
Tú . 69985} . 501021 . 70735| . 50974] . 71472] . 518471 . 72196| . 52718] .72908| ..53589| 53
8 . 69998) . 501161 . 70748| . 50989] . 71484| . 518611 . 72208| . 527331 . 72920! . 53604] 52
9 . 70011, . 50131] . 70760) . 51003] . 71496! . 51876] . 722201 . 52748] .72931 |. 53618] 51
10 | 9. 70023 0. 50145|9. 707720. 51018|9. 71509 0. 51890]9. 72232/0. 5276219. 72943 0. 53633] 50
14 . 70036| . 50160] . 70785) . 51033] . 71521) . 51905] . 72244| . 52777] .72955| . 53647] 49
12 . 70048) . 50175) . 70797) . 510471 . 71533) . 51919] .72256| . 52791] . 72967) . 53662] 48
13 . 70061) . 501891 .70809| . 51062) . 71545) . 51934] . 72268) . 528061 . 72978) . 53676] 47
14 . 70074| . 50204] . 70822| . 51076] . 71557) . 51948] . 722801 . 528201 . 72990! . 536911 46
15 | 9. 70086/0. 50218|9. 70834/0. 5109119. 715690. 5196319. 72292/0. 5283519. 730020. 53705| 45
16 . 700991 . 50233| .70847| . 51105) . 71582) . 51978] . 72304| . 52849] . 73014 .53720| 44
17 . 70111) . 50247] . 70859| . 51120| . 71594| . 51992) .72316| . 52864] . 73025 . 53734] 43
18 . 70124| . 50262] . 70871| . 51134] .71606| . 52007] . 72328) . 52878] . 73037| . 53749] 42
19 . 70136| . 50276} . 70884) . 51149] . 71618) . 52021] . 72340) . 52893] . 73049] . 53763] 41
20 | 9. 70149 0. 502919. 70896 0. 51163]9. 71630 0. 52036]9. 72352 0. 52907|9. 73060 0. 53778] 40
21 . 70161| . 50305} . 70908) . 51178] . 71642) . 520501 . 72363, . 52922] . 73072| . 53792) 39
22 . 70174 . 503201 . 70921) . 51193] . 71654! . 52065] . 72375) . 52936] . 73084! . 53807| 38
23 . 70187) . 503351 . 70933) . 51207] . 71666) . 520791 . 72387) . 52951] . 73096] . 53821] 37
24 . 70199) . 503491 . 70945) . 51222] . 71679] . 52094] . 72399] . 52965] . 73107] . 53836] 36
25 | 9. 70212/0. 50364]9. 70958|0. 51236]9. 71691/0. 52108|9. 72411|0. 52980]9. 73119/0. 53850] 35
26 . 70224 . 50378] . 70970) . 51251] . 71703] . 521231 . 72423} . 52994] . 73131] . 538865] 34
27 . 70237| . 50393] . 70982) . 51265] . 71715] . 52137] . 72435) . 53009] . 73142) . 53879] 33
28 . 702491 . 50407] . 70995, . 512801 . 71727) . 521521 . 72447] . 530231 . 73154! . 53894] 32
29 . 70262 . 504221 . 71007, . 51294] . 71739) . 52166] . 72459) . 530381 . 73166) . 53908] 31
30 | 9. 70274/0. 50436|9. 71019 0. 51309|9. 71751/0. 5218119. 72471|0. 53052|9. 731770. 53923] 30
31 . 70287| . 504511 . 71032) . 51323] . 71763) . 52195) . 72482) . 53067] . 73189] . 53937] 29
32 . 70299| . 50465] . 71044) . 51338) . 71775) . 52210] . 72494) . 530811 . 73201) . 53952] 28
33 . 70312| . 504801 . 71056} . 51352) . 71787] . 52225) . 72506] . 53096] . 73212) . 53966] 27
34 . 70324| . 504951 . 710681 . 51367] . 71800! . 522391 . 72518] . 53110] . 73224) . 539811 26
35 | 9. 70337|0. 50509|9. 71081/0. 51382|9. 71812/0. 52254]9. 72530|0. 53125]9. 73236/0. 538995] 25
36 . 70349| . 50524] . 71093) . 51396] . 71824] . 52268] . 72542) . 53140] . 73247, . 54010] 24
3 . 70362, . 50538] . 71105, . 51411| . 71836) . 52283| . 72554| . 538154] . 73259| . 54024] 23
38 „70374| . 50558| . 71118| . 51425| . 71848| . 52297| . 72565) . 53169| . 73271) . 54039] 22
39 . 70387, . 50567| . 71130) . 514401 . 71860| . 52312] . 72577 . 53183| . 73282) . 54053] 21
40 | 9. 70399|0. 50582|9. 71142/0. 51454]9. 71872|0. 52326|9. 72589 0. 58198|9. 73294 0. 54068| 20
41 . 70412} . 50596| . 71154| . 51469] . 71884| . 52341| . 72601, . 532121 . 73306, . 54082] 19
42 . 70424| . 50611| . 71167| . 51483] . 71896) . 52355| . 72613) . 53227| . 73317) . 54097) 18
43 . 70437, . 50625] . 71179| . 51498] . 71908] . 52370| . 72625| . 53241| . 73329) . 54111] 17
44 . 70449| . 506401 . 71191 . 51512| . 71920, . 52384 „72637. 53256 . 73341) . 54126| 16
45 | 9. 704620. 50654]9. 71203 0. 51527]9. 71932 0. 52399]9. 72648 0. 53270|9. 73352 0. 54140 15
46 . 70474| . 50669] . 71216| . 51541] . 71944| . 52413] . 72660, . 53285] .73364| . 54155] 14
47 . 70487| . 50684] . 71228 . 51556| . 71956| . 52428] . 72672| . 53299] . 73375, . 54169| 13
48 . 70499| . 50698] . 71240) . 51571] . 71968! . 52442] . 72684 . 53314] . 73387 . 54184] 12
49 . 70512) . 50713] . 71252) . 51585] . 71980) . 52457] . 72696) . 53328 . 73399) . 54198 T
50 | 9. 70524 0. 50727 9. 71265 0. 51600]9. 71992 0. 52472|9. 72708 0. 53343|9. 73410/0. 54213

51 . 70537, . 50742] . 71277) . 51614| . 72004| . 52486| . 72719| . 53357| . 73422. 54227| 9
52 . 70549| . 50756| . 71289| . 51629| . 72016| . 52501| . 72731) . 53372| . 73433 . 54242 8
58 . 70561| . 50771| . 71301! . 51643] . 72028) . 52515| . 72743| . 53386| . 73445) . 54256] 7
54 . 70574| . 50785 . 71314 . 51658 . 72040, . 52530 . 42755, . 53401 E as S
55 | 9.70586|0. 50800|9. 71326 0. 51672|9. 72052|0. 5254419. 72767|0. 53415|9. 73468|0. 54

56 . 70599| . 50814] . 71338| . 51687| . 72064| . 52559] . 72778) . 53430] . 73480 . 54300 3
57 . 70611| . 508291 . 71350, . 51701] . 72076| . 52573] . 72790 . 53444 . 49491 . 54314 >
58 . 10624 . 50844] . 71362) . 51716| . 72088) . 52588] . 72802, . 53459 . 73503) . 54329 d
59 . 70636, . 50858| . 71375! . 51730) . 72100) . 52602] . 72814) . 53473) . 73515 . 54343 Ó
60 9. 70648 0. 50873|9. 71387 0. 51745|9. 72112 0. 52617|9. 72825 0. 53488|9. 73526/0. 54358

269° 268° 267° 266° 265°

1440

95°

TABLE 34

Haversines

97°

98°

99°

Log Hav "Nat Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav |Nat. Hav] ’
0 | 9. 735260. 54358|9. 74215 0. 552269. 74891/0. 560939. 75556/0. 5695919. 76209|0. 57822] 60
1 73538154372 . 74902| . 56108| . 75567| . 56973] . 76220| . 57836| 59
2 . 783549, . 54387 „74914| . 56122] . 75578| . 569871 . 76231| . 57850) 58
3 . 73561} . 54401 . 74925| . 56137] . 75589} . 57002| . 76241| . 57865) 57
4 (35/2) . 54416 . 74936] . 56151] . 75600) . 57016] . 76252) . 57879) 56
5 | 9. 7358410. 5443019 . 74947/0. 56166|9. 75611|0. 5703119. 76263/0. 57894] 55
6 .73596| . 54445 . 74958] . 56180] . 75622) . 57045| . 76274! . 57908] 54
7 . 43607, . 54459 . 74969) . 56195] . 75633) . 57059] . 76285] . 57922) 53
8 . 736191 . 54474 . 74981| . 56209] . 75644] . 57074] . 76296) . 57937) 52
9 . 73630} . 54488 . 74992) . 56223) . 75655) . 57088] . 76306] . 57951] 51
10 | 9. 73642/0. 5450319 . 75003/0. 5623819. 75666/0. 57103|9. 76317|0. 57965) 50
11 . 13653) . 54517 . 75014) . 56252) . 75677, . 57117] . 76328) . 57980] 49
12 . 73665) . 54532 . 75025] . 56267] . 75688] . 57131] . 76338] . 57994) 48
13 . 73676, . 54546 . 75036| . 56281| . 75698| . 57146| . 76349| . 58008| 47
14 . 73688] . 54561 . 75047| . 56296| . 75709| . 571601 . 76360} . 58023) 46
15 | 9. 736990. 54575]9 . 7505910. 56310|9. 75720/0. 57175|9. 7637110. 58037| 45
16 . 73711) . 54590 . 75070} . 56324| . 75731| . 57189] . 76381| . 58051| 44
im . 73722) . 54604 . 745081, . 56339] . 75742| . 57203| . 76392| . 58066| 43
18 . 73734] . 54619] . . 75092| . 56353| . 75753| . 57218| . 76403} . 58080) 42
19 . 73746] . 54633) . . 75103| . 56368] . 75764 . 57232] . 76414| . 58095| 41
20 | 9. 737570. 54647|9 . 751140. 56382]9. 75775|0. 57247|9. 76424/0. 58109| 40
21 . 737691 . 54662 . 75125| . 56397| . 75786| . 572611 . 76435! . 58123] 39
22 . 73780) . 54676 . 75136 . 56411| . 75797| . 57275| . 76446| . 58138| 38
23 . 73792| . 54691 . 45147, . 56425| . 75808) . 572901 . 76456! . 58152) 37
24 . 73803] . 54705 . 75159| . 564401 . 75819| . 57304| . 76467] . 58166| 36
25 | 9. 73815/0. 54720ļ9 . 75170/0. 56454|9. 758300. 5731919. 76478/0. 58181] 35
26 . 73826| . 54734 „75181| . 56469] . 75840] . 57333] . 76489| . 58195| 34
27 . 73838] . 54749 . 75192) . 56483| . 75851! . 57347| . 76499| . 58209] 33
28 . 73849] . 54763 . 75203] . 56497| . 75862) . 573621 . 76510! . 58224] 32
29 . 73860| . 54778 . 75214| . 56512] . 75873) . 57376| . 76521| . 58238] 31
30 | 9. 7387210. 5479219 9. 752250. 56526|9. 758840. 57390|9. 7653110. 58252| 30
31 . 73883] . 54807] . . 75236] . 56541| . 75895| . 574051 . 76542) . 58267] 29
32 . 73895; . 54821 . 752471 . 56555| . 75906| . 574191 . 76553| . 582811 28
33 . 73906} . 54836 . 75258} . 56570] . 75917| . 57434| . 76563| . 582951 27
34 . 73918] . 54850 . 75269. . 56584] . 75927| . 57448] . 76574| . 58310] 26
35 | 9. 73929/0. 54865ļ9 . 75280/0. 56598|9. 75938/0. 57462|9. 76585|0. 58324| 25
36 . 73941| . 54879 . 75291: . 56613] . 75949| . 574771 . 76595| . 58338| 24
37 . 73952) . 54894 . 75303. . 56627| . 75960| . 57491| . 76606| . 58353 23
38 . 73964) . 54908 . 75314 .56642| . 75971, . 57506) . 76617| . 58367| 22
39 . 73975| . 54923 . 75325] . 56656| . 75982| . 575201 . 76627| . 58381| 21
40 | 9. 739870. 5493719 . 75336/0. 56670|9. 7599310. 57534|9. 76638/0. 58396} 20
41 . 73998) . 54952 . 75347| . 56685| . 76004| . 57549] . 76649| . 584101 19
42 . 74009| . 54966 . 75358| . 56699] . 76014! . 575631 . 76659| . 58424 18
43 . 74021| . 54980 . 75369|. 56714] . 76025| . 57577| . 76670! . 58439| 17
44 . 74032! . 54995 . 75380} . 56728] . 76036| . 575921 . 76681! . 58453] 16
45 | 9. 740440. 55009l9 . 75391/0. 56743|9. 760470. 57606|9. 7669110. 58467 15
46 > 74055 . 55024 . 75402| . 56757| . 76058] . 576211 . 76702! . 58482] 14
47 . 74067, . 55038 . 75413] . 56771| . 76069] . 57635) . 76713). 58496} 13
48 . 74078, . 55053 . 75424) . 56786] . 76079] . 57649] . 76723) . 58510} 12
= . 740891 . 55067 . 75435| . 56800] . 76090! . 576641] . 76734! . 58525} 11
9. 74101/0. 55082|9 919. 75446 0. 56815|9. 76101|0. 57678|9. 76745/0. 58539| 10

51 . 74112) . 55096 . 75457| . 56829] . 76112! . 57692] . 10755|058553 9
E X 74124 . 55111 . 75468| . 56843] . 76123| . 577071 . 76766| . 58568] 8
3 2174195 E 55125 „75479| . 56858] . 76134| . 57721] . (6777, .58582| 7
947 _. 74146 .. 55140 . 75490] . 56872] . 76144| . 57736] . 76787, .58596| 6
2 9. 741580. 5515419 9. 755010. 56887|9. 76155|0. 57750|9. 767980. 58611] 5
AKI, 21 A8 - 15512 . 56901] . 76166| . 57764| . 76808 . 58625] 4
kn e - 755283 . 56915] . 76177| . 57779] . 76819] . 58639| 3
38 |. 74192) . 55197] .7 - 56065} . 75534 . 56930] . 76188] . 57793| . 76830| . 58654| 2
E t 14203 é 55212 . 74880) . 56079] . 75545 . 56944] . 76198| . 57807| . 76840 . 58668] 1
9. 74215|0. 5522619, 74891 0. 56093|9. 75556|0. 5695919. 76209 0. 57822|9. 76851|0. 58682} 0

264°

263°

262°

261°

260°

~

100° 10

TABLE 34

Haversines

19 1029

Log Hav

9. 76851
. 76861
. 16872
. 76883

. 76893

Nat. Hav | Log Hav

Nat. Hav | Log Hav

103°

Nat. Hav} Log Hav

0. 58682|9. 77481
. 586971 . 77492
. 58711] . 77502
. 58725] . 77512
. 58740) . 77523

0. 59540|9. 78101
. 59555) . 78111
. 595691 . 78121
. 69583] . 78131
. 59598] . 78141

0. 60396|9.
. 60410
. 60424
. 60438
. 60452

78709

. 78719) . 61262
. 78729
. 78739
. 78749

0. 61248|9.

„61276
„61290
„61304

104°

Nat. Hav| Log Hav

79306
. 79316
. 79326
. 79336
. 79346

Nat. Hav

0. 62096
. 62110
. 62124
. 62138
. 62153

1441

OO ND ANNO

„76904
„76914
„76925
„76936
. 76946

. 58754|9. 77533
. 98768| . 77544
. 58783) . 77554
. 98797| . 77564
. 98811] . 77575

. 59612]|9. 78152
. 59626] . 78162
. 59640] . 78172
. 596551 . 78182
. 596691 . 78192

. 76957
. 16967
. 76978
. 76988
176999

. 5882619. 77585
. 588401 . 77596
. 58854] . 77606
. 58869] . 77616
. 58883] . 77627

. 60467]9.
. 60481
. 60495
. 60509
. 60524

78759

. 78769
. 18779
. 78789
-78799

. 613189.
. 61333
. 61347
. 61361
. 61375

79356

. 79366
. 79376
. 79385
. 79395

. 62167
. 62181
. 62195
. 62209
. 62223

„59683]9. 78203
. 596971 . 78213
. 59712] . 78223
. 597261 . 78233
. 59740] . 78243

. 77009
. 77020
. 77031
. 77041
„77052

. 5889719. 77637
. 58911| . 77647
. 58926] . 77658
. 58940] . 77668
. 58954] . 77679

. 77062
„77073
„77083
„77094
„77104

„58969[9. 77689
. 58983] . 77699
. 589971 . 77710
. 59012] . 77720
. 99026| . 77730

. 597559. 78254
. 597691 . 78264
. 597831 . 78274
. 597971 . 78284
. 598121 . 78294

. 60538]9.
. 60552
. 60566
. 60580
. 60595

18809

. 78819
„78829
„78839
„78849

. 61389]9.
„61408
„61418
„61432
„61446

. 60609]9.
. 60623
. 60637
. 60652
. 60666

78859

. 78869
. 78879
. 18889
. 78899

. 61460]|9.
. 61474
. 61488
. 61502
. 61517

79405

. 79415
. 79425
. 79434
. 79444

79454

. 79464
„79474
„79484
. 19493

. 62237
. 62251
. 62265
. 62279
. 62294

. 62308
. 62322
. 62336
. 62350
. 62364

. 59826]9. 78305
. 598401 . 78315
. 59854] . 78325
. 59869] . 78335
. 598831 . 78345

. 60680]9.
. 60694
. 60708
. 60723
. 60737

18909

. 78919
. 78929
. 78939
. 78949

. 6153119.
. 61545
. 61559
. 61573
. 61587

79503

. 19513
. 79523
. 79533
. 79542

. 62378
. 62392
. 62406
. 62420
. 62434

. 77115
. 77125
„77136
„77146
„77157

. 59040]9. 77741
. 59055) . 77751
. 59069] . 77761
. 59083] . 77772
. 590971 . 77782

. 59897/9. 78355
. 59911] . 78365
. 59926] . 78376
. 59940) . 78386
. 59954] . 78396

. 6075119.
. 60765
. 60779
. 60794
. 60808

78959

. 78969
. 78979
. 78989
. 78999

. 61602]9.
. 61616
. 61630
. 61644
. 61658

79552

. 79562
. 79572
. 79582
«79501

„62477
„62491
. 62505

. 62449} :
. 62463] :

U UK KO
E
. 77188
3199
. 14209

. 59112|9. 77792
. 591261 . 77803
. 59140) . 77813
. 591551 . 77823
. 59169] . 77834

. 59968|9. 78406
. 59983] . 78416
. 599971 . 78426
. 60011| . 78436
. 60025] . 78447

. 60822]9.
. 60836
. 60850
. 60865
. 60879

19009

2/9019
. 79029
. 79039
. 79049

. 61672]9.
. 61686
. 61701
. 61715
. 61729

79601

. 79611
. 79621
. 79631
„79640

. 62519
. 62533
. 62547
. 62561
. 62575

„77220
. 77230
"77241
. 77251
. 77262

. 59183|9. 77844
. 591981 . 77854
. 59212] . 77864
. 59226] . 77875
. 59240] . 77885

. 60040|9. 78457
. 60054] . 78467
. 60068| . 78477
. 60082] . 78487
. 600971 . 78497

. 60893|9.
. 60907
. 60921
. 60936
. 60950

19059

. 79069
. 19079
. 79089
. 79099

. 61743]|9.
. 61757
O
. 61785
. 61800

79650

. 79660
. 79670
. 79679
. 79689

. 62589
. 62603
. 62618
. 62632
. 62646

. 44212
. 77283
. 77293
. 77304
- 77314

. 5925519. 77895
. 592691 . 77906
. 592831 . 77916
. 592981 . 77926
. 59312] . 77936

. 6011119. 78507
. 60125) . 78517
. 60139] . 78528
. 60154] . 78538
. 60168| . 78548

. 6096419.
. 60978
. 60992
. 61006
. 61021

79108

. 79118
. 79128
. 79138
. 79148

. 61814]9.
. 61828
. 61842
*. 61856
. 61870

19699

379709
. 79718
. 79728
„79738

. 62660
. 62674
. 62688
. 62702
. 62716

„77325
„77335
. 77346
. 77356
. 77366

. 59326|9. 77947
. 99340] . 77957
. 59355) . 77967
. 59369] . 77978
. 59383] . 77988

. 60182|9. 78558
. 60196] . 78568
. 602111 . 78578
. 60225| . 78588
. 60239] . 78598

„61035|9.
„61049
. 61063
. 61077
. 61092

79158

. 79168
. 79178
. 79188
270195

. 61884]9.
. 61898
. 61913
. 61927
. 61941

79748

. 19757
279167
o EEE
. 79787

. 62730
. 62744
. 62758
. 62772
. 62786

11377

7077387

„77398
„77408

. 59398|9. 77998
. 59412] . 78008
. 59426] . 78019
. 594401 . 78029
. 594551 . 78039

. 60253|9. 78608
. 60268] . 78618
. 60282] . 78628
. 602961 . 78638
. 60310] . 78649

. 61106]9.
. 61120
. 61134
. 61148
. 61163

79208

28292157]
. 79227
. 79237
. 79247

. 619559.
. 61969
. 61983
. 61997
. 62011

19796

. 79806
. 79816
. 79825
. 79835

. 62800
. 62814
. 62829
. 62843
. 62857

. 59469|9. 78049
. 59483] . 78060
. 59498] . 78070
. 59512] . 78080
. 59526] . 78090
. 5954019. 78101

. 60324]9. 78659
. 60339] . 78669
. 60353] . 78679
. 60367] . 78689
. 60381] . 78699
0. 60396|9. 78709

. 61177]9.
. 61191
. 61205
. 61219
. 61233
0. 61248]9.

19257

. 79267
OZTA
. 79287
019297

79306

. 62026]9.
. 62040
. 62054
. 62068
. 62082
0. 62096]9.

79845

„79855
„79864
„79874
„79884

„62871
. 62885
. 62899
. 62913
62927

79893

0. 62941

ONO y aldo -J00 (O

25

8° 257°

256°

255°

1442

TABLE 34

Haversines

105° 107° 109°
8 Log Hav | Nat. Hav] Log Hav | Nat. Hav} Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav] ’
0 | 9. 798930. 62941|9. 80470 0. 6378219. 8103610. 64619|9. 81592 0. 6545119. 82137 0. 66278] 60
1 | `. 79903] . 62955 . 82146, . 66292] 59
2 | .79913| . 62969 . 82155| . 66306| 58
3 - 79922 - 62983 - 82164 . 66320| 57
. 79932| . 62 . 82173, . 66333| 56
5 | 9. 799420. 6301119 . 82182/0. 66347| 55
6 | .79951| . 63025 . 82191| . 66361| 54
7 - 79961 : 63039 . 82200| . 66375| 53
. 82209] . 66388| 52
9 | .79980| . 63067 .82218 . 66402| 51
10 | 9. 79990 0. 6308119. . 82227 0. 66416| 50
11 | .80000| .63095| . 80574) . 63936 . 82236| . 66430| 49
12 | .80009 . 63109] . 80584 . 63950 . 82245| . 66443] 48
13 | .80019 . 63123] . 80593 . 63964 . 82254| . 66457| 47
14 | . 80029) . 63138] . 80603 . 63977 . 82263 . 664711 46
15 | 9. 80038 0. 6315219. 80612 0. 6399119 . 82272/0. 66485| 45
16 | . 80048) . 63166| . 80622 . 64005 . 82281| . 66498| 44
17 | .80058 . 63180] . 80631 . 64019 . 82290 . 665121 43
18 | . 80067) . 63194] . 80641. ` 64033 . 82299 . 66526] 42
19 | .80077| . 63208] . 80650 . 64047 . 82308) . 66539| 41
20 | 9. 80087 0. 6322219. 80660 0. 6406119 . 82317 0.
21 | .80096| . 63236] . 80669 . 64075 EE 39
22 | . 80106) . 63250] . 80678! . 64089 .82335| . 66581| 38
23 | .80116| . 63264] . 80688 . 64103 . 82344 . 66594| 37
24 | .80125 . 63278] . 80697| . 64117 . 82353 . 66608| 36
25 | 9. 801350. 63292|9. 80707 0. 64131l9
26 | .80144 . 63306| . 80716 . 64145 rupi der. a
27 | . 80154] . 63320] . 80726) . 64159 . 82380 . 66649| 33
28 | .80164 . 63334| . 30735 . 64173 . 82388 . 66663| 32
29 | .80173| . 63348] . 80745 . 64187 . 82397| . 66677| 31
30 | 9. 80183 0. 6336219. 80754 0. 6420119
31 | .80192| . 63376] . 80763 . 64215 ore 28
32 | .80202 . 633901 . 80773! ` 64229 ` 82424| | 66718| 28
33 | .80212 . 63404] . 80782! . 64243 . 82433| . 66731] 27
34 | .80221 . 634181 . 80792| . 64257 . 82442) . 66745| 26
35 | 9. 802310. 6343219. 80801 0. 6427019
36 | . 80240) . 63446| . 80811) . 64284 GE 21
37 | .80250| . 63460] . 80820! . 64298 . 82469| . 66786| 23
38 | .80260| . 63474] . 80829] 64312 . 82478| | 66800] 22
39 | .80269| . 63488| . 80839 . 64326 . 82487| . 66814] 21
40 | 9. 802790. 6350219. 80848 0. 6434019 82495 0. 66827| 20
41 | .80288 . 63516] . 80858 64354 . 82504| . 66841| 19
42 | .80298| . 63530] . 80867 . 64368 . 82513, . 668551 18
43 | .80307| . 63544] . 80876 . 64382 ` 82522| | 66868) 17
44 | .80317| . 63558] . 80886 . 64396 . 82531) . 668821 16
45 | 9. 80327/0. 63572|9. 80895 0. 6441019 82540 0. 668961 1
46 | .80336 . 63586] . 80905 64424 . 82549| . 66910 i
47 | . 80346] . 63600] . 80914 64438 . 82558] . 6692 B
48 | .80355 . 63614] . 80923 64452 . 82567 : 66937 T
49 | .80365| .63628| . 80933 | 64466 . 82575| . 66951 11
50 | 9. 803740. 63642|9. 80942 0. 64470l9 i
50 |9. : . 82584 0. 66964| 10
80384| . 63656] . 80952| . 64493] ` 82593
52 | .80393 . 63670] . 80961 . 64507] ` ` 82602 See
53 | .80403| . 63684] . 80970 . 64521 ` 82611 mee
94 | .80413| . 63698] . 80980| . 64535 . 82620 ne 4
55 | 9. 804220. 6371219. 80989 0. 6454919 82629 0.
56 | .80432 . 63726] . 80998 . 64563 ie
SE .82638 . 67046] 4
41| .63740| . 81008| . 64577
ae | 5 . 82646) . 67060] 3
. 637541 . 81017) . 64591 82655
* E . 63768] . 81026| . 64605] ` . 82664 pee 4
$ | C 4 '
0/0. 63782|9. 81036 0. 64619]o. . 826730. 67101] 0
254° 253° P

250°

1443

TABLE 34

Haversines

110° 111° 112° 113° 114°

Log Hav | Nat. Hav} Log Hav | Nat. Hay | Log Hav | Nat. Hav Log Hav | Nat. Hav] Log Hav | Nat. Hav

9. 826730. 67101|9. 83199/0. 67918|9. 83715|0. 68730]9. 84221/0. 6953719. 84718 0. 70337
-82682| . 67115) . 83207 . 67932] . 83723) . 68744] . 84230| . 69550| . 84726) . 70350
. 82691) . 67128) . 83216| . 67946] . 83732| . 68757| . 84238] . 69563] . 84735| . 70363
. 82699) . 67142) . 83225| . 67959] . 83740| . 68771] . 84246| . 69577| . 84743| . 70377
.82708| . 67156} . 83233) . 67973] . 83749 . 68784] . 84255 . 69590| . 84751| . 70390

. 827170. 67169|9. 83242/0. 67986|9. 83757|0. 68798|9. 84263 0. 69603|9. 84759|0. 70403
.82726| . 67183] . 83251, . 68000] . 83766 . 68811] . 84271) . 69617] . 84767| . 70417
. 82735) . 67197] . 83259, . 68013] . 83774 . 68825] . 84280) . 69630] . 84776! . 70430
. 82744) . 67210} . 83268) . 68027] . 83783) . 68838] . 84288) . 69644] . 84784] . 70443
. 82752) . 67224) . 83277| . 68041] . 83791, . 68852] . 84296) . 69657] . 84792) . 70456

. 827610. 67238|9. 83285|0. 68054]9. 83800 0. 68865|9. 84305|0. 6967019. 84800 0. 70470
. 82770) . 672511 . 83294| . 68068] . 83808) . 68879] . 84313| . 69684) . 84808) . 70483
. 82779, . 67265| . 83303| . 68081] . 83817) . 68892| . 84321| . 69697] . 84817) . 70496
. 82788) . 67279] . 83311] . 68095] . 83825) . 68906] . 84330, . 697101 . 84825) . 70509
. 82796) . 67292) . 83320) . 68108] . 83834) . 68919] . 84338] . 69724] . 84833) . 70523

. 82805 0. 67306|9. 83329 0. 68122|9. 83842 0. 68932|9. 843460. 6973719. 84841 0. 70536
. 82814) . 67319) . 83337| . 68135] . 83851) . 68946] . 84355 . 69751] . 84849 . 70549
. 82823) . 67333] . 83346) . 68149] . 83859) . 68959] . 84363) . 69764] . 84857 . 70562
. 82832) . 67347| . 83355) . 68163] . 83868) . 68973] . 84371) . 69777] . 84866) . 70576
. 82840} . 67360} . 83363) . 68176] . 83876) . 68986] . 84380) . 69791] . 84874. . 70589

. 828490. 67374|9. 83372|0. 68190|9. 83885 0. 69000|9. 84388 0. 6980419. 84882 0. 70602
. 82858) . 67388] . 83380| . 68203| . 83893| . 69013| . 84396) . 69817| . 84890) . 70615
. 82867) . 674011 . 83389 . 68217| . 83902| . 69027| . 84405) . 69831] . 84898, . 70629
.82876 . 67415} . 83398| . 68230] . 83910| . 69040] . 84413, . 69844) . 84906] . 70642
. 82884| . 67429] . 83406| . 68244] . 83919| . 69054] . 84421| . 69857| . 84914 . 70655

. 82893|0. 67442|9. 83415|0. 6825719. 83927|0. 69067|9. 84430 0. 69871|9. 84923|0. 70668
. 82902 . 67456] . 83424) . 68271] . 83935| . 69080] . 84438) . . 84931) . 70682
. 82911) . 67469] . 83432, . 68284] . 83944) . 69094) . 84446) . . 84939) . 70695
. 82920) . 67483] . 83441] . 68298] . 83952) . 69107) . 84454) . . 84947| . 70708
. 82928) . 67497] . 83449] . 68312] . 83961} . 69121] . 84463) . . 84955) . 70721

. 82937|0. 67510|9. 83458|0. 68325|9. 83969 0. 69134|9. 84471/0. 69937|9. 84963|0. 70735
. 82946 . 67524| . 83467) . 68339] . 83978) . 69148] . 84479) . 69951| . 84971, . 70748
. 82955) . 67538] . 83475) . 68352] . 83986) . 69161] . 84488) . 69964) . 84979. . 70761
. 82963) . 67551) . 83484) . 68366] . 83995) . 69174] . 84496) . 69977) . 84988) . 70774
. 82972) . 67565) . 83492) . 68379] . 84003, . 69188} . 84504) . 69991) . 84996 . 70788

. 82981/0. 67578|9. 83501/0. 68393|9. 84011|0. 69201|9. 84512/0. 70004]9. 85004/0. 70801
. 82990| . 67592| . 83510) . 68406| . 84020| . 69215| . 84521| . 70017| . 85012) . 70814
. 82998| . 67606| . 83518, . 68420| . 84028) . 69228| . 84529, . 70031| . 85020| . 70827
. 83007| . 67619| . 83527) . 68433| . 84037| . 69242| . 84537, . 70044| . 85028) . 70840
. 83016) . 67633| . 83535| . 68447| . 84045| . 69255| . 84545| . 70057| . 85036) . 70854

. 83025/0. 67647|9. 83544|0. 68460|9. 84054|0. 69268|9. 84554|0. 70071|9. 85044 0. 70867
. 83033) . 67660| . 83552| . 68474| . 84062) . 69282| . 84562 . 70084| . 85052) . 70880
. 83042| . 67674| . 83561| . 68487] . 84070| . 69295| . 84570| . 70097| . 85061) . 70893
. 83051) . 67687| . 83570. . 68501| . 84079 . 69309| . 84578) . 70111| . 85069| . 70907
.83059 . 67701| . 83578| . 68514| . 84087, . 69322] . 84587) . 70124| . 85077) . 70920

. 830680. 67715|9. 835870. 68528|9. 84096 0. 69336|9. 84595 0. 70137|9. 85085|0. 70933
. 88077, . 67728] . 83595, . 68541| . 84104 . 69349| . 84603, . 70151| . 85093) . 70946
. 83086, . 67742| . 83604| . 68555] . 84112 . 69362| . 84611, . 70164| . 85101, . 70959
. 83094| . 67755] . 83612, . 68568| . 84121| . 69376| . 84620| . 70177| . 85109 . 70973
. 83103) . 67769] . 83621| . 68582] . 84129) . 69389| . 84628, . 70191| . 85117, . 70986

. 831120. 67783|9. 83630 0. 68595|9. 84138|0. 69403|9. 84636/0. 70204|9. 85125 0. 70999
. 83120} . 67796| . 83638 . 68609| . 84146| . 69416| . 84644| . 70217] . 85133 . 71012
.83129| . 67810| . 83647) . 68622| . 84154| . 69429| . 84653, . 70230| . 85141) . 71025
. 83138| . 67823] . 83655| . 68636] . 84163) . 69443| . 84661| . 70244| . 85149 . 71039
. 83147| . 67837| . 83664 . 68649| . 84171| . 69456| . 84669 . 70257| . 85158| . 71052]

. 83155/0. 67850|9. 83672|0. 68663|9. 84179/0. 69470|9. 84677 0. 70270|9. 85166 0. 71065
. 83164| . 67864] . 83681| . 68676] . 84188) . 69483| . 84685| . 70284| . 85174) . 71078
.83173| .67878| . 83689| . 68690| . 84196 . 69496| . 84694 . 70297| . 85182) . 71091
. 88181| . 67891| . 83698) . 68703| . 84205) . 69510] . 84702, . 70310] . 85190) . 71105
. 83190; . 67905] . 83706) . 68717| . 84213) . 69523} . 84710) . 70324] . 85198) . 71118
. 83199 0. 67918|9. 83715 0. 68730|9. 84221 0. 69537|9. 84718 0. 7033719. 85206 0. 71131

OOND 23888 >

QC —to0og CO DIOS

245?

249? 248? 247? 246?

1444

115°

116°

TABLE 34

Haversines

117°

118°

á Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav
9. 85206|0. 71131]9. 85684|0. 71919|9. 86153|0. 72700|9. 86613
d . 85214) . 71144] . 85692) . 71932] . 86161) . 72712] . 86621! . 73486
2 - 852221 . 71157] . 85700} . 71945] . 86169) . 72725] . 86628! . 73499
3 . 85230} . 71170] . 85708! . 71958} . 86176] . 72738] . 86636) . 73512
4 . 85238} . 71184] . 85716, . 71971] . 86184] . 72751] . 86643] . 73525
5 | 9. 85246/0. 71197|9. 857240. 719849. 86192/0. 7276419. 8665110. 73538|9.
6 . 85254) . 71210] . 85731, . 71997] . 86200) . 72777] . 86659) . 73551
7 . 85262) . 71223] . 85739] . 720101 . 86207, . 727901 . 86666] . 73563
8 . 85270) . 71236] . 85747, . 72023] . 86215] . 72803] . 86674] . 73576
9 . 85278 . 71249] . 85755] . 72036] . 86223) . 72816] . 86681! . 73589
10 | 9. 85286/0. 71263|9. 85763|0. 72049|9. 86230|0. 7282919. 866890. 7360219.
IR . 85294| . 71276] . 85771| . 72062] . 86238) . 72842] . 86696! . 73615
12 . 85302) . 71289] . 85779| . 72075) . 86246] . 72855] . 86704! . 73628
13 . 85310} . 71302] . 85787] . 72088] . 86254] . 72868] . 86712] . 73640
14 . 85318] . 71315] . 85794] . 721011 . 86261] . 728811 . 86719] . 73653
15 | 9. 85326/0. 7132819. 85802/0. 7211419. 86269|0. 7289419. 86727 0. 736669.
16 . 85334| . 71342] . 85810] . 72127] . 86277| . 72907| . 86734| . 73679
17 . 85342 . 71355] . 85818| . 72141] . 86284) . 72920] . 86742| . 73692
18 . 85350] . 71368] . 85826] . 72154| . 86292] . 729321 . 86749| . 73704
19 . 85358) . 71381] . 85834] . 72167] . 86300) . 72945] . 86757! . 73717
20 9. 85366|0. 71394|9. 85841 0. 72180|9. 86307/0. 72958|9. 8676410. 7373019.
21 . 85374! . 71407] . 85849] . 72193] . 86315! . 72971] . 86772 . 73743
22 . 85382, . 71420] . 85857} . 72206] . 86323) . 72984] . 86780 187056
23 . 853901 . 71434] . 85865| . 72219] . 86331) . 72997| . 86787 . 73768
24 . 85398] . 71447] . 85873) . 72232] . 86338) . 73010 . 86795] . 73781
25 9. 85406|0. 71460|9. 85881/0. 72245|9. 863460. 7302319. 86802 0. 7379419.
26 . 85414. 71473| . 85888| . 72258| . 86354| . 73036 . 868101 . 73807
27 . 85422) . 71486] . 85896] . 72271] . 86361] . 73049 . 86817, . 73820
28 . 85430} . 71499} . 85904| . 72284] . 86369! . 73062 . 86825| . 73832
29 . 85488| . 71512] . 85912| . 72297| . 86377| . 73075 . 86832| . 73845
30 9. 85446 0. 71526|9. 859200. 72310|9. 86384 0. 7308719. 86840 0. 7385819.
31 . 85454 . 71539| . 85928] . 72323| . 86392 . 73100] . 86847| . 73871
32 . 85462| . 71552] . 85935] . 723361 . 86400 . 73113] . 86855| . 73883
33 . 85470| . 71565| . 85943| . 72349] . 86407 . 73126] . 86862| . 73896
34 . 85478) . 71578] . 85951| . 72362| . 86415 . 73139] . 86870. . 73909
35 9. 85486 0. 71591|9. 85959 0. 72375|9. 86423 0. 73152|9. 86877 0. 7392219,
36 . 85494 . 71604] . 85967| . 72388| . 86430 . 731651 . 86885| . 73935
37 . 85502| . 71617] . 85974| . 72401| . 86438 . 73178] . 86892| . 73947
38 . 85510| . 71631] . 85982 . 72414| . 86446 . 73191] . 86900} . 73960
39 . 85518| . 71644] . 85990| . 72427] . 86453 . 73203] . 86907, . 73973
40 9. 85526 0. 71657|9. 85998 0. 7244019. 86461 |0. 7321619. 86915 0. 739869.
41 . 85534) . 716701 . 86006| . 72453| . 86468 . 73229] . 86922. . 73998
42 . 85542) . 71683] . 86013|-. 72466| . 86476 . 73242] . 86930| . 74011
43 . 85550| . 71696] . 86021| . 72479| . 86484 . 73255] . 86937| . 74024
44 . 85557) . 71709| . 86029| . 72492| . 86491 . 73268] . 86945| . 74037
45 9. 85565/0. 71722|9. 86037 0. 72505|9. 86499 0. 73281|9. 869520. 74049|9. 8
46 . 85573. . 71735| . 86045| . 72518 . 86507) . 73294] . 86960! . 74062
47 . 85581! . 71748| . 86052! . 72531 . 86514| . 73306| . 86967| . 74075
48 . 85589| . 717621 . 86060) . 72544 . 86522| . 73319] . 86975| . 74088
49 . 85597, . 71775| . 86068| . 72557 . 865291 . 73332] . 86982} -74100
50 9. 856050. 71788|9. 86076 0. 72570|9. 86537 0. 73345|9. 86990 0. 74113]9.
51 . 85613) . 71801] . 86083| . 72583 . 86545| . 73358] . 86997] . 74126] . e Q
52 . 85621] . 71814| . 86091) . 72596] . 86552| . 73371| . 87004| . 74139] . 87448| . 74899] 8
53 . 85629 . 71827] . 86099| . 72609| . 86560 . 73384] . 87012| . 74151] . 87455 74912] 7
54 . 85637, . 71840] . 86107) . 72622 . 86568] . 73396] . 87019| . 74164 .87462| . 74924] 6
95 9. 8504500. 7185319. 86114 0. 72635|9. 86575 0. 7340919. 87027 0. 74177|9. 8747010. 74937 5
56 . 85653 . 71866] . 86122) . 72648] . 86583 . 734221 . 87034| . 74190] . 87477 . 749501 4
97 . 85660 . 71879] . 86130] . 72661 . 86590) . 73435| . 87042| . 74202 . 87484) . 74962] 3
58 . 85668) . 71892 . 86138) . 72674] . 86598] . 73448 . 87049) . 74215] . 87492] . 74975] 2
59 . 85676) . 71905] . 86145! . 72687 . 86606] . 734611 . 87057 . 74228 . 87499) . 74987] 1
60 9. 856840. 7191919. 86153|0. 72700|9. 866130. 7347419. 87064 0. 7424019. 8750610. 75000 0
244° 243° 242° 241°

>

120°

121°

TABLE 34

Haversines

122°

123°

124°

Log Hav | Nat. Hav| Log Hav

Nat. Hav] Log Hav

Nat. Hav] Log Hav

Nat. Havļ Log Hav

Nat. Hav

1445

9. 87506 0.
. 87513
. 87521
. 87528
. 87535

. 75013
„75025
„75038
„75050

750009.

87939

. 87947
. 87954
. 87961
. 87968

0. 75752|9. 88364
. 75764] . 88371
. 75777) . 88378
. 757891 . 88385
. 75802] . 88392

0. 76496|9. 88780
.76508| . 88787
. 76521| . 88793
. 76533] . 88800
. 76545| . 88807

0. 77232|9. 89187
. T7244] . 89194
. 77256} . 89200
. 772691 . 89207
. 77281) . 89214

0. 77960
„77972
„77984
„77996
. 78008

CONDO PWNr OS

. 87543
. 87550
. 87557
. 87564
. 87572

. 75063|9.
. 75076
. 75088
. 75101
. 75113

87975

. 87982
. 87989
. 87996
. 88004

. 75814|9. 88399
. 75827) . 88406
. 75839] . 88413
. 75852] . 88420
. 75864] . 88427

0. 76558|9. 88814
. 76570) . 88821
. 76582| . 88828
. 76595| . 88835
. 76607} . 88841

. 7729319. 89221
. 77305] . 89227
. 77317) . 89234
. 773291 . 89241
< 77342) . 89247

. 78020
. 78032
. 78044
. 78056
. 78068

. 87579
. 87586
. 87593
. 87601
. 87608

. 75126|9.
. 75138
. 75151
. 75164
. 75176

88011

. 88018
. 88025
. 88032
. 88039

. 75876|9. 88434
. 75889] . 88441
. 75901] . 88448
. 75914] . 88455
. 759261 . 88462

0. 76619|9. 88848
. 76632| . 88855
. 76644] . 88862
. 76656| . 88869
. 76668} . 88876

0. 77354|9. 89254
. 77366] . 89261
. 77378) . 89267
. 77390) . 89274
. 77402} . 89281

. 78080
. 78092
. 78104
. 78116
. 78128

. 87615
. 87623
. 87630
. 87637
. 87644

. 75189]9.
. 75201
. 75214
. 75226
. 75239

88046

. 88053
. 88061
. 88068
. 88075

. 75939|9. 88469
. 759511 . 88476
. 75964] . 88483
. 75976} . 88490
. 75988| . 88496

0. 76681|9. 88882
„76693| . 88889
„76705| . 88896
„76718| . 88903
„76730| . 88910

0. 77415|9. 89287
. 774271 . 89294
. 774391 . 89301
. 774511 . 89308
. 77463] . 89314

0. 78140
. 78152
. 78164
. 78176
. 78188

. 876520.
. 87659
. 87666
. 87673
. 87680

. 75264
. 75277
. 75289
. 75302

7525119,

88082

. 88089
. 88096
. 88103
. 88110

0. 76001|9. 88503
. 76013| . 88510
. 760261 . 88517
. 76038| . 88524
. 76050} . 88531

0. 76742|9. 88916
. 76754] . 88923
„76767| . 88930
. 76779] . 88937
. 76791| . 88944

0. 7747519. 89321
„77488| . 89328
. 775001 . 89334
. 77512] . 89341
. 775241 . 89348

. 78200
. 78212
. 18224
. 18236
„78248

. 87688 0.
. 87695
. 87702
. 87709
„87717

„75327
„75339
. 75352
. 75364

75314]9.

88117

. 88124
. 88131
. 88139
. 88146

. 76063|9. 88538
. 76075| . 88545
. 76088} . 88552
. 76100} . 88559
. 76113] . 88566

0. 76804|9. 88950
. 76816] . 88957
. 76828] . 88964
. 76840| . 88971
. 76853] . 88978

0. 77536|9. 89354
. 775481 . 89361
. 775601 . 89368
„77578| . 89374
. 77585] . 89381

0. 78260
. 18272
„78284
„78296
„78308

. 87724 0.
. 87731
. 87738
. 87745
. 87753

. 75389
. 75402
. 75415
. 75427

753779.

88153

. 88160
. 88167
. 88174
. 88181

. 76125]9. 88573
. 76137| . 88580
. 76150} . 88587
. 76162] . 88594
. 76175} . 88600

0. 76865|9. 88984
. 76877| . 88991
. 76890] . 88998
. 76902] . 89005
. 76914| . 89012

0. 77597|9. 89387
„77609| . 89394
. 776211 . 89400
„77633| . 89407
„77645| . 89414

0. 78320
„78332
„78344
„78356
„78368

. 87760
. 87767
. 87774
. 87782
. 87789

. 75440]9.
. 75452
. 75465
„75477
„75490

88188

„88195
. 88202
. 88209
. 88216

. 76187|9. 88607
. 76199] . 88614
. 76212] . 88621
. 76224] . 88628
. 76236| . 88635

0. 76926|9. 89018
. 76939] . 89025
. 76951] . 89032
. 76963| . 89039
. 76975| . 89045

0. 77657|9. 89421
. 776701 . 89427
. 77682) . 89434
. T7694] . 89441
. 77706| . 89447

. 78380
. 78392
. 78404
. 78416
. 78428

. 87796
. 87803
. 87810
. 87818
. 87825

. 75502)9,
. 75515
. 75521
. 75540
. 75552

88223

. 88230
. 88237
. 88244
. 88252

. 76249|9. 88642
. 76261| . 88649
. 76274| . 88656
. 76286] . 88663
. 76298| . 88670

0. 76988|9. 89052
. 770001 . 89059
. 77012) . 89066
. 77024] . 89072
. 77036] . 89079

0. 77718|9. 89454
. 777301 . 89460
. T7742) . 89467
„77754| . 89474
. 77766] . 89480

. 78440
. 78452
. 78464
. 78476
. 78488

. 87832
. 87839
. 87846
. 87853
. 87861

. 7556519.
„75577
„75590
. 75602
„75615

88259

. 88266
. 88273
. 88280
. 88287

. 76311|9. 88677
. 76323] . 88683
. 76335] . 88690
. 76348] . 88697
. 763601 . 88704

0. 77049|9. 89086

. 770611 . 89093| .

. 77073] . 89099
„77085| . 89106
. 77098} . 89113

0. 77779|9. 89487|C

71191| . 89493
. 77803] . 89500
. 77815] . 89507
„77827| . 89513

. 78500
. 78512
. 78524
. 78536
„78548

. 87868
. 87875
. 87882
. 87889
. 87896

. 756279.
. 75640
„75652
„75665
„75677

88294

. 88301
. 88308
. 88315
. 88322

. 76373|9. 88711
. 76385] . 88718
. 76397| . 88725
. 764101 . 88732
. 76422) . 88739

0. 77110|9. 89120
. 771221 . 89126
. 77134] . 89133
. 77147| . 89140
. 771159] . 89147

. 77839]9. 89520
. 77851| . 89527
. 77863) . 89533
. 778751 . 89540
. 77887| . 89546

. 78560
. 78571
„78583
„78595
„78607

. 87904
29/911
. 87918
. 87925
. 87932
9. 879390.

. 75690|9.
. 75702
„75714
. 75727
. 75739

7575219.

88329

. 88336
. 88343
. 88350
. 88357

88364

. 7643419. 88745
. 76447| . 88752
. 76459] . 88759
. 76471| . 88766
. 76484] . 88773
0. 76496|9. 88780

0. 77171]9. 89153
. 77183] . 89160
. 771951 . 89167
. 77208] . 89174
. 772201 . 89180

|0. 7723219. 89187

. 778999. 89553
. 779111 . 89559
. 77923) . 89566
„77936| . 89578
77948| . 89579

. 78619
. 78631
„78643
„78655
78667

239°

238°

236°

235°

0. 779609. 89586 0. 78679

1446

TABLE 34

Haversines

125° 126° 127°

, Log Hav Log Hav | Nat. Hav | Log Hav | Nat. Hav
0 | 9. 89586|0. 9. 89976/0. 79389|9. 90358
1 . 89592| . 89983, . 79401| . 90365| . 80102
2 . 89599| . 89989| . 79413] . 90371| . 80114
3 . 89606| . 899951 . 79425| . 90377| . 80126
4 .89612| . 7 90002, . 79436] . 90383| . 80137
5 | 9. 89619/0. 9. 90008/0. 79448|9. 90390/0. 801499
6 . 89625| . 90015} . 79460} . 90396} . 80160
7 . 89632) . 90021! . 79472] . 90402] . 80172
8 . 89638) . 90028, . 79483] . 90409] . 80184
9 . 89645) . 90034] . 79495| . 90415| . 80195
10 | 9. 89651/0. . 90040/0. 795079. 90421/0. 8020719
11 . 89658| . 90047, . 79519] . 90428| . 80218
12 . 89665| . 90053| . 79530) . 90434| . 80230
13 . 89671) . 90060| . 79542| . 90440| . 80242
14 . 89678| . 90066| . 79554| . 90446| . 80253
15 | 9. 89684/0. 7885719. 90072/0. 79565|9. 9045210. 80265|9
16 . 89691) . 90079) . 79577] . 90459] . 80276
dn .89697| . 90085| . 79589| . 90465| . 80288
18 | .89704|. 90092| . 79601] . 90471| . 80299
19 3897100 90098, . 79612] . 90478| . 80311
20 | 9. 89717/0. 78917|9. 901040. 79624|9. 904840. 8032319
21 289723]. 90111) . 79636} . 90490| . 80334
22 . 89730) . 90117, . 79648| . 90496| . 80346
23 > 89736]. 90124) . 79659} . 90503] . 80357
24 . 89743} . 90130| . 79671| . 90509| . 80369
25 | 9. 89749)0. . 90136/0. 79683|9. 90515/0. 80380]9
26 .89756| . 90143! . 79694} . 90521| . 80392
27 . 89763) . 901491 . 79706] . 90527] . 80403
28 . 89769) . 90156| . 79718| . 90534| . 80415
29 2990/0 87 90162. . 797291 . 90540| . 80427
30 | 9. 8978210. . 90168/0. 79741]9. 90546/0. 80438]9
31 .89789| . 7 . 90175| . 79753| . 90552| . 80450
32 . 89795) . 90181| . 79765| . 90559| . 80461
33 . 89802| . 90187| . 79776] . 90565| . 80473
34 . 89808| . 90194| . 79788] . 90571! . 80484
35 | 9. 89815|0. 7 9. 90200/0. 79800|9. 905770. 80496l9
36 .89821|. . 90206) . 79811| .90584| . 80507
87 „89828| . 7 . 90213] . 79823] . 90590| . 80519
38 . 89834) . . 90219} . 79835] . 90596) . 805301 `
39 . 89840) . . 90225] . 79846] . 90602! . 805421 . 90971
40 | 9. 8984710. . 902320. 79858|9. 90608|0. 8055319. 9097710.
41 - 898531... . 90238) . 79870] . 90615 . 80565| . 90983! . 5t
42 . 89860| . 7 7| .90244| . 79881] . 90621| . 80576 . 90989] , . 91349} . 81938
43 . 89866} . . 90251} . 79893] . 90627] . 80588| . 90995| . . 91355, . 81950
44 _ . 89873 . 90257) . 79905] . 90633] . 80599] . 91001 . 91361) . 81961
45 | 9. 8987910. 7 . 902640. 7991619. 9063910. 8061119. 9100710. J. 91367/0. 81972
46 . 89886| . . 90270) . 79928] . 90646] . 80622] . 91013| . . 91372) . 81983
47 . 89892) . . 90276! . 79940] . 90652| . 80634] . 91019) ` . 91378| . 81994
48 . 89899) .7 . 90282) . 79951] . 90658| . 80645] . 91025) . . 91384| . 82005
49 .89905| . 7 . 90289] . 79963] . 90664! . 806571 . 91031 . 913901 . 82017
50 9. 8991210. 7 . 90295/0. 7997419. 90670/0. 8066819. 9103710. . 91396/0. 82028
51 -89918 7 . 903011 . 79986] . 90676| . 80680] . 91043 . 91402 . 82039] 9
52 . 89925 4 . 90308| . 79998| . 90683! . 80691| . 91049 : . 91408} . 82050| 8
53 . 89931) . . 90314| . 80009} . 90689| . 80703] . 91055 § . 91414| . 82061] 7
54 . 89938) . . 90320| . 80021} . 90695| . 80714 . 91061 . 91420] . 82072] 6
55 9. 89944 0. 7 9. 90327|0. 80033|9. 90701/0. 80726|9. 910670. . 91426/0. 82084] 5
56 . 89950 7 . 90333} . 80044] . 90707| . 80737] . 91074 : . 91432] . 82095} 4
57 . 89957 éd . 90339} . 80056] . 90714| . 80749 . 91080} . . 91437) . 82106] 3
58 . 89963 .7 . 90346] . 80068] . 90720] . 80760 . 91086) . . 91443] . 82117] 2
59 . 89970 . 7 7| . 90352] . 80079] .90726| . 80772 > 91092), ; 91449} . 82128] 1
60 | 9. 89976/0. . 90358/0. 80091|9. 907320. 8078319. 91098 914550. 82139] 0
234° 233° 2429 231?

130°

13

TABLE 34

Haversines

13 132°

133° 134°

Log Hav | Nat. Hav

. 91461
. 91467
. 91473
. 91479

. 91485
. 91490
. 91496
. 91502
«91508

„82151
„82162
. 82173
. 82184

. 82195|9.
. 82206
. 82217
. 82228
. 82240

Log Hav

9. 914550. 82139|9. 91805
. 91810
. 91816
. 91822
. 91828

Nat. Hav | Log Hav

Nat. Hav | Log Hav

Nat. Hav | Log Hav | Nat. Hav

1447

0. 82803|9. 92146
. 82814] . 92152
. 82825| . 92157
. 82836| . 92163
. 828471 . 92169

0. 83457|9. 92480
. 83467] . 92485
. 83478] . 92491
. 83489] . 92496
. 88500] . 92502

0. 84100]9. 928050.
.84111| . 92811) .
. 84121| . 92816) .
. 84132] . 92821) .
. 84142] . 92827| .

. 91839
. 91845
. 91851
. 91856

91833

. 82858|9. 92174
. 82869] . 92180
. 82880] . 92185
. 828911 . 92191
. 82902} . 92197

. 9151440.
. 91520
. 91526
. 91532
. 91537

. 82262
. 82273
. 82284
. 82295

82251]9.

. 91868
. 91874
. 91879
. 91885

. 835119. 92507
. 83521| . 92512
. 83532] . 92518
. 83543| . 92523
. 83554] . 92529

. 84153|9. 9283240.
. 84164| . 92837) .
. 84174] . 92843| .
. 84185| . 92848| .
. 84196| . 92853) .

91862

. 82913|9. 92202
. 82924] . 92208
. 82934] . 92213
. 829451 . 92219
. 829561 . 92225

. 83564]9. 92534
. 835751 . 92540
. 83586| . 92545
. 835971 . 92551
. 83608] . 92556

. 84206|9. 9285910.
. 84217| . 92864) .
. 84227| . 92869] .
. 84238| . 92875) .
. 84249| . 92880) .

. 915430.
. 91549
. 91555
. 91561
. 91567

. 82317
. 82328
. 82339
. 82351

82306]9.

. 91896
. 91902
. 91908
. 91914

91891

. 82967|9. 92230
. 82978] . 92236
. 829891 . 92241
. 830001 . 92247
. 83011] . 92253

0. 83618]9. 92562
. 83629]. 92567
. 83640] . 92573
. 836511 . 92578
. 83661] . 92584

0. 84259|9. 928850.
. 84270| . 92891| .
. 84280| . 92896) .
. 84291] . 92901| .
. 84302] . 92907| .

. 9157340.
. 91578
. 91584
. 91590
. 91596

. 91602)0.
. 91608
. 91613
. 91619
. 91625

. 82373
. 82384
. 82395
. 82406

. 82428
. 82439
. 82450
. 82461

82362]9.

. 91925
. 91931
. 91936
. 91942

91919

. 8302219. 92258
. 83033] . 92264
. 83044] . 92269
. 83055) . 92275
. 83066] . 92280

0. 83672]|9. 92589
. 83683] . 92594
. 83694] . 92600
. 83704] . 92605
. 88715| . 92611

0. 84312]|9. 929120.
. 84323| . 92917) .
. 84333] . 92923) .
. 84344| . 92928) .
. 84354| . 92933| .

82417|9.

„91954
. 91959
. 91965
. 91971

91948

. 83077|9. 92286

. 830871 . 92292) .
. 83098] . 92297) .
. 83109| . 92303| .
. 831201 . 92308) .

0. 83726|9. 92616
. 92622
. 92627
. 92633
. 92638

0. 84365|9. 929390.
. 84376| . 92944) .
. 84386| . 92949) .
. 84397| . 92955| .
. 84407| . 92960) .

. 91631/0.
. 91637
. 91643
. 91648
. 91654

. 82483
. 82495
. 82506
. 82517

82472]9.

91976

. 91982
. 91988
. 91993
. 91999

. 83131|9. 92314
. 83142] . 92319
. 83153] . 92325
. 83164] . 92330
. 83175] . 92336

0. 83780|9. 92643
. 83790| . 92649
. 838011 . 92654
. 83812] . 92660
. 83822] . 92665

. 84418|9. 929650.
. 84428] . 92970) .
. 84439] . 92975) .
. 84449) . 92981) .
. 84460) . 92986) .

. 91660
. 91666
. 91672
. 91677
. 91683

. 8252819.
. 82539
. 82550
. 82561
. 82572

92005

. 92010
. 92016
. 92022
. 92027

. 831859. 92342
. 83196| . 92347
. 83207] . 92353
. 83218] . 92358
. 83229] . 92364

0. 83833|9. 92670
. 83844] . 92676
. 83855] . 92681
. 83865] . 92687
. 83876| . 92692

. 84470|9. 929920.
. 84481| . 929971] .
. 84492) . 93002) .
. 84502] . 93007) .
. 84513} . 93013) .

. 91689
. 91695
. 91701
. 91706
. 91712

. 82583|9.
. 82594
. 82605
. 82616
. 82627

92033

. 92039
. 92044
. 92050
. 92056

. 8324019. 92369

. 83283] . 92391

. 88251] . 92375) .
. 83262] . 92380| .
. 83272) . 92386) .

0. 83887]9. 92698
. 92703
. 92708
. 92714
. 83929] . 92719

. 84523|9. 93018 0.
. 84534| . 93023| .
. 84544] . 93029) .
. 84555| . 93034) .
. 84565| . 93039| .

9. 91718
. 91724) .
. 91730) .
. 91735) .
. 91741

. 8263819.

92061

. 92067
. 92073
. 92078
. 92084

. 8329419. 92397
. 833051 . 92402
. 83316| . 92408
. 833271 . 92413
. 83337] . 92419

0. 83940[9. 92725
. 83951| . 92730
. 839611 . 92735
. 83972] . 92741
. 83983] . 92746

. 8457619. 930440.
. 84586| . 93050) .
. 84597| . 93055) .
. 84607] . 93060| .
. 84618| . 93065| .

. 91747/0.
. 91753
. 91758
. 91764
. 91770

. 82704
. 82715
. 82726
. 82737

82693]9.

92090
. 92095
. 92101
. 92107
. 92112

. 83348]9. 92425
. 83359] . 92430
. 83370} . 92436
. 83381} . 92441
. 83392] . 92447

. 83993|9. 92751
. 84004] . 92757
. 84015] . 92762
. 84025| . 92768
. 84036] . 92773

. 84628|9. 930710.
. 84639] . 93076) .
. 84649] . 93081) .
. 84660} . 93086) .
. 84670} . 93092) .

. 91776
. 91782
. 91787
. 91793
91799
. 91805)0.

. 82748]9.
. 82759
. 82770
. 82781
. 82792

82803]9.

92118

. 92124
. 92129
. 92135
. 92140

. 83402]9. 92452
. 83413] . 92458
. 83424] . 92463
. 83435] . 92469
83446] . 92474

92146

0. 8345719. 92480

. 84047|9. 92778
. 840571 . 92784
. 84068} . 92789
. 84079| . 92794
. 84089| . 92800
0. 84100]|9. 92805

. 81681|9. 93097 0.
. 84691| . 93102 .
` 84702] . 93107].
` 84712] . 93113 .
| .84722] . 93118 .
0. 84733|9. 9312310.

ONO OOOO

229°

228°

227°

226° 225°

222°

221°

220°

1448
TABLE 34
Haversines
135° 136° 137° 138° 139°
^ Log Hav | Nat. Hav| Log Hav | Nat. Hav] Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav] '
0 | 9. 93123/0. 85355|9. 934330. 85967|9. 93736|0. 86568|9. 9403010. 87157|9. 94318/0. 87735| 60
1 | .93128| . 85366| . 93438 . 85977] . 93741| . 86578| . 94035! . 87167| . 94322| . 87745| 59
2 | .93134 .85376| . 93443| . 85987| . 93746! . 86588] . 94040| . 87177] . 94327| . 87755| 58
3 | .93139|.85386| . 93448] . 85997] . 93751, . 86597| . 94045| . 87186] . 94332| . 87764| 57
4| .93144| . 85396] . 93454| . 86007] . 93755! . 86607| . 94050| . 87196] . 94336, . 87774] 56
5 | 9. 931490. 85407|9. 934590. 86017|9. 937600. 86617|9. 94055 0. 8720619. 9434110. 87783| 55
6 | .93154| .85417| . 93464| . 86028] . 93765 . 86627| . 94059| . 87216] . 94346| . 87793] 54
7 | .93160| . 85427] . 93469| . 86038] . 93770! . 86637| . 94064| . 87225] . 94351] . 87802] 53
8 | .93165 .85438| . 93474 . 86048| . 93775 . 86647| . 94069| . 87235| . 94355| . 878121 52
9 | .93170| . 85448| . 93479| . 86058| . 93780! . 86657| . 94074 . 87245] . 94360 . 87821| 51
10 | 9. 931750. 85458|9. 934840. 8606819. 937850. 86667|9. 940790. 8725419. 943650. 87831| 50
11 | .93181| .85468| . 93489| . 86078| . 93790| . 86677| . 94084 . 87264| . 94369| . 87840| 49
12 | .93186| . 85479| . 93494| . 86088] . 93795| . 86686| . 94088| . 87274| . 94374] . 87850| 48
13 | .93191 . 85489| . 93499 . 86098| . 93800 . 86696| . 94093 . 87283| ` 94379| . 87859| 47
14 | .93196| . 85499] . 93504 . 86108] . 93805 . 86706| . 94098| . 87293| . 94383| ` 87869| 46
15 | 9. 93201/0. 85509|9. 93509 0. 86118|9. 93810|0. 86716|9. 94103|0. 8730319. 94388 0. 87878] 45
16 | .93207| .85520| . 93515| . 86128] . 93815| . 86726| . 94108 . 87313] . 94393| . 87888| 44
17 | .93212 . 85530] . 93520| . 86138] . 93820| . 86736| . 94112| . 87322] ` 94398 . 87897] 43
18 | .93217 . 85540] . 93525| . 86148] . 93825| . 86746| . 94117| . 873321 . 94402 . 87907] 42
19 | .93222| .85550| . 93530 . 86158| . 93830 . 86756| . 94122 . 87342] ` 94407 . 879161 41
20 | 9. 93227/0. 85560|9. 93535/0. 86168|9. 938350. 86765|9. 941270. 87351|9. 94412 0. 87926| 40
21 | .93232 .85571| . 93540| . 86178| . 93840| . 86775| . 94132| . 87361| . 94416) . 87935| 39
22 | . 93238) . 85581] . 93545] . 86189| . 93845| . 86785| . 94137! . 87371| . 94421| . 87945| 38
23 | .93243 . 85591] . 93550] . 86199| . 93849| . 86795| . 94141 . 87380| . 94426| . 87954] 37
24 | .93248| .85601| . 93555 . 86209] . 93854| . 86805| . 94146 . 87390| . 94430| . 87964| 36
25 | 9. 93253 0. 85612|9. 93560 0. 86219|9. 93859|0. 86815|9. 941510. 87400|9. 94435 0. 87973| 35
26 | .93258 . 85622] . 93565 . 86229] . 93864| . 86825| . 94156| . 87409| . 94440 . 87982] 34
27 | .93264| .85632| . 93570 .86239| . 93869| . 86834| . 94161| . 87419] | 94444 | 879991 33
28 | .93269| . 85642) . 93575 . 86249] . 93874| . 86844| . 94165 . 87429] ` 94449| | 88001] 32
29 | .93274 .85652|.93580| . 86259] . 93879 . 86854| . 94170| . 87438] . 94454| . 88011| 31
30 | 9. 932790. 85663|9. 93585|0. 86269|9. 03884 0. 868649. 94175 0. 8744
31 | .93284| .85673| . 93590| . 86279] . 93889| . 86874| ` 94180 SET ABT ievēroti cs 25
32 | .93289| .85683| . 93595 . 86289] . 93894 . 86884| . 94184| . 87467| | 94468| | 880391 28
33 | .93295|.85693| . 93600] . 86299| . 93899 . 86893| . 94189| . 87477] ` 94472| | 88049] 27
: . 933001 . 85703] . 93605| . 86309] . 93904| . 86903| . 94194| . 87486| 94477! 8g058| 26
9. 93305 0. 85713|9. 93611|0. 86319|9. 939080. 86913|9. 9419910. 0
36 | . 93310) . 85724] . 93616 . 86329] . 93913| . 86923 BEE mid 24
37 | . 93315) . 85734) . 93621 . 86339| . 93918| . 86933| . 94208 . 87515| ` 94491| ` 88086| 23
38 | . 93320) . 85744) . 93626| . 86349| . 93923| . 86942| . 94213 . 87525| ` 94496 ` 88006| 22
2 . 93326 . 85754] . 93631| . 86359| . 93928| . 86952| . 94218 . 87534| . 94500 . 88105| 21
9. 93331/0. 8576419. 93636 /0. 86369|9. 93933|0. 8696219. 9422: 5
41 | .93336| . 85774] . 93641| . 86379] . 93938 ` 86972 SE Ee t
42 | .93341| . 85785| . 93646 . 86389| . 93943 . 86982] ` 94232| | 87563| ` 94514 . 88133| 18
13 | . 93346) . 85795] . 93651] . 86399] . 93948 . 86991] . 94237! | 875731 94519 . 88143| 17
: DIM 85805| . 93656| . 86409| . 93952| . 87001| . 94242| . 875821 ` 94523| | 88152| 16
9. 93356/0. 85815|9. 93661/0. 86419|9. 93957 0. 8701119. 7
46 | .93362| . 85825| . 93666| . 86429| 93962 ES RE E
47 | .93367 . 85835] . 93671] . 86438] . 93967) . 87030] . 94256 87611 ` 94537) . 88180] 13
48 | .93372| . 85846] . 93676| . 86448] . 93972 . 87040] . 942611 87621 94542] . 8819
AP sa < 7 .87 ; 0| 12
2 E um . 93681) . 86458| . 93977 . 87050| . 94265| . 87630] ` 94546| 881991 11
50 | 9. 933820. 8586619. 93686|0. 86468|9. 93982 0. 8706019. 9427 7640|9
51 | .93387 .85876| . 93691| . 864781 . 93987 :87070|.942781. seal asa O: 88209 ip
52 | . 93392) . 85886) . 93696] . 86488| . 93991 . 87079| . 94280 87659 ` 94560 . 88227] 8
53 | . 93397) . 858961 . 93701] . 86498] . 93996| . 87089] ` 94284 ` 87669 .94565| .88237| 7
4 - 93403) . 859061 . 93706) . 86508| . 94001| . 87099] . 94289 . 87678| 94570 .88246| 6
55 9. 934980. 8591619. 937110. 86518|9. 94006 O. 8710919. 94294 0. 87688|9. 9457410. 88255 5
7| :93413| - 85927] . 93716) . 86528| . 94011| . 87118| . 94299| . 87697| . 94579 - BE
57 | -93418 . 85937] .93721 .86538| . 94016 . 87128| ` 94303 87707 .94583| .88274| 3
58 - 93423 - 85947 - 93726 - 86548 . 94021 . 87138] . 94308| . 87710| . 94588| | 88284] 2
9 | 93428 -.85957| . 93731 | . 94026| .87148| . 94313] .87726| . 94593 ` 88293| 1
60 9. 93433/0. 859679. 93736/0. 86568/9. 94030/0. 87157|9. 9431810. 877359. 94597 0. 88302 0
2240 223°

1449

TABLE 34
Haversines
140° 141° 142° 143° 144°

Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav

0 | 9. 94597/0. 88302|9. 94869/0. 88857|9. 951340. 8940119. 95391/0. 89932]9. 9564110. 90451

1 . 94602 . 88312] . 94874| . 88866] . 95138 . 89409} . 95396| . 89941] . 95645| . 90459

2 . 94606} . 88321] , 94878) . 88876| . 95143] . 89418] . 95400) . 89949] . 95649] . 90468

3 . 94611) . 88330] . 94883) . 88885] . 95147) . 89427] . 95404) . 89958] . 95654) . 90476

4 . 94616) . 88340} . 94887, . 88894] . 95151! . 89436] . 95408] . 89967] . 95658] . 90485

5 | 9. 94620/0. 88349|9. 94892|0. 88903|9. 95156/0. 8944519. 95412|0. 8997519. 9566210. 90494

6 . 94625| . 88358] . 94896) . 889121 . 95160| . 89454] . 95417) . 89984] . 95666) . 90502

7 . 94629| . 883681 . 94901, . 88921] . 95164| . 89463] . 95421| . 89993] . 95670) . 90511

8 . 94634| . 88377| . 94905) . 889301 . 95169| . 89472) . 95425) . 90002] . 95674| . 90519

9 . 94638, . 88386] . 94909| . 889401 . 95173| . 89481| . 95429) . 90010] . 95678) . 90528

10 | 9. 94643/0. 88396|9. 94914/0. 88949|9. 95177|0. 89490|9. 95433/0. 90019|9. 956820. 90536

11 . 94648| . 88405| . 94918, . 88958] . 95182) . 89499] . 95438| . 900281 . 95686) . 90545

12 . 94652| . 88414| . 94923) . 889671 . 95186) . 89508| . 95442| . 90037] . 95690| . 90553

13 . 94657| . 884231 . 94927| . 88976| . 95190, . 895171 . 95446| . 900451 . 95694| . 90562

14 . 94661| . 88433| . 94932) . 88985] . 95195, . 895261] . 95450| . 90054| . 95699| . 90570

15 | 9. 94666/0. 88442|9. 94936 0. 88994|9. 95199|0. 89534|9. 95454|0. 90063]9. 95703|0. 90579

16 . 94670) . 88451| . 94941| . 89003| . 95203| . 895431 . 95459 . 90071| . 95707, . 90587

17 . 94675| . 88461| . 94945) . 890121 . 95208) . 89552| . 95463, . 900801 . 95711) . 90596

18 . 94680| . 88470] . 94950) . 89022] . 95212| . 89561] . 95467, . 90089] . 95715| . 90604

19 . 94684| . 884791 . 94954| . 890311 . 95216| . 895701 . 95471, . 90097| . 95719 . 90613

20 | 9. 94689/0. 88489]9. 94958/0. 89040|9. 95221/0. 89579|9. 95475|0. 90106[9. 95723/0. 90621

21 . 94693| . 884981 . 94963) . 890491 . 95225| . 89588] . 95480, . 90115| . 95727, . 90630

22 . 94698| . 88507| . 94967| . 89058| . 95229) . 895971 . 95484| . 90124] . 95731, . 90638

23 . 94702 . 88516| . 94972) . 890671] . 95234| . 89606] . 95488, . 90132] . 95735, . 90647

24 . 94707, . 88526] . 94976) . 89076] . 95238) . 89614] . 95492) . 90141] . 95739) . 90655
25 | 9. 94711/0. 88535|9. 94981/0. 89085|9. 95242|0. 89623|9. 954960. 90150|9. 95743/0. 90664

26 . 94716| . 88544| . 94985| . 890941 . 95246) . 896321 . 95501, . 90158] . 95747, . 90672

21 .94721| . 88553| . 94989| . 89103| . 95251) . 896411 . 95505| . 90167] . 95751| . 90680
28 . 94725) . 88563| . 94994| . 89112| . 95255) . 89650] . 95509, . 90176) . 95755| . 90689
29 . 94730) . 88572| . 94998| . 89121| . 95259| . 896591 . 95513, . 90184] . 95759| . 90697
30 | 9. 94734/0. 88581|9. 95003/0. 89130|9. 95264/0. 89668|9. 95517/0. 90193|9. 95763/0. 90706

31 . 94739| . 88590] . 95007) . 89139] . 95268) . 89677| . 95521| . 90201] . 95768| . 90714
32 . 94743| . 88600] . 95011) . 89149] . 95272) . 89685| . 95526| . 90210} . 95772, . 90723
33 . 94748| . 886091 . 95016| . 89158] . 95276) . 89694| . 95530| . 90219} . 95776, . 90731
34 . 94752| . 88618| . 95020| . 89167| . 95281| . 89703] . 95534| . 90227| . 95780) . 90740
35 | 9. 947570. 88627|9. 95025/0. 89176|9. 95285 0. 89712|9. 95538|0. 90236|9. 95784/0. 90748
36 . 94761| . 88637| . 95029| . 89185| . 95289| . 89721| . 95542| . 90245] . 95788, . 90756
37 . 94766| . 88646| . 95033| . 89194| . 95294| . 89730| . 95546| . 90253| . 95792) . 90765
38 . 94770) . 88655| . 95038| . 89203] . 95298| . 89738] . 95550) . 90262] . 95796) . 90773
39 . 94774| . 88664| . 95042| . 89212] . 95302| . 89747| . 95555, . 90271| . 95800) . 90782
40 | 9. 94779 0. 88674|9. 950470. 8922119. 95306/0. 89756|9. 95559 0. 90279|9. 95804/0. 90790
41 . 94784| . 88683] . 95051| . 89230] . 95311| . 89765| . 95563, . 90288] . 95808, . 90798
42 „94788! . 88692] . 95055 . 89239] . 95315| . 89774| . 95567, . 90296| . 95812) . 90807
48 . 94793, . 887011 . 95060| . 89248] . 95319! . 89782| . 95571, . 90305| . 95816| . 90815
44 . 94797) . 887101 . 95064| . 89257] . 95323| . 89791| . 95575| . 90314] . 95820) . 90824
45 | 9. 948020. 88720|9. 95069 0. 89266|9. 95328 0. 89800]9. 95579|0. 90322|9. 95824 0. 90832
46 . 94806) . 88729| . 95073| . 89275| . 95332| . 89809| . 95584| . 90331| . 95828) . 90840
47 . 94811) . 88738| . 95077| . 89284| . 95336| . 89818] . 95588| . 90339] . 95832) . 90849
48 . 94815| . 88747| . 95082) . 89293| . 95340| . 89826] . 95592| . 90348] . 95836) . 90857
49 . 94820| . 88756| . 95086| . 89302| . 95345 . 89835| . 95596 . 90357| . 95840, . 90866] 11 |
50 | 9. 948240. 88766|9. 95090/0. 89311|9. 95349 0. 89844|9. 95600/0. 90365|9. 95844/0. 90874 10
51 .94829| . 88775| . 95095| . 89320| . 95353| . 89853] . 95604) . 90374] . 95848 .90882| 9
52 ` 94833) . 88784| . 95099 . 89329] . 95357, . 89862| . 95608 . 90382| . 95852) . 90891 8
53 .94838| . 88793] . 95104 . 89338] . 95362 . 89870| . 95613) . 90391| . 95856 .90899| 7
54 . 94842. . 88802] . 95108| . 89347| . 95366, . 89879| . 95617, . 90399| . 95860 . 90907 S
55 | 9. 94847 0. 88811|9 951120. 89356|9. 95370 0. 89888|9. 95621/0. 90408|9. 95864 0. 90916
56 „94851! . 88821] . 95117! . 89365] . 95374| . 89897] . 95625 . 90417] . 95868 .90924| 4
57 . 94856| . 888301 . 95121| . 89374] . 95379) . 89906] . 95629 . 90425 . 95872| . 90933 `
58 . 94860| .88839| . 95125| . 89383] . 95383) . 89914] . 95633) . 90434 . 95876) .90941| 2
59 ` 94865| . 88848] . 95130) . 89392] . 95387) . 89923] . 95637) . 90442 . 95880) . 90949} 1
60 9. 9486910. 888579. 95134/0. 8940119. 953910. 8993219. 95641|0. 90451|9. 95884/0. 90958 0
219° 218° 217° 216° 215°

1450

TABLE 34

Haversines

145° 147° 148° 149°

ü Log Hav | Nat. Hav| Log Hav | Nat. Hav | Log Hav | Nat. Hav} Log Hav | Nat. Hav] Log Hav /
0 | 9. 95884/0. 90958|9. 96119/0. 91452]|9. 96347/0. 91934|9. 96568|0. 92402]9. 96782)0. 60
1 . 95888| . 909661 . 96123| . 91460] . 96351! . 91941] . 96572| . 92410] . 96786| . 92866| 59
2 . 95892| . 909741 . 96127] . 91468| . 96355| . 91949] . 96576| . 92418] . 96789] . 92873| 58
3 . 95896, . 90983] . 96131| . 91476| . 96359] . 91957| . 96579| . 92426] . 96793| . 928811 57
4 . 95900| . 90991] . 96135) . 91484] . 96362] . 91965] . 96583] . 92433] . 96796| . 506 =
| 5 | 9. 95904/0. 90999|9. 96139/0. 91493|9. 96366/0. 91973|9. 96586 0. 9244119. 96800/0. 928
6 . 95908) . 91008] . 96142) . 91501] . 96370! . 91981] . 96590] . 92449] . 96803) . 92903} 54
74 - 95912 . 91016] .96146| . 91509} . 96374| . 91989] . 96594| . 92456] . 96807) . 92911] 53
8 . 95916| . 91024] . 96150) . 91517] . 96377, . 91997] . 96597] . 92464] . 96810) . 92918] 52
9 . 959201 . 910331 . 96154) . 91525] . 96381] . 92005] . 96601| . 92472] . 96814| . 92926 | 51 8
10 | 9. 95924/0. 91041]|9. 96158|0. 91533|9. 96385|0. 92013|9. 96604/0. 92479|9. 96817/0. 92933] 50
11 . 95928) . 91049} . 96162| . 91541] . 96388] . 92020] . 96608| . 92487] . 96821| . 92941| 49
12 . 95932) . 91057] . 96165] . 91549] . 96392] . 92028] . 96612! . 92495] . 96824! . 92948] 48
13 . 95936) . 91066] . 96169] . 91557] . 96396] . 92036] . 96615] . 92502] . 96827| . 92955] 47
14 . 95939) . 91074] . 96173) . 91565] . 96400) . 92044] . 96619] . 92510] . 96831) . 92963] 46
15 | 9. 95943/0. 91082|9. 96177|0. 91573|9. 96403 0. 92052|9. 96622|0. 92518|9. 968340. 92970] 45
16 . 95947| . 91091] . 96181| . 91582| . 96407, . 92060] . 96626| . 92525] . 96837) . 92978] 44
17 . 95951| . 91099| . 96185} . 91590] . 96411| . 92068] . 96630| . 92533] . 96841| . 92985 43
18 . 95955| . 91107| . 96188] . 91598] . 96414| . 92076] . 96633| . 92541] . 96845| . 92993| 42
19 . 95959) . 91115] . 96192) . 91606] . 96418] . 92083] . 96637] . 92548] . 96848) . 93000] 41
20 | 9. 95963/0. 91124]9. 96196/0. 91614]9. 9642210. 92091|9. 9664010. 9255619. 9685210. 93007] 40
21 . 95967| . 91132] . 96200] . 91622] . 96426] . 92099] . 96644! . 92563] . 96855) . 93015} 39
22 . 95971) . 91140] . 96204| . 91630] . 96429] . 92107] . 96648! . 925711 . 96859] . 93022] 38
23 . 95975) . 911491 . 96208] . 91638] . 96433] . 92115] . 96651! . 92579] . 96862) . 93030] 37
24 . 95979) . 91157] . 96211] . 91646] . 96437] . 92123] . 96655! . 92586] . 96866] . 93037] 36
25 | 9. 95983/0. 91165|9. 96215/0. 9165419. 9644010. 92130 9. 96658/0. 92594|9. 9686910. 93045] 35
26 . 95987| . 91173] . 96219) . 91662| . 96444! . 92138] . 96662| . 92602] . 96873| . 93052] 34
27 . 959911 . 91182] . 36223) . 91670] . 96448| . 92146] . 96665. . 92609] . 96876} . 93059] 33
28 . 959951 . 911901 . 96227) . 91678] . 96451] . 921541 . 96669 . 926171 . 96879 . 93067] 32
29 . 95999) . 91198] . 96230] . 91686] . 96455] . 92162] . 96673, . 92624] . 96883] . 93074] 31
30 | 9. 96002/0. 91206|9. 9623410. 9169419. 96459 0. 92170|9. 96676/0. 9263219. 96886/0. 930811 30
31 . 96006| . 91215| . 96238] . 91702] . 96462! . 921771 . 96680, . 926401 . 96890! . 93089| 29
32 . 96010) . 91223| . 96242| . 91710| . 96466. . 92185| . 96683] . 92647| . 96894| . 93096| 28
33 . 96014) . 91231] . 96246| . 91718| . 96470) . 92193| . 96687| . 92655| . 96897) . 93104| 27
34 . 96018] . 91239| . 96249| . 91726] . 96473] . 922011 . 96690| . 92662| . 96900| . 93111] 26
35 | 9. 96022 0. 91247|9. 96253/0. 9173419. 96477|0. 92209|9. 966940. 92670|9. 969040. 93118] 25
36 - 96026] . 91256] . 96257| . 91742| . 96481] . 92216| . 96697| . 92678] . 96907! . 93126] 24
37 . 96030| . 91264| . 96261| . 91750] . 96484! . 92224] . 96701| . 92685| . 96910! . 93133| 23
38 . 96034) . 91272| . 96265| . 91758] . 96488) . 922321 . 96705) . 92693] . 96914| . 93140] 22
39 . 96038] . 91280| . 96268| . 91766] . 96492) ` 92240] . 96708} . 92700| . 96917| . 93148] 21
40 | 9. 96042|0. 91289|9. 962720. 9177419. 96495|0. 92248|9. 96712|0. 92708|9. 96921|0. 93155 20
41 . 96046| . 91297] . 96276| . 91782] . 96499| . 92255] . 96715} . 92715] . 96924| . 93162] 19
42 . 96049| . 91305] . 96280] . 91790] . 96503, . 92263] . 96719] . 92723] . 96928| . 93170| 18
43 . 96053| . 91313] . 96283| . 91798] . 96506) ` 92271| . 96722, . 92730] . 96931, . 93177] 17
44 . 96057| . 91321] . 96287! . 91806] . 96510| . 92279| . 96726| . 92738] . 96934! . 93184] 16
45 | 9. 96061 0. 91329|9. 9629110. 91814/9. 96514/0. 92286|9. 96729/0. 92746]9. 96938/0. 93192] 15
46 . 96065 . 91338] . 96295| . 91829] . 96517| . 922941 . 96733| . 92753| . 96941 |. 93199] 14
47 . 96069| . 91346] . 96299! . 91830] . 96521| . 92302] . 96736| . 927611 . 96945) . 932061 13
48 . 96073| . 91354] . 96302! . 91838] . 96525| . 923101 . 96740} .92768| . 96948) . 93214] 12
49 . 96077 . 91362] . 96306! . 91846] . 96528 . 92317] . 96743] . 927761. 96951, . 932211 11
50 | 9. 96081/0. 9137019. 96310)0. 91854|9. 965320. 9232519. 9674710. 9278319. 96955 0. 93228] 10
51 . 96084 . 91379] . 96314! . 91862] . 96536| . 92333] . 96750| . 92791] . 96958) . 93236] 9
52 . 96088] . 91387] . 96317! . 91870] . 96539) . 92341] . 96754] . 92798] . 96962) . 93243] 8
53 . 96092) . 91395] . 96321] . 91878 . 96543] . 92348] . 96758] . 92806] . 96965) . 932501 7
54 . 96096) . 91403] . 96325! . 91886] . 96547, . 92356] . 96761| . 92813] . 96968) . 93258] 6
55 | 9. 96100 0. 9141119. 96329/0. 91894|9. 96550 0. 9236419. 9676510. 9282119. 96972/0. 93265| 5
56 S 96104 . 91419} . 96332) . 919021 . 96554!. 92372) . 96768] . 92828] . 96975 . 932721 4
97 > 96108 . 91427| . 96336] . 91910] . 96557! . 92379| . 96772] . 92836] . 96979) . 93279] 3
58 . 96112 . 91436] . 96340] . 91918 . 96561| . 92387] . 96775| . 92843] . 96982 . 93287] 2
59 - 96115} . 91444] . 96344] . 91926| . 96565! . 92395| . 96779) . 92851| . 96985 . 93294] 1
60 . 96119/0. 9145219. 9634710. 91934|9. 96568/0. 92402|9. 9678210. 92858|9. 96989/0. 933011 0

214° 213°

212° 211° 210°

— E

«K A AA DE

1451

TABLE 34

Haversines

150° 151° 152° 153° 154°

Log Hav | Nat. Havļ Log Hav | Nat. Hav} Log Hav | Nat. Hav} Log Hav | Nat. Hav | Log Hav | Nat. Hav] ’

9. 96989/0. 93301|9. 97188|0. 93731|9. 97381/0. 94147|9. 97566/0. 9455019. 97745|0. 94940} 60
. 96992) . 93309] . 97192) . 93738| . 97384) . 94154| . 97569) . 94557) . 97748| . 94946] 59
. 96996) . 93316} . 97195) . 93745| . 97387) . 94161| . 97572) . 94564| . 97751] . 94952) 58
. 96999) . 933231 . 97198) . 93752| . 97390| . 94168| . 97575| . 94570) . 97754) . 94959| 57
. 97002) . 93330} . 97201) . 93759| .97393| . 94175) .97578| . 94577| . 97756, . 94965] 56

0
1
2
3
[ 04

5 9. 97006/0. 93338|9. 972050. 93766|9. 97397 0. 94181|9. 97581/0. 94583|9. 9775910. 94972| 55
7
8
9

10

. 97009) . 93345] . 97208) . 93773] . 97400| . 94188] .97584| . 94590) .97762| . 94978) 54
. 97012| . 93352) .97211| . 937801 . 97403) . 94195] . 97587| . 94596] . 97765| . 94984) 53
.97016| . 933591 . 97214) . 93787) . 97406) . 94202] . 97591| . 94603) . 97768) . 94991) 52
. 97019} . 93367] . 97218) . 938794) . 97409. . 94209] . 97594) . 94610] . 97771) . 949971 51

9. 97022|0. 93374|9. 97221|0. 93801|9. 97412/0. 94215|9. 97597|0. 94616|9. 97774/0. 95003] 50
11 .97026| . 93381] . 97224) . 93808| . 97415) . 94222) . 97600) . 94623| . 97777| . 95010| 49
12 .97029| . 93388| . 97227, . 93815| . 97418) . 942291 . 97603| . 94629] . 97780) . 950161 48
13 .97033| . 93395| . 97231) . 93822| . 97422 . 94236| . 97606) . 94636] . 97783) . 95022) 47
14 .97036| .93403| . 97234) . 93829| . 97425) . 94243| . 97609| . 94642] . 97785) . 950291 46

15 | 9. 97039/0. 93410|9. 972370. 93836|9. 97428|0. 94249|9. 97612/0. 94649|9. 97788|0. 95035| 45
16 . 97043| . 93417| . 97240| . 93843| . 97431, . 94256| . 97615. . 94655| . 97791) . 95041| 44
17 . 97046| . 93424) . 97244| . 93850| . 97434| . 94263] . 97618| . 94662] . 97794) . 95048| 43
18 .97049| . 93432) . 97247| . 93857| . 97437, . 94270| . 97621) . 94669] .97797| . 95054| 42
19 „97052| . 93439] .97250| . 93864] . 97440| . 94276] .97624| . 94675) .97800| .95060| 41

20 | 9. 97056/0. 93446|9. 9725310. 93871|9. 97443|0. 942839. 97627|0. 94682|9. 97803|0. 95066) 40
21 .97059| . 93453] .97257| . 93878] . 97447, . 94290] . 97630| . 94688) . 97806) . 95073| 39
22 : 97063| . 93460] . 97260| . 93885] . 97450) . 94297] . 97633| . 94695) . 97808) . 95079) 38
23 . 97066) . 93468] . 97263) . 93892] . 97453) . 94303) . 97636) . 94701) . 97811) . 95085) 37
24 . 97069] . 93475] . 97266, . 93899] . 97456) . 94310] . 97639] . 94708] . 97814| . 95092] 36

25 | 9. 97073/0. 93482|9. 97269 0. 93906]9. 97459|0. 94317|9. 976420. 94714|9. 97817/0. 95098] 35
26 . 97076| . 93489] .97273| . 93913| . 97462| . 94324] . 97645| . 94721] . 97820) . 95104] 34
27 . 97079| . 93496| . 97276) . 93920| . 97465| . 94330) . 97647) . 94727| . 97823| . 95110) 33
28 . 97083] . 93503] . 97279| . 93927| . 97468| . 94337| . 97650, . 94734| . 97826) . 95117) 32
29 . 97086} . 93511] . 97282, . 93934| . 97471) . 94344| . 97653| . 94740| . 97829 . 95123| 31

. 97089|0. 93518|9. 972850. 9394119. 97474/0. 94351|9. 97656|0. 94747|9. 97831/0. 95129| 30
3l „97093! . 93525] . 97289| . 93948| . 97478| . 94357| . 97659) . 94753| . 97834| . 95136| 29
32 . 97096| . 93532] . 97292| . 93955| . 97481| . 94364| . 97662| . 94760| . 97837, . 95142| 28
33 . 97099, . 93539| . 97295| . 93962| . 97484| . 94371| . 97665| . 94766| . 97840) . 95148) 27
34 „97103| . 93546] . 97298| . 93969| . 97487| . 94377| . 97668| . 94773| . 97843 . 95154| 26

35 | 9. 97106/0. 93554]9. 97301/0. 93976|9. 97490/0. 94384|9. 97671)0. 94779|9. 97846|0. 95161| 25
36 . 97109| . 93561| . 97305| . 93982] . 97493] . 94391] . 97674. . 94786| . 97849) . 95167| 24
37 . 97113 . 93568| . 97308| . 93989| . 97496| . 94397| . 97677| . 94792] . 97851] . 95173| 23
38 .97116| . 93575| . 97311, . 93996] . 97499| . 94404] . 97680 . 94799] . 97854| . 95179) 22
39 . 97119| . 93582| .97314| . 94003] . 97502| . 94411| . 97683, . 94805| . 97857| . 95185) 21

40 | 9. 97123/0. 93589]9. 97317|0. 94010|9. 975050. 94418|9. 976860. 94811|9. 97860/0. 95192) 20
41 .97126| .93596| . 97321| . 94017] . 97508| . 94424| . 97689 . 94818| . 97863) . 95198) 19
42 . 97129| . 93603] . 97324| . 94024] . 97511| . 94431| . 97692| . 94824| . 97866 . 95204| 18
48 „97132. . 93611] . 97327| . 94031| . 97514| . 94438| . 97695| . 94831| . 97868) . 95210] 17
44 .97136| . 93618] .97330| . 94038] .97518| . 94444] . 97698| . 94837] . 97871| . 95217) 16

45 | 9. 97139/0. 93625|9. 973330. 9404519. 97521/0. 94451|9. 97701/0. 948449. 97874|0. 95223] 15
46 .97142| . 93632] .97337| . 94051] . 97524| . 94458) . 97704| . 94850] . 97877, . 95229) 14
47 97146] . 93639] . 97340] . 94058] . 97527] . 94464] . 07707, . 94856] . 97880) . 95235) 13
48 ` 97149| . 93646] . 97343] . 94065] . 97530) . 94471] . 97710, . 94863] . 97883) . 95241) 12
49 "97152 . 93653] . 97346 . 94072] . 97533| . 94477] . 97713] . 94869] . 97885) . 95248) 11

50 | 9. 971560. 9366019. 97349 0. 94079|9. 975360. 9448419. 977160. 94876|9. 978880. 95254 10
51 "97159 . 93667] . 97352] . 94086] . 97539) . 94491) . 97718] . 94882] . 97891, . 95260) 9

w
(=)
e

52 "97162 . 93674] . 97356, . 94093] . 97542| . 94497] . 97721] . 94889] . 97894) . 95266 8
58 .97165| . 93682] . 97359| . 94099] . 97545| . 94504] . 97724] . 94895) . 97897 .95272| 7
54 "97169 . 93689] . 97362, . 94106] . 97548| . 94511] . 97727, . 94901| . 97899 . 95278 6
55 9. 9717210. 936969. 97365/0. 94113|9. 97551/0. 94517|9. 97730|0. 94908|9. 97902/0. 95285 5
56 ` 97175| . 93703] . 97368] . 94120] . 97554| . 94524] . 97733 . 94914) . 97905 . 95291) 4
57 ` 97179) . 93710] . 97371| . 94127] . 97557, . 94531) . 97736, . 94921) . 97908 . 95297] 3
58 "97182 . 93717] . 97375, . 94134] .97560| . 94537] . 97739| . 94927] . 97911 . 95303] 2
59 ` 97185, .93724| .97378| .94141| .97563| . 94544] . 97742| . 94983] . 97914 . 95309 i

60 9. 9718810. 93731|9. 97381/0. 9414719. 97566 0. 9455019. 977450. 94940|9. 979160. 95315

209? 208? 207? 206? 205?

1452
TABLE 34
Haversines
155° 157°
Log Hav | Nat. Hav | Log Hav | Nat. Hav} Log Hav | Nat. Hav| Log Hav | Nat. Hav| Log Hav | Nat. Hav| '
0 | 9. 97916/0. 95315|9. 98081/0. 95677|9. 9823910. 96025|9. 98389 0. 9635919. 98533 0. 96679] 60
1| . 97919) . . 98084 |. . 98241) . . 98392| . . 98536, . 59
2 | .97922|. . 98086) . ` 98244| . ` 98394| . . 98538) . 58
3 | .97925|. . 98089) . . 98246 . . 98397| . . 98540| . 57
4| .97927 . . 98092 . . 98249) . . 98399| . . 98543} . 56
5 | 9. 9793010. - 98094. 0. . 98251/0. . 98402/0. „ 98545 0. 55
6 | . 97933] . . 98097) . . 98254| . . 98404 . . 98547. . 54
7| :o7936|. ` 98100) . . 98256 . . 98406| . . 98550| . 53
8 | .97939 . ` 98102] . . 98259) . . 98409) . . 98552] . 52
9 | ` 97941) ` . 98105) . . 98262) . 98411] . . 98554) . 51
10 | 9. 979440. - 98108 0. . 982640. . 984140. . 98557 0. 50
11 | .97947|. 98110) . ` 98267) . . 98416| . . 98559) . 49
12 | .97950|. ` 98113| . . 98269| . $ . 98419) . . 98561| . 48
13 | .97953| ` 98116 . . 98272) . ` 98421) ` . 98564. . 47
14 | . 97955} . . 98118| ` ` 98274 . . 98424| . ` 98566 . 46
15 | 9. 979580. . 98121/0. . 98277 0. - 9842610. . 985680. 45
16 | . 97961 . „98124. ` 98279 . . 98428) . . 98570) . 44
17 | .97964| ` 98126 . . 98282) . . 98431| . .98573 . 43
18 | .97966| ` . 98129 ` . 98285 . . 98433) . . 98575| . 42
19 98132 . . 98287| . . 98436) . . 98577, . 41
20 - 98134 0. . 98290 0. . 98438 0. . 98580 0. 40
21 . 98137) . ` 98292 . . 98440) . . 98582 . 39
22 98139) . . 98295| . . 98443| . . 98584. . 38
23 ` 98142 ` . 98297] . . 98445) ` . 98587] . 37
24 98145) . . 98300) . . 98448| . . 98589 . 36
25 . 9814710. - 98302 0. - 98450 0. . 98591
26 . 98150) . . 98305| . . 98453| . . 98593. 34
27 ` 98153| ` . 98307) . . 98455 . . 98596] . 33
28 . 98155| . . 98310) . . 98457] ` . 98598) . 32
2 . 98158| . . 98312 . . 98460 ` . 98600) . 31
- 981610. . 98315 0. . 98462 0. i j
31 . 98163] . . 98317 . . 98465| . 188605 ; Se
32 . 98166). . . 98320) . . 98467] . . 98607) . 28
33 . 98168| . . 98322 ` . 98469) . . 98609 27
ES 98171) ` . 98325) . . 98472 ` . 98612 . 96854| 26
. 9817410. - 983270. . 984740.
36 . 98176 . . 98330) . . 98476! . Tor Gane 24
37 . 98179 . . 98332 ` . 98479 . . 98619 . 96869] 23
38 ` 98182| ` . 98335 . . 98481 . . 98621| . 96874| 22
4 EE å ās „98484. . 98623 . 96879| 21
i i . 98340/0. . 984860.
41 . 98189| . . 98342) . S yp. 103624 GE 19
42 . 98192| ` . 98345| . . 98491) ` . 98630| ` 96894] 18
43 . 98195| ` . 98347 ` 98493 i
43 i l . 98632 . 96899] 17
H EDD Å . 98350) . . 98496| ` . 98634| . 96905] 16
. 982000. . 98352 0. - 984 |
46 . 98202 . . 98355| . 98500 | 19803011904 ae
d ; | . 98639 . 96915] 14
. 98205| ` . 98357] . . 98503) . 98641| . 96920| 13
48 ` 98208 ` . 98360| . 98505 |
b | | . 98643| . 96925| 12
5 SE j . 98362| . . 98507| . . 98646 . 96930] 11
; . 98365 0. o ;
51 . 98215) . . 98367 . Tone ; 34865) ium p
52 . 98218 ` . 98370) . . 98514] . . 98652| ` 8
53 . 98221) ` . 98372 ` 985171 . . 98655 | ` 7
£ ur Å ú i . 98519) . . 98657] . 6
56 . 98228) _ . 98379) . pe | Qon a
57 . 98231 . 98382| . . 98526 ` . 98664 3
58 . 98233 ` . 98384| . . 98529| ` ` 98666 ` 2
59 . 98236| ` . 98387 98531| . i
60 9823910. 9602519. 98389 | QoS A
98533 9867010. 0

203?

202?

201?

160°

Log Hav

9. 98670

: . 98673] . 96990

„98675
- 98677
. 98679

. 98681
. 98684
. 98686
. 98688
. 98690

161?

TABLE 34

Haversines

162?

Nat. Hav | Log Hav

Nat. Hav| Log Hav

0. 96985|9. 98801
. 98803
. 96995] . 98805
. 97000] . 98807
. 97004] . 98809

0. 97276|9. 98924
. 97281| . 98926
. 97285| . 98928
. 97290| . 98930
. 97295| . 98932

Nat. Hav| Log Hav

0. 97553|9. 99041
. 97557| . 99043
. 97562| . 99044
. 97566| . 99046
. 97571| . 99048

163?

0. 97815|9.
. 97819
. 97824
. 97828
. 97832

164?

Nat. Hav| Log Hav

99151
. 99152
. 99154
. 99156
. 99158

Nat. Hav

. 98067
. 98071
. 98075
. 98079

1453

0. 98063

10. 97009]9. 98811
. 97014] . 98813
. 970191 . 98815
. 97024] . 98817
. 97029| . 98819

. 97300|9. 98934
. 97304| . 98936
. 97309| . 98938
. 97314| . 98940
. 97318| . 98942

. 975775|9. 99050
. 97580| . 99052
. 97584] . 99054
. 975891 . 99056
. 97593| . 99058

. 9783619.
. 97841
. 97845
. 97849
. 97853

99159

. 99161
. 99163
. 99165
. 99166

. 98083
. 98087
. 98091

. 98099

. 98095]

. 98692
. 98695
. 98697
. 98699
. 98701

. 97034|9. 98822
. 97039| . 98824
. 97044| . 98826
. 97049| . 98828
. 97054| . 98830

0. 97323|9. 98944
. 97328| . 98946
. 97332| . 98948
. 97337| . 98950
. 97342| . 98952

. 97598|9. 99059
. 97602] . 99061
. 97606| . 99063
. 97611| . 99065
. 97615| . 99067

. 97858|9.
. 97862
. 97866
. 97870
. 97874

99168

. 99170
. 99172
. 99173
. 99175

. 98103
. 98107
. 98111
. 98115
598119

. 98703
. 98706
: 98708
. 98710
. 98712

. 9705919. 98832
. 97064] . 98834
. 970691 . 98836
. 97074] . 98838
. 97078] . 98840

. 9734719. 98954
. 97351| . 98956
. 97356| . 98958
. 97361| . 98960
. 97365| . 98962

. 97620|9. 99069
. 97624| . 99071
. 97629| . 99072
. 97633| . 99074
. 97637| . 99076

. 97879]9.
. 97883
. 97887
. 97891
. 97895

90177

899179
. 99180
. 99182
. 99184

. 98123
. 98127
. 98131
. 98135
. 98139

. 98714
. 98717
. 98719
. 98721
. 98723

. 97083|9. 98842
. 97088| . 98845
. 97093| . 98847
. 97098| . 98849
. 97103] . 98851

„97370[9. 98964
. 97374] . 98966
. 97379| . 98968
. 97384] . 98970
. 97388| . 98971

. 9764219. 99078
. 97646| . 99080
. 97651| . 99082
. 97655| . 99084
. 97660| . 99085

. 97899]9.
. 97904
. 97908
. 97912
. 97916

. 98725
. 98728
. 98730
- 98732

. 97108|9. 98853
. 97113| . 98855
. 97117| . 98857
. 97122| . 98859
. 97127| . 98861

. 97393|9. 98973
. 97398| . 98975
. 97402| . 98977
. 97407] . 98979
. 97412| . 98981

. 97664|9. 99087
. 97668| . 99089
. 97673| . 99091
. 97677| . 99093
. 97681| . 99095

. 97920]9.
297924
. 97929
. 97933
. 97937

99186

. 99187
. 99189
. 99191
. 99193

. 98142
. 98146
. 98150
. 98154
. 98158

99194

. 99196
. 99198
. 99200
. 99201

. 98162
. 98166
. 98170
. 98174
. 98178

. 97132]|9. 98863
. 97137| . 98865
. 97142| . 98867
. 97147| . 98869
. 97151] . 98871

. 97416|9. 98983
. 97421| . 98985
. 97425| . 98987
. 97430| . 98989
. 97435| . 98991

. 97686|9. 99096
. 97690| . 99098
. 97695| . 99100
. 97699] . 99102
. 97703| . 99104

. 97941|9.
. 97945
. 97949
. 97953
. 97957

99203

. 99205
. 99206
. 99208
. 99210

„98182
„98185
„98189
„98193
„98197

. 97156|9. 98873
. 971611 . 98875
. 97166] . 98877
. 97171] . 98880
. 97176} . 98882

. 9743919. 98993
. 97444] . 98995
. 97448] . 98997
. 97453] . 98999
. 97458} . 99001

. 97708|9. 99106
. 97712} . 99107
. 97716| . 99109
. 977211 . 99111
. 97725] . 99113

. 97962)9.
. 97966
. 97970
: 97974
. 97978

99212

. 99213
. 99215
. 99217
. 99218

. 98201
. 98205
. 98209
. 98212
. 98216

. 97180|9. 98884
. 97185| . 98886
. 97190| . 98888
. 97195| . 98890
. 97200| . 98892

. 97462|9. 99003
. 97467| . 99004
. 97471| . 99006
. 97476| . 99008
. 97480| . 99010

. 97729|9. 99115
. 97734| . 99116
. 97738| . 99118
. 97742| . 99120
. 97747| . 99122

. 97982|9.
. 97986
. 97990
. 97994
. 97998

99220

. 99222
. 99223
. 99225
. 99227

. 98220
. 98224
. 98228
. 98232
. 98236

. 97204|9. 98894
. 97209| . 98896
. 97214| . 98898
. 97219| . 98900
. 97224| . 98902

. 97485|9. 99012

. 97490] . 99014) .
. 97494| . 99016) .
. 97499| . 99018| .
. 97503| . 99020| .

. 97751|9. 99124
. 99126
. 99127
. 99129
. 99131

. 9800219.
. 98007
. 98011
. 98015
. 98019

99229

. 99230
. 99232
. 99234
. 99235

. 98239
. 98243
. 98247
. 98251
. 98255

. 97228|9. 98904
. 97233| . 98906
. 97238| . 98908
. 97243| . 98910
. 97247| . 98912

. 97508|9. 99022
. 97512| . 99024
. 97517| . 99026
. 97521| . 99027
. 97526| . 99029

. 97773|9. 99133
. 97777) . 99135
. 97781| . 99136
. 97785| . 99138
. 97790| . 99140

. 9802319.
. 98027
. 98031
. 98035
. 98039

99237

. 99239
. 99240
. 99242
. 99244

. 98258
. 98262
. 98266
. 98270
. 98274

. 97252|9. 98914
. 97257) . 98916
. 97262| . 98918
. 97266| . 98920
. 97271| . 98922
. 97276|9. 98924

. 97530/9. 99031

0. 97553|9. 99041

. 97535) . 99033) .
. 97539] . 99035] .
. 97544] . 99037] .
97548} . 99039) .

. 9779419. 99142
. 99143
. 99145
. 99147
. 99149
0. 97815|9. 99151

. 980439.
. 98047
. 98051
. 98055
. 98059
0. 98063|9.

99245

. 99247
„ 99249
. 99250
. 99252

99254

. 98277
. 98281
. 98285
. 98289
. 98293
0. 98296

O» NOÉ GV O NOS

198°

197°

196°

195°

1454

165°

TABLE 34

Haversines

" Log Hav d
0 | 9. 99254 0. 99081| 60
1 | .99255| . 98300] . 99352| . 98518 ` 99524| . 98910] . . 99084] 59
2 | .99257| . 98304] . 99353| . 98522 . 99526| . 98913| . 99602| . 99087| 58
3 | .99259| . 98308| . 99355| . 98525 ` 99527] . 98916| . 99603 | . 99090] 57
4 | . 99260] . 98311] . 99356 . 98529 . 99528| . 98919| . 99604| . 99092] 56
5 | 9. 99262 0. 98315|9. 99358/0. 9853219 ` 99529 0. 98922|9. 99605 0. 99095| 55
6 | .99264| . 98319] . 99359| . 98536 . 99531| . 98925] . 99606| . 99098] 54
7 | .99265| .98323| . 99361| . 98539 . 99532, . 98928] . 99608| . 99101] 53
8 | .99267| . 98326] . 99362| . 98543 . 99533| . 98931| . 99609| . 99103| 52
9 | .99269| . . 99364| . 98546 . 99535| . 98934| . 99610| . 99106] 51
10 | 9. 99270 0. 9833419. 993660. 9855019 . 99536 0. 9893719. 99611/0. 99109| 50
11 | .99272| . 98337| . 99367| . 98553 . 99537| . 98940] . 99612 . 99112] 49
12 | .99274| . 98341] . 99369| . 98557 . 99539| . 98943| . 99614| . 99114| 48
13 | .99275| . 98345| . 99370| . 98560 . 99540| . 98946| . 99615! . 99117] 47
14 | .99277 . 98349] . 99372| | 98564 . 99541| . 98949] . 99616| . 99120] 46
15 | 9. 992780. 98352|9. 9937310. 9856719 . 99543 0. 9895219. 99617 0. 99123] 45
16 | .99280| .98356| . 99375| . 98571 . 99544| . 98955] . 99618! . 99125| 44
17 | .99282| . 98360| . 99376| . 98574 . 99545| . 98958] . 99620| . 99128| 43
18 | .99283 . 98363] . 99378| . 98577 . 99546 . 98961] . 99621) . 99131] 42
19 | . 99285] . 983671 . 99379| | 98581 . 99548| . 98964| . 99622] . 99133] 41
20 | 9. 99287/0. 9837119. 9938110. 9858419 . 99549 0. 98967|9. 99623 0. 99136| 40
21 | .99288| . 98374] . 99382] . 98588 . 99550| . 98970| . 99624| . 99139] 39
22 | .99290| . 98378] . 99384 ` 98591 . 99552| . 98973| . 99626| . 99141] 38
23 | .99291| . 98382] . 99385| | 98595 . 99553, . 98976| . 99627! . 99144| 37
24 | .99293| .98385| . 99387| . 98598 .99554| . 98979| . 99628| . 99147] 36
25 | 9. 9929510. 98389|9. 99388 0. 9860119 . 99555 0. 98982|9. 99629 0. 99149| 35
26 | .99296| . 98393] . 99390| . 98605 . 99557| . 98985] . 99630| . 99152] 34
27 | .99298| . 98396| . 99391| ` 98608 . 99558| . 989881 . 99631| . 99155| 33
28 | .99300| . 98400] . 99393| . 98612 . 99559| . 98990] . 99633! . 99157| 32
29 | .99301| . 98404] . 99394| 98615 . 99561| . 98993] . 99634| . 99160] 31
30 | 9. 99303/0. 98407|9. 99396 0. 98618l9 -99562/0. 98996|9. i
31 | .99304| . 98411] . 99397| . 98622 . 99563 98999 Beete E
32 | .99306| . 98415] . 99399! | 98625 . 99564| . 99002] . 99637| . 99168| 28
33 | .99308| . 98418] . 99400| . 98629 . 99566| . 99005| . 99638! . 99171] 27
E . 99402| . 98632 . 99567, . 99008] . 99639 . 99173] 26
. 99403 0. 9863519 . 995680. 9901119. 9964110. 99176| 25
36 . 99405| . 98639 . 99569| . 99014] . 99642| . 99179] 24
37 . 99406| . 98642 . 99571| . 99016] . 99643| . 99181] 23
38 . 99408| . 98646 . 99572| . 99019] . 99644| . 99184] 22
n . 99409 . 98649 . 99573| . 99022] . 99645! | 99186] 21
„ 994110. 9865219 . 99575 0. 9902519.
41 . 99412 . 98656 „99576 de i
42 . 99414| . 98659 . 99577| . 99031] ` 99
. 99649 . 99194] 18
43 . 99415| . 98662 . 99578 . 99034] . 99650| . 99197] 17
E . 99417| . 98666 . 99580| . 99036] . 99651 . 99199] 16
. 994180. 9866919 995810.
46 . 99420| . 98672 995821 Ke SE, n
47 . 99421| . 98676 . 99583] . 9904
Å 5| . 99654! . 99207] 13
48 . 99422) . 98679 . 99584| . 990481 . 99655| . 99210] 12
E d ` 98682 . 99586| . 99051] . 99657! . 992121 11
. 99425 0. 9868619 . 99587 0. €
51 . 99427 . 98689 . 99588 Ó IDE F
52 . 99429 . 98692 . 99589] . 99059] . 99660| . 99220] 8
53 . 99430| . 98695 . 99591 . 99062] . 99661. 992231 7
E . 99431| . 98699 . 99592 . 99065| . 99662 . 99225| 6
. 99433 0. 9870219 . 99593 0.
56 604241. 98708 Ies EE SE
57 . 99436| . 98709 . 99596| . 99073| . 99 :
58 99437| . 98712 í posee Be
58 1 . 99597 . 99076] . 99667 .99235| 2
. 99438 . 98715] . i . 99598 . 99079] ` 996
60 99440 0. 98719l9. 99 Bä Eccc ae
í i . 99523/0. 98907|9. 9959910. 9908119. 9966910. 992401 0

193°

192°

191°

1455

TABLE 34

Haversines

170° 172° 173° 174°

Log Hav | Nat. Hav] Log Hav | Nat. Hav | Log Hav | Nat. Hav] Log Hav | Nat. Hav Log Hav | Nat. Hav

9. 99669/0. 99240|9. 997320. 99384|9. 99788/0. 9951319. 99838/0. 99627|9. 998810. 99726
. 99670) . S 3 . : 9| .99515| . 99839| . 99629| . 99882| . 99728
„99671|. ` : : . 99517| . 99839| . 99631] . 99882| . 99729)
. 99672) . : ; : . 995191 . 99840) . 99633] . 99883 . 99731
. 99673) . : ; . . 99521| . 99841| . 99634] . 99884| . 99732

. 9967440. . : l . 9952319. 99842 0. 99636|9. 99884 0. 99734
. 99675) . - : . . 99525] . 99842) . 99638| . 99885| . 99735
. 99677| . : s : . 99527| . 99843) . 996401 . 99885 . 99737
. 99678| . : 3 ` . 99529] . 99844) . 996411 . 99886 . 99738
. 99679) . S . : . 99531| . 99845) . 99643| . 99887, . 99740

. 996800. l m i . 99533|9. 99845/0. 99645|9. 998870. 99741
. 99681) . S E 4 . 995351 . 99846| . 99647| . 99888| . 99743
. 99682) . : 4 a . 99537| . 99847| . 99648| . 99889| . 99744
. 99683) . : k S . 99539| . 99848| . 99650| . 99889| . 99746
. 99684) . - ? , . 995411 . 99848) . 99652} . 99890| . 99747

. 99685)0. E $ : . 99543|9. 99849 0. 99653|9. 9989110. 99748
. 99686) . S ? d . 99545] . 99850) . 99655] . 99891| . 99750
. 99687. < S 3 . 99547| . 99851| . 99657| . 99892| . 99751
. 99688) . : ; 4 . 995491 . 99851) . 996591 . 99893) . 99753
. 99690) . : : ! . 995511 . 99852 . 996601 . 99893) . 99754

. 9969110. Ë : i . 99553|9. 99853/0. 99662|9. 998940. 99756
. 99692. . : ` : . 99555] . 99854) . 99664] . 99894) . 99757,
. 99693) . : : : . 995571 . 99854) . 99665| . 99895) . 99759
. 99694) . 3 . e . 995591 . 99855) . 99667] . 99896| . 99760
. 99695) . : : : . 99561| . 99856) . 996691 . 99896 . 99761

. 99696)0. E E y . 9956319. 99857|0. 9967019. 99897/0. 99763
. 99697) . e s S . 99565| . 99857| . 99672| . 99897| . 99764
. 99698) . f c ; . 995671 . 99858| . 99674] . 99898| . 99766
. 99699| . : ; : . 995681 . 998591 . 996751 . 99899 . 99767
. 995701 . 99859 . 99677) . 99899) . 99768

. 9957219. 9986010. 99679|9. 99900/0. 99770
. 995741 . 99861) . 996801 . 99901) . 99771
. 995761 . 99862| . 996821 . 99901| . 99773
. 995781 . 99862| . 99684] . 99902| . 99774
. 995801 . 99863, . 99685} . 99902| . 99775

` Y K . 99582|9. 998640. 99687|9. 99903 0. 99777
. 99766, . : . 99584| . 99864| . 99688] . 99904 . 99778
. 99767). : . 99585| . 99865| . 99690| . 99904) . 99779
. 99768) . < . 995871 . 99866| . 99692] . 99905| . 99781
. 99769) . ! . 99589| . 99867, . 99693| . 99905, . 99782

„997700. Å . 99591|9. 998670. 99695|9. 999060. 99784
. 99771) . : . 99593| . 99868| . 99696| . 99906| . 99785
. 99772) . 3 . 995951 . 99869| . 99698| . 99907| . 99786
. 99773, . : . 99597| . 99869 . 997001 . 99908 . 99788
. 99774) . : . 99598| . 99870| . 99701} . 99908| . 99789

. 997740. y . 99600|9. 99871/0. 99703|9. 99909|0. 99790
. 99775) . 5 . 99602] . 99871) . 99704) . 99909; . 99792
. 99776) . : . 99604] . 99872 . 99706] . 99910! . 99793
. 99777, . : . 99606| . 99873| . 99708| . 99911 . 99794
. 99778) . : . 99608| . 99874| . 99709} . 99911) . 99796

. 997790. , . 99609|9. 99874|0. 99711|9. 99912 0. 99797
. 99780| . 4 . 99611] . 99875, . 99712] . 99912) . 99798
. 99781) . 4 . 99613] . 99876| . 99714] . 99913) . 99799
. 99782) . : . 99615| . 99876, . 99715| . 99913| . 99801
. 99783| . : . 99617] . 99877, . 99717| . 99914| . 99802

. 997840. E . 99618|9. 99878|0. 99718|9. 99915/0. 99803
. 99785) . : . 99620| . 99878 . 99720| . 99915; . 99805
. 99786, . : . 99622| . 99879 . 99722| . 99916, . 99806
. 99786, . i . 99624| . 99880, . 99723| . 99916) . 99807
. 99787, . 7| .99626| . 99880) . 99725| . 99917, . 99808

99788 99838 0. 99627|9. 99881/0. 99726|9. 99917|0. 99810

PETREA F

Or t dd Ha Ot O» -100 O

188? 187? — 186? 185°

1456

. 99918
. 99918
199919
399919

"99811
. 99812
. 99814
. 99815

TABLE 34

Haversines

Log Hav | Nat. Hav| Log Hav | Nat. Hav | Log Hav | Nat. Hav | Log Hav | Nat. Hav| Log Hav | Nat. Hav

. 99879
. 99880
. 99881
. 99882

9007 11%
20997 Lee
+99971|4-
0999721%

9. 99917|0. 99810|9. 99947/0. 99878|9. 99970/0. 9993119. 99987|0. 99970|9. 9999710. 99992
. 99948 99987

. 99948
. 99948
. 99949

so

. 99921
. 99921
. 99922
. 99922

OO NOU RON O

99920|0.
„99817
. 99819
. 99820
. 99821

99816]9.

. 99950
. 99950
299901
. 99951

99949/0. 9988319.
. 99884
. 99885
. 99886
. 99887

9997210.

2900728
. 99973| .
999731.
SC 99973)"

e

. 99923
. 99924
. 99924
. 99925

. 99923|0.
. 99823
. 99825
. 99826
. 99827

99822]9.

. 99952
. 99952
. 99953
. 99953

99951/0. 9988819.
. 99889
. 99890
. 99891
~ 99892

999730.

. 99974| .
. 99974) .
- 99974) .
- 99975| .

. 99987] .
. 99987] .
. 99988] .

. 9998810.
. 99988| .
. 99988| .
. 99988} .
299989|*:

99989|0.
. 99989| .
99989]
.99989|.
.99990|.

. 99926
. 99926
299927
. 99927

99925]0.
. 99829
. 99831
. 99832
. 99833

99828]9.

. 99954
. 99954
. 99954
. 99955

99953/0. 99893|9.
. 99894
. 99895
. 99896

. 99897

9997540.

: 99975) .
199976]
. 99976) .
. 99976} .

. 99990)0.
7 29990)".
29990017
. 99990} .
299991

. 99928
. 99929
. 99929
. 99930

. 99928/0.
. 99835
. 99837
. 99838
. 99839

99834]9.

. 99956
- 99956
. 99957
. 99957

99955|0. 99898]9.
. 99899
„99900
. 99900

. 99901

9997610.

50997710
2999718.
- 99977|*.
2099789

9999110.
2999017
. 99991

7999911»
29999215:

o

. 99931
. 99932
. 99932
. 99933

. 99931/0.
. 99841
. 99842
. 99844
. 99845

9984019.

. 99958
. 99958
. 93959
. 99959

99958/0. 9990219.
. 99903
. 99904
. 99905

. 99906

. 99934
. 99934
. 99935
. 99935

. 99933/0.
. 99847
. 99848
. 99849
. 99850

99846]9.

. 99960
. 99960
. 99961
. 99961

9997810.

2999/8|%.
. 99978) .
299979:
2999/79

9999210.
29000218
- 99992) .
99992]
. 99992).

99959|0. 99907]9.
. 99908
. 99909
- 99909

. 99910

9997910.

. 99980| .
. 99980| .
. 99980} .
. 99980| .

. 999930.
199993
. 99993) .
. 99993) .
< 999931.

Sz)

. 99936
. 99936
. 99937
299997

99935|0.
. 99853
. 99854
. 99855
. 99856

99852]9.

. 99962
. 99962
. 99963
. 99963

99961|0. 9991119.
299912
. 99913
. 99914

. 99915

. 99981
. 99981
999811"
. 99982) .

99981/0.

. 99993)0.
. 99994] .
. 99994) .
. 99994) .
. 99994) .

. 99938
. 99938
. 99939
„99939
„99940

0
. 99858
. 99859
. 99860
. 99861

99857]9.

. 99964
. 99964
. 99964
. 99965

99963 0. 99915]9.
. 99916
~ 99917
. 99918

- 99919

99982/0.

- 99982) .
299989
. 99983| .
. 99983. .

. 9999410.
- 99994| `.
. 99994) .
- 99995) .
. 99995) .

o

. 99940
. 99941
. 99941
. 99942
. 99942

0
. 99864
. 99865
. 99866
. 99867

9986319.

. 99965
. 99966
. 99966
. 99966

99965|0. 99920]9.
. 99920
199921
. 99922

. 99923

999830.

. 99983) .
. 99984) .
. 99984) .
. 99984| .

. 999950.
- 99995) .
- 99995) .
- 99995) |-
:99995|x

. 99943
. 99943
. 99943
. 99944
. 99944

0
. 99869
. 99870
. 99871
299872

9986819.

. 99967
. 99968
. 99968
. 99968

99967|0. 99924]9.
. 99924
. 99925
„99926

"99927

9998410.

. 99985] .
. 99985] .
. 99985) .
. 99985| .

. 99996|0.
:99996| .
. 99996) .
. 99996) .
. 99996} .

. 99945
. 99945
. 99946
. 99946
. 999471] .
. 9994710.

0
. 99874
. 99875
. 99876

99873]9.

9987
99878|9.

. 99969
. 99969
. 99970
7| . 99970

99969/0. 99928[9.
. 99928
. 99929
. 99930
- 999311"

99970/0. 99931]9.

999860.

. 99986| .
. 99986| .
. 99986| .

99987

99987 0. 9997019.

. 9999610.
: 99996) .
. 99996] .
. 99996) .
. 99997) . o
9999710. 99992]0.

184°

183°

182°

181°

POPE" 79 RW e e U T S v

INDEX

Page
¡Escola denned 5 gs be tasas 206
BSscopesdelined Ee rasa Dm o 911
ALT d ea ee ra yr sies 318
Batracesdeflined- tetas lan et 912
ONMOLANySCOPO- < S Hasta se ia am 335
A, B, C Method”, of, Waller_.....-<=.. 530-531
«A, B, C" Tables for Azimuth, Great Circle
Sailing, and Reduction to the Meridian;
ofgBlackbunnes-- Eer Ee 570
Abandoning ship £ chas < sees = acts 647-649
EX DOO VIB MONS oe cae see o oo os 903-906
on charts, omission of period_____----- 115
use of in chart construction_____------ 894
Bbeamsdefned. Loco oo ores dae s 909
Aberration, causes of- ----------------- 369
EE Eege Ee eR E e 909
discoverviofi acen. tato qe 39
Abney type hand level... cbm. 842
Abraham as astronomer...............- 34
Abscissa, defined - kas tor te - 909, 1031
Absolute accuracy, defined. ------------ 1006
Absolute humidity, defined........... 778, 909
lAbsolute motione ee x o a oer 351
(See also Motion(s))
Absolute precision, defined. ............ 1006
Absolute temperature, defined. ....... 775-776
Absolute value, defined. ` -------------- 1005
Absolute zero, on Celsius and Fahrenheit
gSealegA 4 a E o 959
definedae AR ee eS 775, 909
Accelerating, anode - - ----=--- =< f= Ee 302
Acceleration error, altitude correction for. 428
GIESCXLANL An 4. too Boat ¿Es Eg 417
Accuracy, absolute, defined. ------------ 1006
Olfcharts 2 A b. 34:08 ros 104-106
defined sa 2:6. ði. dies io 679, 1006
relative, defined=2 eg EE, SSS Se 1006
Acknowledgments = iret es te - 74
Acliniclline defined pidt- Aras b= só. = 909
Acoustic navigation, defined- ----------- 909
Acute angle, defined - --------------- 909, 1020
Acute triangle, defined---------------- 1022
Adcockwanterina thee S$ s=5- = See E 307
Addison, Thomas; Arithmetical Navigation of. 34
Addition, of algebraic expressions-------- 1018
arithmetic and algebraic, defined. ----- 1008
of numbers, explained--.--------.---- 1007
Adjacent angles, defined...............- 1021
Advance, allowance for__-------------- 276-278
cCoürseTon defined: eto ZE 66, 218, 919
CGtine Gaeta A ke = sera 277, 909
speedyrofMdefined'eeseso rr ec e See e 948
lActvectiondefinedsses- PFM tase = 909
D EE 807
Aepinus, Francis; electricity vs. magne-
IN fl es. 58
Aerial and Marine Navigation Tables, of
Gingrich Sese IN A, CT 535
Aerodrome, alternate, in air navigation... 676
closedMdefimedeewws e m mw BZ 670
Nerograp hin. Toce AMS. NOUNS S Ta: 787
Aerometeorograph m menen E 787
Aeronautical chart (see Chart(s))
Aeronautical Chart and Information Cen-
ter, publications of------------ 94, 100, 1003
Ageton, Arthur A.; sight reduction tables
of MEI Le 57, 536, 538

Page
Agonic line, defined.............- 116, 162, 909
AROUND, QENE s e eec EE 909

E e ON 725
Adeadsdeüned e "vr í 909
Aid(s) to navigation, changes of, charts
conrected-fopBem sor ER 105
Daily Memorandum on............ 99, 117
Notice to. Mariners onto Nome 99, 117
chartisymbols for on 111=113
uta nee eee 983-998
(See also Chart symbol(s))
defined ate. E e meee 259, 909
descriptions of, in light lists----------- 97
inssailing directions 97
hiStony{ Olas. fe! A PS 28
inahwdropraphicSuryey see aa 861
installation and maintenance of------- 261
IMS POlAITERIONS = SS SS e 630
types of, described_____------------ 259-267
(See also Buoy(s), Buoyage systems,
Light(s))

Airweupersaturaiedzs 7-5 2 Ē 778
temperature measurement. ---------.- 776
(See also Atmosphere)

Awalmanac rdenned tE SE oa 909

Air Almanac, of Weems.---------------- 52

Air Almanac, Americans 222 20828 52-53

Air Almanac, The; altitude correction

tables ins rs OV 439
astrograph setting by---------------- 468
declination by, of moon. 470

of planet tē We sere: naue D = 470

Of starts 17 ose npe m 471

of Sunwell. af: eee 469
description EEN 466, 467
ecliptic diagram in----------------- 479, 586
extension of, to following year-- ------ 479

to lateriyear eee Pt 653

(See also Long-term Almanac)
extracts from eee 1152-1159
hour angle by, of moon-------------- 470

Of planet 2322532 22 3 S5 pem ee 470

Of Star 7 see tacos REO eee 471

of suns eee, ie) Dd. 469
publication of----------------------- 98
risings, settings, twilights by-------- 472-478

in polar regions 2221 eee Cc 639-642
sky diagrams in--------.-2--2------- 591

Air mass defined c EE MM 909
pe RE e a= 800

Air navigation, by celestial bodies. ...--- 675
charts and publications for- ----------- 670
computers for+---------------------- 672
by dead reckoning-.--------------- 671-674
Dec e o 675
denned -e geen ebe 62, 909
Ginectionp < e cee saa an 671
electronics in_------ ------------- 59, 675

(See also Electronic navigation)
flight planning" -------------------- 676
by piloting o setae LL LL 673
pressure pattern--_------------------ 675
principles of _--------------------- 670—676
(See also Doppler navigation, Inertial

navigation, Navigation) m

7

Air Navigation (Air Force Manual 51-40) -
1457

1458 INDEX
Page Pag
Air Navigation (H.O. Pub. No. 216)... 418, 671 Altitude—Continued
Air plot, defined = 2322 e 672 computed, defined. 421, 91
Air position, defined" eee 672 use Of: 2.2 eo es AA A 4
Airspeed„definēd 5 g a a 672 of, cone, defined. o o ae 1027
measurement oi -nam S m 673 correctiongito. es AA 421-446
Air temperature, altitude correction for, air almanac tables--— c
ett , 909 nautical almanac tables------------
tāble:28. 222. Ses CX s 300 Bels 280 (See also Sextant altitude correction(s))
explanation o 1192 of cylinder, defined $ - 3 EEE
(See also Sextant altitude correction(s)) defined, 22 Get nempe EE
Air Weather Service, mission of--------- 787 determination of, graphical methods... . 555-
Aircraft defined des: A 670 1
Aircraft COMPAsses-- EE 672 by map projection- -soono 83, 560-561
Airman's guides, manuals: area- ana 671 mechanical methods------------- 558-560
Airports, shown on charts_------------- 114 _ (See also Sight reduction)
Amway sejās eee ee fom 3 SF NE 674 direction of measurement______-_------
Airy r Georgen. Sāres Je a ME 24 equal, circle of, defined_-__-_----------
Alabaster, R. C.; sight reduction method USO o o eee 449-450
IRA "Ba e e ere Ce 545 defined" "TES PPP 924
Alaska currents: e A 724 ex-Hheridian-.:.. ect see ee 518
Albatross, oceanographic expeditions of... 692 “history EE 48
Alessio, A.; azimuth diagram of--------- 572 high, sight reduction aa 513-514
Aleutianteurreni ss LL 724 HOW, CONTECLONS O SE 442—445
Alexander IV, prime meridian of-------- 48 sight reduction ee 511-513
Alfonsines Dables cono No ee ee 36, 51 use of sextant Tor A 442—445
Algae in sea water 20-00-00 699 measurement of, in lifeboat_________ 654-657
Algebra defined ` "2 2 ce MEE 1017 meridian, defined Ar- oo S 936
rinciples'of SSS A ome 1017—1020 near meridian transit, table 80____ 1308-1311
'Alidadesidefinedi SES ME 153, 909 explanationtof te SPSS 1195
Alignment, of electronic circuit, defined__ 909 negative, of celestial body- -----------
Almagest, of Ptolemy_________ 26, 36, 38, 48, 51 observed defined PTA 421, 450, 938
Almanac(s), contents of________________ 98 parallax in---.—:——2 PROS UA EA 435, 939
defined eee RIM DOOR AN TN 909 parallel of, defned = -_veswer "06 385, 939
early American: (PES SM 52 precomputed 2 e ENER 510, 940
first. official: 580380 > es Pt S oy 52 on prime vertical circle, table 25... 1282-1285
historysof R IE An on es 51 explanation of PES AA 1193
Long-term---. a... Matta Rn 1160-1164 Of prism, defined <i -SIMME ARE 1025
risings, settings, twilights by________ 472-478 of pyramid, defined: 60 MS 1026
at moving craft E Ee 478 rate.of change'of 00 ANo a 551-554
ISG Of: Se. casa! EA a 468-479 rectified, defined- = 437, 943
(See also Air Almanac, The; American sextant defined E 402, 421, 946
Air Almanac; American Ephemeris tabulated, defined? 19 oars ae 949
and Nautical Almanac, The; Ameri- of triangle, defined--_-------22222- 1022
can Nautical Almanac, The; Nautical (See also Celestial body, Sextant altitude j
Almanac) correction(s), Sight reduction)
Almanae, air (see Air Almanac, The) Altitude and Azimuth Almanac, of Japanese
Almanac, Altitude and Azimuth; of Japan- Hydrographic Office. - LL... 541
ese Hydrographic Office... a 541 Altitude and Azimuth Tables, of Aquino__ 537
Almanac, nautical (see American Nautical Altitude and Azimuth Tables for Air and
Almanac, The) Sea Navigation (I. C. S.), of Collins_. - 536
Almanach Perpetuum, of Zacuto____. ____ 51 Altitude azimuth, defined._____________ 910
Almucantar, defined. 1.2... 1 _ 385 formula for ii 567
Alnico, «defined. *esst. ER 909 Altitude, Azimuth, and Geographical Posi-
SE GH Gamma Navigation Tables, tion; of. Littlehales- ------2 2222 56
ey OLGOodwin 8278 C A x 526 Altitude, Azimuth, and Hou ja-
Alphonsine Tables (see Alfonsine Tables) gram; of Dese ods aida 557
CHUA Toten of Davisg cc sc aate 529 -Altitude circle vec: R 385. 910
ernate aerodrome, in air navigation... ; stø 2 A DARREN RE" , A ,
alternating PUE e al 289, ek dub HR defined. ..... 421, 450, 910
Alternating fixed and flashing light, Ititude difference method, line of posi-
NEE See eh, Viet de A 909 a TUE Dod ue. UU M 450, 528, ME
ernatin : SAMA MO: historical 3 cru EN
define ERG kri group flashing light, 910 Altitude factor, discussed ` WW ``“ “vv
Alternating flashing light, defined_______ 910 table-2 es age = See ee 1298-1307
Alternating group flashing light, defined.. 910 „explanation Of tege pane 11
Alternating group occulting light, defined 910 Altitude intercept, define 451, 528, 910
Alternating light, defined... e e CORRI I (See also Altitude difference)
Alternating occulting light, defined. . A10 Attitude intercept method of Marcq St.-
Altimeter, absolute, described... 673 ee Sos
barometric, described... 673, 769 historial. ee E 56
Altitude, apparent, defined... 911 Altitude or Position Line Tables, of Ball. . 529
approximate, defined 911 Altitude Tables for Mariners and Aviators,
calculated, defined... 5. C 915 of Tillman... 41e St Ebene M. 539
of celestial body, defined... 385 Altocumulüszssu sel] hos ued Den 781, 910

Altostratus Bio E D E E 782, 910

INDEX 1459

Page

AM (ante meridian), when used__________ 483

Ambiguity of loop antenna_____________ 305

American Air Almanac, combining of with

| Britishraplerstips 1. ¿relegada snit 53
| publishingiofifirsu- eene eee 52
|... (See also Air Almanac, The)
| American Ephemeris and Nautical Alma-
nac». Thestbistoricaliresa 5119 eed 52
publication and contents of. |... 98, 466
American Nautical Almanac, The; altitude
correction tables inis tedas as 438
combining of with British____________ 53
declination by, of moon 470
OP planet: preeu Celine - Yo ansan 470
Oftstārāts pressure samera hii 471
nmn, erae deimu stendi. ei e 469
described tati. abustal. Leed 466-479
developnientoof...-— o n srl Bs 52
equation: of time byline i e oni nahin! 478
extension of, to following year______-- 479
to later years deL LH) (hint dos 653
(See also Long-term Almanac)
exoracts frome. oo mimermersedo Ls 1136-1151
hour angle by, of moon___----------- 470
OBDlanēts Een cos dun. Les qu 470
OLLA: e UT nid dt 471
ONKUN deinebanBab is arti. Leon 469
lunar distance tables, deletion of... —— 54
publicationohel acier nno. May insit 98
EE DEE creen EE 53
risings, settings, twilights by_------- 472-478
a EU 639-640
time of meridian transit by_----------- 478
(See also Air Almanac, The; Almanac(s);
American Air Almanac; American
Ephemeris and Nautical Almanac,
The)
American Practical Navigator (H.O. Pub.
No. 9), deletion of lunar distance
tables: eret. telar be onitenbinte 45, 54
Origin) it e AER Dava ees 6
revisionfofisemta laniakmmsā. ads 6
(See also New American Practical Navi-
gator, The; New Practical Navigator,
The)
Bowditch, first edition of 1 52-2- 4

American Practical Navigator, The New;
of Bowditch (see New American Prac-
tical Navigator, The)

Amphibious operations--_------------- 737-741
heachitrahicabllitves.— =>. C 740
rea kersianG surfercew€ tm c a 738
currentis in'surf'zone-— ~~ SP 738

"amplifier dede AMA DAA Y L 301

Amplitude, of celestial body, computation
Oro vr me Se De, saml 568

correction of, as observed on visible
horizon, table 28. Jo Ent 1297
explanation of 0L FV Mi CS 1194
cana A £ + 386
reference direction for__------------- 134
CADIZ A OT sar s vong 1293-1296
explanation voheer cer n c 1194
Compasswdetinedapee —— —— — aor 918
defined inai alitas oho ELM Æ de seti 910
grid Wdefned seme oe cer IM ome: 928
magnetic defined ÆU IL EE 934
of radio wave, defined 11.101 10101 22 290
euer So Matte 988 951

(See also Azimuth)

Amplitude balance, defined------------- 910

Amplitude modulation, defined.........- 910
Of radioc waves aD TUNE FAA Oe 300

Anabátictwind EE 806

Anaglyph, use of in photogrammetry_--- 876

l Page

Anchomices otteet Da äaäb Jure 761, 930

(See also Anchor ice)
sta defined serena da sl; 945

Anchoribuoy, defined 22 ut» sh 25d ut _ 910

AnGHOWiCes MORE es ee 747

Anchorage, defined. -- 2222222220 22021 910
in polar regions, desirable features of _ _ 632

Anchorage buoy, defined- -------------- 910

Anchorage chart, defined_______________ 910

Anchoring, piloting procedure____----- 278-279

Anderson, E. W.; sight reduction method
OIbe un kød Hoa; = Ae Tn anise 545

Anemometer «s. ileso sat tote 769, 910

Aneroid barometer, defined------------- 910
described sea BAR tdi 765
precision type____ ee Se M 766
(See also Barometer)

Angle(s), acute, defined. --------------- 909
adjacent, defined --------- "m setu taa 1021
defined199_.04 gi CM) 10483 Bra 911, 1020
kinds and properties of----------- 1020-1022
small sine of 1 and 17s Saute one 959
units of measurement. ........:30..22 1031

Angular distance- C tou ee. asaen a 911

Angular length, of arc, defined- --------- 1031

Amgülar measure-.-.—---w*8e109** Sum 1031

Annéal,_defined s== 1222003 panies sm OL

Annularsdeflined =. oe eee eee 911

Annular eclipse, defined-------------- 380, 911

Anode defined -wedia ieni 911

Anomalistietyearstiītenoēta eet de Mt 370

GEES 24

Antarctic, features of UL aed EE 613

Antarctic circles ov ee Te ane 373

Antarctica, Sailing Directions (H.O. Pub.
NOF27) PMA 01 Coe Preah rets 753

Ante meridian, ler

Antenna; A dcocke2: 22222 een 307
characteristiestobit 39 Nu pv ert 297
Gtossediloopimms css 3 I 305
defined: Loma Takk tee 911
directional, discovery of--------------
loop, direction measurement by. - - -- 304-306
receivingaosid do Nradwgolagno ados _ 301
sense MU Vera Lo He tne 305, 945
transmitting- -=-= AANS cO Mg 301

Antenna array, defined_---------2------ 911

Anthēlionētu a uboši a 035087 ' 10 secant 811

Anticrepuscular raus. 812

Anticyclonehdefined Sse ARAS 805, 911

Antilogarithm, defined-------------- 911, 1013

Antiselenesto.. Dafa tte tee, easiest. 2 811

Aperiodic compass, defined. - ----------- 911

Apex; of cone, defined au e222 saan sas 1027
of pyramidwdetined 2u E 1026

Aphelion defined <<< =. F 855, 911
darthtāat eeneg -Bonpsb spider O 371

Apogeanjcurrent--——— — Z2001O8 gent 714

Apogean.tides.._-. _- 2222022 ADHI 706, 911

Apogee, defined:===-===>= Pene E € 355, 911
moon s distance atveri EV IEEE S 362

Apollonius of Perga, epicycle proposal of- 36
invention of astrolabe by------------- 40

Apparent altitude, defined.......------- 911

Apparent horizon, defined - ------------- 911
(See also Visible horizon)

Apparent motion (see Motion(s))

Apparent solar day.......--.---------- 353

Apparent solar time. - ------=-======- 374, 482

Apparent IN o ss Ls E 374, 495
cle fine Gems en A hen - mc re cre 911

Apparent time, defined..........- 374, 482, 911
findings tor = ee mc ee 495
Greenwich, defined- --=------------=-- 928
lócabadefined- 2. — — — AM TUN Aga 933

1460 INDEX

Page =
Apparent wind, defined. ------------- 770,911 Astrograph-time Star Tables for Air Navi-
Approximate altitude, defined_---------- 911 gation, ot: Ashton. esere su qeu 545
Apsides; line of. Picos coco EISEN 355 Astrolabe, defined - ings. ase Tb. e 912
Aquino, Radler de; sight reduction tables invention of ancient... 2 40

(O d adum E v. A AMNES * 57, 537 pendulum atr +... pes AAN 838
Arabia, early observatories of. ---------- 48 prismatic. 2. £907 enak sth cnin 837
Arabian mil (mille), origin of- ---------- 2 surveying_____- pd nur gi 837
Ane? defnēdā. «=== =<, et 911, 1024 use of in geodetic control survey_-_----- 850

excess of, defned -2 -eRe sad. sar 924. Astrológy....--2- Je meon bas A 374

major and minor, defned 1024 Astro-Navigation Tables for the Common

of sextarnt=t molos huir YO. d s 400 Tangent Method, of Benest and Timber-

EE 1031 lake 02. 22-20-8020 so Ta eee 536 `

cohversion;factors=- ——— — nes 959 Astronomical day, defined- ------------- 483
conversion to time units 484—486 signifieance.of — 49. tel 374

of visibility, defined... ...... 2 911 use of in old almanacs- - ------------- 5228
Arcano del Mare, of Dudley ------------ 34 Astronomical distance, units of_____--- 351-353
Archimedes, celestial and terrestrial globes Astronomical latitude and longitude, de-

G) AA ees TE epu X 36 fined= — nu 81, 912
Arctic, features of- ` 5 —— Mec T 612 and deflection of the vertical---------- 427 `
Arctic Azimuth Tables (H.O. Pub. No. op 569 Astronomical Navigation Tables (British 4
Aretlescircle. sad mm Br 373 Air Pub. 1618) (H.O. Pub. No. 218), 3
Arctic Ocean, features of- -------------- 613 description ofeerginiā qoot Y e" 98, 540
Arctio;ea smoke. .— . temere tí 808 Astronomical observatories- ... 48-51
Arcturus, proper motion of_____________ 370 Astronomical position, defined- ------- 427, 912
Areal units ofsi- enk a do anes 954 Astronomical refraction, defined... 430, 912
Argo, Navis, of Ptolemy- ` 1925222 974n Astronomical tide, defined______________ 912
Argumentādefined CES aes 911 Astronomical triangle, defined. |... 393, 912

OL tableta se cocoa e as 1045 Astronomical twilight, defined-____.--- 368, 912
Aries, first point of. --___---- 373, 471-472, 925 Astronomical unit, conversion factors for. 955
Aries, zodiacal constellation. ......... 373, 374 efined.e sk estie erue e , 912
Aristarchus of Samos, heliocentrie theory Astronomical years «ties soe 370

(Ee Apr ved T rne 36 significance of... .— == seg 374
Aristotle, lunar eclipse studies of... 36 Astronomy, defined 20 2220 351

twelve winds of... ....-..- inei ni 23 historyaofsmesiniA -ost soon vM net 34-39
Aristyllusua 203) ata. uma. es 37 nautical, defined... 222022222 222 351, 937
Arithmefič,defined-s ==. -= = Dl 1005 navigationalštdstvssji_bet X» 351-397

mental trr raene c anne dedita 1016 defined dandi. 5 S O 351, 937

principles Of spēs ae "Kā lo ape 1005—1016 radio, beginnings of: es USE R 39
Arithmetical Navigation, of Addison_____- 34 defined tu). Zen. gud be ØR 942
Atīhdefined. < = po se es quet fe 911 determination of position bs... 60
Armco, defined... eee T ee 911 units of measurement... 351-352, 953-954
Armillary sphere, origin ot... 48 (See also Astronomical observatories,

Arming of lead. z- tegas kakan an 132, 911 Celestial navigation)

Arnold, John; development of chronom-

tr PORN E sumi e A Oe 47
Arrival, point of, defined_______________
Arrival time, estimated, in air navigation_
Arte de Navegar, of Pedro de Medina___-. 32

Artificial horizon, altitude corrections for_ 437
defined... —— ....... A al 911
description and use of 415-416

Artificial horizon sextant, defined. |... 911
(See also Sextant)

Ashley, Anthony; translation of. 22

Ashton, Philip; sight reduction tables of 545

Aslanicharts m 1: 2 20 er a 19

Assumed latitude, defined_____ 1. 912
(See also Latitude)

Assumed longitude, defined... 912
(See also Longitude)

Assumed position, defined____._________ 912
in navigational triangle._____________ 393
insight reduction- ES ele 450, 502
use of pole ass... ten akti Ye 638
(See also Navigational triangle, Sight

reduction)

Astern, defined emen Mc EE 912

Asteroid «e cemaliou. Me cab ion M 353

Astro (astral) (see Star(s))

AStrO Compass EEN 2 22026

Astrograph, principles of. 562
setting of by The Air Almanac________ 468

“ Astro-Scales", of Anderson... 545
Asymptote of hyperbola, defined________ 1029
Atherton, J. W.; azimuth and great-circle
tables of 22 A 569
Atlantic Neptune =a. RE 22
Atlantic Ocean, currents in... 719-723
TARMA A 4 e de 768—755
International Ice Patrol. |... vv 757
lane routes int EZ S a 755
Atlantic Oceanographic Group, Canada... 692
Atlas of:Orteliuss e A MM 21
Atmosphere, circulation of — 794—800
modifications inse e E D 799
constituents of- -sa ARES 959
defined 2... oo te E 912
Of earth: ee M 358-360, 793
electrical effects n= NN 812
jetstream in- sese c A 114
layers of 7:52. 77-2 T 360
of:moon_s se Ban ieee 363
pressure of, altitude correction for_____ 432
table24-* 1 Se A 1281
explanation Of CEE Sn 1193
effect of upon refraction_________ .. 432
measurement or 765-769
semipermanent highs and lows. . ... 799
standard ` "W" om d at 959
units of measurement... 2.2 20 0 765
pressure gradient of Ta 797
standard structure of- TFP m 794

INDEX 1461
Atmosphere—Continued d Boke
ontinue i uu i
temperature of, altitude correction for, prem TRU: 853
table 23... id 1280 magnetic, curve of! Aa 197-199
explanationfofz--——.. 225 m 1192 defined
effect of upon refraction.__________- 432 iria diano Soudu.. mort alo 935
measurement of----------------- 7752778 Otimme as muth def edt o eevee t d 943
upper air observations. - .. 785 fórmulas for- Plasmani 1o Marnar 567
( ča e Ionosphere, Refraction, Ml te: kaa azimuth, defined- ---- 950
Atmospheric absorption, defined--------- 912 true Bëss EE D 961
dedi ai electricity, types of... —— 812-813 work forms fór 9590 FAGO, „10 quf 1056-1057
EEE PE T ME paced ve A i P Lr Epit
Atmospheric pressure, defined. |... 912 bo RI did šāds ka Kees 569
Atmospheric pressure correction, defined. 912 Azimuth angle, defined- ~- ----------- 385, 913
Atmospheric refraction, defined.________ 912 determination of, graphical methods. 555-558
Atmospherics, in radio... 297 by map projection..............- 560-561
Atom, defined Tie podus Merlin i13 289 mechanical methods. ............ 558-560
E da. <... ee rg 293 (See also Sight reduction)
Rituum eocibddisoush eot nda. aia anos3T5 InpcasuremenUuof see ec ate PSS 385-386
Attenuation, defined=========22Habsabo 919 “Azimuth barydefined ae ee == se ae 913
Gfiracdiotwaves---22...... EECH 296 Azimuth by Logs, of Purey-Cust........- 571
Audio frequency, defined_____________ 291, 912 Azimuth circle, defined e E 913
Augmentation, altitude correction for____ 434 description and errors of- ------------ 140
dehnedMas e. gat 912 Azimuth diagram, of Alessio............- 572
ofámoonsries > Mit. Eet Ape 363 ofiConstanse. E Less ts 572
Aura mall defined... ses do wier me geren 912 Of Cornet e-t A ee do Es ote 572
FATIFCO LOS BUS EM GER 811 of German Navy. ese bes at 572
O AN O dj 356, 813 of Godfrey- S. ote Às etes 572
a a mom oe RPM A 633 oftHilsenrath 2322 ges ee ot ee 572
denned e eater qd o E 912 ofiHugonzss dees c t cete Eos 572
TONER OL EE See IBC TEE 00 ui 162, 633 off Motto art A eee sk 572
Murorgaustralis fee seo NETO E 614, 633 ofsRomanoysk yes = cce EE 572
eünned Mtra HS Ot rT Os) UM 9 of Rust RE DES S = SS EE 572
Adroratborealis soe OA 614, 633 OSWeire M aesor fo. 2c Ee Y 572
efi ned C ae zs s IMA 913 Azimuth Diagram, of Weir_------------- 572
INGOTS LPT Ce ee ee ee + eee eee 162. 633 Azimuth instrument---_----------.-.- 140, 913
Defined E EE EE ' 913 Azimuth table(s), of Atherton and Tow-
Australia current, east "sd DATMYNM IG 1107 724 E ER E EE c c f E 69
Australia current, westo TONAS MTI ATT 725 of Blackburne: s ræ 570
Automatic celestial navigation, defined... 913 “Blue Azimuth Tables", defined------- 914
DEINGCIÐIestof Meal ovario ee onc Hr 566 of Burdwoods 2-2 ER 569
Automatic dead reckoning, systems for, in of Cūģle TB ijas aio en 55% de 571
airhavigations era be 673 of Davis, Jobn(E CES eee 569
Automatic dead reckoning equipment, of Davis, Percy EE 569, 571
Chart Projection Tor S HI: 88 of Decanter e, EE 569
Automatic radio direction finder, defined. 913 defined Me ¿E A ee 913
Artun (season) O oe = ERS et 371 ob eege E Pv ao UE AS s 570
Autumnal equinox, defined----------- 913 OR (40 OC WI11 ee SSIS EINA ht 571
Aviation Agency, Federal, publications H.O. Pub. No. 66(Arctic Azimuth Tables).- 569
OLEO bs BSAC US KA AS 94, 671, 1004 H.O. Pub. No. 260 (Azimuths of the
Awash defined Res o Mm 913 SUN A S SNE 97, 569
Axis of cone defined A S 1027 extracts) rom AAA 1165-1167
of coordinate systems---_-_------------ 1031 H.O. Pub. No. 261 (Azimuths of
Oisecylundersidetined S SES EF 1026 Celestial 'Bod1es)' eee eee 98, 571
of dod tat rats etd 141 extracts, from set ur. A 1168-1169
(See also Gyroscope) Johnson m gene ete vea 570
of hyperbolasees m d 1028 6fiKortāzzis X eR C AM 569
major and minor, of ellipse- - --------- 1027 AM S e ee ee 569
Oldpārabola No MEM ie E 1028 Of Lec ec. eebe Talent 570
ere ee See ae 63 Oi vines e ee ts. 524, 569
procession or earths =ar a") ss n 373 Of Perin cen ee EE: 569
ofiprism t denned e MT ae ee 1025 ot Purey-Cust e 571
it y rani Ged etined samme Sre 1026 “Red Azimuth Tables”, defined -- ----- 943
ONTOLAON ON earths Te = 2s EEE 63 AU E e e AS E 569
Azimutdiagramme, of German Navy------ 572 AO E et tp jeā 569
Azimuth, altitude azimuth, defined. ..... 910 S: Southerland Kaes dd coll cietas bs ie 569
formula Toras A De 567 of Symonds 159571
compass azimuth, defined. ----------- 918 EE THU URP AE OR
dinner As CAUCA 385, 913 Table 902, Azimuts (French)---------- 572
deterīninationiofe SEMI 567—572 of Towson and Atherton. - - ---------- 569
altitude azimuth method. ---------- 567 Wainwright o o Sie QU INT 569
time and altitude azimuth method... 567 BE des IT 568
time azimuth method-------------- 567 Wo vestchenkome ss R eee 571
worki forms orsa mee 1056-1057 andano e oo coer eee 571
effect of upon refraction-------------- 432 9 Kauss I E
grid azimuth, defined- --------------- 928 Azimuthal projections (see Projection(s))

1462 INDEX

Page Page
Azimuths of Celestial Bodies (H.O. Pub. Base line extension, defined............- 914
No: 201) atts E 8, 571 of hyperbolic system alge bees JOSTU fe 310
extracts from... —-.._- ases 1168-1169 Basic pulse repetition rate, defined. ----- 914
Azimuths of the Sun (H.O. Pub. No. 260) 97, 569 of loranzz.- ee ie Ob EE 334
extracts [rom 22 esat 1165-1167 Basin of ocean. -..-z0lizasla dogi in. des 700
Azimut- Tabellen, of Ebsen.. 570 Bathymetric chart, defined_------------ 914
Azimuty Svetil, of Yustchenko. - -------- 571 Bathymetric survey, procedure for------- 865
Bathythermograph, defined. .......... 696, 914

Bitrace;defineds-s5. = m ie dee 915 Bathythermograph Observations (H.O. Pub.
of loraniscopetecs arta Šada 335 0; 606-c): 3o IE Serene | hende 96
Babeladowerof...- .-. 35-28 emer. 15 Buyer! John; star names of- -_----------- 576
Babylon, early astronomical studies in. __ 34 Bayer's name, almanac listing of__------ 467
Babylonians, early maps and voyages... - 35 efineda at qe ed 7 O 914
Back, wind direction change, defined__ 805, 913 Of stars 210. basBub. Saro armið 575
Back sight, altitude corrections for__--_-- 445 Beach, effect of upon waves_____________ 737
defined as Rewer. SE Z Mat E 445, 913 rolling resistance of . 25255222. 2020 740
method of taking ad x Ta a 404 trafficability of 41 saskaita ās 740
Backrush, Of waves ao S 738 Beach survey, procedure for... 864
Backstaff (sea quadrant), invention of. - 41 Beaching of lifeboat__________ KE 662
Backstays ofithersunteca tee P 8 - 812 Beacon, chart symbol for, described. .... 111
Backwash, of waves. ———. 391090 2183 3 738 illustrated 3207. tt. Ind, ROMA 993
Die Ara 9 Mc STU TQ euo YO Á 820 day, defined .-............ RA 900 259
Buily/s-Bends-ee-..-..- Dose MP n 379 defined 2 5: 22u2:: tdo sons 259, 914
Bains; Alexander==2222 22 EE Due tada 25 radar, definedzsievsosieīunāius sei ta 942
Baker, T. Y.; sight reduction method of. . D rotating A E 307
“Baker Navigating Machine z+- nen Beam of radio Fange- 289 see rn O 674

Ball, Frederick; sight reduction tables of_ 57, 529
Ball recording sextant:=--=2: YY HA MAME

Ballistic, floating, of gyro compass... 150
mercury, of gyro compass____________ 143
Ballistic damping error, defined... 913
Of gvro-compassssss-- X DEE 148
Ballistic deflection error, defined_-_______ 913
otigyrorcompassssc s 2-22 ones 149
Bandwidth defined === 913
Bar, of tropical eyelonett * 20 SAMU ON 825
Bar'scale, defined - =+ C9 Hen qm 913
Barlow, Pēters. Goa fo adas di 23
Barnard's Starnes gators Mise 370
Barograp hitters o os eee 766, 913
Barometer, adjustment of______________ 768
anercid; defined ETA „NOD 910
correction for gravity, table 12________ 1262
lee 1189
correction for height, table 11_________ 1262
explanation o == amas 1188
correction for temperature, table 13____ 1263
explanationlof- UN 1189
defined: 53 2u 8 LSD, CASIO 913
eTTOIS-Ofe PE € POI IT E nd, Ln ordi 768—769
height determination by... _ 769
imsurveying- Ee EEN 859
Invention'ot PES 2 22 urs DA A 766
mercurial defined! E 936
errors Of === Eð CERAM 768-769
invention and construction of_____ 765-766
DEELER 766
pumping or Saa E AA 766
defined Es v. a ld 941
in tropical cyclones M 825
AE a a ee UP MM 765
Barometric pressure, defined____________ 913
(See also Atmosphere)
Barometric tendency, defined___________ 913
Barrier ice S: 1 S teen 750
Base, of cone, defined______ 777 1027
of eylinder, defined PT 1026
of polygon, defined__________________ 1023
of pyramid;-defined-- (cucu kb. Zen 1026
Base line, defined _ antsy) 4 hires wanes 913
of hyperbolic System. EE DEM 310
of'suryeyy aceuraecy/of. MIE S 853
Base line delay, defined. ....... 914
ofloranct mass duc co To eee 337

Beam compasses, for chart construction. 845, 889

Beam compasses and dividers, defined. . . 121
Bean width defined PS 914
Oobradaree rc EE 322
Bearing(s), on azimuthal projections..... 81
bowand-Deam = 255, 914
collision defined ` 2 2 2 a 918
compass, denned: -zanan een T 918
cross defined S1 e tee E 919
De o 2 e 255, 920
defined" E 6, 914
direction of-charted ON 116
doubling angle on bow_______________ 255
four-point, defined 5 J EEE ERE 926
great-circle, defined "RT 927
grid, defined a atea a dl E] 928
kinds of, defined ms. o E 241
MANIC Cel eC eee RE 935
per gyro (standard, steering) compass,
defined x F MENO ad ee oa 939
inpolarregions 25: = == 3-02 eg MA 631
Mercator correction for... 621
plotting on Mercator chart. |. |... 631
radanjdefimed EE 942
radio, defined PERE" S 942
(See also Radio bearing(s))
Obrange Se To I oe ON 241-242
reciprocal, treatment of. |... . 314
relative, conversion to true bearing... 67
defined eR 67, 241, 943
reference direction ot “Vr 134
resolution of radar R 322
rhumb,dēfinēd EEN 944
CUA ron 249-255
special combinations Of-_-- Vð 255
Seven-elphths) rulers. EN 255
seven-tenths rule =a S 255
sevenzbhirdsirule ERN 255
true denned Ere aa eee ee 241, 951
use Of S$ "T 241, 255-256
visual, in polar navigation__________ 621, 631
(See also Fix, Navigation, Piloting,
Polar regions, Position(s))
Bearing angle, defined________________ 67, 914
Bearing bar- Lods teta deci GER «U 140, 914
Bearing capacity, of beach |... 740
Bearing circle, defined MU Maa an 914

a ee

K s ut co di ia ef su ce KR

INDEX

Page
Bearing line, defined- --------------12 241, 914
Bbelingofzstosda EE EE : 243
Bearing repeater, defined_______________ 914
Beat frequency, defined________________ 309
Beaufort, Francis; wind scale of... 774, 1059
Beaufort scale, defined- ---------------- 914
of) wind speeds. = age Bet. tesis te «x 774, 1059
Bedell, A. L.; sight reduction method of... 566
Beehler, W. H.; “Solarometer” oft... 566
Bobhaim A Martins a Mc K: > DC 17.
Behm, Alexander; echo sounding experi-
men tS ofc BAS 1. AA 58

Beij, K. Hilding; sight reduction method of. 561
Bellas fog signal tio 42s sla bos siens
Bell buoy; defined- -- eee le brea L
Bellingshausen, Faddei F.;explorations of. 691

Bending of sea ice... onstond Sa. seetaga.ls 750
Benest, E. E.; sight reduction tables of. 536, 547
Ben guelascurrentees2 sie eth: nni ibas ond 722
IBenthos, defined. obsah ribas to esse 701
Bentley. a William. isda- zeta ss 3
Bercy Hugo des: 143242 hero teo 23
Pere Ve Ditto e. dāmas o Le ts & 748
Berthoud, Ferdinand; development of
Gnronometersatts de eegene 47
Bertin, Charles; sight reduction tables
MU dou. EE e anf cec ee — ala , 933
Bertin, Maurice; sight reduction diagram
E d^ Serna s per alie e E m 557
shdesulefes evo AN 559
Beset by ice, danger of_________-_--_-- 631, 761
definedēsešsss E Doe: bed 914
Biancho, Andrea; traverse table of___---- 29
Big dipper, circumpolar motion of___---- 368
Kunaudralhearnn gēns cos LA" 742
Hmnaclesdefinedzsee9tee 228 tos 210 914
described ree WE 136
Sariy description otro? PEE 24
es for compass adiustment ___- (ei
. S. Navy 7%-inch, described-------- 175
BIDlopvánfjócetans SN en ote EE 700
Biguadrantal spherical triangle, definition
A ss ss me = = dzī mk PV S 1039
Birdstas eg lee Eegeregie, 660
Bittacle (see Binnacle)
Bjerknes, Vilhelm F. K., and Jakob;
ocean current investigations of-------- 692
“Black Stream" (Kuroshio)_------------- 723
Blackborrow, Peter; The Longitude Not
OUR Olmert ee amt m AM es LA 44
Blackburne, H. S.; azimuth tables of... 570
sight reduction tables of____--------- 57, 525
IBlhckoutrofsradiosešēds MP EUM. CE M 634
BlinkwtrOMSICesne we sm mr REN S 759
Blinking Of loran signal ^ 7-737972 == 338, 914
EAS AE LR RIA al RE 807
“Blue Azimuth Tables" (H.O. Pub. No.
2615 er Sea es «pl tee 98, 571, 914
OXLTROLSTĪTOJND === as mann eege 1168-1169
Blue magnetism, defined" -- --- _------ 914
E moon E S E 810

Blündeville; Exercises of 02 2 SUÐ ANI za 34

Board of “Longitude” A se 45, 46
Boat compass, defined - - _------------- 135, 914
(See also Compass)
Boat sheet, for hydrographic survey - - -- - 859
Boats, lowering of, preparation Tor. ----- 647
Bopping E 7 — 264, 914
Boi de E IAN 365
Bond, Henry; The Longitude Found of... 44
Bora AMES e PAP Tm S 807
Border of chart, selection of. - ---------- 893

Border-scale subdividing device, for chart
CONSTITUCION NS ese e e 890

1463
Page
Bores tidal estes abae Aah. o: Haden 706, 735
Boreas, ancient wind name_____________ 23
Borough; William. ceo < Ze? 23
Bottom, characteristics of, defined___._.. 916
phantom, in echo sounding... ........ 134
quality of, chart symbols for. 997
defmnitiohsa- Sack Ma ae tes be 108
Bottom contours, on charts_____________ 108
accuracy.of..3-6. EE arani 105
Bottompices. 6 l uo t n aaa: 747
Bottom profile, by echo sounder....... 133, 699
use ofiin piloting ` ` ` -Bas s 258
(See also Echo sounder)
Bottom relief, of oceans_-_-------------.-. 699
Bottom sample, defined- -----------+-—- 914
Bottom sampler, surveying_---------- 700, 842
Boundary Waves. op. sk: 735
Bow and beam bearings. ------------ 255, 914
Bowditch, Nathaniel; biography of------ 3-6
CULO GS POL ae eee o5 a MM
simplification of lunar distance method
Dy a EE 45, 54
The New Practical Navigator of______-- 4

The New American Practical Navigator

[0 E TE: TR I att ik ;
translation of Mécanique Céleste of
Laplace Dy ee] sā
Boxing the compass, defined... ...... 137, 914
Braces, use of in algebra FVR 1

Brackets, use of in algebra-------------
Bradley, James; discovery of aberration

and nutation by mmn po mper 39
Braga, Roméo; sight reduction tables of_ 57, 530
Brahe, Tycho; development of sextant by. 42

discovery of error in Mars' position by. 38
andlepicyclic planes E GE 36
Rudolphine Tables =: === me 51
star catalog 01 dato A AS 50
at Uraniburgum Observatory --------- 50
Brazil current ejā S EE ne 722
Breāker(s)ydeined = = cao e 731
fonturestof wee AS eae 738
(See also Wave(s))
Breakers and Surf, Principles in Forecast-
ang (HO PubsNos2394) SS eep een 96
Breakwaters (jetties), chart symbolfor... 114
Breit, Gregory; origin of pulse ranging. - - 58
Breve de la Spera y de la Arte de Navegar,
ANACO ME ST P e ET 32
Brief Celestial Navigation Table (Japanese
HXOPPUuDWUNoO:602)58 9 rn = 539
Brieve Compendio del Arte del Navigar, of
OSSA S T CLE cr tiam AN 22
Briggslogaritninss e E T Se 1015
Brill, Alfred; sight reduction method of.. 564
British Admiralty, Astronomical Naviga-
tion Tables (British Air Pub. 1618)
(ERROR NOs 2S) ES 98, 540
Hydrographic Department, establish-
ment or a A A = 30
Tables of Computed Altitude and Azi-
main 8186) A A 540
British thermal unit, defined_----------- 776
Broad on the beam, defined. ............ 914
Broad on the bow, denned aan 914
Broad on the quarter, defined_---------- 915
Broadcasts (see Radio broadcasts)
Brown-Nassau, “Navigational Computer". 560
BTU (British thermal unit), defined...... 776
Bubble sextant, defined---------------- 915
development of first: - -- ------------- 42
principles|ofss==-==—— < icing gn b: 416-418
a o e a 609
Buildings, chart symbols....----- 114, 989-990

1464 INDEX
Page Page
Buoy(s), anchorage, defined- - ---------- 910 "Calorie? definedes- He IA eee 776
bell defined... 8840 TH PATAS 264 Galvingidefined=eee:--- 22 ass 0998 915
canp«definedzc sers: agree AAA 264, 915 (See also Iceberg)
cardinal system of, defined- ---------- 265 Camera transiti-2:-...---1 00 ee 840
described 30777 ODA quos IU TUUS 976 "Can buoy; defined’? 2230 MUM NE 264, 915
chart symbol for, described_-------- 1127113 ¡Canary current2L Corb MEDAL een SS 722
illustrated al AA = TODA 992-993 Cancellation of chart, defined----------- 888
colors A EE E 205-200 Gàncer,tropic ofi Cata Te SL S 372
combination, defined < m MER 918 Cancer, zodiacal constellation- ---------- 374
described er ecco er ME 205 Candela, defined: -—.---.--2- SEE 915
dansdeBnedi... 1999808 ES NE SMON. 920 ‘Canton; John APS 2000. CURAE 24
Get defined enge «¿EPM IE vē E20 res Horn. current Aeren E 723
efineds3_ SHE $ mags RUP UM RE C : apricorn,tropic of) i. 50. van zeds 373
Bee eae indlightNlist mE Se Teen zodiacal constellation_------ 374
gas) defined ¿do ger en Oc S ` ardinal points, of compass-_------------ 137
gongsdefincd m DOM IS 264 defined»seoiirtontze ; 2b See DUROS 915
fed define dite eee coco, ANT EN 931 Cardinal system of buoyage---------- 265, 976
qurctionjgdefinedcc eae eee a 932 Carnegie, oceanographic expeditions of... ^ 692
lateral system of, defined. ............ 265 Carnegie Institution, dip measurements of. 423
described. e 976 Carrier wave of radio, defined......... 0, 915
lights*onr 9004 4eib TACT). To AVOTI 266 Cartesian coordinates, defined____---- 915, 1031
nīarkeribCACO NO TIES Ss 265 Cartography, defined----------.--2-- 915
S ----------------------- Bag ace Ha de RE ----------- ee gels E 20
DU ss dā ss , assini, Jacques; proper motion, discovery
piloting by, precautions for. .......... 266 AS ET 39
da Sa im on Se eee ML ds ME 265 Cassini, M.; sight reduction tables of... 524
AR en ser EE Sees uuu 265 Cassiopeia, circumpolar motion of_--_.-.-- 368
sound defined cl eesti, 16 MM mee Catalog of Nautical Charts and Publica-
Par:udefinedy»> comridenie m, 16 00M í 264. 948 gone; (Pubs Nos IN) S 96
station defied 6.222.020.5208". Deene Eegen U8. Dav) A
nottsbowinten charts: 80 OÍ ' 133 and Related Publīcations_----------- 96, 1002
telegraph, defied au bat. dd :o8 00 949 Cathode, defined tucanes nd 302, 915
topmark of....................... 950,977; Cathode 2 LaL defined. -............ 915
turning defined. DAM V 1015 CNN ' 051 principles o1------------------------ 302
iypesuofoteM coe co S NA 264— Cat's paWos=t----=-=2:-===5 ee 807
watch, defined. e e T P T 952 tone kesis of--------------- ae
3 EE i projector-*-- S= S 4
ore d UD gee x _ Ollometar, í aaie NE 784
Buoyage, defined ae A P H f K 1 T 7 91 Celestial body (bodies), circumpolar TN 368
Bhoyage eee E al. 1 265, 976-982 Aro ra E 915
istory Of Meee Ty o DEER 29 idenuncauon of------------------- 575-591
Burdwood, John; azimuth tables of... 569 motion of. ---------------------=--- 366
inen of Standards (U. S.), atomic clock Ee rte Serbi one eee MS.
Of AA KO N RIPE ALM 37 a BIONS S SSS ES ee eee 14
radio propagation signals_____________ 683 Epia laws of. ent O ECH
time signals of (WWV).- 492 revolution in orbit___---..--------- 353
Buys Ballot's Law, statement of_________ 805 (See also Motion(s))
in’ tropical eyelones,. S3 seen 827 symbols for.......... = maa so 906
iBygraversiide rules == aaa ae se 559 paer ol ext And setting, formulas for. 642
stial coordinates 22. < = EE YES 381-387
C-band, defined______.________- “Celestial Coordinator", of Hyatt_..____- 560
Cable, conversion faetorg. Ree Celestial equator, defined SES 382, 915
defined. ee Gila Mons EE Cpl plāns oi S MA 383-384
Eck cable. defihed t ER nan 933 Celestial equator system of coordinates.. 382-
en unit, origi
Be HEEN Ó Celestial fix, defined. io ` 915
abot, Sebastian- elestial Fix Finder", of Zerbee________
“Cadameier” OF Pieri ea. Sia n Celestial horizon, define SCT z S d Web ks 386 S
Cage, defined O = E 915 SR laf tude defined. nm F` ea os 387 915
Cako ice e DAD MNE avg ae an elestial line of position, defined________ ' 915
Caloareous defined 21788) 3078: mum ios. leede Ee 387, 915
Calculated altitude, defined... 915 Celestial mechanics, history of...
Cálculo del Punto, of Ménéclier and Celestial meridian, defined____________ 382, 916
Ë Chevalier: = + "On gi 541 diagram ga plane of, defined__________ 9
/aleulus; defined: MAD Sen E RO DEO escriDed -z= ar doo bað að 387-393
principles of (AMR Óli aú 1041-1043 Celestial navigation, in air navigation____ 675
Calendar, Gregorian... 370 automatic doce tadas aces 566
time divisions by. defined: $ ae NN
(See also 'Time) 23. rte EE Bé automation O ss bee, Dë
Calibrate; defined a: sn Je NI 915 and dead reckoning. 72 460
Calibration table, defined... 015 s defined -oeiee o ia tods 62, 916
California WEE iisti WEE 304
California ee, E M 808 i uM Oa a 34-57
nstruments for 398-420

INDEX

Page
Celestial navigation—Continued
modern methods of or e 56
in paar regions: ## ais So) miaa 635-642
radiofastponomy---—-*-—---- Senā
(See also Radio astronomy)
TAdiojsextantjer- wie nas case 304

PUD NO, 601) 7-727757 SU) e, 530
Celestial Navigator for Aviators, of True. . 561
Celestial observation(s), defined_________ 916
in geodetic control survey... __ 850-852
lines of position from... 449—465
nlanmngtof aaieseter votare ev 455—458
In-palam regions sūdus five s 635-637
lines of position from---22222- 222 638
low-altitude siehte 22 636
Celestial pole, defined________________ 382, 916
Celestial sphere, defined______________ 351, 916
Celestial triangle, defined_____________ 393, 916
(elus Anders" C y Pane) 775
Celsius temperature, defined__________ 775, 916
Center, of circle, defined_______________ 1024

of sphere,idefinedtt’ 0x 3. Li syn 1029

Center line, of hyperbolic system... 333, 310

Centering control, defined______________ 916
Centering error, defned 3 916
POLSON GAN Grae ecco ETT 411
Centesimal system of units, defined... 1031
Centigrade temperature, defined_______ 775, 916
Centimeter, conversion factors__________ 958
Central angle of circle, defined__________ 1024
Centroid of triangle, defined____________ 1022
Ceres, IeaturesjOf:£siestss4 oo Ede pene 362
Certaine Errors in Navigation Detected and
Corrected som Wright ==. 22, 30, 34
Chain, hyperbolic system_____________ 310, 333
Challenger, HMS (1872-76), oceanographic
expedition Of i222. 2. Lee 691
Challenger, HMS (1931), oceanographic
expeditions off! S: seeders dale 692
Change of tide, defined________________-_ 916
Channels of radio frequencies, use of... 299
Character of the bottom, defined________ 916
Characteristic, of a light, defined________ 916
of logarithm, defined "esse 1012
Gharge: electrical: 223440220 asist st 289
Charles II, establishment of Greenwich
Royal Observatory mee Te ape da 50
Chart(s), aeronautical, air routes of world . 101
publicationioí--33 Māstsanes mera 100
CY PCS Of e i lati 670
value of for marine navigation. _____ 100
(See also Air navigation, Projection(s))
anchorage defined. Sāka cube 910
Annee ccn qus OE 19
azimuthal equidistant, publication of. . 101
(See also Projection(s))
bathymetric, defined W V N IA 914
Catalog of Nautical Charts and Publica-
tions (Pub: No: 1=N)=-22 222222222 96
checking accuracy of, by survey------- 865
classification by scale qe = _- 104
coast chart, defined------------------ 917
Geseribed=ety. E pecht 02022 pU sag 104
corrections to, ozaguides for__-------- 888
sources Of ola eee asa 99-100
current chart, defined---------------- 919
datums for (see Datum (s))
defined t REESE Sees Tr mi NER 69, 916
direction measurement on. ----------- 214

discontinuance of, defined. ----------- 888

1465
Page

Chart(s)— Continued
distortion Ofe- -ds En PUB de 1491 91
for electronic navigation... 96

(See also Electronic navigation)
equatorial chart, defined_____________ 924
field chart, defined 221202 2_- wav 888
fishing chart, publication of... 101
form-hines'on gs Ee do aoe ram in 114
general chart, defined -MEAN 926

deactibēdsas sea ee o M 104
great-circle chart, defined_____________ 927.

described s 2... 400a gti AA 230

publication of 4) motto SM 100

(See also Great circle(s), Projection(s))
offend variation. 4 Da 5 100
harbor chart, defined. esee 929

described seme juan detta de re 104
history of Teimer At 20023 ats 18-22
lee chart, defined" 00 teen g 931
importance Of <= AMA: 3d AN 93
Index catalog of nautical charts and

publications == ee EE 96
index chart, defined... m- X zs 931
Information on Hydrographic (Oceano-

graphic) Office charts and publica-

HONS otto Int Ad de 96
isoclinal defined PM DOM NOT S MER B) 932
isogonicsdefined = -SINO mar AES 932
isomagnetic, defined_________________ 932

described o a wt 162

publication and features of_________ 100
isoporic defined 2.5... SEE wt 932
Lambert conformal (see Lambert con-

formal chart)
forland navigation -r I ee 664
loran, publicationtot Sem PIDA 96

(See also Loran)
mapneticikdelined< ` < E Ems 935
maintenance, of--€ Eeer Lara 197
marine defined CERED 19 Muri 69
Mercator (see Mercator chart)
miscellaneous === HAGO $e 100-101
GER TEE HEN rats no D O 103-118

ACCUTACY. Of a Ss o.c ai 104-106

aids to navigation on- -Sr MiS

accuracy OA e 105
illustrated et 342.30 meon 983-998
(See also Chart symbol(s))
bottomseontours onec 108
accuracy, ol ls 223 m map LY 105
bottom quality, definitions of__----- 108
symbols forsee: Eu a pe E 997

classification byjscales.o 2422-2 a 104

coastiidescribed e e eae es 104

CONSE CUO MO 888-894

(See also Chart construction)

contoursonssssas= ss SE 114

controlling depth EEE ses a 108

Correction of- V ee 117, 118

(See also Daily Memorandum, No-
tice to Mariners, Publication(s) )
dangersion. 2123. blk ds EE 110
symbols for.s- be mag Ere THH GE 995

data adeqglüacyzoL[----- k eee 106

daterof3+=- = Efe ecl n pipe ME Sale se 106

GaN SHOT e. SES Eu e E 109

(See also Datum(s))

detined see E ās 69, 103, 937

depth units of various nations......- 999

distance measurement on..........- 215

general described <- a esas 104

great-circle, described_------------- 230

(See also Great circle(s), Projection(s))
red og, glas damen), seess ess 104

1466

Chart (s)— Continued
nautieal— Continued

heightstont_ esie ede 110
illumination ofte erem vue 118
improvements EE te iEn 886
of Intracoastal Waterway.........- 104
land areas on. beten Ier 32 114
landmarks on, chart definitions of... 114

symbols for-2--J. If rs 983-998

lebtering:on.. Vus dn 107
light characteristics on------------- 261
light/ridnges:-0n 02217 se 263
magnetic information on_---------- 116
(See also Compass, Magnetism,
Variation)
maintenance of----- vt ries SE 117
sources of information_-_-_------- 99-100
miscellaneous features described___ 115-116
notes printed on = INN. ven 116
plotting great circle on___________-_- 229
preparation for using_-------------- 116
production of -nese ejās 886-899

GE IA TE 2 895-899
(See also Chart production)
production methods- 22
projections tor- sod 103
(See also Projection (s))

for radar comparison - _ 1 42 300 1 324
radio bearings on---------------- 314-315
reading theme = V EE 106-116
Thumb} line onc ee is hne zL Hal 228
sailing, described ' v: eee ee 104
scaletof ERU oes) terreno pe tod 108
scale suitability of- -Ten 106
shore) line on__ V Je ast 107
soundings on, accuracy of__________ 105
obtained by echo sounder- -----_- 134
symbols for S - "e 107—108, 996
tidal effects upon. ___.._..._- 267
sources of data fors cce PN 887
stowage of ire de gaīsor dl Gee 117
SULveyv2accuracyc-- Ss Va 104
Symbols 00342 e E A 106
definitions oft T 114-115
Uluüstrated-- -wa Sep i Al 983-998
(See also Chart symbol(s))
terminology of IN 888
titles Of: De ee cda sr] 116
use! off 9 77 Ee 116-118
Water areas'o0n < c ME 107
neat line.of 20 &cnitdüob villain mod 72
new (edition), defined_______________: 888
of North America, spheroid used______ 62
numpering zoi AM: T ee 94
Obtaining E do ee Eegen 7 94
oceanopraphicmee eR 95—96, 1002
outline; publication of < A eS 101
pllotiebart defined 939
issuance ofS sva e di M qute asā 94
publication and features of. 95
plotting chart, defined______________- 940
description and use of... iL 18 100
publication of e EUR 100
(See also Plotting sheet(s))
of polar regions, adequacy of__________ 617
plotting on... SENA Se 620-622
projections fór === REN 85-88, 616
(See also Polar navigation, Polar regions,
Projection(s))
Portolan- 3455244320700 CAI 20
projection of, defined: 222211 916
bypestof3 2401 x roma Joe) e wg 69-89

Chart(s)-—Continued

(See also Projection(s))
and publications, for air navigation----- 670
sourcesiofett 3 93-102, 1002-1004
(See also Publication (s)) -otin
radar chart, experimental, publication
f

of ac reve CL See eas 98: 96
reprint ‘of, defined sobtm aL tins use 888
Fetter E iiO
sailing chart, defined-: mw ACT o Ra 944

describediecenel) sidad. ai red x 104

scale of (see Scale)
scale conversion factors______--------

sources:of- -<< en diat iuh ele 93, 94, 1002-1004
star chart, publication of__-___------- 101
rectangular projection for___----_---- 77
transverse Mercator projection for___ 76

symbols and abbreviations, Nautical

Chart Symbols and Abbreviations
(Chart: Norl) ëtt shies 101
Hlustrated 23.020 542s bee Hab men 983-998

(See also Chart symbol(s))
synoptic chart, defined
terminology 0f=.ce 255 SA
tidal current chart, publication and

features of..-- ss ebestekisi Sa 95
time zones of the world, illustrated... 489
publication of s» aaa o E 101
titles of ES TAN EE 116
track chart, defined... med AE 951
publicationsofs. x ee 101

Of variations noh iaa To CATE ge Ja 100, 162
(See also Loran, Mercator chart, Polar
regions, Projection(s))

Chart comparison unit, defined__________ 916
prineiples.of ......390H9D Ae la i8 324
Chart construction, borders and scales... 893
charted/details*: eg, NCS 5 894
dāturt muc oder o ERE 892, 1000-1001
(See also Datum(s), Tide)
drafting instruments for... 2 888
drawing material for ......- 00S 891
elements off [88 (SUID PRECOR 888—895
reductionēmethods === s. MONI 891

standard symbols and abbreviations. 894—895

illustrated 228 _ Aa 4 SV RA VS 983—998
(See also Chart symbol(s))
Chart original, drafting of_.____________ 896

Chart portfolios=- ZV MKD 94

Chart production, compilation. _________ 896
drafting chart original. ~.__.________- 896
estimate of the situation. ___________- 895
record of 1 RIO Digit Te 899
reproduction processes- -------------- 897
requirement, ior as cM 895
research and planntng 1... 2 895
reviemandiedit22 HOYA Ue eae 896

Chart reading, defined. `` "Rr 2221 916
described =+ S Æ 826 a ee 106-116

Chart record, of production_____________ 899

Chart symbol(s), for adjectives, adverbs,

et6 cuui coc E DE. Spee 986
for aids to navigation.... 111-113, 991-993
forn bottomiquality se PEN 997
Iorsbuldinpsee em 989-990

for buoys and beacons 992—993

for coastifeaturesi Ee 985
for coast line. asa pase 984
for compass information______________ 998
tor “control points. SIR 986
for currents, described (Ed U2 3 116

illustrated. - AA 998

|

INDEX 1467

Page Page
Chart symbol(s)— Continued
NlLustrātod asm 4 RSA SDIS y 995 Chronometer watch, defined-__-_-_----- 916
A e R dl oe 114-115 Circle, circumscribed, of triangle_____... 1022
pomdepth'eontoüurssese£ee cores use U 997 AS ICONO SECUIONS ETS eee ee eee ee 1027
for distance finding station__________- 113 of declination, defined_____________- 382, 916
ia EN S Ec de talle q 994 description and properties of... . 1024-1025
Ilustrada 983-998 of equal altitude, defined- ------------ 916
Ionkolp m eran prp err le RIS 110, 995 VTM E V a seer 449-450
for land, areas and structures________- 114 of equal declination, defined. --------- 916
artlticidkiedvuressā ss ea ook Ke 988 inscribed, of Lriangle -aaa 1022
patural features; c EE EE 985 olslautudes denied =o ee 387, 916
LOYSI Ø D i eee TEN. 111-112 of longitude, defined. .--- --- 387, 916
d'Ee sao Rn a EA 991—992 parbhehosmes e E eee
IOPMOOKOUU AA An 115 OI EE ÉIER eebe 449, 916
for miscellaneous stations_____________ 990 prime vertical, defined. . .......... 385, 941
ONPE en Sees SL VO rr 110 principal vertical, defined__________- 385, 941
Tonporuand'hanborgsecs sekas eeh 987 of right ascension, defined___________- 16
ROPA Eeer a 113 ottuncertainiy VSK eee ee 685, 916
for radio and radar stations_________ 112, 994 vertical dci ss ==" eee a= a= ue 385
ORALES seer eee MR 113 Of visibility defined en eegene EEE 917
forirockssreeis, etc. rr 110. Circular cone, defined E 1027
CEA pea E. S 996 Circular cylinder, defined--------------- 1026
EE 115 Circulation, of atmosphere_----------- 794-800
aj? (e ETI DR ee UNE va E E o C 110 prevailing westerlies_ ---------------- 798
for tides and currents_-_--_-------_--- 998 Ürade*windsseee e e ERE RU 797
O Rm 115 Circumference of circle, defined. - ------- 1024
for units of measurement____--_------- 986. Circumborizontal arcu eee tem 811
use of, illustrated. ...between 106 and 107 Circumpolar, defined..................- 917
TOTAURFIOUS limits E TN EUER > 996 mE Circumpolar émotions REM 368
IDDENRUBPERIOHS NR Eer 107-109 Circumescribed' circle: e c 1022
TOLEWreC Ks Mtr nr ere ee (10 Circumecriped halo S D 811
Chart symbols and abbreviations. ..... 894—895 Circumzenithal arc_______------------- 811
Insorated A oe 983-998 Cirripeda, defined__--_---------------- 109
Charuterminologys ma ee 888 Cirrocumulus eo) m 780, 917
W@narted depth denned Sr. meu a1 " DIOR Cirrostratus tes eee Sees SEE 780, 917
Charted visibility, defined "22222222 T6 MO eee En 780, 917
Charting agencies, federal. - ------------ SIM Cities Ont Charts ee EET EE 114
Oraner denned est a 888, 916 BymDols fór T ia = oe re 989
Chemistry of oceans 2 eo 693-695 Civil time, change of almanac to. ......- 52
O emopause E S S See A 360 conversion to mean time_------------ 53
(EA sat ena sae ee 360 Greenwich, defined. ----------------- 928
GbreopsMPvramid'of***-*- 9 o EU LE 35 local Reh DBO. Mec Ee 933
Chevalier, Roberto; sight reduction tables Gio wilightedennedaass= S SE 917
dg A ieget 541 limits Or See. in i yr Eeer gea is 368
Chiesa, Stefano; sight reduction tables of. 531 Clamp screw, defined. ----------------- oT
Chimney, chart definition of------------ 115 Clamp screw sextant___.-.----------- 401, 917
China, early contributions to astronomy. - 39 Clarke, A. R.; spheroids of. ----=======--= 357
PONO UP E A lle 806 Clarke spheroid of 1866, adopted for North
WEE EE 25, 127 American charts ooro. te se eee 62
in lifeboat navigation---------------- 651 dimensio oM oe eae 956
Chiorinity of sea water "n= -..- 695 meridional parts for_- -------- 71, 1237-1245
Chord’ of circle, defined PS SET Mm Tet 1025 Clarke spheroid of 1880, dimensions of-- 956-957
Chou Kung, early Chinese astronomer. - - 35 (See also Spheroid(s))
Chronograph, survey timing equipment.. 839 Clearing mark, defined_---------------- 259
Chrononeter EE i sus 419 Climate”defneds — — 9 E05 193
Bt op on Wake ec Hip REM TR 418 and ocean currents_----------------- 725
denned ME WE COSE EE 920 Zones of caa Viņai suse non pcr T 373
determination of... — 490-491 A Glinometer.-.—------- eed MESES xe 784
A E Š ta 916«- Gloud(s), defined e LL su beet 917
description and use of-------------- 418-419 families ol as E a ass tesla 780
Barly “anes Of) ieies se NETS 17 height measurement of___---------- 783-784
error or e ato 418, 490-491, 916 high, middle, and low, defined. - - - ---- 780
toyota o ere lopi (8 s 45-47 types of, described- ---------------- 779-783
Ee eg A 418, 490-491 vertical development. .............--- 780
for survey timing equipment. ........- 839 Cluster of stars. - - -—---===============- 366
Lunsbosec cu cms IE) Clutterdefined--2 ------ eebe ap 917
(See also Greenwich mean time, Time, on radar scope ------ -----=---------- 323
Time signals, Watch) Colitis ppt E 0
Chronometer error, defined- ---------- 418, 916 EE 917
uo ee EE 490-491 Coarse delay, defined___--------------- 917
Chronometer rate, defined_____------- 418, 916 (See also Delay(s)) =
determination of- ee EEE EEE = 490-491 Coast and Geodetic Survey (U. S.) (see
Chronometer Tables, of Percy L. H. Davis 57, 525 U. S. Coast and Geodetic Survey) $
Chronometer time________------- 418, 490, 916 Coast chart, defined- ------------------ 917

Use OIMAM ANA PM P 2a ee 483 description A ape eee eae 104

1468

Coast Guard (U. S.) (see U. S. Coast
Guard)

Coast pilot(s), defined = c+ + ae 917
description and contents of. |... 97
INOGEr neers aem A eee ee eee 23
supplements and changes to__________ 97
otslūnitedEStates=S= SSS S ee 31

Coastipilotingi/defined S C S 917

Coastal current, defined______________ 718, 917

Coastal refraction, defined______________ 917
of radio wayes*ee se AS ea e 293, 313

Coasting sxlefineds_. 0-2 . 2 iaa 917

Coastwise navigation, defined... 917

(Codeclinationme tec E 394
defined Meet n 7 n rc 917

Codingidelay,.of loran e ee ae 337, 917
(See also Delay(s))

Coefficient, of compass deviation, approxi-
mate vales Or o S EE 189

defined E99 39053745 Vc E 174
of thermal conductivity E 698
of thermal expansion_________________ 698

Coercive force, defined... .. 7! 159

Coercivity defined eee S n 159

Colatitudeza sēdās ee A 394
defined 3 5 be E O $ 917

Cold airímass defined oe 917

Cold front, defined aaa) E 801, 917

Cold wall of Gulf Stream. 721

Collimation error of sextant- 0. 414

Collins, Elmer B.; sight reduction tables

Ol Star? Bam Ee oe ae eg AN 536
star finder and identifier of. 586

Collins, Oliver C.; sight reduction method
Of DR A a dei vy harð eee 555

Collision, prevention of by radar______ 324-325
Collision bearing, defned Th 918
Collision course... a o E 327
Cologarithm, defined EE 918
explainedsf-9 pe AE E 1014
Color, of light, effect upon refraction_____ 432
Or SeA water en SE E 699
Columbus, Christopher, 19, 23, 26
Coma oi cometa p mum 364
Combination buoy, defined_____________ 918
eege TU een 265
Combined method of double interpola-
lionrc ge oo lali re edo el Lo ee 9
Combined Time and Altitude Table, of
Johnsont o o Rr errr 570
Comets=features'of us 363-365
Command, establishing, in lifeboat. _____ 647
Common log (speed indicator) (see Log)
Common logarithms e iE EE 1012, 1015
modulus or SR $9 Ee 959
Common tangent, defined... __— 1025
Common year, conversion factors... 955
Comparing watch, defined... yy _ 918
described: 9m». o c o LM i 419
Comparison frequency of Deeen 345
Compass, aireratt. ¿7 meu 3 672
aperiodic; defined r 911
ASIO S SREE S A A 626
Dearm e Ue II, 845, 889
boa tle See 135
boxing the? defined Pe "e 137, 914
celestial) types ofin —- 5 < $ 625—627
deadbeat; defined —— < 921
defined 1 vs LU k ees 918
direētional"gyrot g -- < A es 672
drys defined: x. . .. Ma eee OE 923
dumb, ‘defined SA SS THE NOCHE UM 923
earth inductor, defined... EEEE 923

Compass—Continued
gyro; aircraft 200093 n AE
ballistic deflection error____________
defined ms: SA
correction curves for polar regions,
construction ci
dampingroiene 21005 ERA
dampingierror olo o ee
computation of in polar regions...
defined soo IE CTRA ee

description and principles of____-- 143-145

errorstof stas Tansee "S 25 ee 146-151

gimballing error, defined___________
explained E Gf = eae

gyro principles: ME see ee ^
history ‘of Harare Jeo tara vg EN
intercardinal rolling error, defined...

explained
fordand navigation oss S
mereūfyDāllistics 5395 SS
in polar regions, correction curves

forest tenes! 230: 300 151-153
USO "o S TENERE 625
precession of Ee JE 142—144
quadrantal error of SS SSS ES 150
repeaters Tort S EEN 153
speed error of, computation of for
polar regions 2] 6 5. M 151
defincd ASP far - se A 948
explained? 1.0 J oÐ 146-148
use of in polar regions_____-_____. 151-153
Gyro; Plux: Gate S4 PE A 672
liquid defined AAA Che Se AS 933
magnetic, accessories for_____________ 140

adjustment of (see Compass adjust-
ment)

compensating coils for___________ 207
compensation of (see Compass com-
pensation)
defined A x F S T 935
described < S 135
deviationiof:$ 1-0 19 166
(See also Compass adjustment,
Compass compensation, Degauss-
ing, Deviation)
die E E A 139
effect of ship’s magnetism DO HESE 171
EE Eden eee 164-169
(See also Deviation)
history Ot EC E 23
installation and care of. __ 136
for land navigation -o S. 5) 666
limitations ORCOS 139

removal during magnetic treatment.. 207
routine procedure at sen. 195
shielding factor tor. eM 182
types of. .. Ly See EC 138
U. S. Navy 7%-inch, described... 137
U. S. Navy 6-inch, described... 137
inaster ¡defined ión. 7777 eg 153, 935
navigational, desirable characteristics of. — 135
kinds frei p Pi a 135
points of cl a 137
definede = rl lge ESTE 918
points to degrees, table2... . 1217
explanation ol. "d 1186
portable, for land navigation... 7 666
radio, defined EP EE E egenen OA
Temotesindicatingl 5 tas CE S 944

145-146 `

INDEX

| Page
. Compass— Continued
y defined sor IO ciar eotia! 947
explained SoN rA Am vysede Brie 627
standard, defined. TECH 948
described. ten ta MAA Toles 1411350137
RRC LINE AO e 5 2 knáur v 135
defined... 2-4 DSD 10 vg nu 948
SUN oT STI. ŠATAVBJST GU Hul 626
fomlandinavieationses ose nr fee 667
twilight, defined.+.<.<...10. BERTA sīt 951
explained... 4... DOS Jal 627
Compass adjustment, analysis of devi-
AI (e LA ` 189-192, 195
coefficients, approximate values of — 189
dehnedo cenare ence + + | x ` ` 174
constant deviation, treatment of... 186
defined. E < as aco ONY 918
Dyutetlector esc ty omy eh ce E 201-203
(See also Deflector)
for degaussing fields o... . E 203-209
(See also Compass compensation, De-
gaussing)
ECOS IO a rt or ocr ay ! 172
E-link defined t to ` morem C seo! 923
useiof- .—— KE SOMME sunna Jj 185
finding the deviation______________- 195-201
by magnetic bearing or azimuth_____ 199
by magnetic headings. ------------- 199
by,range SUR matt sat esu 200
by reciprocal bearings- ------------- 201
Flinders_bar, defined --------------B2 925
description of. be ssi moe A 179
effect of permanent magnets upon... 188
length determination_____________ 180-183
drop-in: 4 method noor: s0 eIn] 188
Testing Ol Lo — eet a wint3 32) Tn 180
(See also Flinders bar)
Gaussin error- < =- ER se cena 20t 193
heeling adjuster, defined- ------------- 929
deseret "S zonas vet. (Sep 188
heeling error, cause of--- ----.. Jem 186
CORFE CLIONOle= a a= A = 187-188
denned ee a =. eae: een Ap Ye 929
expldined ees e 186
instrumental determination. ..... 187-188
heeling magnet, defined__------------ 929
WEISE rds e so E A 187
for induced magnetism, in asymmetrical
horizontal soft iron “ð eer an 185
in symmetrical horizontal soft iron. . 183
insverticalisoftdtori$ SS Le d 178-180

Kelvin's rule for improving----------- 183

magnetic fields of a ship------------ 170-172
(See also Magnetic field)
for permanent magnetism.. .......- 176-178

placing vessel on magnetic heading.. 195-197

by azimuth of celestial body. ....... 197
by bearing of distant object. - - ----- 196
bya ey ro compass R emere Pauls? te 196
by magnetic compass-------------- 195
Procedurēfforēd act Bees Ta gr 192-195
atktnoorting-0-38U 850595320. SUIS 192
Swingin gisipes: t= NINE RUM 194
My Soe bee: Saree SSeS 193-194
quadrantal corrector, defined. - - ------ 941
effect of permanent magnets upon. 188-189
TES O e 184
(EG Ūū: trad quiae tær jean 183
reasons OLA a ts te 172
routine procedure at sea_____--------- 195

vertical force instrument, described... 188
(See also Compass compensation, De-
gaussing, Deviation, Magnetic field,

Magnetism)

1469
Page
Compass amplitude, defined... .. 02 918
Compass azimuth, defined... 918
Compass bearing, defined_____________ 241,918
Compass bowl, defned 2.222 2 918
Compass. cards ------7-—- Ee ett 136, 137, 918
history-ot£-— 2.5.2: B0mBuh ia 23
Compass compensation, defined_______ 172, 918
degaussing- ddes nane OO Simone: 203
principles-ofi0uIstot inate Lae $1ed i. 207
procedure-forz-— Ia man 208—209
type “K” installation, described... .... 207
(See also Compass adjustment, De-
gaussing, Deviation)
ComDpass_correctioh card 2. rst ee 672
Compass course, defined_______________- 918
Compass error, correcting and uncorrect-
A Deieren nidos Si 168
defined = 2. te o UNO nido tec 918
discussed ==> agéiert d agin 164
magnetism, magnetic Doles ----------- 159
theory. 0f e DEE STE 158
(See also Magnetic field, Mag-
netism)
(See also Compass, Compass adjust-
ment, Compass compensation)
Compass heading, defined--_----------- 918
Compass north, defined == F -----— 164, 918

Compass points, conversion of to degrees,

table-2.---- celda IE Ee 217
ešplānationiof MO JO den Sate 1186
defined? Los MARA e tin in 918
described: o m prem 137
Compass repeater, defined--_--------_-- 918
Gompassirosešonēcharis tocata - 116
defined: 2 sec ecw ete rro co Minh 918
magnete SE JA mu 164
use ortin plottiūg (EO CE aE 214
Compasses (plotting instrument), defined. 918
description and: user0lo-22 c enoli" 121
Compensation, of com pass 203-209
Gefined ses.) ce JAA nope: 918
(See also Compass compensation, De-
gaussing)
Compilation of chart details. - ---------- 896
Compilation mosaic, use of in chart pro-
duction su: =: hemBah Potete 896
Complement, defined. ..-..........- 918, 1021
Complementary angles, defined... ...... 1021
Composite proof, defined MBE 72223 888
Composite sailing, defined. - ---------- 221, 918
example Ot IM: crew mum 235
Compressibility, coefficient of----------- 697
of sea water"! 9. eva abel sal se 697
Computation, forms for__---------- 1052-1058
Computed altitude, defined----------- 421, 918
Use Oe betes EE ees 450
(See also Altitude)
Computed Altitude and Azimuth, Tables of
(HO. Pub No. ZA) NEHME mom 98
Computed point, defined - -------------- 918
Computer(s), for air navigation___-_-_---- 672
for “clearing” lunar distances, of Richer. 558
for reduction to meridian, of Vilkitskiy__ 518
Sightreduetiongby eee pe 558-560

(See also Altitude, determination of;
Azimuth angle, determination of;
Sight reduction)

Comrie, L. J.; sight reduction tables of... Ko

Concentric circles, defined. ------------- 2
Conductivity, electrical, of sea water....- 698
thermal, of sea water- --------------- 698
GondūetorVeleciricalssss 2222-23-52 m 289
Cone, description and properties of. - ---- 1027
secant cone, defined- -------------- 70

(See also Conic sections)

1470 INDEX
Page i
Conformal projection, defined----------- 918 Conversion tables, arc-time, in almanac- -

properties Of_--_---_ Eeer Jika 69
(See also Projection(s)) ha
Conformality, of azimuthal equidistant

projeetion-:-.---—. 5 ee Bee gs
‘of, chart defined 5 sees = 69
of conic projection (simple)----------- 79
of gnomonic projection_-------------- 82
of Lambert conformal projection. - ---- 80
of Mercator projection--------------- 71, 87
of modified Lambert conformal pro-

jectiónz -pesuserthn. - sepe sus sa de 88
of polar azimuthal equidistant projec-

EA dt eee ox 88
of polar charts..-=.---Beekee atvest 25 86
of polar gnomonic projection---------- 88
of polyconic projection--------------- 81
of stereographic projection------------ 88

(See also Projection(s))

Congruent triangles, defined-_---------- 1023
Conic projection, defined_____-_-------- 918
described? Aa arre ME salda aan 78-81
(See also Projection(s))
Conic sections efe use CE - 1027—1029
(See also Cone)
Conjunction, of celestial bodies---------- 377
defined tes delas”... Tue do 375, 918
Connaissance des Temps, first official
Almanac A o NR 5
Consecutive number of U. S. Navy charts. 94
Consol, in air navigation. ES 675
brief description _of- --- 2 - Bee 346
British name for sonne 308
definediz2 C _ em ome eee 918
development o A 59
intpolariregionsia se < mom c 635
principlesiofol A$... ea e 316
Consolan, U. S. name for consol--------- 308
US stations ec... Je Modes eene 317
Constan, P.; azimuth diagram of-------- 572
sight reduction diagram of____________ 557
Constant, defined_ el 1041
Constant of the cone, defined___________ 618
Constantierror----. 249120 asa LSS! 680
defined 2:24: ab Fc. stas ales! 918
Constellation(s), defined_____________- 366, 918
names, meanings, positions of------- 974-975
Contact flight, defned 113542 222025 670
Continental shelf______ 552251. 08202 601, 699
Continental slope ee 700
Continuous wave, defined______________ 919
of radio, discussed: 32-5 9959-2 V a 300
(See also Radio waves)
Continuous wave systems, development
E a eed abr NRY 58
Contour(s) on charts- a ` 114
defined +5: < li ga 919
of depth, defined met Ee ha 921
(See also Bottom contours)
Contrary name, defined________________ 919

Contratación: Casaidenm ea et (ase 20

Control in hydrographic survey, types of 857
Controlling depth, dene... 919
discdssed...2.2....2: cat MOKKO 3 108
Convergence of waven _ 2:111 a] 737
Convergence constant, defined__________ 919
Convergency, defined__________________ 618
Conversion, arc-time_________________ 484-486
Conversion angle, defined... 919
for great. cifele. 20 lo elsa situa 231
for radio bearingse- - rð fee i tere 314
Pale essc ce sein Mf. 1198-1216
explanationvof ieee Ma arab 1185
Conversion factors-__-:.-99.ĪB0. son 954—962

Cook, James; explorations of...........
Cooperating observers, information for-- -
Coordinate(s), eelestial 3 i
celestial equator system of___------- 382-383
defined Å
ecliptic system of, defined. -----------
fictitious, on transverse Mercator pro-
jections- es sti ts Depto
galactic systēm/of<_C_-+i4- banu” de
geographical, defined cÜ. -bos Lig
explaihed:.- 25.4225: nfegdasibs. Æ
geometric, systems Of... ee 22
horizon system of, defned 4
described EE te 384-387 ©
navigational, table of. 2422
oblique, defined
polar defined! 52.58 7072. Mba
rectangular, for chart erids ----------

Spacer Yu. cv E A
Sphericgit ee ee
“Coordinate Transformer”, of Hyatt...
Copella, Martianus; Satyricon of-------- 36 `
Copernicus, Nicolaus... 19, 36-37, 38
De Revolutionibus Orbium Coelestium of. 37
Cordouan, lighthouse at________________ 28
Coring device, for bottom samples. ...... 700
Coriolis force, altitude correction for —— 428
defined? 35... ... .barBah 180 a < 1919
éffect upon ice drift2002.-.. Le seite 753
Corner reflector, defined______-_.------ 322, 919
Cornet, azimuth diagram of____________ 572
Corona of sun or moon_______________ 380, 811
Corposant (St. Elmo’s Brei... 297, 813
Corrected print of chart, defined________ 888
Correcting, compass error______________ 168
defined.------.... heeftah seme 919
Correction(s), for atmospheric pressure,
defined.---*. .2.. iol oe meme ee A 912
for'dip, defined-------- ... ie nodes 922
height of eye, defined. uc? 929
index, defined... data 931
instrument, of sextant- 012014 412
of nautical chart (see Chart(s))
hase, defined- ebria Ea 939
olaris, defined 9232 ` 00100080 bn be 940
sea tilt, defined___. si Jing fend 945
sextant altitude, defned 0022. 946
tide; idefined__ fia, 2102. Leal track 950
wave height, defined_______._________ 953
(See also Error(s), Sextant altitude
correction (s))
Corrector, defined- 1103340 Jomas 919
quadrantal, defined-- 2 2002.2022 941

Cosmographia, of Ptolemy- 707

Cotangent, defined_____ d eer, ver. "1032

Countercurrent, defined... ` 718, 919
(See also Current(s))

Counterglow vg PO Abe do 365

Course. PORTADAS 319101117603 dor Ta 66, 919
of advance, defined... 0 66, 218, 919
in air navigation, defined... ` 671
collision

INDEX

Page
Course—Continued
compass, defined. ...........201007.3 918
direction of charted 2 115
final great-circle, defined... 925
great-circle, defined. aa 927
pridtdefnined AVIATION 0 ia a =
initial great-circle, defined____________
made al SOOT RA E 66, 218, 919
TE EE EE WE gee
mmagnebie;'definedsex«- deba 20109 9001 935
over ground, defined------__---_ 66, 218, 919
per gyro (standard, steering) compass,
defined Wiig 9. . — .. Hna wh 939
thumb; defined... Zpeeaive la ney bus a 944
true; defined: Ire pudo da (2 951
Course angle, defined. ---------------- 66, 919
A ss sos ds se rrr 66
Course computer, for air navigation... 675
Course error, defned. 2 222222 919
Course indicator. --- LLL. 153
Goursepline: V gan 2001 da anise 66, 216, 919
in air navigation, defined_____________ 671
AN IA Ea 216
asilineof positionicr.... seer SEENEN 453
plotting of iss... bee Beth lae 216
Onfpolanuchartssss = A tp legāts 622
Course recorder, defined________________ 919
Aoc a 155, 220
Woversiiie, denel oo o aa 1032
CUracióninfco Sh REY. 9007 PESADOS 204 750
Crepusclilanraysme wanes 0 812
Crescent moon, explained- ------------- 377
Crest, of radio wave, defined____________ 290
of water wave, defined_______________ 727
Critical range, defined________-_--------- 919
Goran waves: Ui si aran + 11918 bee 337
Critical table, defned 4 Jursa ni e sun, 919
usefofēmis Ama Wee BEMOL eeti_a 1045
Cross bearings, defined. -.-------------=- 919
Cross talk, in radio receiver_------------ 302
Cross-staff, description Of-------------- 41
Mabe defined" -Verrete Poderlts. 1025
of a number, defined................. 1010
Cube root of a number, defined. ........ 1012
Oubit, length unit, origin of_----------- 26
Cugle, Charles H.; azimuth tables of----- 571
Cugle’s Two-Minute Azimuths----------- 571
Culmination of celestial body, defined.. 383, 919
Giniture; defined (CS: EZ Ust es teeter 919
Cumulonimbus_____----.------------ 783, 919
Gdumulustētms træk AC LO 3a annen 782, 919
Cupola, chart definition Of-------------- 115
Current(s), allowance for, in dead reckoning. 217
Ne UA 252-254
ADOPCAD == me eee e E 714
average, in celestial navigation. - ------ 461
computation: OFF === uM 276
chart symbols for, described. --------- 116
eler A 08 998
coastal defined =E === tE ee tit 718, 917
definitions-of -—---===-===22=--- 222 919
determining, in celestial navigation___-- 461
jnsdead' reckoning:----—---— m 217
by geomagnetic electrokinetograph- 60, 128
diagrams, described-=-========= eer 275
direct, defined - 2301 fov me Sara 20T 922
direction OL See oe S eee H 920, 922
discussed. =. E ES 217
distinguished from tide---------==-=-=- 703
diurnal defined a se. det sex Es 922
discussed 15-70 T2 LE. RT 713
drift of, in celestial navigation. - - ----- 461
dica A a a 217, 923
discussed*e cue E 712
rift current sea m a E 718, 923

1471
Page
Current(s)—Continued
ebby defined. AA 923
SUrengthiofesoosies lada Alden 712
effect of, upon running fix__________ 249-254
UPON speed. PA CUE Ba) 218
ŪPONFWāVESs => 00d OAL Wf 730
of electricity, defined_______._______- 289
Inducedsaul simus ot sug... Sqneda 289
equatorialeoIl.. ger (ënn) esie. 714
favorable, defined...........J9D21 31 924
feeder sues nsus AA diera 3 740
Hoodsdefined vl... Dao mb maraathr a 925
strēngthofaNsobā Ms e eec omnei 712
greater ebb (flood), defined... ....... 927
hydráulic ¿24014 DAI .dokosub 3 712
mduceduitkazina.defuuu. aa sar mam: 3 289
information on, sources of... 97, 716
(See also Publication(s))
tns horemdefinedšāssssss5558.2 390 718
lesser ebb (flood), defined_____________ 933
longshore, defined... 22- JEDVA 5224.4 718
described E A AM 739
lunicurrent interval of. - ------2---22- 268
maximum ebb (flood), defined--------- 935
mixed; definedibaidaf eat label 0 713, 937
Monsoon odina ¿Lit coco. DCK
neapsiecjavec.c MONDO nortisod qut 714
fiontidai, dēfined 223 12202 JÆ 800m 1 711
nontidal flowfteffect:ofs=s»>=»-=» P9 M 714
observation ofa Jo reinen. z Odds 716
in hydrographic survey----------- 844, 860
In OGeáns-.---.--.-.o080110990 10 889718 718-726
(See also Ocean current(s))
Oftshore,-defined:===+2=====2=10 ROMU 718
perigeanget. 0f Unos 18 Y Diseno: 714
periodic;'defined** 1022269920000 718
permanent, defined. ................- 718
piloting Te r 1999 Ma 268
in polar regions). .-aodamioi lo 290 629, 725
deflection:of -APAS anaE 094 615
(See also Polar regions)
predictions of, precautions in using---- 268
at reference stations__------------- 273
at subordinate stations------------- 273
pulsating; definēd- ===? age. 1⁄2 3 289
relationship to tide--_--------------- 267
Teversing: ines. Æ bs ooo lui 712
rip current! 31A JIAN BEE 740
in rivers and channels vm 2 222222 268
rotary,defined+==+=========3=JI 190015 944
described 2... 22 2420S), qr non ese ptr 711
inequalities.of-!0 MOosta02 DOMA: DOK 713
seasonal, defined +: 0U1 USE T DV 92 718
semidiūrnalji 01 904: nal 713
defined DUROS M BAR OO Lb 945
set of, in celestial navigation---------- 461
definedo 5941 SER. 10 110128 217, 712, 945
slack water, defined... ...........-- 712, 947
time computation of_----------eec- 274
speed of, finding by table------------- 274
relation to tidal range Sha 3009.52 715
Spring eo EE sa RRO OO ANC 714
stream current, defined............- 718, 949
strength of, defined gegen EE 40 949
In isurf zone owe bOI ee 738
surface and subsurface, defined-------- 718
survey observations of_-------------- 844
tidalPdefined- 050-399 Pon +010 SENJA 711, 950
in piloting fe EC 18018: Yo OC 267-268
relation to time of tide__----------- 715
reg eee deeg eegen RE 713
variations and eycles--------------- 714
initidālšwātērs ss sss) a= EL. iem 268
and trde 2243 oe 1 »9 ME EMT 267, 703
time computation of_---------------- 274

1472 INDEX
Page Page
ais C es Y. tr 7 714 ¡Danger bearingit ^ Eeer 255, 920
unfavorable, defined ___-------------- 951 Danger buoy, defined. --------------2-- 920
variation of, with depth-------------- 716 Danger: line, defined ¿2000 AAA 920
across estuary --------------------- 716 Danger sounding, defined_____---------- 920
velocity ratio ot 5 ES ES 274 A xx sta P teg 257 .
wind current, defined. --------------- K Dangerous semicircle, defined- - E 5 5 920
nt a ere DAPAC (see Danger Areas in the Pacific
Cer ola i current(s), Tidal cur DÓx4egésqubet ice Gi 302
Current chart, defined AA RA 919 Bars Charles; impact of upon oceanog- Le
t di m, defined: ---22- SÆ _ 920 raphYāģmres Codtoðr fees) 0298
DEE as, MA 1 1 S. 275. Date line, defined -------.-*---*- tam 920
Current difference, defined-------------- 920 origin andcuse'of --—- 77-7 IMM Aa 486
Current direction, defined_..._--.--.s2u5 920 Datum(s), of chart, defined------------- 916

Gurren tometer eee ae 716, 844, 860
defined. === ea as str 920

Current pole in hydrographic survey----- 860
Current Tip a tejo Msn. 740, 920
Current rose (ellipse) ______._.--_-_-_--- 412
Current tables, tidal- - ----- 222222 95, 273, 716
defined 222223. 9252.2 __: AS 950
extracts from: cs Je 47 9 1132-1135
PEO <br E A ele jas 273-276
(See also Tidal current tables)
Gursor,defined?. SS 5 S 920
of plan position indicator------------- 318
Cusp of moon. 22.225 .2-. usa (Vis 377
Cut, defined... ¿2.2226 øgn ed Jems 920
Cycle, defined: — "osse 290
@ycloid, wave. as... fare: SP io 727
Cyclone, areas of occurrence___________- 820
defined: -- —- (etn S sss eate os 920
description of = V aa A 805
extratropical- "= 2. ae eee 806
observations of, by Air Weather Serv-
ice m si £ jo E ee 787
tropical defined n 951
theories of formations rn 824
(See also Tropical cyclone)
Cylinder, description and properties of... 1026
Cylindrical projection (see Projection(s))
D-layer of ionosphere----------------_ 293
Da Costa, Fontoura (see Fontoura da
Costa, A.)
UN Memorandum, chart maintenance
A Se yr a SMS A eon 117
distribution of- 2.420. T AS 99
iceuntonmabionjnee ee ae 758
publication and contents of___._______ 99
(See also Hydrographic Office (U. $.)
publication(s), Notice to Mariners,
Radio broadcasts)
Daily rate, of chronometer_____________ 418
determination of. e 490-491
defined fe ase. T e Mies ee 920
Dump haze ten EE 809
Damping ¡defined 2 503 d a ees E 920
Damping error, ballistic; defined________ 913
OffevroRcOmpassMe a. see CNS 148

computation of for polar regions_____ 151

Dan buoy defined. Sn 920
Dana, oceanographic expeditions of______ 692
Danger(s), chart symbols for, described. _ 110
illustrated = a UVa e ee de ee 995
information on, source of... 97
publication of latest information_____._ 99
Danger angle, defined... 22:5 e Lose 920
horizontal eee se. e SSL 256-257
DEE GE allustrated: c d EE 256
eruca e EE 257
Danger Areas in the Pacific (H.O. Pub.
Nov TO) cer EE 101

definitions of various____________~_ 709-710
discussed Eege E 109
types of Huet eu ee JE 301 erin 892

(See also Tidal datum(s))
general definition.of.-======- PUBS
North American, of 1927. -.-------- 427, 892

as origin of measurements... .......... 427
tidal defined -= sec de == EE 950
of various areas__--_--_--------- 1000-1001
vertical, «defined:-======<. ass A 892
Datum:level of. tides--5----2 819 C 709
Davidson: HE AP 723

Davies, T. D.; sight reduction method of__ 563

Da Vinci, Leonardo (see Vinci, Leonardo
da)

Davis, John; determination of longitude... 44
invention of backstaff by... s-t- 41
latitude by lower transit__-__-------- 43
prime meridian. of 22 _ == Hp n 48
The Seaman’s Secrets of___-_--------- 34, 41

Davis, John E.; azimuth tables of_--__--- 569

Sun’s True Bearing or Azimuth Table
of ce 2225 et 57

work continued by Percy L. H. Davis__ 571
Davis, Percy L. H.; Alt-Azimuth Tables 3
f IS E r a 529
azimuth tables of CC S nN 569, 571
Chronometer Tables of. 57, 525
Requisite Tables ori ase CUTE AN 57, 528
sight reduction method of____________ 5

Sun's True Bearing or Azimuth Table

Day, apparent solar. =-=====< Dona 353
astronomical, defined________________ 483
significance: ofe.=4--=-=-=--5 ce eee 374

use of in old almanacs. _ 222 2222 52
defined: «an aal mi sat samnorotla tee 482
kinds of, conversion factors___________ 954
length of Æ Som. ote e EE 659
lunar. == Ane da en Bee 375, 482
and, tides.» o AEN 708, 709
nautical, defined, A 483
historical = 2% EE 518
sidereabs wi eee eee da E, 375, 483
defined: == * s e ro ee AN 946
solar, astronomical significance of______ 374
defined SEENEN 947
tidal.» dacsaesua ation etai e me 482, 709
defined = - = AA 950
Daybeacon, chart symbol for. 111
defined Ý wee. cr 7 AAN 259, 920
Daylight saving time____________ 482, 488, 920
Daymark, defined... 01: 1101) bevels 259, 920
description of, in light et. 97
Day's run, defined: == ss ee pan 920
Day’s work, defined" 12% Luisa tos 920
described 2-5 «e med > es O 597-601

| X
|
1
4
i

INDEX 1473

Page Page
Dead astern, defined "` kenali an 920 Declination—Continued
T AS 213-239 for lateniyearsisita er bab s HØVI - 653
ISI AVIGAUION Sn me nm id 671-674 finding by almanac—Continued
MO Me es A 220 Of, MOON netic e ccs Jana da soba 470
inair navigation... hatos be taltauus 673 E a oem eoo e RVM J 470
and celestial navigation... 460 Of Stare acortar. Dial de 471
hy coamputation__- scs Ä 220-228 ARMA IES A CH 469
course made good, defined____________ 218 finding without almanac, of sun... 653-654
course of advance, defined____________ 218 gudadefinedat, ti cone ca 928
course over the ground, defined._______. 218 magnetic; defined... -a 161, 935
A, ht eer Fede 217 measurement of- ==- Eege 382
defined_______ mitre bla. 62, 213, 921 parallel of, defined __ —— Eh Ae 382, 939
departure, taking of. 222202002 216, 597 precession of equinox in_.-__---_------ 373
Doppler method, described ___________ 220 Declination table, of Zacuto____________ 32
effect of current upon. ............. 217-218 Decometer, Decca. -_---22 20 coo 345
ION AAA 304 Deduced reckoning, defined_____________ 62
ADM ents 64 55 oec «ies AAA 220 (See also Dead reckoning)
A IA PA fee 18 Deep, definedurmenud. : 49417. pedum nel 921
A FR td tS U 627—629 on,lead-linGwels a. nf 2. atto pt 132
inertial method, described... 220 invocean«delinedi = os es 700
Mand navigation. 1 5-0... Sere. | 664 ` Deep scattering layer, in echo sounding_-- 134
leeway, allowance for... 219 Of, Sea Water de a bras <b te cae 744
donned do DEE TEE dari = 219, 933 Deep sea lead, defined- ---------------- 921
in lifeboat navigation. casso 649-653 description of- eee h Te 131
Originjof expression ape. (esejas Jas sa 25 (See also Lead)
ly ploteo patilla fele fee Arps 216 Deep sea sounding Ines ee 869
laspolariregions ` 2220022. hg 622-630 Deep water layer, of sea water---------- 743
probable erromof. Lect... kage 685-687 Definite integral, defined_______________ 1043
MS E AAA ee 2212236, ` Definitions, basic -ss do pad da hatt 62-68
(See also Sailing(s)) Deflection error, ballistic, defined___----- 913
speed made good, defined------------- 218 Deflection of the vertical, altitude correc-
speed of advance, defined... .......... 218 tonora- ebetan Ms deo teris 427
speed over the ground, defined________ 218 defined amr tt dit 921
(See also Navigational errors, Naviga- (See also Vertical)
tional practice) Deflection plate, of cathode ray tube__-_-- 302
Dead Reckoning Altitude and Azimuth Deflector, compass adjustment by------- 202
Table (H.O. Pub. No. 211), of Ageton, defined... tres o. hea bss 921
contents Ol ee E EE NES eh 98 of De Colong,described______________- 203
AA A Bee ep 538 ofsKelvin, described ferran 202
Dead reckoning equipment, defined__-_-_ 921 principles ofe = "2 ve eee a 201-202
RADO lar regions =< > «fe: ahs 630 DeForest, development of vacuum tube by. 58
use of transverse Mercator projection Degaussing, compensation of compass
Vay tf EE EE EE EE ee 88 TA A EE AL eee 207-209
Dead reckoning plot, in air navigation... 672 definedz.. 228 A a 3 pr 203, 921
deBnod Nee E hað gads 921 deperming, defined- ---- eee ae 921
Dead reckoning position, defined. ... 62, 213, 921 described v€ == 28222 Jae eps 207
Ciscussedes =D ei 213 flashing defined sess a sae sa ee 925
(See also Position (s)) described thue x. ts se eere 207
Dead reckoning tracer, defined_---------- 921 magnetic treatment of vessels_-__----.-- 207
principles OLA Mu c ee SE 155, 220 principles of- e eee a ara hatos 203-209
Dead reckoning track, defined. --------- 921 (See also Earth, Magnetic field, Mag-
iDeadiwabteries* bs Se E ë 735 netism) : e `
Deadbeat compass, defined _------------ 921 Degaussing coils, direction of current in-_ 206
Decante, E.; azimuth tables of_-_-----.-- 569 effects Of sen. EE E ees 204-206
A A Hee eredi 312 "reversal" method of securing_--------- 206
UNT D ppm ber meta GE 345 types of--- ===. inna A 204-206
unsaimnavigabon----------e ae ===> 675 use of, during ship SWINGS K cce 194
COVERT ee Se eee 346 "Degaussing folder". ....... bes passi 204
eCOM Cele -e trenes: tes 345 on reversal method for securing degauss-
defined. AA AAA An 921 a COUS = eie Eeer 206
development ofi- Se CC sedas 59 Degaussing stations, function of_-------- 204
principlessof edo. < asā K 344-346 Degree, length of, table 6-_-_------- 1246-1247
iDccembersolsticeset-- — de osas 373 _ explanation OLA E EE 1187
Decibar, unit of pressure measurement.... 696 unit of art- AAA E 1031
Decibels defined! 2.22. _- . .. bea das ais 921 Deimos, features Of:-_-_--- = sens 361
Decimal, mixed, characteristics of......... 1012 De Jonge, Joost H. Kiewiet; sight reduc-
repeating notation fort: < Æ e ert 1011 fon method ols aa eee e ecce 548
Deak oa abies! da ot 5 814 De Colong,I. P.; deflector of 203
Deckilogadefinedm si 54: Pedes encore 921 Delay (s), base line, defined............. 2
inifeboatinavigation------ basse E 649 coarse, defined AS ts at
Declination, circle of, defined__--.----- 382, 916 coding defined: o ease Ju
definedee bak rines Due epee 921 tinetdeinēdēs teure sr. ice etie ait ie
equal, circle of, defined. ____-_-------- 916 half pulse repetition rate, defined. -- - - - oe

finding by almanac, for following year.. 479 ¡ra = a: Jasas

1474 INDEX
Page Page
(See also Loran) Deviation—Continued

De FIsle, Rollet; sight reduction diagram reduction Of t -Padierna ce MN 170-189
Ge o eee 557 residual, defined... PORO 944

Demodulation, defined_---------------- 921 determinationof== 2 == =ð 166, 194
Ofsradio waves 2 tes < 300 of properly adjusted compass. ------ 172

Denominator, defined------------------ 1005 semicircular, cause of- PMA 174

Density EE, EE ee 752 defined E OI 945
Ofisea water. Kia Speed MBA.) 696 standard. <=... adds DODE ASE 681
Units Of ce AOS E INT 696 (See also Navigational errors)

Departure, defined. - ----------------- 65, 921 from’ vertical softtiron = = OR NE 171
pointrofadefineds ca 0 Ten 940 (See also Compass, Compass error,
position of, defined DE 216 Magnetic field, Magnetism)
taking AS METI hr anb 597 Deviation table, defined---------------1 921
(See also Longitude) preparation of: 7 — ihe) AOSTA 39 194

Dependent variable, defined- ----------- 1041 USCOf =... 3.9. RI SOT 166

Deperming, defined__-2922-22 a om 921. Dew; defined=t=-_- se. SE PUN 778
described... ee Et ex 207 Dew point, defined... 4122028 921

Depot des Cartes, Plans, Journaux et explained ceca EIN 778
Memoirs Relatifs a la Navigation; temperature of, table 17__________ 1268-1269
origin Of a. A ro oi ee avs 30 explanation of EG) „HO 1191

Depot of Charts and Instruments, estab- Diagonal, defined =--2 HE eae 1024

lishment.of^2 a= eee eee eee 31 Diagonal metric scale EE ES 844
publishing of first American Ephemeris for chart construction -------<- PM 890
and Nautical Almanac by----------- 52 Diagram, current, defined____---------- 920

Depressed pole, defined_____________- 382, 921 on plane of celestial equator________ 383-384

De Principiis Astronomiae, of Frisius____- 32 on plane of celestial meridian, defined... 922

Depth, allowance for tide___.___________ 267 described empre. MAA 387-393
charted, defined — ... Saas oir 916 time, defined senn 1 ITI E 950
contrasted with height of tide_________ 267 described = «o. S sa 383-384
controlling, on charts] summ 108 vector, defined "` "` `" EE 952

defined esu mis gotu iti in. qi 919 Diagrammi Altazimutali, of Alessio. 572
measurement of, methods........... 131-134 Diameter, of circle, defined_____________ 1024
by Posidonius MS R 691 of sphere, defined 9 -S 0008 ER 1029
predicting of, in piloting.___________ 270-273 Diaphone defined"*: ^ lene pe 922
units Of 2007 CT EK 27, 124 as fog signal, defined (22 48 266
on charts of various nations________ 999 Diaphragm horn, as fog signal, defined___ 267

Depth contour defined oe ee 2. 921 Diapositive, use of in photogrammetry___ 876
illustrated 7: er ee O 997 Diatom, defined ` ed aes 109

Depth finder, sonic, defined_____________ 947 Difference, of distances, measurement of
ultrasonic, defined RES 951 309-312
(See also Echo sounder, Sounding ma- of latitude, defined... See 922

chine) explained (229 10789 HUA, 2879 Tesh S 64

Depth measurement, importance of. |... 131 of longitude; defined--- 20 922

De Revolutionibus Orbium Coelestium, of explained? ANDA ADSL] SOHO 65
Nicolaus Copernicus. ...............- 37 of numbers, defined: EE 1009

Derivative, defined" COTA 1042 Differential "defined PLE IED IJ 1044

Desert? deyil C ee aen b 807 Differential equation, defined___________ 1044

Desk computers, sight reduction bn __ 560 Differentiation, defined Mal 1042

Destination, defined 3430 Tasman n 921 process of, explained "Cu C920 RM 1041
poinv'otzdefined AS 940 Diffraction, of radio waves_____________ 295

Deviation, analysis of... 189°192,195 Digit, defined FRAGD AI Bee 1005
application o 168 Dihedral anglexdefined--..____)) mm 1022
Causes ors. UNE vo cm rae a JM 166' Dip, defined. ee Panne eun Fi 922

the single-pole concept_______...... 171 geometrical, defined "Be ATI iy Lat 927
coefficients of, defined =" MIRE 174 of horizon, altitude correction for____ 422-496
constant, treatment of_______________ 186 from difeboatsse o c 657
defined: <: A quu uui 166, 921 computation of----— DERE 422-423
effect of compass location upon... 175 defined-I= dr 922
effect of latitude upon... 173 effect of refraction upon____________ 423
finding dð ld y 195-201 effects of weather upon. 423

by magnetic bearing or azimuth_____ 199 fluctuations of... UL fuso 424

by magnetic headings______________ 199 formula for se 2 edge o TORMO 423

by range ees ICONE 200 measurement of PM 423

by reciprocal bearings-- e 201 in polar regions 4907 Ji ig to on 637
Flinders bar origin. ofe. e DNE 24 magneticrdeinedi aeai 162, 164, 935
Gaussin error FANNS LOA EE 193 short of horizon, table 29. 1278-1279
history OŠEA ees "tādas DORA 24 explanation of- Tn 1192
from horizontal soft iron __ E 171% .Dip'cirele; dee dona 922
from induced magnetismo se AUR MD d 171* Dip-correction, defined. -..-....Do009 5. y 922
Kelvin's rule for improving compass Dip needle, defined... iuo Teed 922

adjustment i EE RU D 183 as vertical force instrument... 2 __ 188
magnetic fields of a ship____________ 17029172. Dipole antenna naa 297
from permanent magnetism___________ 171 Dipsey lead (see Deep sea lead)
quadrantalica ise ot ON 174 Direct current, defined... 289, 922

defined x TA C M A MM 941 Direct motion, of planets. AA rR 3

INDEX

Page
Direct wave, defined___--.__ 22302 922
Direction, in air navigation... 672
compass- E Ja 66, 166
Of current, defined__teseenueseut los 920, 922
denned r Haba manos) sals 4 66, 922
and distance, by electronics... 313-331
On earths! SM Weer. .(niekiecnali 66
of fictitious rhumb line on transverse

Mercator projection--. W Sisi Joad 88
eridadefined 999 CITEA AAR 618
E plotnpiol uoce eter EEE MS: 622
eege hae. 627-629
in land navigation, instruments for... 665-668
in lifeboat Navigation brunn 649-651
MNO CbIG == 2s naa 164
Of magnetic Held CC eines Ja noir 159
measurement of, on chart sieste Ja sob 214

on Mercator projection____________- 71

Methodsts 51 SOME OB < medus 134-157

Dy radio GU E 304—306
PIOU KO O NUBE + hg AE 214
in polar regions, use of grid for... 91
bf Teferengele9 Hau. n biorg 66, 134

of magnetic cOMpasses_ ::_ 30 Hs 164
Of relative movement tt trna mad 326
of underwater sound waves, measure-

Ment Of eer e adds 742
of waves or swell, defined.______ 922, 949, 953
of-wind,“defined= tase huniteh 922, 953

Direction finder, automatic radio, defined. 913
deviation of; defined... hese 922
manual radio, defined- ME kran 935
adio defined: i m J eor haeneh an 942

(See also Radio direction finder)
Direction finder station, functions of... 313
tadiotdetineds=--sssasbsaāsk. 15 8f

Direction theodolite- Lir- divessa + 3911. 839
SCO 0 Attig vær dn fade nis 851

Directional antenna, discovery of____---- 58

Directional gyro compass, for aircraft... 672
taeckibya e = ees A TS l 88
(See also Gyro . . ., Gyroscope)

Directional transmission, of radio signals. 307

Directions, sailing (see Sailing direction(s))
Directive:force, defined... ..-... 355-5 t. 01922

iDinectrix of parabola---.--5s2355- 6 1028
Discontinuance of chart, defined--------- 888
Discovery II, oceanographic expeditions of. 692

Dispersion of light, effect on refraction.... 432

Disposition of lights, defined... ... 922
Distance, angular, defined... .. 134, 911
astronomical, units of l e 351-353
deme A E os $ 65
difference measurements____________ 309-312
differences of, measurement of___--- 309—312
and direction, by electronies. ....... 313-331
great-circle, denned eee ee VA 66, 927
to horizon, en SE DSL: agri OI 1254
explanatiobrob e cc e = 1187

cc rm EIC m 627—629

in land navigation, discussed____----- 668
merge gedeterraln RAS a= an 665

inwfeboatmavigatione ses 651

measurement of, by electronics... ... 313-331
VISS TEE ENEE 842
on Mercator projection. ...........- 71
Methods: 408828 -12 2. «set 4 125-131
onmauticalicharte< 232-0600 P NOTE 215
on polar azimuthal equidistant pro-

Je CliON metas a de E o 8
bysradiod- ieu etse ELIO 2122 308—309
by two bearings, table 7........ 1248-1253

explanatio or- 109 JO mue P: 1187

by underwater sound. ...........-- 742
by vertical angle, table 9_---_---

Page
Distance— Continued
explanation ef Arie E sabio. 1188
plotungioor ewm. CO eds <szaassdi 215
polar, defined___________- sor SS 382, 940
rhumb lines Lorri aim fuia lo „gr 66
dēfinēdētt ten: Sot pavers tb ye 944
scale of, on azimuthal equidistant pro-
jection E st ca | 83
on gnomonic projection_____________ 82
Skip, defined £5 3290 Hom bas qoia 947
explained }iacan 335195 303 4613518. ye 294
O E, DL ral 26, 65, 124
(See also Units of measurement)
sett IMO POLO cs sette A 243
venith;idefined we Lëtze Birra 385, 953
Distance finding station... 309
chartisymbollor==... 2.2222 IR 113
defined. 35€. TNE Pere. Ze 922
use Of renz Sey br S. IA 315
Distance marker, defined_______________ 922
Distance measuring equipment__________ 317

Distance off, determination of, from life-
bost. vee Øl «4 de are MBA bes 661

an piloting 22 444, *9. JO eae 257
Distance, speed, time; table 19_____- 1271-1275
explanation of S EE 1191
Distance vector. use of... 1017
Distances Between Ports, Table of (H.O.

Pubs No. 15011 Job ab dani HE < 97
Distances between U. S. Ports (USC&GS).. 98
Distress information (see Radio broad-

casts)

Distress signals, source of information on. 96
Dittmar, C. R.; sea-water analyses of. ... . 692
Diurnal’ defined- 9 6 2222222555 De 922
Mirna circle PED. EE A 367, 922
Diurnal current, defined---------------- 922

discussed? SP. GETTA Ada sioe al ada 713
Diurnal inequality of tide or tidal cur-

rent) "defined. 992v9e-9e "Uie aede 922
Diurnal libration of moon. Er 553255 n: 3062
Diurnal motion, defined. ----... —-.... 922
Diurnal tide ts MUTET ocn 705, 922
Divergence of waves as = 137
Dividend "defined 32222222 EE E 1011
Div iderswdetsne das ee A oe 922

descrippion and: use or. = =e EE 121

proportional ea 845

proportionalfandispacine coc" 889

SPACING = == << sees aren J See earn: 847

vise omin plotting====25230 nae 214, 215
Division, of algebraic expressions__------ 1018

by logarithms: te VESTEJON suet seu 1014

of numbers, explained__--------------- 1011
Divisor=defined = seeks METS ANW. SECHER 1011
D’Ocagne, Maurice; altitude-azimuth

RTR, GE EEUU r ee a HO MIC 555-557
Docek defined Seba. ISA - cm eoa 922
Doldrums+weatherins cou 797
Dolphin, definition and chart symbol. - - - 110
Dome chart definition of- -= ===" == 115
Doniol, R.; sight reduction tables of------ 532
Doppler efect dened? mmc 922

principles of, in speed measurement- 308
Doppler navigation, of BEE een ech 60, 673

described 220, 567

DESIDIA TING meee ae ee es 608
Doubledenned= em 2 ejā 922
Double interpolation, defined- ---------- 1045

methodsifor es Se 1048-1049
Double pulsing, defined. -----2========= 922
iDouble3star.---- = ease Zeg e BOS, 366
Donbleltide sea. BOT 706, 923
Doubling angle on bow, defined__-_------ 923

1476 INDEX
Page
inspiloting Mee: 7 ee 255 Earth—Continued
Dozier, Charles T.; sight reduction method secular change ofuolionitsa Us uL ME
AA AS aj 548-549 magnetic field of —Continued
MDraftfdētinēdēs $$$. o. ber m» 923 units of measurement-__------------
Drafting, of chart original. ------------- 896 (See also Compass adjustment, Com-
Drafting instruments, for chart construc- pass compensation, Magnetic field,
ereechen betian ee 888 Magnetism)
for hydrographic surveying----------- 844 magnetic poles ofa. SHE eerte RAS 1
Drafting machine, defined-------------- 923 motion of, cause of seasons- -------- 371-373 `
description and use of =---- tes 123 oceans’ on, extentioft —_ EE 1
Drawing material, for chart construction. 891 orbit;of.. Ls eae. Leer eee
Dredge, bottom sampler................ 700 orbital speed, of eerste << S
Dreisonstok, J. Y.; sight reduction tables polaraxisrof sJeeerrrisat waltagiven he
ofr E dm m 57, 98, 526, 534 positionions_.... =... taa sea
Drift, of current, in celestial navigation__ 461 precession- of axis- en S AN
E E E gi 217, 923 revolution of, effects Of_--------------
discussed. = cdc cee oran a 712 rotation of, effects Of----------2222 367-369 ©
Of icon. Enim Sees ee | Ma 753 Shape:of.. ...... did Tota
Drift angle, in air navigation, defined... 672 historical-.:-f052.35.. ... a
Drift correction angle, in air navigation, size determination, by Eratosthenes...
defined 2252. Sa ee pando pato om 59 672 by. Picard #: ¿2 A
Drift current, defined________________ 718, 923 by: Posidonius: bite M Sais setae? BR 9
Driftlead, defined: AZ avn EE 923 asispheroids esis EE 357, 427
Drogue;detned dfe ss Ee 923 troposphere of eebe eia en 358-360
Diy compass, defined ea ME 923 Earth inductor compass, defined________
Drny'haze-se EE Ta ae 800 Earthshineton mooner ofro cule
Dry-bulb temperature (thermometer).... 779 East Australia eurrent. 2202
Duet; ofradioswawest- eege eae 292 East Greenland current... 22021
Dudley, Robert; Arcano del Mare of... 94 Hasting, defüned.......3. .. banh MN
DuFay, positive and negative electricity, Ebb, of current, defined________________
discoverycofzibe M engt ae tented e yt discussed: ze utl: 54 haies Te ee
Dumb compass, defined... ... 2 923 time b ste». dus ste do BM
Dunn, Samuelómsdtet o manas lpp 34 greater; definedt. 2-2 As
Dusinberre, H. W.; sight reduction lesser, defined bat oi 0 ni ad
method Of + 2. 2s 25> o = IA 564 maximum, definedG@il_ mhart ES
Dūstīdēviiše serene matte — a 807 strength of, definedé Seas AAA
Dust whirlae. debas. BemBeh dom ú 807 Ebsen, Julius; azimuth tables of.
Dutchman’s log, history of... «c JM 24,127 Eccentric point of survey, defined________
in lifeboat navigation 2: 22 #205224 1 652 Eccentricity, of conie sections, relation-
in polar navigation. ..... cll. í 1 í í 2 5. 629 ships ¿GIULIA agi TAR LA
Dynamic pressure, of water_____________ 128 Dellt pe, SAA. x OS EE
Dyne, unit of force, defined_____________ 765 of hyperbola sem reik- es nie
of orbitsse.2 bro uodsetraanadd Tomo
Hlayerlof(ionospliere ss 293 of parabola--culz uu 22 val USE ano
Elink, denned ā. --c... Beara bu 923 Echo, of radarzóyado.. ab sna
described eee 185 Echo ranging, defined. 2221
Earnshaw, Thomas; development of chro- Echo sounder, defined)” ISS EN
DO meter A e eee ET E 47 descriptiontof 4 OH NT A
Earth, atmosphere Of ---------- 358-360 development Of e nd
axis [or TO CA LOM Ol = =e A 63 early methods---.--..-..-. eet
precession Of A pe oe ake MR 373 O SOT eas a ES EE
ER e ae V 63 phantom bottom IE ERN 134, 744
elimaticizones'of= SS S. 373 in polar NEE: 635
compared with other planets__________ 964 principle of__________ O A 309
ANMERSION O s aa 62, 357, 956-958 (See also Bottom relief, Navigational
direction on F ` Te ER 66 practice, Sound)
distancejonāms - te. ee a 63,65 Echo sounding, defined... 923
escape velocity from. 358 Origin OL = sae AA 28
features Of Biren tp de be pate ada 357-360 Eclipse, annular, defined_____________ 380, 911
AIP UTES KO feed rey yeaa See eg 956-958 defined... ie ee ir ' 923
as Geld if, aute sera desir -. 358, 427 explained s. es conos e eee 379-381
magnetic field of, anomalies_________ 161 longitude: Dy + => S EE 38 44
E Eet pr T Zei d 162 partial. to CN 379
diurmnalšchnangejo [g ej 161 SArOs CY Cleat. x n Vn 381
elements (components) of________ 161-162 total. 3 opos tee EN 379
geomagnetic coordinates |... Ge = 162 Heliptie, defined... 0. 5 aoe 370, 923
at Mg altitudes e. ee 162 and moons Orbit. <<... ele Lect aie 381
infensus Ole ce sa LENT 161 motions of celestial bodies in________ 370-373
at magnetic equator... 161 obliquit yjor a TR 370,955
Ainas neble poles NER 161 significant points of. 7157 seine 371
ene NON of BUS RITA 162 system of coordinates on_____________ 387
AL TCCIONS ms. ee MENOS iptic di j
properties of H tr Ee ` 68 SK of Air Almanac A "vijās, 479, Se

INDEX

Page

star identification by-----lucadiae ias 586
Ecliptic pole, defined. --------------- 387, 923
Ecliptic system of coordinates, defined... 923
SLATS amatā Ārā, 387
Eddy, chart symbol for. - 23022 110
Eddy current, defined__________________ 718
Eddy viscosity of sea water... 697
Egypt, early astronomy In... 35

Ekman, V. W. ; ocean current investigations

OL a eo a e AA 692
Electric current, defined___________2 ez 289
Electrical conductivity of sea water______ 698
Electricity, first communication by... 58

AAA PA o S 57

(See also Electronics)

Electrode, defined... ... foem e 923
Electromagnetic energy, defined. |... 923

reflection of, Marconi on... 58
Electromagnetic Jop eee 128
Electromagnetic radiation- ------------- 290

(See also Radio waves)

Electromagnetic spectrum____________ 290-291

Electromagnetic theory of light, historical. 58
Electromagnetic waves (see Radio waves)

SCO RRS aS o oce s 7 289
CUR CONAN EEE ROME IL o c eio 58
A A m qnia 293

Electron gun- _ 2. Slimi] sals 302

Electronic computors, inspeetion tables
computed Dyer. saree. mE N 59

Electronic control in surveying__________ 858
Electronic navigation, of aircraft_______ 59, 674
charts: forsee EE get 96
(See also Chart(s) )
donned austere? Eege 923
Ihistosy OEM AT een BETA QI 57
Onslandeerest ec OO PISOS tee 669
IN polar regions- ær 633-635
publications: toro IA BEL oM 96
hs OS DA Hom O sump pa 1003
COPIA me wb M adi es > eal € 62, 304
(See also Radar, Radio, Radio waves)
Electronic navigational aids (See Radio
Navigational Aids)
Electronic position indicator------------ 330

develobment'of Mones 1 1 C 59

Electronics, defined------------------ 304, 923
direction and distance by----------- 313-331
first application to navigation......... 58
STO o e co com 57-59
OEA Ee 304-312

in celestial navigation-------=2====== 304
intdcadreckonipr = oe ees ee 304
in'pilotinp A e & 279, 304
in"Dolamregionseeceece EE 633-635
padioNexuanpes e cR S C 304

use of for weather observations___----- 59
(See also Electricity, Electronic naviga-

gation, Radio propagation, Radio
waves)
Elektra e ict cael 307, 317
Element, of cone, defned 1027
of cylinder, defined " ` cocoa Ba 1026
Elements of Navigation, of Robertson. --- - 34
Elevated pole, defined. - ------------- 382, 923
Elevations- on'charis--——-—-5772--.--77* 114
lizabethtlst esiet ere 50
Ellipse, description and properties of_---- 1027
Ellipsoid defined esas: F e 923
of revolution, earth assem ase == 22 = 357
Ellsworth, Lincoln; polar tables of------- 638

Page

Ellsworth Tables, for polar navigation... ` 638
EIN ño described ties. 0100007 eg 701
Elongation, greatest, defined____________ 927
of planet,,explained..2.......2. -Paniki 376

Endless tangent screw, defined__________ 923
Endless tangent screw sextant__________ 401
Engine revolution counter, defined_______ 923
Engineers, Corps of (U. S.); maintenance

of aids to navigation by_------------- 261
Engineers level T 18:014 MOLI ege I 841

Bihberingibont- ce c ECT eee SEM
Ephemeris defined -s= 4-242252- JONS
of Regiomontanus___________________ 51
(See also American Ephemeris and Nau-
tical Almanac, The; American Nautical
Almanac, The)
Ephemeris and Nautical Almanac, The
(see American Ephemeris and Nautical
Almanac, The)

Ephemeris time, defned ------------- 375, 496
Epicenter of seismic sea waves__________
Epicycles, plan Of 32 ecc a va SA” eee 36
Epistola de Magnete, of Peregrinus de
NI bebe Et 23
Epitome of Navigation, of Norie-__------ 34
Epoch, defined. < eee pa 12 ah 924
Equal altitudes, circle of, defined________ 916
defined ee e cee ee Eee AM 924
(See also Altitude)
Equal areas, Kepler's law of 38
Equal triangles, defined. --------------- 1023
Equation defined- co... eee DAS 1017
differential, defined--..-- 221202 "5f 1044
Equation of time, defined. - ---------- 375, 924
Dy nautical almanacs eco. AD 478
USE Ol e een AO 495
Equator, celestial, defined- ----------- 382, 915
defined "rece SVS 64, 924
fictitious, of transverse and oblique
Mercator projections_-------------- 74
Galactic se e female entr 387
geomagnetic, defined______________-_-_- 927
magnetic, defined eerste 164, 935
earthsifield ate- ee AA 161
(See also Celestial equator)
Equatorial Azimuth-Table, An; of Goodwin. 571
Equatorial chart, defined --_-_---------- 924

Equatorial countercurrent, in Atlantic

CORD AA ES, E A 719
i Indian Ocean. eegen 724
MPAT LEE «10815725
Equatorial current, in oceanic circulation. 719,
723, 724
Tidal var E dv le Ee 714
Equatorial cylindrical orthomorphic pro-
jection (see Projection(s))
Equatorial horizontal parallax, defined.- 435
oftimoon mess ee Tou amet iine hem 362
Equatorial projection (see Projection(s))
Equatoriabtide:--——. —— — Peu 06, 924
Equiangular polygon, defined. ---------- 1023
Equiangular triangle, defined. - - -------- 1022
Equilateral polygon, defined. ----------- 1023
Equilateral triangle, defined. ..........- 1022
EquinoetialsdeBned ee eere Sour 924
(See also Celestial equator)
Equinoctial tides, defined--------------- 924
Equinochialiy ear c Ee e e RR 370
Equinox autumnal 222 em e 913
Aina Ee 924
explained EES ZS 371
Marcha sec, PESOS 94 3 mt tr OI H 373, 935
September ti Jn roo LEGAME 37

1478 AD

Page
vernalezsa sa deepen alni 301 iMm 371, 952
Equinoxes, precession of, defined. ------- 940
discovery. of -beedeL. tes q 37, 48
explained-..-.--.-.-- ses 373
rate ofc. Zi sātstetsms see. 955
(See also Nutation)
Equisignal, of consolei se. eee T 316
Eratosthenes, armillary sphere of-------- 48
determination of earth's sizeby-------- 18
Winds-of.. err. E itka ties cd one
Error(s), acceleration, altitude correction
Mo o es x 428
of sextant... 2. caos. e. Po bo MER 417
ballistic damping, defined. ----------- 913
ballistic deflection, defined............ 913
of. barometer: eve eT nere 768-769
centering, defined. NES EEE 916
Of sežtantsāssāā - ¡sta E Bae. Seem 411
chronometer, defin ed +t +420 am 418, 916
determination of- --------------- 490-491
collimation, of sextant_-___---.------- 414
tčombinations ofiss es pe «tes ae 682—685
compasssdefined----— S ei gð 918
(See also Compass error)
CODSUSDU eR EE 680, 918
course, defined. ar Jr sesso os. des 919
damping, of gyro COMPAsS------===--- 148
computation of for polar regions. _ 151
GE DEE 678
fifty percent == = c cae aes 681
Gaussin, defined" te ql oer 193, 926
gimballing, defined. - aenean sre 927
OE yIO/COMPASS ES BS 150
graduationsdehned- —— es 927
offsextant-5...-..Beg WAS SUMI s 411
gyro; dened: =- rer- 5882005 he 146, 929
būt POMPTON Saas ose Se 625
heeling cause of eg tenes 3 186
(See also Heeling . . .)
indexado de eme bep 413-414, 931
installation, defined. sr eee Tem 931
instrument Ee 931
(See also Instrument(s))
intercardinal rolling, defined- --------- 931
Ot gyro Conipass ie. ee eee 150
loran; sources of- mas RR 4- 338-339
mistakeehoos domi ās ēnu | 679, 687
navigational (see Navigational errors)
normallcurye off. IO. e 681
periodica S occi e MN 682
of perpendicularity, defined___________ 924
personal o EM 408, 422, 939
polarization, of radio waves... 295, 314, 940
prismatic, defined E 941
Oigsēxtani "e E a 411
probable, in dead reckoning--------- 685-687
defined=- figa EVE Sa) tā 681
guadrantal,'defined__--------.--/---- 941
of gyroicompasst =" ELM 150
ofsradiolbearinpgs e OM 313
random /defincd/ c NEN 943
discussed... D Aten Bātas vut 680-682
EE aleja Salen 682
TOO IM e ans quar e M RM 681
scale, on polar stereographic projection . 88
of sextant, acceleration -no r eE - c 98 417
centering r- Caleta Tana EN 411
collimation = E - feme sane A 414
graduationsec--— "row NA 411
horizon. glass: ca. e ae 412-413
index 30 Sn s 413-414
indeximimot Tae ne oe 412-413
instrumentalis oe ME 412
prismatoxwe--- < M 411

Page
Error(s)—Continued i
shāadēs- sies sed ciere 411 _
of sextant—Continued k
E EE 413 `
telescope.-.---..:.. BA Sodas Tuam EEN
(See also Sextant, Sextant altitude
correction(s))
sextant error, defined------------+----- 946 `
shade, definedenediJteBales al 2 946 |
of sextantiissusiige-tunpsassa- MY 411
side, defined Æ cometer 946
of sextant..--...... =o eee 413
speed, computation of for polar regions_ 151
defined... -nobesienauros dex B 338 948
olieyrojconipasss = EM 146—148
standard deviation... (sn rð se 681
station, defineds 52 — —— hartsk ah 948
swirl, defined. «ef ceno sija 949
Systematic... He Poma M - 679—680, 949
telescope, of sextant-.-...2----52259z 414
temperature, of barometer..-........- 769 .
defined... <> 2. - LLL EE eai 949
terms'defined-.-.-.-.-- Conan: Adu 678-682
tilt, defined seit ida scada alee 950
of sextant. oH. Ø 0211283241 ziedo mis 422
Ü:shapedz- ere EE 682
watches EE PEE 419, 952
determination of... — 48 492—494
(See also Correction (s))
Escape, velocity of, from earth------_--- 358
from: moons ēd ENIM 363
Eskimo Place Names and Aids to Conversa-
ton (H.O. Misc 10579) 2 == ae EE 101
Establishment, defined___-------___.-__ 924
of the, portž eege -ad iea n 268, 709
VATI CY HMM etd i a e 709, 952
(See also Lunitidal interval, Tide)
Estimated position, defined____________ 62, 924
in piloting 723 2 arar E NER 258

(See also Navigational errors, Position(s))
Estimated time of arrival, in air naviga-

Lë el EE SSS 676
Eudoxus of (Cnidusi-@- cao 36
Eulerian motion, defined- -------------- 370
Euphotic zone, defined__-_-__--_--------- 701
Eurus, ancient wind name______________ 28
Evening star, defined" Sm 377
Excelsior Azimuth and Position Finding

Table of Blackburne 1 uae 525
Excess' of are, defined YC Saka 924
Egercises, of Blundeville S Coma 34
Ex-meridian altitude, discussed_________ 518

history off. Ose er AN 43
Ex-meridian observation, defined________ 924
ExosphereX 2500 A a EE 360
Expansion, thermal, of sea water________ 698
Experimental Air Navigation Tables, devel-

opment'of SS = eee 545

Heard's modification of- -2721 I5 545
Explement defined 112 UDS s 924, 1021
Explementary angles, defined___________ 1021
Exploration of the Sea, International

ouncil for; Copenhagen_____________ 692
Exploratory survey, procedure for... 862-863
Exponent. emos tab m 1005, 1010
Exterior angle of triangle, defined... 1023
Extracting a root, defined -e C TRR 1012
Extragalactic nebula... a a 366
Extrapolation, defined______________ 924, 1045

principlesiot e nN 1050
Extratropical cyclone “1 x 9 806
Extremely high frequency, defined_______ 924
Eye, of the storm, defined_______________ 924

described. 22 soldar ising oke aim 824

INDEX

Page

adoos tale ta 824
EA O MI A E 204
-layer of ionosphere. .._.............. 293
F-Tafel, of German Navy______________ 536
Face, of polyhedron, defined____________ 1025
of pyramid, defined o- -<ne 1026
Factoring of algebraic expressions_ ._____ 1018
A sioe AR R 924
Bading, of loran signals-C. 20222. _ 2. 337
Oradiojwaves 25 esca sah in 0 295

Fahrenheit temperature, defined_______ 775, 924
iain tide defined Lecce aa hiss aree 924
Raimwind «defined: esconde Pesto ox 924
SITO RU es. su Metin peers) ol 17, 44
iballclandicurrent ues serbe. tiem ALLS Līva 723
PUR cr Si PV 807

Falling tide, defined: el 924
False cross, southern, movement of pole
Ee EE ee 373
posoniofes- a= E EE 580, 582
False horizon, defined... .............. 924
EA e od ecu. POR f 7 675
MarkvanešdefinedS RL mor Dime SOS C 924
Faraday, Michael; electromagnetic induc-

ONE A S du cec eg NIT: T 58
Blas ticam ne jee T II ta S 74
Fata morgana, defined... ... 950 809, 924
Fathom, conversion factors_____________ 958

CEM c-r E 924

Origin ofs- 5. rM TO A3 gotas (1 26, 27
Fathom curve (line), defined. |... | 924
Mathometer, defined SAU u Tol Pf (NL MIÐ I 924
Fathoms, feet, meters; table 21_________ 1277

explanation.of- COEM STE 88. In 1192
Favé, L.; sight reduction diagram of___-. 557

sight reduction method of. 563
Favorable current, defined______________ 924
Pavorable wind, defined OM N NM 924
Federal Aviation Agency, publications

OLA A sa st. 94, 671, 1004
Federal Communications Commission... 1003
Reedemcurrents.. 2299990 IMITA vr 740
Heel the. bottom, defined? ee. 924

Feet, fathoms, meters; table 21__________ 1277

explanation ole === "SUPE TOTIS 1 1192
Ferrel, William; psychrometric formula
CAP E EE A 1190, 1191
Fessenden, R. A.; discovery of directional
MATA C 42 4. „A 58
Hetch of-wave, defined e =. 727
Fictitious coordinates, on transverse
Mercator.projection3* "s 88
Fictitious craft, defined ea A 925
«Bletitlonsperaticules SE 74
Fictitious latitude (longitude), defined---- 925
Fictitious meridian (parallel)------------ 76
Buetitiousspole TE Rn Lee d s 74
Fictitious rhumb line, defined- --------- 76, 925
COMED OTIC TICS FE s E n 618
Fidelity of radio receiver. ..... ......... 301
Held OLiCela E eget er Tod err ne 749
magnetic (see Magnetic field, Mag-
netism)
ireldtehart?defined*-————— doe ge 888
Biftvepercenterror-* eee e 681
Filling of low pressure area____________- 802
iltervofesextants Æe san ate di telde 400
Final great-circle course, defined. ------- 925
hinesdelay defined 9 de 2 925
Finite number, defined šās ss e rere 1005
IBireba ll em se). een [ard 365

Cle fine dee ee EE e e
First point of Aries-----====- 373, 471-472, 925
First auarter of moons. EE 378
uso rechoesitron E 134
SOUNC ro ee ore eee eee 742
Bishistakes denned mee ate ee a 925

1479

Page

Rismngachartsee ce <<. -9.. TÐ 101
Hixi0elestiāliefssas eet el 547-550
computation of without plotting.___- 547
defined octies oo. a. A 915
AA een cde OTE 550-554
plotting of, discussed____________ 455-458
defined Maen ted eec tnt AI 925
by horizontal:angless o aura 245
Corrections DEE 446
laDelingiofiia te Ae ae a 216

by nonsimultaneous observations____ 246-249

running, allowance for current______ 252-254
by bearings on single object______ 254-255
by bow and beam bearings--------- 255
by celestial observations__________ 458-460
defined A ál Æ ka oy ud 944
discussed ðn morc 248
by doubling angle on bow_________- 255
effect of current.uponzs 5 2 D 249-254
error Olas See oe ei D eee 248-254
methods of obtaining____-________ 248-255
by seven-eighths rule: ------------- 255
by Seven-tentbhsrule 255
by seven-thirds rule_______________ 255

typesior discussed RE E 243-245

(See also Navigational errors, Position(s),
Sight reduction)

Fixed and flashing light, defined__________ 925
Fixed and group flashing light, defined_.__ 925
Bixedilishtsdetined me NEP 925
Flagpole (staff, tower), chart definition of.. 115
Flamsteed, John; first Astronomer Royal. 50

staninumbers ofc c Oc eee eres 576
Mashing defined ee ee, 925

described". Ls L ip M 207
Flashing light, defned ee daa 925
Fleet Weather Central, Navy----------- 815

Fleming, John A.; development of vacu-
UM tube by tot CARS Se TM 58

Flight Information Publications---------- 671
blightzplanning A MIS 676
Flinders Matthew cS 24, 179
Enders bar defined E 925
description of RA ee 179
determination of length, “drop-in”
method rk prie EE 188
effect of permanent magnets upon_-_---- 188
length of, determination of__------- 180-183
Origin (Olestas A PATCR e e e 24, 179
removal during magnetic treatment ... 207
routine checksror ae ee eee 195
LEStIN EIA de HR SE AS 180
(See also Compass adjustment, Devia-
tion)
Floatachart:symbol {ores ee 113
Float chamber, defined M AV 925
Float gage for tide measurement... .... 844
Floating ballistic of gyro compass. ------ 150
Floešidefinēd HBO Ms Ace sei ein. m bkn MET 925
formation ors d T ae 749
Filoeberg defined meee 925
Flood, of current, defined--------------- 712
lesser, defined... lr euh i cór ir ie 933
maximum demmed aae 935
strengtheot dened =a." P se 712
Flood current, denned A 925
time computation off HL e es 274
Florida EEN ENEE EE us 721
Flux Gate (see Gyro Flux Gate compass)
Flyback of cathode ray tube------------ 303
Roam line of rip current -qI S9 S 740
HēcālWēngthYdetinedēāseseseecs P 2528 925
Focal point defined S eec 925
Oise lipse RI EE 1027
ofzhyvberbolase e meti sea ees 1028
Opara bold cce ce SEE eei 1028

1480 INDEX
Page e
Hocus; defined. -.=- hoc pos. ES 925 ` Front, cold, defined" BS 91
Of ellipses e282 e ee 1027 defined a a S
of hyperbola sean teena lo ote ES 1028 occluded- EE 802, 938
of psrapola sr eS = on cr ER 1028 warm, defined. "` V yg en SEE E 801, 952
Rocusinp'anodeces--sc ee 302 Frontal surface, defined.---.-----2--- 801, 926
Foehn 7t. A See 806 Frost, defined=-- = SS :
Ege ady cuon mccesecc c p as 807 Frost smoke s- S mem COE. 614, 808
Californias =<: cnl cer rp 808 defined. ee caco 926
defined tas: we De A EE 719, 925 effect of on sextant observations.......
CO A n KE ee 808 Frustum of cone, defined --——---— E 228 1027
navigation E cels sesa art (ei 004 Fucus; defined. ieies Iesms
tadigtion fog- in- ecu 807 -Eull moon; explained: C ES
steam) fog, definedat ssec 948 Function, defined — EE 1041
types OR 807 (See also Trigonometry) i
Fog signal, chart symbol for, described... 113 Functional Glossary of Ice Terminology, A
Mlusiratedes-s c n 994 (EKO SEub No 009) EE 762
defined ss ceo e ee 925 Fuss, V. E.; sight reduction tables of... 57, 537
description of, in light list.-___------- 97
maintenance EE EE EES 3 SE
SE EE SCH Ey EE HEC IU eas s ete S
a da Costa, A. etlecher dlactieedģustor_ E SM A
a QR King era gle 539 Galactic latitude and longitude, measure-
Foot, British, conversion factors_________ 958 ment E ——À M! Hem d
length unit, origin of... iecēss 26 Galacticmebulas. es A

United States, conversion factors......
(See also Units of measurement)

Horamuniterd sce tine cess aes eee 109
Horce, unto Rb v Eo eR m a 765
Forecasting the weather______________ 815-817
Hormeline sone EE 114
denedi sm TE Syne ae MEA 925
Bormstceomputaion ð e eee 1052-1058
Foucault Leon ee, 24, 141
Roucanlipendalun mEnE 141
Inu erg HE, denned S maa 925
EE 317, 675
(See also Radio range)
Four-point bearing, defined a n mn 926
Fox, Charles; sight reduction method of 548
Fractions, rules for handling--------2-2- 1019
Fram, oceanographic expeditions of______ 692
Eramerobsextant# e cS css as 399
Freight ton, conversion factors__________ 962
Frequency, audio, defined____________ 291, 912
bcapwe EEN 309
COMPARISON AO MD ECC 345
denned s EVE e E e ee 926
extremely is Tee 924
nigh defined = secre E 930
low denned ssn E EE 934
maximum usable, of radio waves______ 294
medad 936
radiogdenneds o. eae ee 942
of radio waves, channels of___________ 299
effect of on transmission... _==___ 298—299
maxmmumiusaple ee olo. 294
regula tio nous s RS 299
a TREE 290
Supershieh define dia. =a. NE 949
Den uginn, basket 951
id a O rT 290
Very niche defined to SANAE 952
very loy, defined on ne NM 952
and wave length, interconversion of____ 200
Frequency bands. M eee 291, 322
CIIanae ETIS UC KO IM 298—299
Frequency channels, radio n mnnnE 299
Frequency modulation, defined... 926

Frequency spectrum 2.2 M NN 290
Erigid zones 5 ss eon A ee 373
Frisius, R. Gemma; De Principiis Astron-

(71101610 E E cR 32

Galactic system of coordinates_____-----
Galathea, oceanographic expeditions of...
Galaxy (galaxies), defined
features Of 5409 +, < q A NN
galactic system of coordinates_--_------
Galilei, Galileo; contributions of_____----
determination of longitude by_--------
improvement to telescope by----------
pendulum as time keeper--_--->-------
on TOLAtIOM OSUNA cce ðið"
on theories of Copernieus_------------
Gallon, conversion factors... cll
Galvanometer, reflecting, of Weber
Gamma, magnetic unit, defined_________
Garcia, “short” method of
Gas buoy- defined sais ao ay een 4
(See also Lighted buoy) 1

Gauss, Karl; reflecting galvanometer of. . 58 8
Gauss, magnetic unit, defined_________ 203, 926
Gaussin error, NER 193,926 á
Gee, defined AAA A HER 926 .

development of S MEI 59 3

principio mesti ee 343-344 `
Gégenschein nta. A TO 365
GEK (see Geomagnetic electrokineto-

graph)
General chart, defined_______________ 104, 926
General precession of equinoxes_________ 373
Geocentric latitude, defined___________ 382, 926
Geocentrie parallax, defined__________ 435, 926

of moon3. c Nene A 362
Geodesic, defined 63
Geodesic line dēfinec NN RENE 926
Geodesy, defined... ee 926
Geodetic. control, defined NEC 854
Geodetic control survey, defined_________ 848

procedures fone eee EMS NNNM 0-857

926

of lights 35 si 263
Geographical mile, defined... 65, 926
Geographical position <a Je uses 449, 926

of celestial body, in navigational tri-

angle a S 2 S SS 393

INDEX

Page

Geographical positions, maritime. ... 1060-1100
Índex of a o a cid e Ja Ce? 1101-1128
Brood, defined swe Luci ell al Dui 386, 926
CONT UCI E ES a 358, 427
Geoidal horizon, defined______________ 386, 926
ANO TS EE KEE 699

determination by coros ad 60, 128
denned «4S sekstes Seegen Din, t 926
onBsubmarme coe See ee 608

Geomagnetic equator, defined... 927
Geomagnetic latitude (longitude)... 162
Geomagnetic noon (midnight) 162
Geomagnetic pole, defined. |... 162, 927

unit of measurement in... .... DI _ 161
Ceomagneticntime: sete e viet: C 162
Geomagnetism, defined e-n au 927
Geometric projection, defined__________ 69, 927
Geometrical dip, defined______________. 927
Geometrical horizon, defined__________ 387, 927
Promeury, defined. -- -aah 1020

Drmcemnlesope oe Kea 1020-1031
Geophysical Institute, University of

Bergen gNOLWA V No as eae ens ini nh 692

Georef (World Geographie Referencing
ESENE HA a I M adu 91

Meostrophichwind sees J CW ja 797
German Hydrographic Institute, Ham-
(Dūjas e op a cl M TAO O 692
German Navy, azimuth diagram of 572
sight reduction tables of TL TT 536

(Germanús Nicolaus! - es 1590 26

Getting qmderways saki dc 596
(Ghostsdefineds,eetdeējiā sāns E 927
entlornabDacopec- c.c. Beim nen 335
Ia dar a o M) TORIO 323
VESKO VIN dl ci def MT 343
Gibbouskaetned OMESTI Ve TEE < 927
«ubbousiphaseiofimoonsq = Mb E 378
Gimballing error, defined_______________ 927
oovro compasses eut 10 EE vn 150
eumbalssdetünedescew- c STA NT S 927
Gingrich, John E.; sight reduction tables
UA AN. peg o BR PE TUA 57, 535
ien Blayio ot Amalfi s Ben eom Æ 23
Glacier .detined e- as Jee | Puig 2 927
ROTM ATION: OL se see See Ee 747
Glacier, USS; largest iceberg reported. |... 748
Gloðiserina defined... EE 109
(LORA 2 2 A AO 811
Glossaryee DRAR ITO YMO M 909-953
Gnomonic projection (see Projection (s))
Godfrey, Hugh; azimuth diagram of_____ 572
Godfrey, Thomas; development of sextant ;
ut e eda ues M HAMO TOC T 4
Goetz, Roy F.; sight reduction tables of. . 542
Goldberg, E. D.; solutes in sea water. ... 694
Goldsborough, L. M.; of Depot of Charts
andi mstruments e ES 31
Gonsbuoyndetincd SR 264
E EI OO 2 306, 927
Goodwin, H B.; azimuth table of... 571
sightireducuon tables tol. E ex 017" 526
Grade KUITOLEA TC a EE 1031
Gradient-«defined es ve I 927
Gradient tints, defined SSS RO ROT 927
(eradieniswindsvkseš=:s< Ab 797
Graduation error, defined 999 e e c 927
Olas CX LAN LAA ARS o E 411
Graham, George; development of chron-
ometer FM. M pU NR A AE 46
diurnal change in variation----------- 24
Grain fconversionstactors FAA 958

1481

Page

Gram, conversion factors_______________ 958
Graphsdelined asete renses dinee aa M 927

103, 893

of Wave Refraction
Diagrams (H.O. Pub. No. 605)

Graphical solutions: eege age A gaer
use of stereographic projection Tor. 83

Graphique d’ Azimut, of Cornet_ 2
Grass denned- 22s mera se. coco 927

om loran- scope Ae < M dm 338
Graticule, defined e dkūssas: am, A 70, 927

Gravitation, universal law of. 38, 355

Gravity error of mercurial barometer____ 768

(Gra VILY/WAVeBĀs ee MU AD 727

Gravure, reproduction process, described.. 897

Gray, Stephen; conductors and non-
Conductors sc ee ME NOR russ 57

Grazing angle of radio waves___________ 291

Great circle(s), on azimuthal projections. . 81
on azimuthal equidistant projection____ 84
defined Esate ENA TIAS, Pele PIE 63, 927, 1029
discussed. VM ae 228-229
on gnomonie projection= S 82, 100
on Lambert conformal projection______ 80
eeh 65
on Mercator projection---------- 71, 228-231
on modified Lambert conformal projec-

PON wer Rotam a SAVA 88
on oblique Mercator projection-------- 77
Plottingrolea= sr: sa IE TEE 100
Oa HOW? [HO E DEE 87
EH secondary a 1029
on stereographic projection----------- 83
transferingpspoints Oi =e Ss el 100
on transverse Mercator projection... 87
EE 229
(See also Chart(s))

Great-circle bearing, defined____________ 927

Great-circle chart, defined-------------- 927
(See also Chart(s), Projection(s))

Great-circle course, defined "Tð an 927
finabsdefimedssow st eet E 925
ben, mëtteg deer a A a 931

Great-circle distance, defined__________ 66, 927

Great-circle sailing, altering track_______ 235
Dy; CHAT trek fee Soe re cM pees Pa E 230
byscomputavion 225 E Soe 232-234
byiconversionancie ae eee 231
detmnedz..-----.- este 349 Lenta 221, 927
discussed £2552 PRS lini y pili. 229
example ses cor TO. eee 232-234
finalCOUnSe === D v c 231
geographical position, destination as... 232

ITS CO Vg EE E 30
ANUS COUTSE dem EE

Onepolarrchian tem Po T
Dwttabletes Le ol ES 234-235

WOrk form (Ores < « EO 1053
Great-circle tables, of Towson and Ather-

[or e EN lietā 569
Great-cirele track, defined-------------- 927

discussed. o EE 66, 229
Greater ebb (flood), defined-----2-=22====
Greatest elongation, defined___________-
Greece, early astronomy in------------- 35

Greekval hab ete Rum le 3 nr 908
(Green flash ðs E, WT 811
Green moons e m PROMO ZB 810

1122

Greenland current, east (west) ----------

1482 E

Page
i time, defined = = 928 Gyro sextant, defined -12an mm

Si E SCH a Ele A S 495 Gyroscope, axes of___------------------

Greenwich civil time, defined. ---------- 928 directional (see Directional gyro com-

Greenwich hour angle "= see eee 383, 497 pass) "
Change ofvalmanactO= seo S 52 origin of e e aa
defined — 9 = do o epee tee 928 principles: of... 2255 = 1 925523225 141-1449
(See also Hour angle) (See also Compass, gyro)

Greenwich mean time, defined. ....... 482,928 Gyroscopic precession_----- LIII „Daļā
finding..-...-.2+--=---2-=:---J=++22: 1487 Gyrotron vibratory gyro, principles of
(See also Chronometer, Mean time,

Time)

Greenwich meridian, defned 928

Greenwich Royal Observatory, history of. 50
asprime meridiano pte 48, “Hachures! on charts- 25 ICM

Greenwich sidereal time, defined___--- 497, 928 defined}: 922200 Uus uev RO
(See also Sidereal time, Time) Hack watch, defined? e

Greenwich nme- o- S tee AS 375 Hadley, John; development of sextant by.

Gregoriantcalend ar alegre ee ae 370 Hagger, A. J.; sight reduction method of...

Grid SMadctincd =. Lo Pl d 928 Hagner, Fred; “Position Finder" of...
perspective, construction of... 879-880 ' Hakimite tables cse OPEN

use or Mea erst e I A 881 Half pulse repetition rate delay, defined. .

polar, description and use of-------- 618—620 ofilóran 7 2 Ina ee vore SEN

typos of discussed A 91 Half-üdelevel--..— ES 710, 929 `

Universal Transverse Mercator- <76 191 Halley Edmond ON 24

(See also Coordinate (s)) development of sextant by____________
Gridvamplitude) defined 928 . proper motion, discovery of__________-
Grndrazimuthedelined memen ee 928 Halley'sicomet 2 300010 RONS 364 `
Gridtbearing, defined =e ae 241,028 - Halo, types of 21 =e. c 810-811
Gxidacoursewdehned s "E 928 Hamilton, W.; sight reduction tables of. _ 3
Grid declination, defined. ------------- 9152928. Hand! lead defined e AN
Grid'direction defined e eee 618-620 description of A 5 ==

plotting iol =. e Se as 622 history of esi (OSes EN

Gridiheadingsdefincd ep 928 (See also Lead)

Grid latitude (longitude), defined-------- 928 Hand level, types of.

Grid mavigation, defined TT 928 Handsen, Ralph; middle-latitude sailing__
gras cdt OE A eee 91 Hannibal, Pelorus as pilot for___________
referencesdimecuonforee 2.222 22 134 Harbor chart, defined en: Ur

(Gridimorthyad efinre tiem eee E 928 description ob eee

Grid variation seq E 100, 162, 618, 928 Harbor radar, use of_._____ sie 2

Grivation (see Grid variation) Harbors, sources of information on...

Ground, of radio transmitter____________ 301. Hard iron, defined PS

Groundhog s a ssr EE 127 Harmonic analysis of tide observations...

Ground speed in air navigation, defined __ 672 Harmonic constants of tide predictions...

(Garoundiswelladefinede es 928 Harmonic tide plane. MiP m
CHE COLONES lil) e d 731 Harrison, John; development of chronom-

(See also Swell, Wave(s)) Sept bye ee UN 46
Ground tackle, defined_________________ 928 Harvest moon, defined_________________ 379
Ground wave, defined_--_----------.- 294,928 Hassler, Ferdinand; director of USC&GS. 30

of loran, characteristics of. |... 33/2338. Haul denned Soo E I 929

(See also Radio waves) Haversine (s) denned c ME 929, 1032
Grounding Scauses ot =e mnn 280 table $4022 025 Ee 1421-1456

defined «2. 22-220 Opel OI EE 928 explanation ols: RR 1197
Group flashing light, defined___________- 928 Hawkesbee, positive and negative elec-

Group occulting light, defined___________ 928 tricity, discovery of ce AE I 57

Group velocity of waves_...__._________ 729 Haze defined. OD a ELM 929

O A Es 748, 929 described... ret Lts aoe ME 809

Guericke, Otto von; invention of “electric Head of feeder current... S 740
machine kbye a de e 57 Heading, in air navigation, defined_______ 671

Güincascunren sss II cH 722 compass, defined... 5) EEE 918

Gültsotrcan ad as a ENEE 721 defined. cS €. cds PA 929
enection Uponimeiraction= EE 432 discussed su...) eeneg Gal EL AM 66

e 23 grid, defined -aana waste de
E E A enc 34 magnetic, defined 2214. erg

Quit ote toque 807 placing vessel on Sm 195-197

Guyot, defined. _ DIT 699 per gyro (standard, steering) compass,
üserofsinspilotns 22 ee 258 definéd:< LA AA 939

Gyrolcompass dende 929 true, defined z- 227 sd NER NM 951
(See also Compass) Heading angle defined sen amen alee 929

Gyro compass repeaters. 22-32-12) _-_-. 153 Heading line, defined OUR 671, 929

Gyro error, defined E eee 146, 929 Heading-upward plan position indicator,
ini polarregions ee ae 625 defined waa d c S 929

Gyro Flux Gate compass--------------.- 672 Headway defined. EE 929

Gyro pHotsdehned- = eae 929 Heard, John F.; sight reduction tables of. 545

Gyro repeater, defined: SES UM 929 Neat, units of ee M MM 776

described aa. cc ae AO. NE 153 Hestligktning S N eee 813

INDEX 1483
Page Page

Heaviside, Oliver; theory of ionosphere.. 58 History of navigation—Continued

Hebrews, early astronomy Of ya Ft Tona ia 36 during twentieth e Ada eS 17

Heel, defined E R 929 earth, determination of size of________ 18

Heeling adjustor, defined. 929 eleotronicda DEE EEN 57-59
desorbed MES Ee teh A 188 hydrographic offices. --— 2 30

Heeling error, cause of... 186 inspection tables, development of hie 57
computation of, on various courses _ ____ 192 latitude, finding ol. slew = Aia 43, 518
correctionion ag: 24. 253.3200) besa 187 line of Bano. discovery of. 54
defined 2.2.27 ... dae M nido soucis 929 logs ett, Ad RD a 24
o A AAA A IA 186 longitude, by lunar distance__________ 4, 44

Heeling magnet, defined. ........ _ 929 (See also Lunar distance)

POSIMODI GOL Las sa eec o ee 187-188 by time sights. ep RE 54, 523

Height, determination of, from vertical (See also Time sight)

photograph EC E ee 878 navigational triangles ms 53
on nautical chart 2 2-2 0 E 110 piloting and dead reckoning__________ 18-34

Height error of barometer______________ 768 pilots profession... els 7 a 28

Height of eye correction, defined_________ 929 Primemeridjan Varna 48
eer MEA, oA coser 422-426 sailing directions test ss uot del oo 16
(See also Dip, Sextant altitude correc- (See also Sailing direction (s))

tion(s)) sailings tie e e A 9

Height'of tide, defined-- -7------- | 929 Seta Et ee A 39-43

Heliocentric parallax, defined__________ 365, 930 soundings e EE eres 27
discussed HARAN e Newer S 352 Burnessipnalsst SAS PONAT EIE 47
OUStarsias. eke ee are odo d 485 units of measurement_______________- 26

Heliocentric theory, origin of------------ 36 MATI bonita ee So AS 23-24

Helland-Hansen, ocean current investiga- wind rose, of Eratosthenes___________- 18
ONS Of cA EE Ld Lase ela eon 692 batün-s o CEN 23

Hen e TS mde e MAE ma 7 50 Portolan fre soc Dd sec (R e 20

Henrys “bho Navigators aa test < 49 (See also Wind rose)

Herschel, William; discovery of Uranus by. 39 (See also Sight reduction)

Hertz, Heinrich; reflection of electromag- Hitchcock, R. B.; of Depot of Charts and
neto Waves o Ee 58 Instruments + £ < EE eee 31

AA: Nate qee a aii a 36 B George G.; sight reduction tables

Hevelan halo t 2 e lem 7 SLO Sage Ol ARAS E E ke RA 541, 542

Hexagon defined A V C 1023 Hóhonaida nach Sternzeit, sight reduction

Hickerson, Thomas F.; sight reduction table EA ee 541
tahes eren st < M Ps Eat, se Se) Homer four windsioi Man 23

Hidaleo features of NEE 36217 Hominedelined X = `. Ee 930

High altitude method of sight reduction. 513-514 on radio Dearing <c sap em RE 314
defined yl S SR e e om ce 930 Hommey, Louis; sight reduction tables of. 524

iHügh:frequencyv, defined". - de 930 Hopadefüned Sk Md 930

High Latitude Celestial Ne ea Table Horary tables defined Sepe === a= - 623
KE OSEUD NO #230) SSS c 542 Horizon, apparent, correction of ampli-

High tide (water), defined_____________ 704, 930 tude tor table:28 prete eee MES 1297
TNFR OUTED A c E E 267 explanations ieee ae eee 1194
(See also Tide) defined gare ee jās 911

kHighiwatejādācunss e pear) yee 710 artificial, altitude corrections for------- 437

High water full and change (HWF&C)____ 268, defined Bs ee eee Ae AE 911

709, 930 description and use of___--------- 415-416

High water inequality, defined___________ 930 celestial defined A ae 386, 915

High water lunitidal interval______ 268, 709, 930 defined 5-5 E55: BA itis 3 930

Higher high water, defined______________ 930 SE eg EE 922

Higher low water, defined______________-_ 930 altitude corrections for..........- 422-426

Hilsenrath, Joseph; azimuth device of_--- 572 (See also Dip, Sextant altitude cor-

Hiltner, W. F.; sight reduction method of. 565 rection(s))

Hipparchus, chart projections of... 19 distance to, table 8------ Ju uan 1254
Andearlwalmanacs e e ee eee 51 explanation, ofa esee sce BEEN 1187
precession of equinoxes, discovery of____ 37, 48 jalsewdefinedee seo ares es ute 924

Hiram of Tyre, pilots supplied by- ------- 28 zeordaladefined qc ce E 386, 926

ISA oh eke Aie Mes toy dre ER 330, 930 geometrical, defined Wee eee 387, 927

ElistorvofnavligatHon ð sm c c Í 15-61 Kinds fe ee o se see IM 386
aids tonayigation SEE EEE 28 as primary great circlen 22222200282 384
AiMAanacs We e a o e EE EE 51 zadar defined. e šās e 30 942
DRETTEN 34-39, 575-576 discussed O 1 320
Ce Ale EE 568 radio defined ses Msariegšes V 942
celestial ca MEME eA ipio eoe Ee 34—57 discussed IFTE ergeet Ee 292
CHATS AI EC 18-22 Ravionalwidetine da a 943
Chronometer sākās) ee a ee 45-47 discussed itt. a sese he eye 386
Compasses - MIS cm E onem 1 23 sensiblo denned VMR PV 945
determination of latitude_____________ 43 bus alles AM gi lā < Lr. 386
determination of longitude_-___________ 44 system of coordinates__-_---------- 384-387
AN A BVI ES 24 Pocero MT 952
during pre Obristiamera tl em 11 15 discussed c PA i arn eg che d SCH
during sixteenth, century 2573.7. 27. 16 Horizon glass, of sextant__------------ ERE
during eighteenth century------------ 17 SIE =

1484 INDEX
es Int tional (
i see
defined". ARA oo eae sean see 930 Hydrographic Bureau, Internationa
orcas stan of coordinates, defined... 48 A å haki V Bureau)
ibed see a EH 384-38 ydrographic control, O
Hohen tul angle, measurement of, by Hydrographie Division, Maritime Safety
sextante San OE TIT 245 Agency, p EE
corrections for Vr HÁTT H [ur Manual ( Uh VT:
Horizontal danger angle__------------ EE
Horizontal datum, defned .- 892 Hydrographic omo Zeg x (see U. $.
Hor on ma Ee 161 EE (U S j publication]

Det toe ABE woe IS. S
Horizontal method of double interpolation 1049 Daily Memorandum, issuance of------- 94
Horizontal parallax, defined. ----------- 290 distribution um A 1002-1004

discussed: eg eler H.O. Pub. No(s).: LN, Catalog of Nauti-

Of moon. ss sus u we RO 362 cal Charts and Publications... 96
Heec e PAI 25 1-V, Catalog of Aeronautical Charts S

ss ji et Ee acl artes bate PT E and Publicationsz. TT eg
Hour angle, defined. .......- lo ER dod 9, American Practical Navigator (Bow-

finding by almanac, for following year-- 653 ditch) (see American Practical Navigator)
fenis cu Rd 470 27, Sailing Directions, Antarctica... 753
e SER A AC IB MC QE :. 470 66, Arctic Azimuth Tables (Schroeder
OL plane aiva ska a 471-472 and Wainwright)------- cede Jae bbe
Si E RE 469 103, f nternational Code of Signals (vis-
: a an ER a T TE uah Ss A a ee
fini wp Roten DAS Soma 104, International Code of Signals (ra-
Aries. - ------------------------- ees dio) ise ac ee eet ico ÓN 96
Sor en d RU: 110, Danger Areas in the Pacific... ... 101
(See also Greenwich hour angle) 111-116, List of Lights. ---.------- 97, 261
local o Mi MES i TA 383 117, Radio Navigational Aids-------- 96
defined o E 933 118, Radio Weather Aids Sara 97
finding Set. TES Jae Nr ee 497 119, Weather Station Indez......... 97
measurement of eM 383 150, World, Port Indes. -= Lm 101
sidereal ABI EE 383 151, Table of Distances Between Ports- 97
defined Saat See ere ae eee 946 201, Simultaneous Altitudes and Azi-
discussed ire MOE. EE AS 383 muths of Celestial Bodies---------- 530

AaNALTIMG a een I ee 497 203, 204; The Sumner Line of Position

(See also Meridian angle, Time) Gëf of Celestial Bodies (Littlehales)__ 526, 547
Hour circle, deftned , 208, Navigation Tables for Mariners
House, chart definition of. _-------- --- 114 and Aviators (Dreisonstok)____-- , 534
Hues, Robert; determination of latitude 209, Position Tables for Aerial and

Dy EE ccs = 56 Surface Navigation (Pierce)------- 538
e Tables for Sea and Air Navigation, Eo 211, Dead Reckoning Altitude and

of Comrie- ------------------------- Azimuth Tables (Ageton)-------- 98, 538
Hugon, P.; azimuth diagram of--------- 572 214, Tables of Computed Altitude and

sight reduction tables of------------- 57, 531 Azimuth a A RTN 57, 98, 540
Hulsmeyer, Christian; development of extracts from... . Tm 1170-1176
Hun ars Mis os EA a ON pos (See also Tables of Cra Al-

MIN ALO nere e a == EEE titude and Azimuth
Humidity- ------------------------- 778, 930 SOEN 671

absolute, defined... EE 778, 909 217, Maneuvering Board Manual____ 99

effect of upon refraction- - -----------2 431 218, Astronomical Navigation Tables. 98, 540

measurement of oca 778-779 220, Navigation Dictionary... 101, 903, 909

relative, defined. .................- 778, 944 221, Loran Tobes Hmm 96, 338, 340-341

table 16---------------------- 1266-1267 extracts from NEE KCI 1177-1179
v op AV ie EP E ar kājā 225, World Atlas of Sea Šurface Tem-
ere Sa mate ates eS peratures SEE DER 695
Hummocked ice __------.------------- 750 226, Handbook of Magnetic Compass
Hunt, defined Spee Gg as aia ro 135 Adjustment and Compensation ____- 99
Hunting, SC SE socks ES 350 he Alan Celestial Navigation
A a SE adea S O ES ables (Goetz) RN 542
Hurricane RE a ea Se ae ese P c 819, 820 234, Breakers and Surf; Principles in
Hurricane and storm warnings, informa- Forecasting RPM 738
Mot gp sources OË n 96 249, Sight Reduction. Tabl ue
radio broadcasts of. E - 100 Navigation. ze EE
(See also Navigational warnings, Radio extracts from =>. > au 1180-1182
broadcasts) ` ` (See also Sight Reduction Tables for
Hutchings, C. H.; sight reduction table of. 542

Huygens, Christian; development of
chronometerd 2 8 cc 0 op 45

HWF«C (high water full and change)... 709
Hyatt, Delwyn; “Celestial Coordinator"

and “Coordinate Transformer" of _____ 560
Hydraulic currents... ccoo soe 712

Air Navigation)

261, Azimuths of Celestial Bodies... 98, 571
1168-1169

attitude ERE T ee ee CC A

INDEX 1485

Ë Page Page
Hydrographic Office (U. S.) publication(s)— Ice—Continued
Continued o E A A etu MI 747
H.O. Pub. No(s).— Continued Cakedcesed sore 1! 749
601, Wind, Sea, and Swell: Theory of dead reckoning jn... 627-629
Relations for Forecasting._________ 96 Deck daos Mesta aeren 814
605, Graphical Construction of Wave density of 284s ic SEA to Ju ect, Eé
Refraction Diagrams_________..--. 738 detection of, Aot oom seat 758—760
606-a, Navigational Observations____- 101 direction and distance In... 627-629
606-b, Sonic Soundings....... 96 drift:of - asan DOT 301 wë: 753
606-c, Bathythermograph Observations . 96 effect of, upon navigation... 746
606-d, Ice Observations___________-_ 96, 762 UPON Waves. 20 case O MI 731
606-e, Sea and Swell Observations... 96,732 extent of in sea.. 753
609, A Functional Glossary of Ice Ter- fást doe... eee os UE Be Minas
MInology = eth i er. anise 762 Mocha dct EDO MORIA. QU 749
705, Oceanographic Atlas of the Polar forecasting: of 22. =. EE 762
Deas id a gege io styac 3 1002 formation or aka -mhon Lo. golatan: 746
2102-D, Star Finder and Identifier__ 85, frosh waten from... ARO 752
1 x 586-590 influence on navigation_______________ 746
SP 44, Visual Wave Observations... 732 information on, publication of... 758
SP 58, Tables of Sound Speed in Sea on land, formation of---- - .....- 25. 747
Witeri Cia da Lhdbt < tas! 744 land ice, ¡defined:44 US: ¿UA eee 932
NEE EE EE 671 leadēķinisassss--3 vere tet ba Ads 750
Notice to Mariners (see Notice to Mari- mpped by, defined 22255 Saree mah aaa 761
ners inBNorth'Atlantjc Se enm 753-755
(See also alphabetized titles, Chart(s), observing ofiss 7 MA Jame 762
Publication(s), U. S. Navy Hydro- operatiohsin:c dat CEET 760-762
graphic Office) Dancake:ices 95.2%) e nae 749
Hydrographic offices, history of... 30 pressure ico ¿bad ah «alo al ent 750, 940
Hydrographic survey, aids to navigation. 861 pressure ,ridge..._ =). bash ale atte 750
controlinsce Æ eee au ted 857 Fotten lees: 02 00 0 Dags d 752
current observations 01 M Joo 844, 860 sea ice; bending, rafting, tenting of---- 750
defined st <= MER. eie ae han ta 848, 930 defined: 4... 2) aten meii samt 945
distance measurement, instruments for. 842 formationtof -trari er ioe skumpar eua 748
drafting instruments for... 844 fresh water fron : "`` rie E 752
electronic controls sae ees oet 858 kinds of - "ewe solus 748-750
geographic namessteut eno eT. met 861 salinity o9 c A cope RM 752
hydrographieifeatures--— ` a 859 Thicknessiot- CCS FC ee EI 750
instruments: fors 232. em mH 837-848 shelf ‘ices! pothe vs or aia ane hs 748
magnetic measurements_-------------- 861 speed measurement in________________ 629
miscellaneous information, acquisition SPICULES Of se "rm TE pes HAFTEN IU 748
of c oc D eid Pu x 861 weathered ice" <? e m 750
plottingisheetsfor---—-— ÆV ekur. 859 young, defined” RP ee 953
procedure torn ues xc ertet oue 848-867 (See also Polar navigation)
records fort Mau enbical olas Teto 862 Icetanchori. AE EE 761
tide and current observations. -_----- 844, 860 defined t Eent BEE quomm 930
dora gc tor AE aa 845. Icetbarriert2020.- BU dat IES 750
timing equipment for- .--..---.-...-- 839 defined: Stee eere eer MS At 931
EE ET act nta _ 850. O AAA 9915. lanatus 759
Visualtcontrole messes puse? wu 857 Ice bulletin, broadcast of ` TR 758
wdreidragtuseiofie=._Jreubā MOE 860. Tcesbuoy defined TR 5 tbe E 931
Hydrography, defined______-_-------- 8484930) Tee eg Kee EE SE 749
Ey drolants E ee 10039307 Teefcape?.-. E nie 612, 747
Hydrometeor, defined-------..---.--.-- 930) Icefchartidēfinedsētess < A 981
kludropacs tem S e ds 100,930 Tog field eene M) 749
Elydrophonedefined2222 2222-32. 3 930 defined 225% $96 55. Hd Jena. 931
Iesse A O hoahuuges eokdat gūt 808
Hygrometer, defined Wo2- < 930. EE 748
described [3292 TE 13. ip RA 778 Teerhummo c kte 3S8 A 750
Hygrothermograph a E 779 Ice island i 748
os a a a. ogi
"as measure of distance difference______ 310 Ice Observations (H.O. Pub. No. 606-d) - - 96, 762
Hyperbolic line of position, defined. -~ - --- 930 “Ice observation service”, definition of. - tās
Hyperbolic system(s), described. ------ 333-348 Ice pack------------------------------
Drinciplesvol tego PT eean 309-312 approximate center pa BEER 750
Hypotenuse, defined-----------...----- 1022 Ice Patrol, International; establishment
Hypsometric tints, defined. ............. 930 OLA A E E 31
nvNomod did ssesbssas ee ee 757
“Ice patrol service”, definition of_------- 758
I. C. S. Altitude and Azimuth Tables for Ice pole, definition and location--------- 750
Air and Sea Navigation, of Collins. - - - - 536 Ice reports and predictions, broadcasts
iceman chor LOLs. SS A E 761, 930 RC cad de shen kn Sete 100
al Te UE S Še < ae t 747 Ice Seamanship, Manual of (Pub. No.
beset, by, danger of ff m3 ==. 631, 761 551)------------------------------- 96

1486 INDEX
x helter, defined
¿2 aga 613 Instrument shelter, defined-_-----------
crdi Sis o os a jā 931 Insular shelf- O TA NA 601, 699
e defined SANI ER 931 Insular’slope!ct Hr
AES R 747-748 Insulator, defned O o L iun DN
defined A lux (ierasts UE tM 931 Integral, defined._---_------ 45i rcr
Identification of navigational stars_____ 965-972 Integration, process of, explained____--.-
(See also Star identification) OM p RR points? 35e ee ER
iti i A ons aes efined. .. 422 ermal ee mercem
COND KO d OLE a= 26, 130 Intercardinal rolling error, defined.......
Inch, conversion factors_--------------- 958 of 'gyrorcompass NESEN
Incidence, angle Ol aki ER 398, mt Mog un Sets EM anl
inati tic; defined efined_____ sidered as qot aed
SE defined ERIS 1043 (See also Altitude difference)
Independent variable, defined__________-_ 1041 Interference, radio LM S
Index arm of sextant = s o enS 400 controlorii Eea FR ERR
Index catalog of nautical charts and A taterior BRE ot triangle, defined________
ications. 5295057 Set Ausis 9 nternal waves: d- E inn. C
tes eur AUT c. HM agreste ars 931 International Code of SE Vol. I (H.O.
Index correction, defined ae SO RU 931 Pub. No. 103) (visual 222 35 Ses
of Sextant. 5*9 E ee en ei 414, 421,657 International Code of Signals, Vol. II (H.O.
Index error, defined. 22.5. BeuPabc ant 931 Tub. No. 104) (radio =. —
of sextant, adjustment for... 413-414 International Correspondence Schools,
Index mirror, defined_________________- 931 sight reduction tables (Collins)........
Oh sectantes EE Ate 400 International Hydrographic Bureau, es-
adjustment ol RN 412-413 tablishment ofsO0 Tann NE
Indian, American; migration of. |... 15 Systems of Maritime Buoyage and Beacon-
Indian Ocean, currents in 7 9 E age Adopted by Various Countries ES
Indian spring low water, defined______-. 709 (Special Pub No39) ae E Miss
Indian tide plane, defined______________ 709 j "d
Indirect wave, defined_________________ 931 International Ice Patrol.___________....
Induced current Huot- sane A 289 establishment of______ scale Eë 31
Induced magnetism, defined__________ 158, 931 International nautical mile, defined____-. nea
j M i origins:* a Aa Šprē sea onn
acu cere Le cea peta International spheroid, dimensions of__ 357, 957
Inertial navigation, of aircraft_________ 60, 673 (See also Spheroid(s)) —— ^. j
denne n am 931 International Telecommunication Union,
described ses =: so da 220 Bureau 0f 27 D Ee 96, 1003
direction and speed measurement by.. 308 Interpolation, defined_______________ 931, 1045
GUTE Lee 567 double, methods for HEN 1048-1049
of submarine. BP. Oh.” le 2 pā 608 methods foras2-« eS Haero h Gene 1045-1050
systems hip (SINS) oso ee eee 608 single, methods fori. fos 1045-1048
Inferior conjunction, defined____________ 375 triple, method for =m n 1049
Inferior mirage. ff SM 809 Interpolation tables_______ Los Hð 1050
Inferior planets----- 55-399 9 0 357 Interrupted quick flashing light, defined_ 931
Infinite number, defäned 1005 Intersection method of visual survey con-
Infinitesimal number, defined... .. 1005 trol -ods aso S t ME 858
Information Manual, Airman’s_________- 671 Intracoastal Waterway, charts of debi t 104
International Flight-_..._____________ 671 Inverse cylindrical. orthomorphic projec-
Infrared, defined. 2 hiva 931 tion (see Projection(s), inverse Mercator)
Initial great-circle course, defined________ 93] Inverse function, defined_______________ 1037
Innertplanets eee s e 357 Inverse Mercator projection, defined___ 70, 931
Inscribed angle, defined________________ 1025 (See also Projection(s))

Inshore current, defined Saa 718
Inspection tables, computed by electronic
COMPUCOTS MEM RT 59
Story TOLIMA eg 57
Installation error, defined... gg 931
Institute of Oceanology, Vladivostok_____ 692
Instrucion Nauthica, of Diego Garcia de
Palacios E OUS 3. Eo AO 34
Instrument (s), for celestial navigation__ 398-420
defined yt APA apses he du c 121
directional se eet ine 134-156
funetion'of easel Ta Aa TERN 134
(See also Compass)
for hydrographic surveying... 837-847
for piloting and dead reckoning. 121-157

for weather observations- ___—_ 765—790
Instrument correction, of sextant._____ 412, 421
Instrument error, of barometer. 768

Inversion. vs tð. 509208 OI 807, 931
lon, defined: 25... mēs ez T OL REM 293
lonopausez..U.- 0059. 0 E ONE 360
Tonosphere; defined ES 931
discovery-of Eeer 58
Kennelly theory of mmm 58
layers et A eee 293
during magnetic storms- --_----_-____ 294
nature Off EE MEN 293
position of e EM 360
radio waves in? JV UM 293-295
in polar regions": 5 EEE J 633

21090 e 633

Irminger cuca PERENNE 722
Irradiation, altitude correction for... 433
defined. IENA ETA ewe A 932
Isobar, defined TT T! "OP ee. Saree 932
onisynopticichartos EEGEN 765
Isoclinal, dēfined < S AS 932

932

O— Ov

INDEX

Page
Isoclinal line, defined________________.. 164
Isodynamic line, defined. |... 1. 164
eege defined... EU. 932
Isogonic chart, defined_______________._ 932
Isogonic line, defined. _______________ 116, 162
Lon Ee 932
COR ESI QT SEE INE PRISE a 618
Hsogtiv chart, defined. . . ..... 932
Isomagnetic, defined _ ` ne 932
Isomagnetic chart, defined... 1. 932
sodali ba gare ee eset it iig 162
publication and features of... 100
or reti nc] Ee A 932
on isomagnetic charts______..________ 164
BOOT COATES a sa Gert. Lea os 164, 932
Isopyenic line, denned se e S E 719
Isosceles triangle, defined_______________ 1022
Isorbermadefinod sv i" XE <. C 932
Istituto Idrografico della Marina (Italy),
sight reduction tables of... 537
Italian Navy Hydrographie Institute,
sight reduction tables of... 587
Jamming ofradio AES S ES 297
Japan Stream (Kuroshio)__.____________ 723
Japanese Hydrographic Office, Altitude
and Azimuth Almanac of... 541
sight reduction tables of________ 530, 539, 541
Japanese Navy, sight reduction method
Oty = 556Seas et 565
Jeremiah On Winds- < es 2 23
Jernes, Leiv; “Nauticator” of----------- 557
ENS Ca ee eg 794
Jetties (breakwaters), on charts_________ 114
Johnson, A. C.; azimuth tables of... 570
On Finding the Latitude and Longitude in
Condy Weather ot Ti oe A 56
Jones llano EE 34
JEAN GENE e AA ES 484
Junction buoy, defined ` ee 932
Ee E e SSS" taa m 373
Jupiters features Of SES cs 361
satellites of, determination of longitude
DA C m Sone Emi 44
Kepand denned se == ` sata e 932
Kahn, Louis; sight reduction method of_- 564
Katabaticnwind "easy Cee a set eir 806
Kelienphur Datum- EE 892
Kelp chart symbol for es < ce 110
Kelvin, Lord (William Thomson); com-
pass improvements of_______-_----- 23, 24
deflectorof*-- 2 fen IL No d 202
inspection tables c ee 57
sight reduction tables of_------------- 524
sounding machine of- er eer SE 28, 132
temperature scale EE 716
Kelvin temperature, as absolute temper-
ADE rd E E 2 WEE 776
definede sa ee EEN 932
Kelvin’s rule for improving compass
adjustment re ua 14189
Kennelly, Arthur E.; theory of iono-
Sphere ed a al. l 58
Kepler, Johannes; laws of 22. 122422 52 354
effect of upon seasons-------------- 372
Origins. Wie yee E tæ ER b 38
d udolphine: Tables E a 51
Uraniburgum Obaservatorx. 50
iKüloeyele- defined kde oe = 290, 932
Kilogram, conversion factors_-_----------- 958
Kilomegaeycle, defined- 122222 290
Kilometer, conversion factors----------- 958
Gefine dees e M See ee d 932
Kirwan Richard e ge bs 3

1487
Page
Kleist, E. G. von; discovery of Leyden
| ie A Bee O TS 57
Knot, defineds aio. aida. MT Toys 66, 932
SDeedauniUxorigintohe e ae ee 25
(See also Speed, Units of measurement)
Knudsen, Martin; sea-water studies of... 692
Koppernigk (see Copernicus, Nicolaus)
Kortazzi, I. J.; modification of Kelvin’s
tables. Pee a CR 525, 569
Kotlaric, Stjepo M.; sight reduction
inethods ORTA tenent MES quen 589, 550
Kremer, Gerhard (see Mercator, Gerard-
us
Kuroshio (Japan Stream) e 723
S-band denned <Ar SE E 932
lxcolAMdetnedtes om Ei REO 206
Labels for lines and positions---_-------- 216
Isabradoricurrenüsece c NM 722
Labrosse, F.; azimuth tables of. 569
Lagrange, Joseph Louis; celestial mechan-
10 BANET S p cnn PME 38
spherical triangle formula of... 558
Lalande, Jerome; sight reduction tables of. 524
Damanon Laude 24

Lambert, Johann Heinrich--------------
chart projections of E e A 22, 80
(See also Projection(s))

Lambert conformal chart, bearings on.... 631
in polar regions Toom ee RN 621
(See also Navigation, Plotting, Polar

regions, Projection(s))

Lambert conformal projection (see Projec-
tion(s))

Lambert conformal projection, modified
(Ney’s) (see Projection(s))

Lamplough, F. E.; sight reduction method
Of = GM SE FA MI E 562

Land, effect of upon tides_--------------- 268
Sipnsiof APS wen A SE 660

Land areas, chart symbols for----------- 114

Iand?breeze Soe ese EE < sd S 806

Land effect, defined 2433282 932

on TAdiO waves- E ae Še 293, 313

Land ice, defined... ea ans em 932
Land mile idebined:- S Mo Ee eee 65, 932
Dandinayigation A 664-669
byacelestialibodies S nr 669
charts Lor Sivas. oe OA AOS ad 664
byadeadtreckoning AAA 664
defined <r eee see ae 62, 664, 932
directional instruments------------- 665—668
distance measurements--------------- 668
in ruggediterrain AAE VE AA 665
byelectronicimethodsi mmr 669
odomētērins ratos aa e BS V 668
pedometer in Ase. E Sene ENS 668
by piloting eee Su Dee 669
position instruments for e eee 665
Sex tant Oreos EE EE 669
sun compass for k- ro seen 667
(See also Navigation)
Landis A ee O ete 759
Tandil A A 601
denied A o 932
Landmark(s), chart symbols for_------ 983-998
denned. oe es s 932
ONEDAUCICACHAT US EE e a E 114
IN polan RAMON A E M E 630
GE SCH
UE
defined A e or een kads 932
Lane routes, in North Atlantic_--------- 755

1488 INDEX
Page Page
Langevin, Pierre; development of echo Lead (for sounding)—Continued

Bounder a sa EE? , 58 hand, backgroúnd'of- -5901p UCT 278

La Pérouse, Jean Frangois; explorations defined: ces itin TEMA 929
ee Sia AES I Ee, 691 sounding, defined -=-= 1 APE
Laplace, Pierre; celestial mechanies___--- 38 (See also Sounding machine)

Mécanique Célestexote as 2s m 5,39 Lead (in ieejai ei 750
Laplace azimuth, defined------------22- 853 Lead line, defined. .....-..-..-------- 933
Laplace correction, defined... --..------- 853 marking Of... 22. O PME 131
apse Tate, denned sass secet 932 Leader cable, defined Sora. Aa e 933

of temperature S Pa 794 Leading light(s), defined---2----2--222 933

effect of upon terrestrial refraction--- 9425 Ecap years 12 === SES 370
Large scales defined- TA eae se 932 conversion factors e 955
Last quarter of moon, explained......... 378 Leaving porti: 9. SE 596
Lateral system of buoyage------------ 265, 976 Lecky, S. T. S.; azimuth tables of------- 570
Eatitude assumed =e. d SS ES 452 “Wrinkles” in Practical Navigation of__ 34

in. sight reduction: ore eeo n NE 502- Lee, defined- ¿IA Conn AE 933

astronomical, defined- sous -mM 381,012 "Lēeways E vc c ae eee 219, 933

and deflection of the vertical_______-_ 427 allowance forse 0000. DO eee 219

celestiabsdefinede r-re- NE 887,915 ` Leg, defined ^ ea ee ID ON 933

from celestial observations-2---------7 547 of triangle: defined FORCE AA 1022

ciclo iden 387, 916 Legend, defined 2 NSS m 933

defined Ses ass te tae ae cee 64, 932 Leick, A.; sight reduction method of_---- 563

determination of, by ex-meridian alti- Length, units of, conversion factors_-_---- 958

tude Tue: nm oem A 43 Lephyrus, ancient wind name----------- 23
historydofe-oec oo EEN 43,518 Leroy, Pierre; chronometer of----------- 47
from lifeboat, by body in zenith_____ 659 Lesage, electrical communication by----- 58

bylengthiotiday < e eee 659 'LëSortb; computer of A AA 560

by meridian altitude-----------7- 658 Lesser ebb (flood), defined______________ 933

by Polarigues Tinas de dt ar 658 Letterpress, reproduction process, deseribed.- 897

by variation of the compass------ 609 Devel; Abney type ee 842
at lower transita Sek 43 engiheens C5 desa SD 841
by meridian altitude_________ 517-521, 658 kand, Locke type smo 842
byābolaris setā m ere ee 9215523008 "Ibevierrier) Urbaine- -n aR 39

difference.of, defibéd.- —. .. me 922 Connaissance des Temps of 52

explained: >: Usos eee ee Le 64 prediction of Neptune by_____________ 39

effect of, on deviation. 2 ecc rn 173 Leyden jar, discovery and development of- 57, 58

onirefraction a a sae das 432 Libra, zodiacal constellation. ___________ 374

fictitious detnede EA se eee 925 Libration of moon Tann 362

galaetig- de ode o a 387 Lifeboat navigation- A PK 645—663

geocentric, deined +) X. c 382, 926 abandoning ship. -<20 EE 647-649

geodetie, defined. SS -= es 381, 926 altitude measurement 222222 654-657

geographic, defined. E 381, 926 approaching land 660

GE 162 beaching theron EE 662

Sid Gd ekine layer sae A 928 byseelestial bodies m S TINE 653-660

length of one degree, table 6______ 1246-1247 byedeadireckoning === EN 649—653

explanation of os. BB 1187 defined... A cec c DEBERE 62

lengths of one minute of.__----------- 65 determination of distance off. 661

libration in, of moon e. ee 362 direction by celestial bodies_________ 649-651

masnevic defined. =. ue. Sanwa ee 162, 935 distance measurement in_____________ 651 8

muddle mid) defined e EE 64, 936 emergency kit for. 2o. A 645 3

(See also Middle (mid) latitude, Sail- equipment for < ye ITEE 645-647 1

ing(s)) estimate.of situation Ai TOL TENE 647 .

observed, detined - . wusste 453, 938 finding aivilizations =- ONE 662

parallel of, defined a 64, 387, 939 importance of ship's position... 647

expansion of on Mercator projection. Ol keeping togethers. ase) SOMMER 649

RM eod the lolas Deer ct ES latitude determination. __________-___ 658

Se O a E longitu i i
Latitude and Longitude in Cloudy Weather, aitas MAR PITS GE

On Finding the; of Johnson... 56 preparations for see ERR 645
Latitude factor, denned a rE 932 selecting route sarao o. o riel oe 648

pr GAS S oct e ME 1286-1292 sextant altitude corrections___________ 657

Bex DIAMS WOU oec c RE 1194 sight reduction______._.- 658
Latitude line, defined. Seege e 453, 932 signs of land 000 o. Il ONE 660
Latitude, Longitude and Azimuth by the speed determination — 651

Sun or Stars; of Hiekerson---.-------- 530 Aime determination EEN
keen denned Ss ere DR E T trayersertable for- -< M CN 652

A ES a S r ight(s), aeronautical, chart symbol for_- 113

Lava, defined-.......... EE TM 108 as aid to navigation_____- $ 293 CEET
Lead (for sounding), arming of. 132 SE EEN 909-910

deepisea== non DN el EE Eecher ee 27 bobbing a described 4.) Seaman 264, 914

deme dak Seki r Ss AM 921 on buoys 2222552 EEN OM 266

deseribedzes ir naan S Oe os 131 chartisymDbolskrór ann 112

defined? EE beds ME 932 characteristics of, on charts___________ 111

desorbedossas2: ass ae ae 131-132 defined suc. e de cue eee ee 916

lee take Ke 923 discussed t EE 261

INDEX 1489

Page

Light(s)—Continued
chart symbols for, described__________ 111

MINIS E ted Berne eer ee ed RA E 991-992
denned EE S LT 933
dis persiontoism E ee Vējā 482
disposition of, defined-222222 20200 922
electromagnetic theory of, historical... 58
Ai AA E 925
fixed and flashing, defined____________ 925
fixed and group flashing, defined... 925
flashing, defined anh Ry ada wens 925
peoseraphic range obo aee 263
group lashing defined Se RON - 928
group occulting, defined... tul 928
interrupted quick flashing, defined... 931
leading EES 933
luminous EE Ee 263
navigational, in light lists.__________- 97
GEO, cue 938
pernod denned Ne 3» eso co at 261
pilotinphbys SSS, UE ghe. jun 264
power of, as aid in identification_______ 264
quick flashing, defined ---_--------- 941
AO CN a 261-264
Eeer mm A 943
sector of, definition and chart symbol

10T A k. GOL 113
EE delinear qure <bec 945
short-long flashing light, defined_______ 946
speed of, conversion factors__________- 961
HENO (iu oc tere a LM 261—264

compütationfof Seer ire b 263-264
Er Mee clas er A 365
(See also Lighthouse(s), Lightship(s))

Light characteristics, defined------------ 916

Inehihsue defined sta. MES An 933
publication and contents of______- 97, 99, 261

dughitectorMs iy wes Set P UC sc qe JE 933
bharusvmnbolforst PARA 113, 261

Light table (box), for chart construction. - 888

lljphtsvesseledefinedeece cce. ecce c. corre 933
(See also Lightship(s))

«ipbied buoy, defined Dosar. oes E 265
(See also Buoy(s))

Lighthouse(s), chart symbols for_------- 111
denned t: cb. ern MPO au 259, 933
description of, in light list__---------- 97
IS COnVROL CM C Herr ccc e 28
OU discussed EE 259
(See also Aid(s) to navigation)

MA A o 812

Lightship(s), chart symbols for. - ------- 112
defined ewe IAE ME santos 259, 933
noliePors MM AMAS i BUT 261
OT UE 7 discussedi- ce 2-22 See 261

lA a SLES 352
Conversion factors Por UEM EK S 955

Empr (E ee oS 933
OF sertan t SMS stas ts DE 400

Ihmekbasēdēfined$ mms 2.00. 913
daneen defined eee EE 920
datemdetined Zēstes SL EEST 8 920

ongin and Use:of BIL o P 9v 397 N 486
denned EAA SE IDA, 1 1020
of force, defined Soa quel se, 3024 159, 935

CHectholeship ponte 203
Peodesicwd chin ed Meese Hes 926

(See also Geodesic, Geodesy)
geodetic defined ees see. SEN 926

(See also Geodetic . . ., Geodesy)
hea dings, defined Ee 929
¿social defined = secar RA 164
isodyna mic ¡defined co ee 164
ISOSOMIC denned en ae Ee 162

Oase, denned Sen 719

Page
Line—Continued
lštitudo dan an að 932
lead (see Lead line)
longitude, defined SSos CE Ian 934
lubbers, defineds TR 934
OT nodes E SA OE Fee 381
of position (see Line of position)
nnumbdefinediis = ===. fatten ES 944
sounding defined sa PE RET 947
speeds defined eege MS ee ee 948
sumnerWdeünede c ce r e 949
(See also Line of position)
Line of position, accuracy after adjust-

MENT OM Ra e d cm Pii 247
adjusted rla Delne oie 248
advanced defined- V k nE 909
advancing (retiring) cmane mee S 246-249
celestial, advancing and retiring of_____ 455

Shiite Pv a ee ee s 915

determination! Of sre eee 450-453

historical m 56
byiSUmnDermeio de 547
bytes E 56

explained ME oO eee 449-465

plotting of in polar regions_________ 688

ESO um ee Pe pha io estais dus A ete 453
coca A ERE 449
course iia dec 919

(See also Course line)
denned” AR AN A 933
discovery oT Em ta r 54
ACUC c T PEE 240
hyperbolic) defined e 930
labello c we T ee ORE 241
latitudeuline denned ss] s EEE 453, 932
longitude line, defined_------------- 4583, 934
Eeer ET e es 339-343

tables for (see Loran tables)
plotting of E AA 241, 451-452, 638
retired Pacino ee e 944
by St.-Hilaire method —---------- 56, 528, 944
(See also Navigational errors, Posi-

tion (s))

Line of Position Book, of Weems-------- 534
“Tine of Position Computer”, of Poor__-- 558
Line of soundings, defined__------------ 933
Ini pilocin AAA Tac 258
(See also Sounding (s))
Linear interpolation, described. ..... 1045-1048
Lippershey, Hans; invention of telescope i
Liquid cómpass, defined ee 933
Lists of Lights, of U. S. Coast Guard... 261
Liter, conversionmactorssas=e= sae eae 962
Bitho'proof defined kN aa 888
Lithography, reproduction process, de-
seribed IA 2 eta NE E DIO M 897
Littlehales, George W.; altitude and

azimuth angle by map projection---. 560
Altitude, Azimuth, and Geographical

Position Ola ARI- ema HUS. ert SO 56
altitude, azimuth, hour angle diagram Ge

UE E AS Se oe
sight reduction method of. - --.-------- 564
sight reduction tables Of--------==-=-- 526

Local apparent noon, defined. - --------- 933
discussed AR ae eee eee 496
finding Cime ok eme PE 519-521

Local apparent time, defined------------ 933
(See also Time)

Local attraction, defined. - ----------- 116, 933
Local civil time tdeined T TmT 933
(See also Time) !
Hocalbhour angle. oda E = 383, 933

Local magnetic disturbance, defined... 161, 933

1490 | INDEX:

Page Page
Local mean time, defined_-------------- 933 Longitude— Continued $97

finding fans 2-20 5092 e 494 determination of, by compass variation. 660

time conversion tables for. 269 Dāvis on. c.c O 44

(See also Mean time, Time) by eclipses er - =e eee 38, 44
Local meridian, defined------2 12022222 933 history m Ch RE MT ter) Arye 35, 14529
Local sidereal time, defned ------------ aoe AME ron 659

finding ==> "fare ee que Se aor MN NIIS A RN
Trocal time, defined sees so EE 375,482 > by qu UMS e Rod maser qu de cs z =

(See also Time) SE Rer

(See also Lunar distance)

Local winds, types and names of__---- 806-807 by magnetic variation, historical... 44
Locke type hand level e ee 842 by meridian transit________________ 659

Lodestonta.== cados E M E ? 158 by rising and setting of celestial
Log Chip loge $T: ee 25, 127 bodies. 660
in lifeboat navigation. ------------- 651 by time sight: «est 54
COMMON co Rese e ror ee eae 25 in lifeboat- = <=. han Nee TN 660
deck log, defined. ..-................ 921 difference of, defined < Se 922
in lifeboat navigation: “Mrr 649 explained 1... st! bag: E 65
defined e sas ee ae ee 934 fictitious; defined... .. Cem aes 925
Dutchman's, history of_------------- 24, 127 galactie en 0 Ð E 2 k 387
indlifeboatmavigátion == mon 652 geodetic defined TT 381, 926
in polar navigation Een oe ee == 629 geographic, defined... 381, 926

electromagnetic m 128 geomagnetic 77.17. * EES 162

ground log RAE 127 gridjdefined* 0. aa eae 928

history of e 24 length of one degree, table 6....... 1246-1247

Impeller-type em cu e E 26, 130 explanation ef 5.35 452904 ee 1187

mechanical ar A os 25 librationtinofmoon E 362

patent log, defined. e a 939 observed; eege 453, 938

"RistOr$ Ol zt EEE ES 25 origin of; on charts? moc 116
itotstaticara A 128-130 and time z irr sadi Á a lee 486

developmentof-- cio e 26 variation of... pe dae e A 370
rough, origin of A 29 (See also Meridian(s))

EE ee 25 Longitude factor, defined_______________ 934

smooth, origin of.-.— ........ 2 3 29 table 2606/25 0. 0925 au a END 1286-1292

speed measurement bs. 127-130 explanation of S ie 1194

SE 25 Longitude Found, The; of Bond. 44

taffrail, defined... Es 949 Longitude line. defined PP Pm 453, 934

description and use of_____________- 127 Longitude Not Found, The; of Blackbor-

(See also Revolution counter) TOW. ga ura a e E 44
Log board 5 See eee as Wi ee 29 Longley, C. D. N.; sight reduction method
Log:ehip e et, 2 i, sect MEER 25 Of II 01 det ee 562
Log glass AN E Fest 25 Long-range navigation, defined__________ 934
Log line MM TT Sect ee AN 25 Longshore current, defined_____________ 718

in hydrographic survey_______________ 860 described ag 59793. 2. La rā 739
Log reelz SES E 25 Long-term Almanac_______________-_ 1160-1164.
Logship t S «ne E 25 Lookout, in lifeboat m 2 649
Logarithm(s), addition and subtraction by. 1015 Lookout station, chart definition of._____ 115

Of Briggs- uE 10000 EE E 1015 Loom. “defined: c in c 934

characteristic of, defined____________- 1012 Looming??. ARM da, A 809

commons 32 hM eser ele EK, 1012, 1015 Loop antenna, direction measurement by. 304-

modulus of ee E 959 306
defined Wer: «07 be S 1012 rotating: nc rd ares Se 306
of haversines, table 34___________ 1421-1456 Lorac, development of_________________ 59

explanation of- TV 1197 principles of ee ie 346

Kindsiof 390.0. Le Meca AN 1015 Loran, aceuracy of. .-.. eebe 338-339

Of Napier ts et eege eta a 1015 in air/navigation van 675

ED Oe Ko) NY places mm 959 charts for, publication of____.________ 96
naturale ees M C SE ER 1015 USE Ola e eee 341
of numbers, table 32 M 1357-1375 defined æ= 19. SOM 934

explanation O MN 1196 delaygoftetc toroo MN 337
of trigonometric functions, table 33. 1376-1420 development of aa aan ÓN
explanation ofra 1196 Errors sources or EN 338-339

Use EECH 1012-1015 ground waves, characteristics of_____ 337-338

Logarithmic function, defined... 1032 luneto fi positioniby sm 339-343
ong-distance navigation, defined_______ 934 tables for (see Loran tables)
Longitude tassumedi asec: m 452 low frequency AIS 335

defined Vara a 912 in polar regions... A 634

in sight reduetion vv 503 Principles OPONE AKA LM 333-335
astronomical, defined______________ 381, 912 pulse repetition (recurrence) rate(s) ____ 318,

and deflection of the vertical... __ 427 334, 941, 948

BoārdofiLongitude C a 45, 46 receiver-indicator, grass on... 338

celestial detned 1 LE 387, 915 principles of 6-20. 1 "ON 335

from celestial observations. |... 547 reading thes. 2.62 6 oat ME 336

SS WEE 387, 916 signals, blinking of. 0 di Ale 338

efine

‘INDEX

Page
Loran—Continued
signals—Continued

EE EE Sa at 337
Es il REIS ME 337
ground- and sky waves, characteristics

OP E va EA 337-338
identification and use of... 337-338
matchingiof- is Seca an need A 336
sphtting'ofzse sides. semita ten 338
sychronization of_........_..._--__ 338

sky wave, characteristics of.________ 337-338

corrections Hora eee e 339
sky-wave synchronized (see SS loran)
Souloranvdefineds Senne eae aes ee 333, 948

Moran chain anger tus 310, 333
Loran charts, use of electronic computers
TO age tat y eene, nan 59
oranda t tices! fe E eur ees 310
Boranirate defined. os... Sere 3 335, 934
Loran reading, obtaining a___________ 336, 339
Loran tables, computation of___________ 59
denedi oa ea M Bis Dena 934
Loran Tables (H.O. Pub. No. 221)______- 96
sky-wave corrections in... ----------- 338
ŪSPOfSĀSS MOSQ o w (ur inn 340-341
Poran=L to de turca sene bereet s 335
Low: frequency, defined-_---.------ 2E 934
Bowstrequencysloran Cs- cio eaa ee 335
Low tide (water), defined_____________ 704, 934
tidal datums, diacussed 7f
(See also Tide)
Low water, mean, defined______________ 709
RNS DUONG: A e eS cu 267
Low water datums- = cc 1 22 709—710
Low water inequality, defined:____.----. 934
Low water lunitidal interval, defined____ 934
Low water springs, defined- _—----------- 709
Low-altitude observations, altitude cor-
reetions (OL eee E EC 442-445
reduction methods -==----_--_----- 511-513
usešoisextantifor = E 442-445
Lowell, Percival; discovery of Pluto..... 39
Lower branch, of celestial meridian.... 382, 934

Ofpmeridianvoleart be eee ee a ee 63, 934
Tower high (low) water _ E aa 934
l'oweniimbsesesme eo ko eee ee 402, 934
Lower transit, defined "` ' 81 ð 8 P 383, 934
Lowest low water, defined__-_---------- 710
Lowest normal low water, defined___---- 710
Hoxodrome; definedes. eee 66, 934

Loxodromie curve, defined_------------- 66

I mbberzsinesdefined SS Sese e 934
of magnetic compasso se e rnm 136
Luminous range, defined. .............- 934
Ofslightsee WI "ees ot dv 263
Lunar (see Moon)
Dunapdayseeveme = ite aL. 375, 482
anditidalšēvcliestessssea. ee vem 708
anditidal da yu O mērs pt 709
Lunar distance, Bowditch's simplification £s
O tc uae Dou I ;
“clearing” of, computer for---------=- 558
deletion of almanac tables for--------- 45, 54
description of method---------=------- 53
historyaofeet e. P do DA 4,44
tabulations off ES a 52
Lunar Ephemeris for Aviators, origin of_-- 52
Lunar month, and tidal cycles.........- 708
Lunar tide, defined ee ca 934

Lunar UNG EE tt - 375, 482
Lune defined Zem Bete! iss era
Lunicurrent interval, defined. ----------
PDunindal Interyal 2 s NT
Luynes, Chevalier de; hydrographer-----

1491

Page
Lynn, Thomas; sight reduction tables of. 524, 569
Lynn Azimuth Tables 24, 569
Lynn Horary Tables 524

M=co defined 103322. MBA AS 204
e Merlin A.; sight reduction method
(0) EE O AP wn E n 555
MacMillan, Donald: B- ð 101
MeMillen, D. A.; sight reduction method
ALA A t R ieri M 565
E eg ri Me 673
Mach number, in air navigation, defined... 673
Madrepore, defined- Ee eva 21 _ 108
Magellan, Ferdinand------------------- 17, 26
Magnete, Epistola de; of Peregrinus de
Maricourtss22= tefle ur ru puts 23
Magnetic amplitude, defined. __________ 934
Magnetic anomalies. -_-----------=-- 161
Magnetic azimuth, curve of ......... 197-199
defined! VE sia th — aes eee 935
Magnetic bearing, defined- ----------- 241, 935
Magnetic chart, defined---------------- 935
Magnetic compass, defined- - ----------- 935
Magnetic compass table, defined- ------- 935
Magnetic course, defined- -------------- 935
Magnetic declination, defined--------- 161, 935
Magnetic dip, defined. ........... 162, 164, 935
Magnetic direction me ME 164
Magnetic disturbance, local----------- 161, 933
Magnetic equator, defined------------ 164, 935
earths neld-at S$ S < etu eee 161
Magnetic field, defined_---------------- 935
degaussingsfor sa ee dede eee 203
(See also Compass compensation,
Degaussing)
dirēctiontof A AA eee 159
of earth, anomalies of --------------- 161
charts, of f= 2-02 se c Sa a 162
dinrnalichangero == == === ae 161
elements (components) of____---- 161-162
geomagnetic coordinates__----------- 162
at high altitudes am a TN 162
LEES 161
at magnetic equator VV 161
atimagneticipoles Ar 161
measurement o 162
in hydrographic survey ----------- 861
in polar regions e ees. ee 616
properties ob:2=== "E02 160-162
secular change of A 161
units of measurement of___--------- 161
(See also Earth, Magnetism, Pole(s))
of electric curren tee a es sete b 28
mtensity O Unison 161, 203
lines of- -force in 159
of moving electric charge------------- 289
SE EE NEU EE PA 158, 160
Ofiradiotwavess! SSS Sedans 289—290
ofsātsnps ye SS cell e 170-172
almeria oo S pieši o pem 207
components Of 4-2-8 C tc 204
effect on compass rara == === 171
parameters 0 f 211358 e ee 173
(See also Compass adjustment)
shielding factor re Ss 182
(See also Compass adjustment, Com-
ass compensation, Degaussing,
arth, Radio waves)
Magnetic force, of moving electric charge- 289
Magnetic heading, defined-------------- 935
placing vessel on- 2222 195-197
Magnetic inclination, defined. - ----- pt 162
Magnetic information on charts, specifica-
tION SKOT eee ac Mee O 116
Magnetic latitude, defined_----------- 162, 935

1492 INDEX

Page Page
Magnetic lines of force, defined__------ 159,935 Map projection, defined. ..............- 935
Magnetic materials: == ee Ss 158 (See also Projection(s))

Magnetic meridan, defined- ------------ 935
Magneticomin ese err 203
Magnetic north, defined..........----
Magnetic observations, where made......
Magnetic permeability, defined... ....... 159

Magnetic pole, defined ` = - 2! 20 a 935
(See also Pole(s))

Magnetic saturation, defined_----------- 158

Magnetic signature of vessel.......... 204, 946

Magnetic storm, defined---------------- 935
TAGIO, propagation Inte e 294, 633

Magnetic track, defined- --------------- 935

Magnetic treatment, of vessel----------- 207

Magnetic variation, defined. .......... 161, 935
_(See also Variation)

Magnetism, blue, defined_--------------- 914
coercive force, defined___-------------- 159
E EE 159
Oman soft A A AE NA 158
of earth (see Magnetic field)
(EIERE EE 158

ofishipscc. nmm M onto e 170
induced defined Se ER Ee 158, 931
deviationiromt se eee 171

intensity Of units o 161
of iron, characteristics of----------- 158-159
linesiot ee 159

magnetic field (see Magnetic field)
Magnetic; poles: s- S 159

of moving electric charge------------- 289
permanent defined1 e 158, 939
in;natüurese4 stop Me qw M M 158
Offarship esc. E EE 170
permeability, defined________________ 159
red defined? 2 0 EEN MN 943
remanence, defined N E 159
residual Adeincd RENE 158
retentivity, defined 2222222 O 159
Saturation== S CARA! y AE 158
ojala hipo o A 170-172
EIERE EE 171
parametersio sae aa MEME 173
(See also Compass adjustment)
shielding factors 182
Oe 160
Osips EES 171
theory ol raose A Se NE 158
(See also Compass adjustment, Mag-
netic field, Radio waves)
Magnetometer, airborne .. 162
Magnitude, of celestial bodies___________ 353
defined A A TT 935
of planets, by almanac_--__-_- 479
Magnitude ratio, defined_______________ 353
formulasfór ee o eoe NIRE 955
Majohplanets.....—, «2.09, Dow mur ee 357
Maneuvering board, defined... 935

zO)ftorsradariplottunc onn 325-329
Maneuvering rules, for tropical cyclone_ 828-832

Mantissa of logarithm, defined___________ 1012

Manual for Ship’s Surface Weather Ob-
SOTVALLONS re n ee AA 788

Manual of Celestial N avigation, of Ageton. 536

anuscript Tables, of Weems___________ 536
Map(s), of ancient world... 19-21
de NCGS -assas reaa A E 69, 935
ouvlinespūblicationof 0 SES 101
topographical, of U. S., publisher of... 94
Wecalliersdefinēd CE cs ene 953

March eguinox------------- <= 20 249 15,09
Marconi, Guglielmo; radio communication
Pyirtizetaeia tt ere: ades ferum
on reflection of electromagnetic energy.
Marcq St.-Hilaire- ES S2u hee aS 56

Margetts’ Horary Tables __-------------- 555
Maricourt, Petrus Peregrinus de---_----- 23
Marine Biological Station; Naples, Italy... 692

Marine chart, defined: $2--:- 2. -- ez 69
(See also Chart(s))

Marine Laboratory, University of Miami. 692
Marine navigation, defned ----------- 2, 935
Marine sextant, altitude corrections for__ 437

defined iepel, T6 nt PE AA 935

(See also Sextant, Sextant altitude cor-

rection(s)) .
Mariner's Compass Rectified, The; of
Wakeley:. 2.2 - oia o ada 568
Mariners Mirror, The Spieghel der

Zeevaerdt) ; of Waghenger
Maritime) positions. eae

index 0f s... C vai
Mark} on lead lines... 520 EE
Marker beacon, on buoys____-_----_-____
Marl, defined. 2“ 232 2 — ._ ==) UA
Mars, features oi _-___- eee Sa ES

orbitfofe_ «5 4. ea TP
Martelli, G. F.; sight reduction tables of_-
Maskelyne, Nevil; first British Nautical
Almanac 2: 222282 O 508b nem NM 52

Mass, units of, conversion factors________ 958
Massey, Edward 3222232622. ae een 25
Mastericompas cc eer ` 153, 935

Master station AAA 310, 935

Mathematical expression, defined________ 1017
Mathematical symbols______________ 906, 1017
Mathematics 1005-1043
symbelsfort-t 855 EE 906, 1017
Matte; defined! E RUN 109
Maud, oceanographic expeditions of______ 692
Maury, Matthew Fontaine; cf Depot of
Charts and Instruments____________ 31
log-book analyses by mr 691
sailing directions of 5. 5s ee 23
soundings by ðr 27
“Steam Lanes Across the Atlantic"... 755

Maximum ebb (flood), defined__________ 935
Maximum (hermometer -------------—- 776
Maximum usable frequency, of radio

WavVes2-- m ee Co 2 RA 294
Maxwell, James Clerk; electromagnetic

theory of light A EN 58
Meades Ranch, U. S. datum. < 252-92 427
Mean high water, defined... 710
Mean high water lunitidal interval______ 709
Mean high water springs, defined________ 710
Mean higher high water, defined_______. 710
Mean low water, defined_______________ 709
Mean low water springs, defined________ 709
Mean lower low water, defined__________ 709
Mean lower low water springs, defined... 209
Mean refraction, defined_______________ 430
Mean sea level, defined______________ 710, 935
Mean sidereal time, defined... 20. 496
Mean. solar time. NN A 374, 482
Mean'sun defined S 9 8 374, 935

discussed... 2 2 Do K RN 495

INDEX

M Page

Mean time; defined seg else 482, 936
Croci wich, defined 2... ooo a be 928

ES EE ECKE 487
focaleidefined sees) Mes ET E 933

LE E POM AA 494-495
reversion of almanacs to... í 53
SOlar defined =V c = Pantiin balling 482
time conversion tables for... 269
(See also Time)

Measured mile, on charts, discussed _____ 115
Bet Oty Ss a J ma EN 936
in speed measurements. |... 02. 181
speed table for, table 182222222222. 1270

exnianatonsofsee dm 1191

Measurement, units of (see Units of
measurement)

Measurement ton, conversion factors... . 962

Mécanique Céleste, of Laplace___________ 5, 39

Meecbanicallog:tecrebatiila vui roð ie ts 25

Mechanical solutions. e eee 558-560
Median, of triangle, defined_____________ 1022
Medical advice, broadcasts of... 100

EE T 96
Medina, Pedro de; Arte de Navegar of... 92
Mediterranean mile, origin of... 26
Medium frequency, defined... ... 936

Megacycle.defined = _-- eee 290, 936
Ménéclier, Víctor; sight reduction tables

OA EN IO II e 541
Mentalaritometic sea a e S 1016
Mercator Gerardus- EE 21, 70
Mercator chart, construction of. 72-74

plotting on, in polar regions________ 621, 631

radio bearings One pees 314-315

(See also Conversion angle, Plotting,
Projection(s), Radio bearing(s))
Mercator correction, of radio bearings... 314-315
of visual bearings, in polar regions... 621, 631
(See also Conversion angle)

Mercator projection, defined... .... _ 936
inverse defined iets s et 931
HOM Ma vical chante. ==. EE 103
oblique defined ta) MEA SAA. SER ce 938
TE OR Pen a RIMI ro Ee 103
mansyverse defined === == see sean at 951
(See also Projection(s))

Mercator sailing, caution_______________ 228
¿Evo eio. c ete rece ON 936
GISCUBSe CMR Ls ae ao 5 Oe 221
EXAM plexo la. Bess ap Se 2 as A 227
Orio a Tad UL APK LL 30
OLMO AA Tee m S ot 1053

Mercurial barometer, defined___________ 936
invention and construction of_______ 765-766
(See also Barometer)

Mercury (planet), features of -_-------- 360
KEE da wie 376

Mercury ballistic of gyro compass. ...... 143

Meridian(s), on azimuthal equidistant pro-

ECHO qa "Pl. qo DUM. MO s 83
on azimuthal projections. ------------ 8l

GE EE 86
branchesiofadefined RE ET 382
celestial defined E cec 382, 916
on cConiciprojecthions === eee NEE 78
CONVer gen cy Or STA E 618
detec ee ese o a 63, 936
expansion of on Mercator projection. . - 71
A e see ec c. BMC 74-76
geomagnetich IRE LA 162
KEELT 82
O ereenyicnēdeined 6 ` S 928
localwdefinec Mes Kādas M Pelee ste 933
lower branch of, defined__-_-__--- 63, 382, 934
magnetic, defined SE EE A 935

1493
Page
Meridian(s)—Continued

numbering of, on charts-.------_---22 116
on oblique Mercator projection... 76
on orthographic projection____..______ 83
on plotting sheets se aan en ee 88, 101

on polar azimuthal equidistant projec-

Hond Aes e bs te ear Rearing 88
on polyconic projection______________ 81
prime, defined S dra 68, 941

estaplishmentiota n. Aa EE e 48
reduovionstott ee 518

defined 9 sek EA iil 943

device for of Vilkitskiy@esessee 2022 518
on simple conie projection___________- 78
standard stis s ocho ddr dad Rr 482
on stereographic projection___________ 83
time'meridian, defined C 950
oOfftimeyzone= E AA ss eee 482, 487
on transverse Mercator projections... 76

fórpolaðregions "mT an
upper branch of, defined___-----
(See also Longitude)

Meridian altitude, defined______________ 936
determination of latitude by__________ 658
(See also Latitude)
obtaining from lifeboat...........-.-- 658
sichtreducion qme MEER 517—521
Meridian angle, for body on prime verti-
calicincio table 25S ES 1282-1285
explanation Oi ass 1193
defined starsat: Melee n? Id 936
disCussedez. Hero IRALA 383, 497
(See also Hour angle, Time)
Meridian observation, defined___________ 936
Meridian passage, defined. ------------- 936
Meridian sailing, defined____________- 221, 936
Meridian transit, defined------------- 383, 936
longitude determination by----------- 659
time ofe ucc VITA aen VJ Jw 519-521
Meridional difference, defined__________- 936
use of in chart construction___________ 72
Meridional parts, conversion of, table 4__ 1236
explana EE 1186
defined Pe Zo SAS SEA N 936
explanation EE 71
OCIO es see = ee EE Ae 21
Meridional parts, table 51 4-5 H 7 1237-1245
explanation on Sora 1186-1187
use of in chart construction__--------- 72-73
Mesopause a E PE 360
MesOsphere SEE sone ee ee eee a ae 360
Messier 51, spiralmebula sm eee 367
Meteorrieatires oinn Es 365
Meteor, oceanographic expeditions of... 692
Meteor sho wer A 365
Mfeicorijswarīns ses A T 365
Meteorite eea EEL riti 365
Meteorological tide, defined------------- 936
Meteorology, denned mees Sg 936
ipolenEpeolonswere E ere 614
units of measurement, conversion factors- 959
(See also Weather)
Meter conversion factors coo 958

¡aa nīty OA O ss eee 27
(See also Units of measurement)

Meters, feet, fathoms; table 21___-_------ Dea
explanation or ssa ee seen S 1192
IMetricescalesdiagonalae sss M = =a n= =e 844
(eng ls RRE HIER == = ae == === 890
Metric ton, conversion factors. - -------- 959
Wicrobarogiapiiamas= =a = E E 768
Micrometer drum, defined____---------- 936
Micrometer drum sextant, defined__----- 936
clescribecN A ee 399-401

(See also Sextant)

1494 ee

Page
Page e
i jection,

EE EE MA

na (denies we T TIA 308, 936 (See also Ney’s projection, Projection (s)) a

Mieroseisms- e 036 auipiitede modulation, EEN

oum A EE e 291 Fettes modulation, EE wie TN ķi

dei diez kāps so sos goes i defined 2 2200

Mid-channel_buoy ' ee ECCE 266 pulse modulation,

Middle Ages, word mapsiofse me cS 20 of radio wavesc---9 EE 200890028017 2d

Middle ground, defined... ....-...-..-- 936 Modulator__--- Akas ÓN ud

Middle (mid) latitude, corrected, dis- Molfino, azimuth diagram of........-..- 2

cussed k sms JM c 295 Monsoon, features Of = Es S == e

defined iYi a a eea aE 64, 936 Monsoon current---------------------- SEN

use of in measuring distance 215 Month, kinds of, conversion factors_-__--- a

(See also Latitude, Sailing(s)) . lunàr.2:7. 22-09 mk ee de
Middle-(mid-)latitude sailing, caution. ... 227 sidereal, of moon. ...-....----------- em

defined si 22: epe emt se q a um 221, 936 synodical of moon n=- =e === met

example of 20-231 e mre 225-227 Moon, age of, defined__-------------- er:

Ori ginko KE c es cr eee 30 altitude corrections for.........- ae
Midnight: defined e 482 (See also Sextant altitude correction (s) 3

geomagneticias tac See Stee eee ae 162 atmosphere of__---.~--------------=- pe
iMidnightüsuns. dee een S 368 nugmentation'of-- 2526222 a at
Mil (mille), Arabian; origin of------------- 26 ble See a ieee ee eee m
Mile, geographical, defined- ----------- 65, 926 cusp oin Ton o EE ate

international nautical, defined________ 65, 931 cycles of, and tides. ee ne

land defined". - M aaa e 26, 65, 932 distance of_------- ume cic ccc d

measured defined. er 936 at apogee and perigee------------- Mex

speed table for, table 18------------ 1270 eclipse pnenomenā..------3e4a <
explanation Oh == ae 1191 (See also Eclipse) M
Mediterranean, origin of... 26 escape velocity from 2
nautical, conversion factors_----------- 958 green: ide EE 2

conversion to statute mile, table 20__ 1276 harvest Ma sus et ASI 4

explanation of e c o- === 1191 bunter'S-...- 323523 P 379
defined ed "se aee EE 65, 937 SE Of ... dece EE on

Lëtz Gutt) är gies 26 mock... e. SS

Rojas MEC s e. cV WIES. 20 motions Of_---- 48 €— 362-363, 377-379

Roman, origin of- "` A 26 nodal period of, as tidal cycle--------- 708

seandetined E e ee De 945 orbit: of eege, e EUM 381

statute, conversion factors____________ 958 parallax of «— se. e EE 362-363

conversion to nautical mile, table 20. 1276 phases of... ds Mea 377-379

explanation o 1191 byalmanac Ze — A 1 479
defined ZE EE 65, 948 rising and setting of, almanac time of. 475-478
origin and length oles M 26 in polar regions -- S. Ee 640—641

(See also Units of measurement) (See also Moonrise and moonset)

Military genda =ð gcc c 91 semidiameter of, by almanac.......... 479
Milk ya Way ===. c pe T ey ee ee N 366 size Of Vs EE 363
Millibar, conversion factors_____________ 960 synodicalumonth e E 362

unit of pressure, defined________ 696, 765, 936 terminator of < cu Cn E 378
Millimeter, conversion factors... .... 958- -Moondog < S SAS SM 811
Millisecond defined sane T 936 Moon oer 811
Mine magnetic =Y m eee IT 203 “MoonbowF e ee TRENT 810
Miniature Navigation Table for Altitude Moonlight, duration of, in polar regions.. 640

and Azimuth ORE ODIO ERE 532 Moonrise and moonset, computational
Minimum thermometer... ..... an 776 formulas ee EE 642
Minor: planets soe ee eee CN 357 at/moving craft eee REM 478

features ofc. Che e = SAEIMU 362 IN polar regions Tr 640-642
Minuend defined A 1008 tables of in tide tables 269
Ve, WHR Git Psoe 1031 time of by almanac o NN 475-478

unittofatinne e sae ae SE 484 in polar regions 640-641
Mirage ttypes: ora Sts e ee 809 Work.fórm Æ oc «v fece AN 1058
Mirifici Logarithmorum Canonis Descripto, Moore, John Hamilton; The Practical

Ol EN API e MEL 34 Navigator of... VE IE IM 4
Mississippi River Commission, charts Moore, Jonas Ee 34

published DA 94 establishment of Greenwich Royal Ob-

(See also Chart(s)) BEE EEN TA lia EE 50
IMISt aS EEN ee ee ee 8083936 Morning star dened. maa 377
Mistake, defined e NE 679 Most probable position, defined_________ 937

detectiontor A 687 discussed EE ton A e CAE 685-687
Mistral STV ST c PNE IM 16, 807 distinguished from estimated position. 455
Mixed current, defined 8 22. 713, 937 ini piloting: ea. S28. << TN 258
Mixed decimal, characteristic of log of 1012 Motion(s), absolute, defined____________ 351
Mixed tide;defined. =). 2 a. ee) 705, 937 apparent, of celestial bodies_________ 367-370
Ntocktīnoons: s V LIII MN 811 defined "dS Sus E 351, 911
Mock SUN e Eo aa EE 811 apparent effects, of earth's revolution. 369

Modification des Tables d’Azimuth de

of earth’s rotation 367-369
Thomson, of Kortazzi

M E 525, 569 of motion of celestial bodies________ 290

INDEX

Motion(s) —Continued d
Olscelestial bodies, 3.5 acre due sel 366
apparent. effects of. 22. -Lensi 370
Keplers laws gehale, A be sn 354
planets- 2 io wi sadi 353-356
Giteumpolari S Be fers ale a ce Í arce 368
direct, Of planets s Poudoss aide sem ete. 377
e E Reeg I aa 922
ulérian. defined... ......isbace 370
ORM OON Ess. miks cee rct 362-363, 377-379
INewion's Jaws of a oremus , 354
NORTE AA P E 370
proper cdenned. m P a A ek ad 941
ICO E beds sal 39
radial, of celestial bodies_____________ 366
relative (see Relative movement)
retrograde, defined... ua n ss 944
IDO d a rs 377

TN TI as aM 39

space motion, defined______ 353, 366, 370, 948

OfSUNe A eee wa cai M 356
Mount Wilson Observatory, founding of. 51
Movement, relative, defined... 944

(See also Relative movement)
Mudge, Thomas; development of chro-

OMG LET ee e US 47
Müller, Johann (see Regiomontanus)
Binibpniesinr. S A geg 366
Multiplicand, defined EX sole 1010
Multiplication, of algebraic expressions___ 1018

Dyrlogarithins: EMU et eg 1013

of numbers,'explaineds... = ss. 1009
Multiplier defined sss Cen 1010
Mumetals defined r y e e 937
Murray, John; bottom-sample analyses of. 692
Museum of Oceanography, Monaco______ 692
MOSCA A 612
Musschenbroek, P. van; discovery of

Leydenajar.-——— AE EE, o 57
Myerscough, W.; sight reduction tables A

(ASES an HC. — NMORNM CNET vr aper 5

Nadir defined AA e 9 O 8,
NakrwanDatun SC S

Name(s), ¿defined sie e ere S 937
pronunciations and meanings, of con-
stellationss Fe 4 A 974-975
of navigational stars and the planets.. 973
Aansen Dottie tez. achter o n 693
reversing thermometer for... 696
Napier, James Robert ------ < a *- 166
Napier, John; Mirifici Logarithmorum
Canonis Descriptio Ee 34
AECA Le Spare e E 1039
Napier diagram, construction and use of.. 166
Naperian logarithm? ss ss es 1015
basetotito 12 places == C EE ea 959
Napier rules- toa oa loo ras oe 1039

National Institute of Oceanography, Great
Britain e cm E Dl v E

tableo eege, Seger Be, Se EE

explanation, OA toi seo 19
Naltüral'logarit IMA ce c € 1015
Natural seale of charts... ee 103

denne dar E ey a 937
¡Natural Eeer A i S 370
Nautical almanac, defined. |... .... EE A097
Nautical Almanac, first British-___------ 48, 52

(See also Air Almanac, The; Almanac(s) ;

American Ephemeris and Nautical Al-

manac, The; American Nautical Al-

manac, The)
Nautical astronomy, defined___------- 351, 937
Nautical Astronomy, with New Tables; of
Symonds A COT e 571

1495
Page

Nautical chart, defined________ a e 937
(See also Chart(s))

Nautical Chart Symbols and Abbreviations
(Chart No. 1), description and publica-
A owen sh mt: «23088 101

Nautical day, defined MuE Im H lar 483
historical zie 532 bagus roza DA RØ ÓN 518

Nautical mile, conversion factors... 958
conversion to statute mile, table 20___ 1276

explanationsof Sc DEI 1191
defined Ht). eo AS AMA. 6) ABA eg 65, 937
international, defined_______________ 65, 931
OTIginkof sien, LM Wiel aea 26
(See also Mile, Units of measurement)

Nautical Slide. Rule/!o: 9 d. cu uror eon 125

Nautical twilight, defined... . 368, 937

*Nauticator", of Jernge 2 200222 207 557

Nautilus, Wilkins polar expedition in... 692

Nautische Tafeln, of Bose 532

Naval Observatory (U. S.) (see U. S. Naval
Observatory)

Naveam,. defined. vs C alba ts 100, 937

Navegação Moderna, of Newton and Pinto.. 534

Navigable semicircle, defined... . _—_ 937

Navigate, derivation of... 62

Navigation, acoustic, defined___________ 909
aid to (see Aid(s) to navigation)
air (see Air navigation)
in amphibious operations ... 787—741
automatic celestial --_---%_ es 566

denned kisss- -aeee MANMAN do 8 913
celestial, defined <-- feet AUTO M 916
history rofi ee ... DANNA Soeur sú 34
indlifeboat-———---- a NEM 653-660
(See also Celestial navigation)
coastwisex.defined 2222220 ein oml 917
dead reckoning (see Dead reckoning)
denned. ¿msc AA SIT. 62, 937
(Dopplerimethodēs . Jv1V MLL Marui 308
(See also Doppler effect, Doppler navi-
gation)
effect of-ica upon o Bit J Joes side 746
electronic (see Electronic navigation)
eleetronics-in---.-----: EE WE 304-312
errors in (see Navigational errors)
in fog DOs LO e ea Ses ei AS UA TA 604
grid navigation, defined... .. 928
(See also Grid navigation)
(RI dEr uon AAS 15-61
(See also History of navigation)
injcet.-»Mi un | Ea e See 627-629
inertial, defined-.-. = 2-3 EE 931

(See also Inertial navigation)
instruments Top ---.------
land (see Land navigation)
lifeboat (see Lifeboat navigation)

121-157, 398-420

long-distance, defined: 2 934

long-range, defined______________--_-- 934

byplorans ceca E A309 333-343
(See also Loran)

marine idea kee 62, 935

in narrow waterways, sources of instruc-
ON AA o Ser 97

piloting (see Piloting)

polar (see Polar navigation) Á

practice of (see Navigational practice)

Dreëssure pattern ` eer es 675
(See also Air navigation)

ee lee oe 323
(See also Electronic navigation, Radar)

radio defined aaron abortu 62, 942
(See also Electronic navigation, Radio)

radiofaidētodetined Ee 942
(See also Radio)

short-distance, defined - ------------- 946

1496 INDEX
Page Page
Navigation—Continued Navigational triangle—Continued
short-range, defined___--------------- 946 solution of—Continued
insmalleraftzet -Gan nece tote J 605 historieali:-i:22:.::99 B9 0 ES 56-57
sonic defined use 8-7 62, 947 inspection tables for. --.------------ 57
BDAC aoe = eee re es ees 676 by orthographic projection. - - ------ 83
submarine (see Submarine navigation) “short” methods Ee: 56-57
surface, definedee EEN , 949 by stereographic projection. ....- ad 83
underwater, defined-----=----------- 62, 951 (See also Sight reduction, Spherical
(See also Submarine navigation) triangle) J .
by underwater sound. ..............- 742 Navigational warnings, first radio trans-
Navigation, Aids to Marine, of U.S. (CG— , missions Of ---------------------- 58
193) x 2+ 222590 eee ee eee 102, 1004 information On:sss es 3529 a 96
radio broadcasts:0f7-======= SBS 99

Navigation Dictionary (H.O. Pub. No.
220 101, 903, 909

Navigation manuals, history of__-------- 32
of sixteenth century--------------- 32
post sixteenth century - - ----------- 34

Navigation Tables for Mariners and Avia-

tors (H.O. Pub. No. 208), of Dreisonstok. 98, 534
Navigational aid, defined------------- 259, 937
Navigational Aids, Radio (H.O. Pub. No.

117) (see Radio Navigational Aids)
Navigational astronomy, defined. ..... 351, 937

“Navigational Computer”, of Brown-
Nassauss tent... Na patrie em 560
Navigational coordinates, table of___---- 963
Navigational errors------------------ 678-688
barometerferrors es (see ear os _- 768—769
chronometer error, defined.......... 418, 916
detenminationgofs--—- 255 eem 490—491
circle ofguncertainty= 2005. pe 685, 916
compass error, defined. -__--.--.----2 918
course error, defined: ---.---- T5 eese 919
tā. Ot venenas dd 146, 625, 929
indexserror ft i see feta} 413-414, 931
installation error, defined__------------ 931
instrument error, defned ------------ 931
loran errors, sources of_____--------- 338-339
most probable position------------- 685-687
(See also Most probable position)
in*piloting:2=:= tk 222. === AR 280

probable error, in dead reckoning.... 685-687

quadrantal error, defined------------- 941
OÍNEYTO, DOLL DEER eee 150
of radio bearing nar de 313
scale error, on polarstereographic projection. 88
sextant errors ect. tale 2 411-415
watch:error 6=Lagliestukt Det asla 419, 952
determination of ES 492-494
(See also Correction(s), Error(s))
Navigational Handbook with Tables, of
Hickerson--3--et--2-- feme. Lab 539
Navigational lights, light lists on________ 97
Navigational Observations (H.O. Pub. No.
606-a), description of ________________ 101
Navigational pnlanets 357, 937
Navigational practice k- a E 595-606
advance) preparation. NE ETA 595
CESAR A ee e M 597-601
entering sport... =... See ae 601-603
ip. lc m MUR T, 604
following great oirele 222222220 229
getting Underway- EE ME 596
landfals-- 12. ..... ieee eon anh 601
leaving port... («abbey asi dat 596
night órdembookem teena ee Ce 601

ABlsen e e 2 o ENS MERE NM 597-601

taking departure 597
Navigational publications, sources of. 97-99, 1003
Navigational triangle, components of... 393-395

defined sett evita cli cta aate 393, 937
description ots- Ta P E 53
solution of, by cosine formula_________ 56

by cosine-haversine formula________ 56

(See also Daily Memorandum, Danger(s),

Notice to Mariners, Radio broadcasts)
Navigator, responsibilities of------------ 60
Ņāvigatorsnotebooksess == =e «S
Neap. currents. 3-2
Neap tide: 5t ode PE 706, 937

Nent'lne'om charts--— P9 no 72
Nebula, kinds of, defined-----——- m 366
Neck of feeder current_____------------ 740
Negative altitude of celestial body------- 387
Negative number defined PORRAS 1005
Nekton} defined E AS 701
Nemedite ses cosas 2205223320 101
Neptune, ¡discovery loe PS 39
features 0[.--.. 22:2. 0 0 oee 362
(See also Planet(s))
Neutrons LUTES EEN D A 289
DN ee =022222232502322022 SE 747
New Altitude and Azimuth Tables, of Ogura_ 534
New American Practical Navigator, The; of
Bowditch; first publication of--------- 34
purchase of copyright of------------ 31
simplification of lunar-distance method
ÍDesskbissssodSpcasðsðsfrar gak asi 54

Ship's Position at Sea by Projection on
Mercator’s Chart, A; of Sumner-------- 55

New chart, defined =====2:=2:>:222 32258 888
New edition of chart, defined- ---------- 888
New Line of Position Tables, of Weems... 536
New moon;-defined22 esse S 371
Newton, Isaac; development of sextant by- 42
law of gravitation of, origin of... 38
shortcoming of-------2--9SE UAR 39
laws:of'thotion'of SMS ASID BITE 38, 354
Principia of, translated by Bowditch _ - 3
Newton, J. A.; sight reduction tables of. . 534
Ņey siprojēction ot st eee 86, 937
(See also Projection(s), modified Lam-
bert conformal)
Night effect on radio waves....... 295, 314, 937
Night order book, contents of----------- 601
defined-=:22722 222522 UI 938
Nightmark defined m. ERE 259, 938
Nimbostratus c ETE 782, 938
Ņimbus e17 euer EE, 780, 938
Nipped by ice, defined ----- 2-22. 761
Noah.--$:-- EE BRUM 15
Nocturnal, description of--------------- 42
Nodal period of moon, as tidal cycle... 708
Node(s),lineofzs--2--T9— OMIM 381
of moon's orbit- ee 5 RERUM 381
regression eegen 377
Noise, atmospheric, defined________.____ 912
defined 272 L TD eee 938
radio, causes of "rs PP ERES 297
Nomograma degli Azimut del Sole, of
Molfino Seely DE DEA HERE di2
Noon, geomagnetic S eTEN E A 162
local apparent: 2 C DRM ME 496
sidereal: ca. ¿2 000 IEA 483
Noon constant, defined. |... 938

INDEX 1497
4 Page Page
Noon sight, definedssast se ssl st 938 Oblique Mercator projection, defined. .... 70,
Note, J. W.; Epitome of Navigation of ___ 34 74, 76, 938
Normal defined core beta on 1020 (See also Projection(s))
Normal curve of random error__________ 681 Obliquephotography...... _ 879-881
Norsemen, voyages Of ats do ale kanuas r: 1 15 Oblique plane triangle, solution of... 1037-1038
North, compass, defined_____________ 164,918 Oblique projection (see Projection(s))

grid, definedoss - 320b. oboe a hl Bieter ix 928 (Obliquespheres iiu een bal 368

magnetic; defined 5... 2152s side 164, 935 Oblique spherical triangle, solution of_____ 1040

as reference direction... 134, 164 Oblique triangle, defined. |... 2... __ 1022

Bre, defined. aie aia Ai d ann n 9910 gei use lege to, let plett astredic 330
North American Datum of 1927______ 427, 892 Observatories, astronomical_____________ 48-51
North Atlantic, ice In. 753-755 Observed altitude, defined________ 421, 450, 938

International Ice Patrol] |... 2... 757 Observed latitude, defined____________ 453, 938

establishment of E Sas} „<. 31 Observed longitude, defined___________ 453, 938
fanegoules In... háslish. adam acs 755 Observers, cooperating, source of infor-

(See also Current (s)) maton Tor s 4s ET 873
North Atlantic current________.________ 721 Obtuse angle, defined... a 1021
Merth: Cápé current. S222 066 2. tres 722 Obtuse triangle, defined________________ 1022
North equatorial current, in Atlantic Ocagne, Maurice d'; altitude-azimuth

Canals Cremas EE a 719 graph of... 2 Siam aaa ap 555—557

indian Ocean... ss. M (24) Oecluded frontsatdue bas labas wiles 802, 938

MARSCH C OCEAN 5 2 10 1231 MACU TION pen an 375
North Pacific current- az, 723 Oceulting light, defined. |... 938
Northeast drift current in Atlantic Ocean. 722 Ocean current (s), in Atlantic Ocean.... 719—723
Northeast trades: 5:159 LB HI diario 798 CAUSES A A ere 718
Northeasterlies of arctic... 2... 799 anduclimātes see Basle, deere 725
Kirthernteross P? pun ruqaigomssso 584 defined ss O c coU ue 718
Dorthingsdefined***-----—- «PARI 938 and density differences... 719
North-upward plan position indicator, extentrofit mēs ener 691

DeEnod E BOLE 938 geplor yO ou c e Ma nie 699
Norwayicurrent e nete (40 Sto 722 in Indian Ocean- -eanan Bee te eR 724
Norwood, Richard; The Sea-mans Practice EN EAS A WEE be 743

(IR S nc ee EE thee O 34 oceanic circulation... c ceci in 719
Notice to Airmen (NOTAM), contents of.. 671 Origin. Of. a i IS ani 693
Notice to Aviators, contents of____________ 671 in Pacific Ocean. 222 be 723-724
Notice to Mariners, chart maintenance by... 99, in polarsregions 4 Ee bs wd 725

106, 117 types, ot "e sabes Testers sakir 718

e DEEN 99 Wind. 2 tots Pe ea iur inn jac 718

OESOTO wie e inns ep ut 31 (See also Current(s)) i x

publication and contents of... 99 Ocean currents (alphabetical list):

publication maintenance by__-_-_-___ ae 97 ‘Australia, east... co salia. te 4 724

(See also Daily Memorandum, Hydro- west. 222-4... Orem ie WI de vieta 725

graphic Office publication(s), Radio Benguela -seti -anuos oido ein 722
broadcasts) Brazil... EE E leben ne PO nlla 722
Notus, ancient wind name__ .. 23 California" Ee 723
Nouvelles Tables Destinées à Abréger les Canary EE 722

Calculs Nautiques, of Perrin.________-. 569 Cape;Horn casas eee 723
Nouvelles Tables Pour le Calcul de la Droite Davidson. `“ 2 FE 181282 b ears del 4 723

de Hauteur a Partir du Point Estimé, of eastēAustralia taa Seed ee 724

Hugon see lo! ed die o ee 531 east Greenland me Der A ees e 722
NO RR cr AE eu 366 ANI 9. £e oe ee AE CE 701
Novara, Domenicao Maria. ...... 36 equatorial esc recie fumer ---. 719, 723, 724
No-wind position, in air navigation, de- equatorial countercurrent, in Atlantic

io CR S es ML eie 672 cean m qon ute Ód ee Ate 719
NSS, radio time signals, of Naval Observa- in Indian Ocean- f em cu a ae 724

EOL Y NN OT EPA: A E aa 492 in Pacifie.Üccans- e g es ee 723
Nucleus ofconiettmmed ola tie 363 Falkland orere ee A e 723
ILLE. Locos A eee 305, 938 Ed lt date géet 721
Numerator defined c (2 UT e 1005 Greenland” m en e Catia 722
Numerical scale of charts- -------------- 103 eer E E esas levcitont 722
Nun buoy, defined. dur rs taa 264, 938 Gulf Stream usse Hotian) van tie sane 721
Nunes, Pedro; fix by use of globe- -------- 32, 56 Irminger Monee Bee shy lied. $6 qeda 722

Tratado da Sphera of 30, 32 Japan Stream domos 10 IM sr NIA 723
Nutation, defined..........*:0560: “Aly 370, 938 Kūroshios see M ee ee ME 723

discovery Of rones IA bino: 39 [A EOS CIMA rernm A UNA 722

Y 109%: WM. MAR e SUE osos 721
Oberkommandos Nak: ie Un: (Ger- EM At Pim Cr MANIERA res 722
many).azimuth'diagrauiofzcz-..D531039572. Se ule ei UA Rea :

sight reduction tables of... 536 Sie E ee ey
Oblate spheroid, defined... 62, 1030 in Indian Ocean.............---.-- e

i jn' Pacific Ocean mc eU 6 ae E
Oblique angle, defined______.__________- 1021 x 723

i i NOLON d Bee eer
Oblique coordinates, defined_____-_---- Sek 61031 A AE 722
Oblique cylindrical orthomorphic projec- northeast drift, in Atlantic Ocean. - - -- 799

tion (see Projection(s))

UNI OT W a V Sete E ooo

1498 INDEX
Page Page
Ocean currents (alphabetical list) —Cont. Ordinate, defined.....-.-.---------- 938, 1031
ru AM eMe AA a) acu aa eee 4 Origin, of coordinate system, defned. 1031
JE d ere oe 629, 725 of-survey, defined EEUU PE MEE 850
à R AA VA 725 oe (see History GR eue, ai
oüth Atlantic t ua BNS 2 *Orion"' instrument, of Voigt------------ 56
poua SC Se in Atlantic Ocean___-- 719 Ortelius, atlas of- ds SEO) RES 21
inj Indian Ocean 151227 rs n 724 rime-meridian of YF AS 48
in Pacific Oceans sorum 723 Orthberaphie projection, defined. ... 70, 83, 938
southeast drift, in Atlantic Ocean. .... 722 (See also Projection(s))
p (Svalbard) Secc es 722 Orthomorphic projection, defined........ 939
sushima ee E 723 (See also Projection (s))
LOO ER eee m a ocu ue n
3:7 MONAND SDIS Poy scillator radio: = 094 SS
west wind drift EE 723, 725 submarine, defined ` 220 38. AREA 949
Ocean station vessel, defined-..---------- 938 Oscillatory wave, defined. .-.-----.----- 730
SC p =? D ES ua o d 727-736 SE princi de Of ABRI See 528
ee also Wave(s unce, conversion factors- - ------------
Oceanic circulation. ------------------- 719 Outer planete:--2 2.222222 3097000 Di 357
Oceanic soundings-_------------------ 868-873 Overfalls, defined---------------------- 939
(See also Sounding (s)) Oyashio. -2-1 7 222.2: eee esse sā 723
Oceanographic charts and publications. 95-96,
1002
Oceanographic Institute, Sweden. ....... 692
Oceanographic institutions_------------- 692 P-band, defined. 2-3 geesde eae
Oceanography 691-702 Pace, length unit, origin of ee Ec iim 26
boitóntirellot GA ae 699 Pacific Ocean, currents in. __---------- 723-724
A e ad 693-695 Pacific Oceanographic Group, Canada.... 692
dened... ooon donnen E Ce E C eses o per
exploration- eo ER ' 691 Pack Jegen eer 5387385 200
: operations ins = 2 ` - 5 0 760—762
History o NES ec BESCH 691—693 “oT k
impact of Darwin upon..............- 691 p ( d EE SE pack)
institutions for see -c<9.-e-<-M es 692 Pa 5 Aa Use ahs pee ja E 20
Wants blolozy ace... alabada 700 age, Robert M.; development of radar by- 59
e EE 699 Palacio, Diego Garcia de; Instruction
marine sediments.................... 700 Naulhica of------------------------- 34
origin foton RIEN. > ales uS 693 Palomar Mountain Observatory, found-
sea water, chemical properties of... 693-695 P RGA soci pooh Pate IIR 51
physical properties of- ----------- 695-699 D kel e ZE EE D. 4 Wee d pue
testing methods for---------------- 693 O IPIE DE ERE MR 119
Oceanography, Departmert of; Texas Pantograph for chart construction....... 888
A de M. College. .. x , 692 Pantograver for chart construction. ..... 888
University of Washingion-.......... 692 "zs description and . properties e
Oceanography publications (see Hyd ro- A A 102 1028
graphic Office publications) = (ð ae Paral see acta eS x
edis ent ------------------- 1023 Parallax, in altitude, defined__________ 435, 939
O SS O o moon massae 36
CES iosa EE SE
defined e
SE for and Sen EE 668 denned NS AENA IRURE bee
or as sign of E BEE 661 i EE dað ia] Obi ‘
Oersted, magnetic unit, defined. ...... 161, 938 36 pee APR a he paths ec abe
Off soundings, defined.................. 938 geocentric, defined- 435, 926
Offset, reproduction process. ------------ 897 of mogh 4 ETE ORT ' 362
Offshore» defined Sass cu: ane 938 heliocentric, defined. ................ 930
Offshore current, defined. .............. 718 of stas es TRAY RNC SIDE 352. 365, 435
Ogura, Sinkiti; sight reduction tables of. 57, 534 horizontal, defined----------------- * x 1 920
rio ee E — 435
Omnidirectional, defined. e (988 "kinds of 5000 EN 435-436
Omnidirectional range (see Omnirange) Parallel(s), of altitude, ‘defined________ 385, 939
Omnirange, air navigation system. ---- 317, 674 on azimuthal (zenithal) rojections _ _ "re
On Finding the Latitude and Longitude in of polar regions je sd th abe í 86
Cloudy Weather, of Johnson. ---------- 56 on azimuthal equidistant projection... .
On the beam, defined- ----------------- 938 of polar re ion per rd eU pego cm
On the bow; defined Ssnan nmn 938 on Kon EE BEER ee =
On the quarter, defined- - -------------- 938 of polar M ions 27 >= r vē ie 2
On soundings, defined------------------ 938 f declinati B E RS ts zd
Ooze, defined ERO. RM 108 denda lon, defined FAA APRA 382, 939
Opposition, of celestial bodies, defined... 938 Set ne reri aes IPA SCH
GEES ol od tbe E EB uA E xd
Orbit, of celestial body, revolution in... 353 of latitud Aen ENEE BE
Kepler's laws of 8, 354 Buide) defined Ti (1 64, 387, 939
SE ae ee ES on orthographic projection............ 83
(See ARS Motion (s)) A on plotting sheets- Sok IA ti Øl 89
Ondindr y v šā 7 on polyconic projection- ------------- 81
as IAA T eS ae m siju 370 spacing of, on polar projections. ...... 86

Jd

INDEX

Page
Parallel(s) — Continued
standard, of conic projection... 78
of polar regions. etch a 86
Red Lo o ce IRN 948
of Lambert conformal projection____ 80
on stereographic projection___________ 83
on transverse and oblique Mercator
TOJCCL ONS meee E E a dads 76
Parallel lines (surfaces), defined_________ 1020
Parallel rulers, defined... seng k to +. 939
description and use of... 121
Parallel sailing, defined... 221, 939
early importance of_____ eege 44
SAME t NOTE C ats ee di ros 224
nup Mor Fforest. alt eae 30
Bee ere E MP UR ANI Par 367
Parallelogram, defined_________________ 1023
Parameters, of ship's magnetic field, de-
CA ua eege, 173
(See also Compass adjustment)
Daranuhehondea F Absa Me 811
iģarantisēlenes N ee ee pe 811
Ara Selene wee mer ense ` 811
IR Circles) ee ee 811
Parentheses, use of in algebra___________ 1017
Rarhelicicirclesnet tes ss" e eps mr 811
Earpelionsr RAR VI cron 811
IA bal a e a A nerij 352
conversionifactors. sit ME < T 955
«Barbalfeelipsetetsdepme NET" CT A 379

Parts Around the World, of Pytheas______ 22

Babent:lorydefined e 5“ SVS OS
(See also Log)

Fául,(Vvoyage'to Rome "002225 T 27

Peak of radio wave, defined_____________

Pedestal on loran scope----:. ^. MI 7 336
Pedometer for land navigation__________ 668
EOI $a eege ro, E 939
description, and. use of.---—e9 nep 3 154
Pelorus, pilot of Hannibal..---:-----.-- 23
Pendulum studies of Schuler____________ 150
Kentaponssdefineds o 9 <: 1023
Penteado, F.; sight reduction table of---- 539
Per gyro (standard, steering) compass,
CORCUERA RA eee 939

Peregrinus de Maricourt, Petrus; Epistola

del Vagneleioteās s a 28
Pereire, M. E.; sight reduction diagram of.
Beripean current. coc ses
PErigean Spring tides c eerte 706

Berigean tide* Bts ssh sese 706, 939
perigee wdetin ed == AS spei 0 355
moon distancerab co Ee 362
Perihelion, defined ` 8 5. 554125 355, 939
earth at ss S de € ive ere del 371
Perimeter, of circle, defined_____-------- 1024
of (eylinderydefined& 2254 33453-2-523455 1026
Of polygon, denned < eS EE 1024
Period, of navigational light, defined..... 261
owaye EN le APRA TO OME

Period (punctuation) (see Abbreviations,
on charts)

Periodic current, defined_______--_-___- 718
IBeriodicferror "NES SEE S 682
(BeriDLUSNOISCYISSIMNE ES ee 16, 22
Īperīnafro su MM RM ULL 612
Permalloy defined Mee Ner 2 939
Permanent current, defined___-_-_-------- 718
Permanent magnetism, defined... .... 158, 939
Permeability, magnetic, defined. -------- 159
Perpendicular lines (surfaces), defined.... 1020
Perpendicularity, error of, defined. ...... 924
Perrin, E.; azimuth tables of 569

Personal equation (see Personal error)

1499
Page

Personal error, correction of sextant alti-
tudejtor setosa sab Roe oa 422
definedss! 7 4 .. mientaniend wis 939
in sextant observations_______________ 408
Perspective grid, construction of______ 879-880
MSChOLS roo a kīra nasa 881
Perspective projection, defined_________ 69, 939

(See also Projection(s))

Reruycurrent..---s22--- 3... hen ah e 724

Phantom bottom in echo sounding. ... 134, 744

Pharos of Alexandria. cocoa. Ju 28
Phase; of moon. Ma utah La indt epi 377-379
OL radio Wave. Huici areis 290
Phase correction, defined_______________ 939
for sextant altitudes = 9 ee 434
Phipps, deep sea sounding of. 27
Phobos; featuresiof2GuL Li... e 360
Phoenician astronomy, influence of______ 35
Phosphor Anies EE PE MI 302
Phosphorescence of cathode ray tube____ 302
Photon proof defined 25 Doa. soi 888
Photogrammetry SE EE IS 874—885
anāgiyph:juseējofi SS CSS TM 876
camera orientation.-_-_--__-_---------- 874
defined: ===. [serie Jo heer saiti 939
oblique photography, high and low____ 879
mapsjfrom-. -- -..- Some K wan 879
perspective grid method------------ 879
procedure for "fP AA 879-881

by, trimetrogon= sums: IRM O 7
perspective grid, construction of..... 879-880
use: of. -- 5. ES ear he 881
photography classifications, defined... 874
photo-interpretation_______________ 882-884
Dlanimetrickns pi ses ane = 1" 10 876
principal point, defned 880
radial line plots = esat da: 876

terrestrial photography, procedure for. 881
tilt correction, radial-line intersection
method yee S pesos ce MS 876
vertical photography, diapositives from- 876
features Of... sie ee e al sua 874
height determination by------------- 878
procedure for emana rem a A 874-879
scale of. - - Keglet tcs diam 876
Photo-interpretation----------------- 882-884
Photolithography, reproduction process. . 897
Photosynthesis: 2.2.22 a eee 701
Bhototheodolite-- oa ee ve ER 841
Physical libration of moon. 222 362
Ēhytoplanktons es momen eee 701
Pi (m), numerical value of______-------- 959
Pibal,defined-. se. enter. 785

Picard, Jean; determination of earth's
circumference: -aee SA S S 2 PUN 19

Picture tubes —— EE GEES 302
Pierce, M. R.; sight reduction diagrams of. 561

sight reduction method of. --_-------- 555

sight reduction tables Er e 538
Piles) chartsymbolfon ec 455 110
Pilot balloon, described. - - ------------- 785
Pilot/chart(s)y defined" S 939

publication and features of__--------- 95
(See also Chart (s))
Pilot rules, Rules of the Road—Inter-

nanona OP ee tt Eye a 102
Rules of the Road— Western Rivers ---- 102
Pilot-stationsidefined seeds ence 34 pde 939
Pilotewaters, ¡defined 2 2 = seesaw 939
Pilotage (see Piloting)
Pilotage services, history of__----------- 28
sources of information on__----------- 97

1500 INDEX
Page er
Piloting XS 240-286 Planimetrie map-------322 79 9 --— e 876
VAN and transfer, allowance for.. 276-278 Plankton, defined. ........------------ 701
aids to navigation in-------------2- 259-267 Platen, defined.......----------------- 876
in air navigations- Esas ar e 673 Plot, dead reckoning, defined. .........- 921
anchoring procedure: -------------- 278-279 ēfined AAA AA S PÐ Ge
bearings and angles in- - ----------- 255-257 Plotter, defined 5.2 A LU SES e E
bottom:profile An 258 description of NEP os pr 122
by buoys, precautions for------------- 266 for polar charts "22222 PEN M MEE 621
coast,.defined:. 2.31 72 06 eee GEO? 917 use of----- eee eee 122, 215
in current Mavs PIS dd au 200 VE 268. “Plotting, of direction" SES EE EE 214
defined E AERO ST 62, 240, 939 of distance-__----------------------- 215
determination of distance off.......- 257, 661 of great circle_---------------------- 100
by distance measurement. ------------ 243 labels used in----------------------- 216
electronics int -n= 9er SET 279, 304 of lines of position--------- 241, 451-452, 638
errorsdn-cu cce. IRA AI 280 ofloranlinese-$eededeeeecez 39-34
grounding, causes Of_---------------- 280 on Mercator chart. .......----------- 71
history Of aa. 30 aee ted m 18, 28 in-high latitude IRE 631
in'land:navigationged- eet name 669 on polar charts_-__----------------- 620—622
lights TAPA se: es. eee MP 264 of position. ---..--------.-----2--. 214, 216
in polar regionsseemsese= la sees 630-633 of radio bearings: = -777----.- —.-4914-915
position finding byeee -S.E Ss 240-259 on Lambert conformal projection... 80
practice OÍ e ccc cet m 280 ofrhumb!lne*"*-***- "e ee 215
precise: S 3-5 2000 du de Y 276-278 of ship'simaneuvers-- AS 325-329
predicting depth of water..........- 270-273 suggestions torne ce C LLLA 216-217
predicting speed of current..........- 274 Of voyages TS e Eee omnee 216
preparation fors et esse Ts 240 (See also Navigational practice)
rõünding a pointi SEO ee 257 < Plotting chart, defined: -^-----*7—— 940
soundings INE M SENS 257-258 (See also Chart (s))
tidal co 20 MS a 267-268 Plotting sheet(s), defined. .............- 940
influence of land upon. ............ 268 described st = se as ES 88, 101
(See also Navigational errors, Naviga- for hydrographic survey -------------- 859
tional practice) principal juse! of 32245 eh ee 101

Pilots (see Sailing direction(s), Coast pilot(s))
Pinpoint, in air navigation, defined. ----- 4
Pinto, J. C.; sight reduction tables of... 57, 534

Pipe gage for tide measurement......... 844
Pitch of ship's screw: Sok INLA 130
Pitot pressure of water__..-.----------- 128
Pitot tube roð. Atala See E TIO < 673

defined eee «EE C DAB 940

water pressures by. -CNET LIEL 128
Pitot-static log, description- ---------- 128-130

development. of: Pr 26

Plan border, use of on charts----------- 893
Plan position indicator, defined- -------- 940
heading-upward, defined... .......... 929

interpretation of 321-323

north-upward, defned. 938
principles of SEE SES e 318-320
(See also Cathode ray tube)
Plane (surface), defined................ 1020
Plane geometry, defined-------------2-- 1020
Plane sailing, caution-------------12 1L 223
defined 24 2 sað ee D gek 3 940
discussed 2322... 6660: - a Me 221
examplejof >. 6602: E OE uM 222
historykofenente de o te = ate SE AS 29
Plane triangle, defined- -- --------------
solution olse See ea eae 1037-1038

Plane trigonometry, defined------------- 1031
Planet(s), altitude corrections for_______-
(See also Sextant altitude correction(s))
classifications -of SNI EM 357

configurations o ses T 375-377
elongation of, explained______________ 376
featurestofa Misā 205 a R 356-362
tabulated e ME o EE 964
magnitude of, finding by almanac- ---- 479
MOONS o oes mee cc SE S 377
names of, pronunciations and meanings. 973
navigational t a , 937
GEHEIT 375
EE EE 377
satellites Ofte MET. E a eee 357
EELER D JV een E 375
Planetary configurations, defined_______- 377

projections. for. = E eee 89

pūblication of 73 te 101
radar, (H.O. 4665 serie)... 22 325
small area, on Mercator projection, con-
struction Ofs=<= Score 020 89—90
universal, defined. - 22002022222 952
description Of 2-7 SIE A 91, 101
instructions for using-------------- 91
O PE A M hs MEME 89
(See also Chart(s), plotting chart)
Pluto; ¡discovery otd de AES 39
features of. 2252225324454: 322222008 362
PM (post meridian), when used... ....... 483
Pogohip.-=-= 2932000252323 SOIN 808
Point(s) Lig curi. 00457501368 > AE 1020
of arrival, defined == 212350 Ee 940
of compass 5222252252290 MA TUE 137
conversion to degrees, table 2_______ 1217
explanatiomof=2222 PM 1186
defined.-2-<222222=2 TOURED I 918
of departure, defined_________________ 940
of destination, defined_______________ 940
of tangency, defined_________________ 1025
Pola, oceanographic expeditions of------- 692
Polar axis of.earth----- BON IES 63

Polar azimuthal equidistant projection. . 86, 88
(See also Projection(s))

Polar icircies defined 373
“Polar Computer”, of Weems__________- 563
Polar coordinates, defined______________ 1031
Polar current 629, 725
Polar distance, defined_______________ 382, 940
Polar gnomonie projection______ PES ie 86, 88
(See also Projection(s))
Polar grid, description and use of______ 618-620
Polar horizontal parallax, defined________ 435
Polar motion P9296 5 14 NME CE 370
Polar navigatione OS 612-644
celestial DARA 20 na MELLE 635-642
charts for ^09 78 melitas Ha 616-622
dead reckoningisei 2 pa: shapes 622—630
defined. 2 et ICON ION a 62, 940

INDEX 1501

Page Page
Polar navigation—Continued Pole(s) —Continued
EE DE INSA "DES OURS AMP 625 magnetic; defined. 211 1 í! FL svn 935
correction curves for... 151-153 of-éarth, flóld-at eee e vð 161
magnetic compass, use of... 622-625 location'of35t:.... o 39 vag quán Ye 161
PHONG EL Ek AA ees eee ee Jas 630—633 polarity-of LE DH ees ior 159
Plotting -see std ee ee 620-622 of 'shipt Aurei oN tev deen LA. 170
polar grids =". L: 223322 D00 0000) mom : 618-620 (See also Compass adjustment)
preparation forse UI T2 369119 al 642 north celestial, movement toward
Soundings 222222222 MONO 30 „mā 631 Polaris. -——— ere renee merce LÍA, 373
tide, current, and wind 616, 629 wandering of M03 NM NOMU "EDT NN 370
visual bearings in 5-375: ISu AE 621, 631 Pole of inaccessibility (see Ice pole)
(See also Ice, Navigation) Polo, "Marco Sane oe NA OSTIAN ag) 29 23
Polar projection, defined______________ 69, 940 Polyconie projection, defined________ 70, 81, 940
(See also Projection (s)) P he EA P rojection(s) ) testet 1023
Polar regions, aids to navigation in... 630 VIO Sui es RU Nan pentes
: Polyhedron, defined =V J 4 be tp SEMU 1025
anchorages, desirable features of_______ 632 Kind d*bidbērtisl of 1025-1026
celestial bodies, apparent motion of |... 614 ashes SS ann gr ts Ý
` EC Polynesians, voyages of. E 15-16
celestial navigation in___________.=. 635-642 Polynya, defined 750
celestial observations in------------ 635-637 Eden
à trage d Polyzoa, defined —----—:----2--.:.: 29K 109
charts for (see Chart(s); Projection(s), Poor, Charles L.; slide rule of TBI Mál 558
polar) | 620 vos p Ort entering - 220210 PIB PLA 601-603
currents D. a e y establishment ora E 268
detlectionio EE EC Ee ER 615 leaving 596
(See also Curr ent(s), Ocean current(s)) Port facilities, sources of information on- - 97
deadireckoning in-- « ae «Ee 622—630 Portolanceharts 20
dead reckoning equipment mm... 630 Parolan miles: ecectrerore 7. OMEN 20
dipfotwhorizondns-- spots EHS 637 Poriolato Big. dqosmoTra 10: BOLA do 22
direction in, use of grid for__________- 91 Posidónins "MDoR(UN átmullur) ie 27
electronic navigation in--.......... jās. eet determination of earth's circumference- 19
geography of------------------------ 2 ocean depth measurements of_________ 691
gyro compass in--------------- 151-153, 625 Position(s), assumed, defined___________ 912
high-latitude effects_------------==--- 613 in navigational triangle... 393
landmarks in_---- due ge bag - edis: 630 pole as ZER I 638
magnetic compass in--------------- 622-625 este nN tered uC ClO Tl A 450, 502
meteorological effects SS c. 614 astronomical denne d A 427, 912
moonlight duration Kette 1 640 from celestial observations__________ 547-550
navigation in- ------ 2537 see + E 612-644 wathontsplottino A 547
(See also Polar navigation) circle of, defined- 0 449, 916
piloting in__--_---.----.---------- 630-633 coordinates of, measuring on chart___-- 214
plotting lines of position in. -_-------- 638 dead reckoning, in celestial navigation 454
preparations for entering. ...........- 642 defined Ls oe DOMINA, EUG 62, 213, 921
rising, setting, twilight in----------- 639-642 in lifeboat navigation_____________- 652
sallineidirechions for”. -----<: see 632 defined" Pte ro DICO SI TA 940
soundings ini =, .- ==+- Shean ye 631 of departure, defined- 216
summary of conditions in............. 616 EE A AT 64
tides and currents In... 615, 629 ErrectoPeurrent L HOR: 249-254
wind in_-___---_-----.------~---=-- 629, 799 estimated, from celestial observation_- 454
(See also Compass, Current(s), Dead defined 2-4 «E.» A 10 27 62, 924
reckoning, Ocean current(s), Polar eet ls == MR QUE Y 62, 213
navigation, Tide) int piloting? Uds EE 258
Polar stereographic projection-__-_------ 86, 88 Peodetice defined e ««e ine T VIDEI MIRI TS 853
(See also Projection(s)) Reographicaladenned ere 449, 926
Polaris, determination of latitude by, line of (see Line of position) N
explained Dl tics deso ies 521-523 MOS proba ils, baak oeren rier 937
historical------.----.------------- 43 A mE eae 685-687
Ga e seu esL. m3 c Y 658 distinguished from estimated posi-
work ronn Nir tdēgodsoiei lauder 1056 TIO eius M Bie tro mme a HET 455
(See also Latitude) We E Ca eech a 258
movement of north celestial pole navigational, symbols for------------- 906
toward--------------------------- 373 poi m A TASA 240-259
Polaris correction, defined... ... 231 940 A A E 214, 216
Polarization of radio waves_-----_------- 291 (see Plotting) s A
Pole(s), as assumed position------------ 638 from single-body observation. ...... diro
celestialdeftinede- eese OV nue mel 382, 916 by zenith photograph--.-------.- uh
of circle on sphere, defined... ......... 1029 E der Navigational errors, Sig
: EE reduction
PO OIT F Bostontancionde inci 940
E a Husa e RE eee dT 395
depressed, defined _----.-.--------- 382, 921 Position at Sea by Projection on Mercator's
ogeclipticte MA de ae sideris 387, 923 Chart, A New and Accurate Method of
elevated defined O O 382, 923 Finding a Ship's; of Sumner---------- 55
hodtious ARM. [potros TL orm ct 74 Position Finder”, of Hagner-_--------- 566
geomagnetic, defined. .............. 162,927 Position Line Tables, of Smart and Kai
ice pole, definition and location. ...... 750 sliētianes:" zs eter :

1502 INDEX
Page Page
Position Tables for Aerial and Surface Prime vertical circle, defined---------- 385, 941
Navigation (H.O. Pub. No. 209), of meridian angle and altitude on, table
Pierce Ses m... 25 EDO een 538 25. ietsad.- E ee AE 1282-1285
Positive number, defined. -------------- 1005 , explanation of------------------ 1193
Post meridian; defined- <= 0404 ¡Prince EE OU 4
Potter, A.; sight reduction method of.... 545 Prince, Jobim? S 3
Pound, conversion factors. ............- 958 -Principal point, defined. ..........----- 880
Power of a number, defined___---------- 1010 Principal vertical circle, defined. ------ 385, 941
PowersupplyBed-..---- ass 301 Principia, of Newton- -------- EE 3
PPI (see Plan position indicator) Prism, description and properties of..... 1025
Practical Navigator, American (H.O. Pub. Prismatic error of sextant- - ---------- 411, 941
No. 9) (see American Practical Navi- Pritchard, H. C.; sight reduction method
gator) Of kas weet. Ge po go E 562
Practical Navigator, The; of Moore. ..... 4 Private aids, chart symbol for..........- 113
Practical Navigator, The American; of Probable error, in dead reckoning. - - -- 685-687
Bowditch sese = ⁄ ESSE seta 4 defined ait Bc pe Fun OF PORRA 681
Practical Navigator, The New American; of (See also Navigational errors)
Bowdite aan. t e es plat 46,349 ‘Producthidetined if == swe = = ees 1010
Practical Tables for Navigators and Aviators, Profile*defined------.. M SOS 941
ofsRustr c RETI = DE 525 Projection(s), for automatic dead reckon-
Precession, defined Y 36-22 e cde 940 ing equipment S A AA 38
Ke ¡AXIS =: e EE LENS 373 azimuthal, bearings on: ``“ ð -T 81
of equinoxes, Ee 940 defined esoo fees sete S K 70, 913
discovery tor I ME 37, 48 features Ofí===<: eee MO 81
explained svag. oL 232 See eae dies 373 great circle’on #222 <2 00 E 81
rubte OC o EE 955 for polariregiong---- ss PME 86
OfYgyroscope A <= ES 142-144 azimuthal equidistant, defined- ------- 913
Precession axis of gyroscope (see Gyro- distance ONssis6es:+ec 308 AOS 88
scope) features: of. 04.1 ME 70, 83-85, 88
Precipitation, defined - -------========-=- 788 great circle On ==: 15 ARA See 84
REELLE HEEN 788 for polar regions +22- HA 85, 86, 88
Precipitation gage -erens -begkpsa- ssk 788 principal uses Ob ee 84
Precision defined A 679, 1006 scale:onz«£2----.-.. 5208 H8 ARMS 83
relative defined AS E 1006 azimuthal orthomorphic (see Projec-
Precomputation, in air navigation-. ----- 675 tion(s), stereographic)
fór sight reductions E 510-511 chart projection, defined__------------ 916
Precomputed altitude---------------- 510, 940 classification-0f "Tomas 69
Preparation Iori voyage: s c EE 595 conformal, defined--------—--- 21 TO 918
Pressure, atmospheric - -~ --- Æe 4502 912 properties of IDOL 69
altitude correction for, table 24______ 1281 conic, defined= ss MA 918
explanation tol == pliss 1193 features of... "03 Dom S 70, 78
effect upon refraction.------------- 432 for-polar regions 4017009. eee 85
measurement of_------- cele d apte 765—769 standard parallels of------------- 86
sea level, defined.................. 768 of Ptolemy = S. tel Bao tossed we 19
semipermanent highs and lows...... 799 simple cónies=:-2-4-2 ol EB 78-79
station, defined 222222. e = 768 standard parallel of---------------- 78
unit conversions, table 14.......... 1264 for polar regions______-__--------- 86
"explanation of EE 1190 transverse. OI SE 78
units of measurement. ------------- 765 (See also Projection(s), Lambert con-
(See also Atmosphere) formal; Projection(s), polyconic;
barometric, defined. ................. 913 Projection(s), secant conic)
conversion fāotofac leca <= EE 960 cylindrical, defined. ----------------- 920
dynamic of waters. ¿ases basis 128 features of. eier 70
Pitobwolowater- d ass EE 128 for-polar regions locus n 85
OL soaswater ==... == Ee 128, 696 defined “WE, Unilned 4% STA 69
static sof water oo oe oa ee 128 distortion: ou 200 A 69, 91
total, EVERE a 128 (See also “features of" under indi-
units of----- SES 696, 765 vidual projections) i
Pressure correction, atmospheric, defined- 912 equatorial, defined________________- 69, 924

Pre Erden deünod s eR S 197 equatorial cylindrical orthomorphic.... 69-70
O SE ISE E 50, 940 (See also Projection(s), Mercator)

Pressure pattern navigation______--_----- 67 A

Pressure Hades, of d D IM a ET MEN 750 JONN: C; defined- =~ = 72322222028 69027

Pressure tendency, defned 802 gnomonie, defined. .------------- 70, 82, 927

Prevailing^westerlies--.. 2 ease 798 features of. 82

Primary, of celestial body .. 353 great circle on. =< SEE 82, 100

3 great SIS HX eset qae e mor EE 5 1029 principal use of SA ee 82
rimary radar at inde e rd 09, 940 icati

Primary tide station, defined____________ 940 P a DE CS PET. 18,82

Prime meridian, defined. _------==---- 63, 941 graticule of, defined EIE 70, 927
establishment 01 gas S tooo 48 of Hipparchus EE jo T9
(See also Longitude, Meridian(s)) inverse cylindrical orthomorphie___ kāti 70

Prime vertical denned * S = e 385, 941 (See also Projection(s), transverse

findingttimeon co es. es a 526-528 Mercator)

NT

INDEX 1503
A i Page Page
Projection(s)—Continued Projection(s)—Continued

inverse Mercator, defined____________ 70, 931 rectangular, defined... 943

(See also Projection(s), transverse features OTE vh. 82 SMS. Boe "ei

Mercator La CT 77

Lambert conformal, bearings on_______ 631 secant conic, defined_________________ 80
defined A E eese sss JOR 80, 932 (See also Projection(s), conic; Pro-

TORO MA EA 70, 79-80 jection(s), Lambert conformal)

A AA A TA 0 ias SAS RR

A A EE 22 for polar regions 2.202.222 9979 86-88, 617

Dor polar regions... seas su 0€ 80, 621 cade Spe sO. a seh 78-79

radio) bearings on__-_-_-J_.29E». 80, 314 (See also Projection(s), conic)

(See also Projection(s), conic) stereographic, defined____________ 70, 82, 948
map; defined itin bw, amo 69, 935 features Or on dit av ās 83
Mercator, bearings on... 631 Origino Sesi TO ro 19

construction Of- sea ees _ Main 72-74 (See also Projection(s), polar stereographic)

o AR RCA 936 transverse conic, defined_____________

expansion of parallels and meridians_ 71 transverse cylindrical orthomorphic (see

¡EN E IA R 70-71 Projection(s), transverse Mercator)

preatieircle,.0n-.— ——. E 71, 228-231 transverse Mercator, dead reckoning

(See also Great circle(s)) equipmentiwibhisss O NE 88

originkol Sade, wayiuaiios. E acu. 21 defined Gees oibus Ye cits 74, 76, 951

rbumbliline;0n-2-5 <=. Oe 71 features of c.n I nM 76

Skil P oS ds MET 71, 103 fictitious graticule on------- 74

(See also Projection(s), cylindrical; preaticircleron ee 87

Projection(s), orthomorphic) tor polar! regions..—-—-——_ IU 76, 85, 87
modified Lambert conformal, defined _ 86, 937 principal’ uses-of + omen maman 76
féntures ofc R nog € ovotunihal toties 88 (See also Projection(s), Mercator)

great/eirclel'on.SduJ ve epos) enin 88 byYpes'OfEs res Dnm. onto 69

foripolar/regions.-- -Hani an 88 zemthaljdefined--— —-——— 0 70, 953
foh nautical charts- oeo gets 103 (See also Projection (s), azimuthal)
NAAA ENER 86, 937 (See also Chart(s), Grid(s), Plotting,

(See also Projection (s), modified Lam- Plotting sheet(s))

bert conformal) Projection-ruling machine 888
obliquedefined-Mistasagsd west als. 69 Projector, vertical, for chart construction... 888
ODIGUIN C en erea 78 Prolate spheroid, defined... ..... 1030
oblique cylindrical orthomorphic (see Prominence, solar- ------- wae SOA IO. 380

Projection(s), oblique Mercator) Proof; photo, litho, composite, and water-
oblique Mercator, defined. .... 70, 74, 76, 938 cote: of charts semen, eS. AQ 888

reatures! of ins o, 16 ROO: 76 Propeller of ship, pitch and slip of----- 130-131

fictitious graticule on... 0 74 Proper motion of celestial bodies... 366, 370

fictitious rhumb line on------------ 76 AA E Ss i A 941

greatecirclesone= =e oe au eres 77 discoyeryuol ct ss 7:2. 39

meridians and parallels on__________ 70 Ereportion, «defined...» DO 1020

fOrtpolarsregions_-AHddaviveto vatiem 85 — Eroportionaldividērs EBM I 845, 889

principalsuse ee wet | 76-77 Proportional parts 941, 1050, 1196
orthographic, defined- ----------- 704831938: Protone teta os So ee 289

features of NaH DIRA IL D 83,86. Protractor, defined-- ==. = 941

originsofec (aet pc Oren fiado: 0 0985 19 descriptiontandlusclol EM 122

principaltuse-of. tH. € Heb. Ma c 83 three-arm (see Three-arm protractor)
orthomorphic, defined---------------- 939 üselofdinplotting - 220129 SRP Ae 215

properties Ofte 4 fa. e 69 Provins, Guyot de....... — s 23
perspective, defined? 22185 L Entis 1 69, 939 ` Prutenicae, Tabulae; of Reinhold--------- 51
for plotting sheets. 1820 AL ós Æl N 807 Psychrometer sores eee ad. 0 PROA S E
polar: defined sss de gien 69, 940 defined: Ho eee d

features of various projections....... 8 Psychrometric tables----------- 779, 1190, 1191

o AA 87 for dew point, table 17_---------- 1268-1269

meridians and parallels on---------- 86 explanation jolie T DEG Ram 1191

selection off 3-28). Zou E 86-88, 617 for relative humidity, table 16----- 1266-1267

types commonly used-------------- 7,88 Pi explanation GE r A Grp

i idi eropododehlinedeecsere ae EE
M one ped end sigs. i ps a Piolemy, Claüdius ; Almagest of_ 26, 36, 38, 48, 51

(See also Projection(s), azimuthal constellations 01, te TT. SASE qs

equidistant) Cosmographia of----- E uae

: 86898 determination of longitude by.........
polar gnomonic, features of____-- = > ; idisnzof 48

(See also Projection (5), gnomonic) simple conic projection d 78
polar orthographic, spacing of parallels MOTORS eir cruris no nein 19

MA e Hms NO" S su Publication(s), for air navigation_------- 670

(See also Projection(s), orthographic) Catalog of Aeronautical Charts and
polar stereographic, features of__---- "- ,88 Publications (H.O. Pub. No. 1-V)... 96

(See also Projection (s), stereographic) Catalogs of acronautical charts and
polyconic defined T mee 70, 81, 940 Publications e cams. 96

features carie 12... obasgdied- «s 81 for electronic navigation----- os à 96
propertiesjol TA Tr 69 (See also Electronic navigation)

SE eh A AT mad 69 importancetone ĒST, 3 93

1504 INDEX
Page ie
Publication(s) —Continued Rabal, defined. .....------------------ ZE
information on Federal Aviation Agency Race, ‘defined tuos elle, 2 aay
publications S 222.222 ue e 94, 671 Racon, in air navigation_--------------- a
miscellaneous a e -3-- = = sai 101-102, 1004 chart symbol for- - -----------------
obtainingietes ss S Basis m 94 defined. ....----=--=+#+----+=------35 di
Oceanographic s-a- ra m 95-96, 1002 principles of - - --------------------- 318-329
Periodical Hee A 99 Radar....- E RE RATA 675
sources oOf___-_------ 93-94, 97-99, 1002-1004 in air navigation- -.-----------------
beam! width ss S Ze 322
terminology, of „< 345.2 EE 94 914
(See also Hydrographic Office publica- defined _-_--+--------------------=- 322
tion(s)) bearing resolution. - Eg (Pia m SCH
Publications and charts. -------------- 93-102 chart comparison unit__-------------- 96
Puddles, fresh water from... 752 charts for- - - ----------------------- 323
Pulsating current, defined- ------------- 289 clutter _-_------------------++------- Ws
Pulse, definedisoemis cetus. Gee Bases anto. 941 RE peda eise smt --------------- rev:
double, defined... 2 deb a nt 922 collision prevention by------------- m
electromagnetic, discovery of_-------- 58 corner reflector for__----------------- 942
Pulse duration, definedss 425525 std) maitas 941 defined_-_-_----.-----------------=5-- 58-59
Pulse interval, defined _ salsas amg 941 development of. - ------------------ X
Pulse length, defined._____------------- 941 frequency bands-_----=---=----+---=- 300
Pulse modulation of radio waves.. 301, 309, 941 thost-s-ss- em AE Bal
Pulse ranging, origin of________-------- 58 for harbors- - ----------------------- 220
Pulse repetition GRE) rate(s). 318, 334, 941 horizon 0f ------------------------- sia
basic, defined <tesz kas 28 HA 334, 914 ice detection by--------------------- S
specific, defined A + 11193347948 maneuveringibyeeeedire CO 325-3
Pulse separation, defined- -------------- 941 Marconi onsē=t.erssiec Isdaed BA 58
Pulse systems, development ofpe wale = 58-59 plan position indicator.......-.---- 318-320
Pulsestraingdefined "> = = M 941 (See also cous ray tube, Plan posi-
Pulse width, defined ageet TL var tion indicator
Pumice, defined sir s Hier orkadan- 109 in polar regions. .........----------z 634
Pumping, of mercurial barometer__ 766, 825, 941 HELENE 309, 940
Purbach Georges Er ipai ee 36 principles of. eu EE 318-320
issuance of first almanac__________-__- 51 TAMāTK A se ata. PE E E 323, 943
Purey-Cust, H. E.; azimuth tables of... 571 (See also Radar beacon(s))
Pyramid, description and properties of... 1026 range resolution. ..........---------z 321
Pyramid of Cheops -= -= -zentas ja 35 scope Weier: Las. fanga: dE
Pythagorasteesd wt stes cus nies 36 sea return. evoca sa lla el ee f
Pytheasvof Massalia- o a 16 secondary 4. .---. -Beuboh moter 309, 945
Parts Around the World of------------ 22 storm detection by. SS 788
tracking Dy--22=2= cepo ads t Kristi:
true motion Om. ege sue! des d) 1
Qiband' defined == 5 = 0 S 941 We air observatione by 2-89 o ts
«coilxdefineds 3-5. E D ee 204 use of, in tropical cyclone............-
deslinda of circle, defined -......-.... 1024 in weather observations. ---------- 59, 788
COMMONS Rd ss Rank 40 virtual PPI reflectoscope_------------ 324
defined eee, A E E g 941 (See also Navigational practice, Radio, i
ofiGodtrey 3 cs n E e 42 Radio propagation, Radio waves)
e AA GEET 415 Hone peaqon (8), chart symbol for.....- 112, WE
BEE e tada Ee m ee eee mea 41 e EE E a
Quadrantal correctors, defined___----.- 183, 941 principles 0f ss = es 5-9 SS 323
during magnetic treatment of ship... 2074 Radar bearing, defined. S V CEE 942
effect of permanent magnets upon... 188-189 Radar chart, experimental, publication of. 96
routine checksior e -c ca 195 Radar comparison unit, charts for_------ 324
Ke E e EE Et T 184 Renan BCE ohieciu defined------- 942
USCO ts meer << e E E ie 183 adar horizon, defined...........--..-- 942
Quadrantal deviation, defined... ........ 941 discussed. 22-22-0022 O 320
Quadrantal error, defined... ------------ 941 Radar navigation + ET C sene 323
HE DONS 150 Ruger Plotting Manual (H.O. Pub. No.
ORTadio OT Te e A 313 A A EI ee 99
Quadrantal spheres, defined..... ....... 941 Radar plotting sheet (H.O. 4665 series)... 325
(See also Quadrantal correctors) ` = Radar reflectors, on buoys__--.--.------ 265
Quadrantal spherical triangle, definition defined... 942
and solution gl ENEE 1039 Radar shadow, defined___._____________ 942
Quadrature of celestial bodies, defined... 377 Radar target, defined: 213
1 ,denneqm 3t aco en
Quadrilateral, defined_--------_=------ 1023 Radial, of omnirange. i ai 674
Quarantine report stations, sources of Radial line plot... 876
information On..-----------------.- 96 Radial motion of celestial bodies- ------- 366
Quart, conversion factors 962 Radial-line intersection method of photo-
Quick flashing light, defined____________ 941 grammetrie tilt correction- ----------- 876
interrupted, defined LSe O M 93] Radian, conversion to are units________- 959
Quilter, E. S.; sight reduction method of.. 546 defined E OE 942, 1031
Quintant DAR do o i era S EMEN 415 941 Radiant energy, defined cuia Med M eR. aaa 942
: , Radiation, defined ES eu 0914 942
of circle, defined: - -TONNE HM UNAM 1024 Radiation fo 807
Quotient, denned NETT: te EEN 1011 BA eee

Radio, chart corrections by____________- 117

As ee CC mo "I

AT

INDEX 1505

Page
Radio—Continued a5
o E A o benc 942 Radio propagation, antennas for________ 297
direction measurement by... 304-306 characteristics of, by frequency band. 298-299
distance measurement by... 308-309 classification of V mesu RT 300
early communication be... 58 critical range, of loran waves__________ 337
frequency channels Of... 299 direction mensurement. ------------ 304-306
information by.l-.. o. berg Bak, sdt 96 directional control of--+-------=----=- 307
ünterrerenoe wa MEA AA 297 Dër Lu eege maron AN A TE 295
EE Of P ===». b3520b-acbe 299 Inbenterende oa S S e el 297
Hamming Of teste eer fn. oh AS 207 ingionospherese uses. fee. MUTET 293-295
Mole causen of sed tv: UCU ge 297 JAM OL A NILS 297
receiver, components of ____________ 301-302 ofdloranwavesso.--_ cenas fe 337-338
speed measurement by_______________ 08 maximum distance of- --------------- 295
for survey timing equipment__________ 839 met, DÉCK 0 a UA A 297
(See also Antenna, lonosphere, Radio ingpolamfegiohe-|. ooh eek nee, 633
propagation, Radio waves) A A 294, 947
Radio acoustic ranging. 309 Skip zonen Use. hes O es 294
definedžrm!: e errar da 942 speedsopmem ee eee 289, 290
Brinciplos of 1105. C fes buena D. sin 316 (See also Electronics, Ionosphere, Loran,
Radio aid to navigation, defined_________ 942 Radio waves)
(See also Radio navigation, Radio- Radio propagation signals, of WWV..... 633
beacon(s)) Radio rangei ak M UARVI zale dl 59, 307, 674
(Racdiojantennāsst_ 59 no Beta) nals. 297 defined. ELC (laine geng HIRE 942
(See also Antenna) omnidirectional sede D H A 317
Radio astronomy, beginnings of... 39 principlestof Ave. o pakā 317
E AA 1.7, 5 042) Radio "sextante = el 304
determination of position by__________ 60H Radio'spectrumssse+s2eu) die M vaig, 290
RENIO bearing (S) ESE — oss 3135315" Radio stars te 1o Abe! pan age 365
coastal refraction__--_-______- fear 293, 313 discovery: of 08r jas 39
conversionangle 0222. Care ba 314 Radio station(s), chart symbol for------- 112
EMAIL AA o eM TN 942 commercial broadcasting, on charts. ... 116
Brrorspinwbeemnm. Gene c — de kp eut 313 sources of information on___-_--------- 96
bomme Dy 85 Sea palala pise alow 314 Radio time signal, defined______________ 942
land oe een A ss kadla _ a T 313 (See also Time signals)
night e ect --—-—-—----------2----- 295, 314, 937 j rt S mbol for
Biotütg ot 21 hacia sceteucyen dādzātijā "ote uiuo. a s A
(See also Plotting) Radio track, defined- -MEA 307
polarization error.............. 295, 314, 940 — Radiotrafficstations, sources of information on 96
quadrantal error- ------------------- 313 Radio transmission, classification of... 300
reciprocals, treatment of. ------------ 314 Radio waves, absorption of------------- 296
use of EE EE 314-315 amplitude of, defined- --------------- 290
(See also Radio navigation, Radio propa- Attenuation ót- es 1... bantsh o3 296
gation, Radio waves, Radiobeacon(s)) bliackoutiof "Es. s cobeodob «iki 294
Radio plackoutt ad secs B SAD VOTA 1 294, 634 characteristics of, by frequency band. 298-299
Rādiošbroadcāsts<Cenēss Ito Ye 99-100 classification Of SS v ROTER 300
(See also Radio Navigational Aids, Radio coastal refraction of--------------- 298, 313
Weather Aids) defined ev v4 sx viv ee Par 917
Radio communication, International Code critical range, of loran signals. .......- 337
of Signals, Vol. II (H.O. Pub. No. 104) defined TIREE, OS ee omma. qo 290, 942
(radio) Bae mre ALBO "sedg. ntur 96%. o ol IDU M 300
Radio compass, defined- --------------- 942 diffraction of. -----.----.-2----.--
Radio direction finder, automatic, for air direction measurement of..........- 304-306
naviention A AA A 674 directional transmission of...........- 307
defined RENS 913 ne 292
chart symbol fori- astea I 112 Te EE 295
defined” ēst y rr 2 942 loran O HAS 337
deviation of, defined "22002 922 firstiproductionko f n NT 58
first utilization of: Se se eee E 58 frequency bands El
manual defined===""= ienes 935 car eee S 322
an’ polar Fegions: OXIDE TU IU 634 e e ee nee ates aoe E 290
principles of Te 208 200094 SOLE ZA 313 grazing Angl eTO T e o eee 291
upper air observations by-- ---------- 785 ground waves, defined_____-------- 294, 928
Radio direction finder station (s), defined. 942 ARE e y A cae e 337-338
functions of------- ------------------ 313 horizonšof ARS F Me la 292
sources of information 0n...........-- 96 interference Oiana o. a i one FE
Radio frequency, defined--------------- 942 indionospherc ee Ce m es eee F
Rø dio. Bar 255; GE CM AIR AR 942 in polar regions_------------------ 633
discussed TE A EE 292 land effoct see e AS + TOA 293, 313
Radio navigation, defined. .. ---------- 62, 942 EES SE
(See also Electronic navigation) magnetic field of... Ioue 289-2
4 Kap Aids (H.O. Pub. No. during magnetic storms. ----------- 294, 633
Radio Navigational Aids (H.O. 316 maximum usable frequency of........- 294
I), consol tables in- - - - ------ 96, 304 313 MICLOWA VES i See a 291
ane ds DEDECUS oo uenti modula onol acc... SE a
corrections tO----- SS ore a Dightfefrect of ee eee = 295, ,
information on radio broadcasts in----- n paths ot MOERS se 294—295

publication of-----------------------

1 506 INDEX
Page 3 Page
i — Continued Range(s)— Continue
i iet > šu Lu SOL AS OES EE 290 of tide—Continued

polarization of. .___--------------.-- 291 relation to current speed -- - -------- 715

polarization error of- ---------- 295, 314, 940 variations in---------------------- 706

propagation of, in polar regions. - - - - - - - 633 tropic, defined... 294 DPTO 951

Speed Of eee MEE 289, 290, 308 use of __._------------------------ 241-243
(See also Radio propagation) Ofvisibility, definedseceec ee SES 943

Tango Mosen = 295, 298 ENEE deer 308, 674

reflection Ofes ere SE Z 291-292 Range finder, defined. ----------------- 943

refraction ols Sessa Udo Een SEE 202 Range lights, defined... ===. «Loma 943

representation of-.-..-----------2--27 290 Ranging, pulse------------------------ 58

EE 296 radio acoustic, defined. - ------------- 942

SENSCIOL rean ae an APA ee 305 principles A ese 316

Skip idistance of Att a IS ee 294,947 Rankine Ls eee defined. ....... 776, 943

sky waves; defined- ---------------- 294, 947 Raob, defined...-.-------------------- 787

otlórandveek- ar MA 337-338 Rapid Navigation Tables, of Myerscough

SOUufrceofeene ier tm tee A 289 and Hamilton: 22==.». = ence Aes 536

Speed OA 289, 290, 308 Rate, of chronometer, defined..........- 916

Supenrtefractioniofis ss = 292 (See also Chronometer)

terminology Olesen E 290-291 offoran; definedact See eee ase tee S 335

transmitter for AS aer 301 (See also Loran)

(See also Electronics, Loran, Magnetic Of:watēlit is ee d 419, 952

field, Radio propagation) „(See also Watch)
Radio Weather Aids (H.O. Pub. No. 118), Ratio,defined.:--......---- IOS BOSS 1020
contents < as AS 97, 304, 817 òf ranges, definede-_< dec LES 943

corrections tor- Ē SENĀ ono PM 97 Ofirise; defined = EE 943

information on radio broadcasts in. .... 100 Rational horizon, defined..............- 943
Radioactivity of sea water-------------- 698 diseissedz 25244208 58: TON MN 386
Radiobeacon(s e cc = ee 313 Ráwin$definedzci55.---——— ea 787

on buoyss5es3n3 JOSS es Made UO oma 265! Rawinsonde, defined___. 2 =- EE TS 787

chart symbolfors i Mae DAS 112 RáydistL:..--.----———-—2--tect ee E 309

defined r tt: gu. meas es 942 development of.---- 2 ES EA 59

first installationrof OBE EN 58 hyperbolic, principles of rc 346

information on, sources of- _----------- 96, 97 pure range, principles of------------ 309, 330

inmpolarsregionse erc c 6300 Read; Natbanc-"-.----——— ccc c 3

NEE 307 Réaumur temperature, defined........ 775, 943
Radiolaria, defined E 109 Reciprocal, of number. ....---------2--- 1007
Radiosonde, defined. .................- 942 Ofivectori M ... casts osu OMEN DENS IN 1017

describeds-i4 iesist ein trios is 787 Reciprocal bearings, treatment of____---- 314

upper air observations by... ........- 785 Recording tide gage, automatic, portable. 843
Radius, of circle, defined. .............- 1024 Stándard 02.2 0 E AN 844

olusphere defined 22-222 Æ eee 1029 Rectangle defined Si uses Ee 1024

of visibility, defined -as =e sees 943 Rectangular coordinates, defined. ------- 1031
Radius vector, defined. ---------------- 1031 Rectangular error O 682

of planetary orbits_----_------------- 354 Rectangular projection, defined. -------- 943
Radomerdefined-.--=.-2== -t¢ 5-2 e å 943 (See also Projection (s)) Å
e x EE 2 2 ip 347 Rectified altitude, defined____..------ 437, 943
Rafting of sea ice. Lp asai eel 750 Recurrence rate, pulse, defined__________ 941
Railroads: on chars 114 (See also Loran)

Ramigage recording == c 788 “Red Azimuth Tables" (H.O. Pub. No.

(See also Precipitation gage) 260) Ste CERRO - E A 97, 569, 943
Rainbows, types of=--1 5 ee eens 810 extracts romo HS 1165-1167
RámwWof'ice-stmE 40-44 eee E 748 Red magnetism, defined. ............... 943
Ramgark? defined as ss Ls ee 043 Redisector defined- 1 A ees 943

principles: ofre 5 2022 ae cM 323 Reduction defined au c 943

(See also Radar beacon (s)) Reduction methods, for chart construc-
Random error, defined. ---------------- 943 tion (8 EORR 891

discussed ee oe ads 680-682 Reduction to meridian- 22 518
Range(s), chart symbol for. ............ 113 defined. eet deseas IA 943

critical eet eet, Zeene 919 device for, of Vilkitskiy_-------:-----. 518

defined RRE E e 943 (See also Altitude factor)

OUT COUTO SES SSS TOM eee eee er ME 317 Reed horn, as fog signal, defined- ------- 267

geographic, defined Tnm 926 Reference direction -----:------------- 66, 134

OË e He cometes En steep: 261-264 (See also Direction)

on char ege 263-264 Reference station, current predictions for. 273
(See also Light(s)) defin Ee 943

objects dh Me" se a NES 241 tide predictions fors eem MC 269

rádio defined: setae Ee 7 942 of itiderta bles TAn mið met ee eee 269, 711

ofradio'signals= < SPa sa ss 295, 298 Reflection, angle of__--..-.---------- 398, 430

Se .— E EE 943 of radiouwaves ars ape eee A 291-292

resolution of, radar. 321 E underwater sound” SU S 744

Ooftidecomputātionrof (0! JEM 270 e a "S gt ned SS 205

defined = aaa ee s. => zs In 704, 943 O ll RS IE SET? 942
defined. -- , Reflectoscope, chart comparison unit... . 324
inipilotingeweseess- n 207 Reflex angle, defined------------i------ 1021

INDEX

Page

Refraction, abnormalities of... 431-432
altitude corrections for... 429-432
orrors in tables teere fe 431, 432
fromslifebonts- e o si 657
astronomical, defined ______________ 430, 912
atmospheric, defined............... 430, 912
Coastal, definteds tes < sakari 917
obiradio Waves latas. See 293, 313
defined ie LEA a M sk eras 943
erect Ofuponrdip. Ee ee te 423
effect of various conditions upon____ 431-432
bouzontalbdefüned- santa a 431
Index otis sl: uzdodu ban skon 430
Meana OLN Cds EE he 430
Oboceantwaves dl Jalan d nasa bi s 731, 737
Ka polāršregionss «des -__Jabedies 637
Of radioiwavefsiikdatas nt mill a L urnas 292

terrestrial; defined tame Jamal unu 430, 949
emechiol upon AiD- = eae asalvo: 4
effect of temperature upon__-_-_------

IEDeorydgof-. s PAD hes 429—430

otjunderwater/sounde------.-.- etx 745
Refractive index, of sea water----------- 698
Regiment of the Pole Star, The; of Wakeley. 568
Regimento do estrolabio e do quadrante_ __- 32
IKievioinontanus. - eo an ee ene 36

issuance of first ephemeris_----------- 51

DALIA distance: eee aa 45

Nuremberg Observatory--------=====-- 49
Register ton, conversion factors--------- 962
Repression of nodes.-------20 24 uz sia 377
Regular polygon, defined_-------------- 1023
Resulsariprism, defined 2 v e 1025
Regular pyramid, deine 9 UxL 1026

Reinhold, Erasmus; Tabulae Prutenicae of . 51
Relative accuracy, defned
Relative azimuth, defined. .............
Relative bearing, defined---------- 67, 241, 943

reterencejdirectjionof-------——— see 134
(See also Bearing(s))
Relative humidity, defined............ 778, 944
pablo M 3e 1266-1267
explanation ois TENITA tus SCR 1190
Relative movement, defined- ----------- 944
directionxotee erase eme 326
principles of ** — 2807 991o1n ct eere 325-329
Relative movement line, defined--------- 325
Relative precision, defined... ........... 1006
Relative speed, vector of. 327
Relativity; theory ofito.: Sr Munn. 39, 355
(ieliet tonichartss 5522. eee IE 114
CIRIE da si es EEN eT e 944
Remainder<defined.- 0-2 Møn x xu 1011
Remanences'definedss==-==- En 3⁄4 159
(See also Magnetism)
Remote-indicating compass, defined. - - - - 944
Repeater, compass, defined. ------------ 918
defined. DEE, ANUM DY + (LV Á. 944
EE E 929
described ene MELOS Se 153
Of Pitot-static loger == «P2 130
Ol TACAT SCODC ssa ees rec ee nau 319
Steering” Celine aes ses ae E 948
Repeating decimal, notation for........- 1011
Repeating, theodoliter co eer ect 840
Repetition rate, pulse, defined..........- 941
(See also Loran)
Reprint ot chart denned e S:TA 888
Reproduction of charts, processes for----- 897
Requisue fables, of Davis 57, 528
Resection method of visual survey control. 858
Residual deviation, defined - ------------ 944
RESOLUTLONM ORO CATIN Dare ae re E NE 322
efi de NM eee E 944

Oia ses PD < ease 321

1507
Page
Resultant, of vector additon. 1017
Retentivity., e 159
(See also Magnetism) ;
Retired line of position, defined_________ 944
Retrace, of cathode ray tube____________ 303
defined E aldo de a ee 944
on$lonansscopes =s E 335
Retrograde motion, defined--_--------.- 944
Qf planetar ce ee edet. E 377
“Reversal? method, for securing de-
gausime- toils: vv mi eeu y 206
Reversing current -e-n bah 5 EE 712
Revolution, of celestial body, defined... 353
Of moons dr EC EC e me ka 362
sidereal» defined 3. Fx atar da Rn 353
sybodicsdefnedses eee 353
Revolution counter, origin of____________ 25
speedoDy Ea ta sekos S 4x. gadā 3 130—131
Rhomboid defined “boss. bare 8 1024
kHhombūsydetinedeimes. ae < alu ms 1024
Rhumb bearing, defined sa eee re 944
Fhbumbrieourse defined. == =e 944
Rhumb direction, for dead reckoning
equipmentidXxWc Hem. i 88
Kambing defined s E 66, 944
neotitioussdeiined snus eg E 76, 925
ORnNpolan EIE e ac a ae 618
On Mercator projection: ee sana 71
onmautical charts. c E 228
plobtingtopm TANE S te ée 215
owpolarnc harta ee EE 620
Rhumb line distance, defined. ---------- 944
Richer, Jean Francisco; computer of... 558
Ridgefüse ofin piloting- b sese = 258
Richtranele defined = a t 1021
Right ascension, change of in almanac- . - 52
le e EE 916
defined sites EA E nm 383, 944
fnndinebyralmanac i Hr 479
precession of equinox In... 373
Richt conerdenned -nan E ee 1027
Rightieylinder defined e. 9 rut 1026
Rightainesidefined -e-n eee 1020
Right plane triangle, solution of--------- 1037
Rughtiprismwdefinedi* Ae Tan E 1025
Right/pyramid denned ERN 1026
Right spheres SPSS YO aar deja 367
Right spherical triangle, solution of_----- 1039
Rightatriangle, defined]. A T 1022
Rip curenti- Torana fare ata T lo ae 740
(See also Tide rip)
Ripples! defined 2&3 osas Meer 727
Riseotstides defined: BON A JE 944
Road$on'ēharts I-an eae enm 114
Road pen, for chart construction. ------- 890
Roaring forties se ee EET 798
Robertson, John; Elements of Navigation di
A Ee exe caesis oc ERE AH ES
Rockefeller General Education Board. ... 51
Rocking the sextant, defined.......... 402, 944
Rocks, reefs, etc.; chart symbols for. - - - - 110
Rodmeter, of impeller-type log... ......- 130
Of Prtobssuaticdogeeertoccm t ee 128
Rollet del'Isle, sight reduction diagram of. 557
Rolling resistance of beach. ...........- 740

Romansmilesorigin-olss-= 22s 26

Romanovsky, A. A.; azimuth diagram of. 572
Romer, invention of transit instrument So
Root, extraction of, defined............. 1012

Root mean square errors. mm 681
Rose, G.; sight reduction tables of------ £
Rossa, Battista Testa; Brieve Compendio

del Ante del Navigar Ole OE 22
RosseMcurrent sm EE

1508
Page
Rotary current, defined. --------------- 944
Fal ege eee ON
inequalities of----------------------- 713
Rotascopo rn eee eee 24, 141
Rotating beacon----------------------- 307
Rotation, of celestial body, defined. - - --- 353
Of moon ae d M 362
sidereal, defined_-------------------- 353
synodic, defined...........---------- 353
Rottentice=s= see ee ee eee 752
Rough log, origin of. ------------------ 29
Round of sights, defined--_------------ 455, 944
Rounding off, procedure for___---------- 1007
Route, selection of, in lifeboat- - - ------- 648
Routes in North Atantie 755-757
Routers cateo EU 22
Rude, Gilbert T.; star finder of___------- 586
Rudolphine Tables, of Kepler et al_------- 51
Rules of the road, area limits on charts. - 116
Rules of the Road—International— Inland. 102
Rules of the Road—Western Rivers------ 102
Running fix, from bearings. - --------- 249-255
from celestial observations. --------- 458-460
ere AA ee a eee 944
effect of current upon-_-_------------ 249-254
(See also Fix)
Running survey, procedure for__-_------ 864
Rust, Armistead; azimuth diagram of... _ 572
sight reduction tables of_------------ 57, 525
Rutters utero c cR DE 22
S-band «defined EE 944
Sadler, D. H.; sight reduction method of-- 545
Sailing (s), composite, defined.......... 221, 918
example 022300 oso eee wo 235
defined HE nUn ni! m. oss ELS 221, 944
great-circle, altering track___--------- 235
pykchart -oe ss gs eoe a 230
by computation------ 222582522 22 232-234
by conversion angle------#--------- 231
defined ess een MEINES cm 221, 927
diseusseds-—-.-— . etaed c 22
examplejog$-5$—5- .-.. ms 232-234
final.course-3e0d*ottuioE nc ās 231
geographical position, destination as. 232
listoryaof-cc 22... Sk om 30
LOUIS 231
onfpolarchart AA 620-621
byātāble: taa See 234-235
tables of Towson and Atherton...... 569
worksform SOT ó ee 1053
historyaO[m- e US MET 29
Mercator, Caution. = EEE 228
defined sa 5-0 =. nep v 936
discussed etenam e 221
exampl of so. €. e IAE 227
origin Of ar Æ 9e eee WE E n 30
worksforms for e ns ee 1053
meridian tdefined s 12 NS 221, 936
middle-(mid-)latitude, caution_________ 227
defined. 3 seduce dada setos de 221, 936
example of- 35i e c S 225-227
Origin of.:s.55..—-. . e deep ed 30
parallel ¿defined eee c 221, 939
early importance O IES 44
example offers des Si 224
Origin (Ofiss cle T race da X. EE 30
planējšicautions? {2.24.2 re 223
defincd e E ÓN 940
discussed). te: Es IB Id ye eee 221
exaumnpiefoi 6: see cce EE 222
history? ole EE. sal n ec 29
quantities used in, defined... .. 221
spherical defined X 948

INDEX

Page

Sailing (s) —Continued
traverse, defined. - - --------------- 221, 951
example of == Aa a 223
het 29

(See also Dead reckoning)

Sailing chart, defined. - ---------------- 944
description of__--------------------- 104
Sailing direction(s), contents of.--------- 97
corrections to, in Notice to Mariners... - 99
defined es diseetssiesss RJ 944
history of EE 16, 18. 22-23
for polar regions--------------------- 632
supplements and changes to. - -------- 97
St) Elmo's fire-= e85 se DE 297, 813

St.-Hilaire, Marcg; celestial line of posi-
tion, methodiofe- e MEM 56, 528, 944
Saint-Pierre, Le Sieur de; establishment of
Greenwich Royal Observatory - - - ----- 50

Salinity of sea water. 695
Same name, defined. ........-.-------- 944
SantatAna«wind)seec-- XEM 807
Sargasso Sea_...---------+--55-4-=--=- 722
Saros, eclipse cycle- ------------------- 381
Satellites of planets____..-.---------=-- 357
Saturation, magnetic, defined. ---------- 158
Saturn, features, of___.--.------ S 361
Satyricon, of Copella. - -----===========- 36
Scalar defined z-a- eunana MEE 944, 1016
Scale, on azimuthal equidistant projection 83
chart classificationiby: 23252225" ue 104
on conic projection- == == =e 79
conversion factors for---------------- 955
defined seb obs sast ee 103, 944
as factor in projection selection... ...- 88
on gnomonic projection. - - ----------- 82
graphic, of charts... eto bet we gaga 103, 893
on Mercator Grolection. 71, 103
on modified Lambert conformal pro-
jection 2.5. da „ tøsd ða eee eee 88
natural, of, charts. ere Ee 103
defined +2 o EvR 937
numerical ofichartso SS ee 103
of plotting sheet for hydrographic survey 859
on polyconic projection. ---_--------- 81
small, defined. ss - 252-46 --- ea MO EU
on stereographic projection- ---------- 83.
suitability Of 31-5453. Ani! derent 106
Scale border, use of on charts. ---------- 893

Scale error, on polar stereographic pro-
jection, reduction ofa. í LEskeðbali NE 88

Scalene triangle, defined---------------- 1022
Scatter of radio waves- CE mmm 296
Scattering layer, deep---------------- 134, 744
Scheduled shooting: EE 675
Schist, defined 7522 `". erbe p e 108

Schoner, Johannes. eesti ES 17

Schroeder, Seaton; azimuth tables of----- 569
Schuler, Ivan; pendulum studies of__----- 150
Seintillation of stár. A 575
Scoopfish, bottom sampler.............- 842
Scope, defined. 225. to Os 945
principles Of ea AS sc 302
(See also Oscilloscope, Radar)
Scoria, defined. Sēde + a = 109
Screw, pitch and slip of- ee s 130-131
Scripps Institution of Oceanography, Cal-
ifornia. esee SS TETUER 92, 694
Seylax, Periplus 0f -a E eee ee 16, 22
Sea, appearance of, under various wind
speeds s= 9. ere e 774
color of pasisign of, land 26 EE 661
and:winds ed de E Ger? 773-775

(See also Ocean current(s), Oceanography,
Sea water, Wind)

INDEX 1509
Page

Sea anchor, defined____________________ 045. 9Seichenustiho ev. £ e

pra and Swell Observations (H.O. Pub. No. Seismic sea wave.................... 833, 945

zd "Mag BØ Sé 96, 152 8 UM der Of cse a MUL OU ONT 733

iS COR sae nn EDU CH electivity of radio receiver------------- 301

See buoy “defined RES VL 945 “Self-acting Sounder”___---------------- 27

NI ga A ODD 746-762 Self-synchronous alidade, defined........ 153
bending, rafting, tenting of... 760°. Semicircle sk sarsa oco emer 1024
AN rr s JUMS: (T 945 dangerous and navigable, of tropical
Tormation'o so roses s QUO. [T 748 cy clone?? Aula LANES. epu. ve 828
ee ra from ME 752 Semicircular deviation, defined........ 174, 945
: ja EE A er ic Er ded o pa correction for... 433-434
BUG rd rom lifeboat-:..-----.---- 2m 0e 657
thickness 'of Seege QU 23T 750 f circle, defi

Sea level, defined_________________-_-_- 945 of sphere, tt Age „bocieb. 35d 1029
means defined 3 €. VI 710, 935 of sun and moon, by almanac. jos unalo 0479

Goy EF Pee defined = Re VE ep Eri er defined "e age 22 ler 945

eNdeninedessmon 0I MU M. emidiurnal Tu ——

Sea quadrant, invention sinea un. pm 41 Imera kr [A 5, LASS eS. Zn 945

Bea return defined: dem» nma ner 320,045 Semidiurnal tide--======*======<. Jl 11.37 5, 945

Sea Toom defined). Studien. graph do 945 Semimajor (semiminor) axis of ellipse___- 1027

RES LEE SS EE Dem 614, 808 Bens highs and lows.......... 799

ee also Frost smoke enso defined 222223. cea TIE LA BUE 945

Sea state codes, and Beaufort scale______ 1059 Sense antenna...-.----------------- 305, 945
(See also Weather observations) Sensible horizon, defined. -------------- 945

Sea tilt, altitude correction for__------ 426, 945 discussed. - - - ------ PS SS 386

Sea water, analyses of, by Dittmar...... 69 Sensitivity of radio receiver.------------ 301
chemical properties Of_--_---------- 693-695 September equinox- ------------------- 373
compressibility of.______----__------ 697 Set of current, in celestial dis tri 461
condneUyatv Olas. bet fb 698 defined----------------------- EET 127045
density of... 696 Seven-eighths rule------------------- 255, 945
E a vu uiis See aa qe 255, 945
E QUIET ESAE Tx Dea a 062 even-thirds rule. ....... JEU RS SEE 255, 945
physical properties of -222 -2 2 695-699 Sexagesimal system of units, defined. .... 1031

: Sextant, adjustment of--------------- 411-415
testing methods for - = 693 e
: altitude: by 2... 2049-1102 103 402-409
thermal expansion of____------------- 698 : :
(See also Sextant altitude correction(s))
dE c < 696, 743
: ? arc of defined... Caotbseen. Se 400
totalspressurejoi S TTT T K EC - 128 neal hori t 416-41
Sea-air temperature difference correction, e O l 5
AE EE i „MAJA ANVI 945 altitude corrections for-------------- 437
for sextant altitudes---_------------ 424—425 ewen SE S

Sea-mans Practice, The; of Norwood. -_---- 34

Seaman’s Secrets, The; of Davis... 34, 41, 43, 48 di of Mott. fede aah Ut rp

Seamark defined si- -s-ben tug Tue 25 : 945 ādkubmarine eater qoxisod Ludo Mt 609

Seamount, defined--------------------- 945 use Of at.sea.-.- Flia aldeas 417-418
use of in piloting: es als 24-26 eeng 258 “ball recording” type_--------------- 422

Seaquake, waves from_______----------- 733 bubble type, development of---------- 42

Seasonal current, defined. ..........---- 718 principles of... ard tette na 416—418

Seasons, causes SR Be framed 371 (See also Sextant, artificial horizon

Eee nels defined EOS UE VUES RED n type)

eaway, defined- 44282528 = deos 45 CM Poco hee GR EE? 409

Secant, of circle, dene. 1025 eg defined. EE 1024

pf ana definedal 35 sastdsst Tak 199 corrections to (see Sextant, errors of) aes
Bele éso Se = eebe defined eeepc rote ee

Secant cone, defined- ------------------ 70 description of -aeea a 399-401

Secant conic projection (see Projection (s)) tege Of äeren bray dd S reine 411-415

Secant Time Sight, of Weems------------ 526 acceleration. so 417

Secchi disks «d^ FMS UU USS 699 adjustable" EE 412-415

Second, unit of are ------------------- 1031 eege jen
unit of time ne ae We tie leans tratte 484 collimation E Ss CU SA pr L

: @ TAC UAL] Oa EEE ee 411

Secondary, great circle as--------------- 1029 horizon glass +2 ak 412-413

eng St radar_--_------------------- n indexes M aene Stai "uin

efined as N l a sb nde MITT OLS es E je

Secondary tide station, defined. .....--.- 945 instrumento 2: oso ee 412, 421

y)

SECOND Eus ecc XH 945 nonadjustable zas pee les as E 411
of circle, defined- < 522 see 1024 prismatic T Ec TEE te
of lights, definition and chart symbol ghade poo EE ege E? 413

A ee ee a aa ae 113 m BEE bi iB inner ccce 414
Ne UK quB E EE ce Tosti D. 3 10422

Sectored light, defined- - --------------- 945 (See also Sextant altitude correction(s))

Secular, defined -- --------------------- 945 LEE e vra sasa inai iru 400

Sediment, of oceans_------------------- 700 gyro defined a -s =- 8005 929

Segment of circle, defined. - - - ---------- 1025 history A C ery s 39-43

1510 INDEX
Page Page
Sextant—Continued Sextant altitude correction(s)—Continued
horizontal angles Dy- 222 SS == 245 for refraction- ------------------- 429-432
corrections for 2 ss 446 errors in tables == en 431, 432
index correction sees 414, 421, 657 from lifeboat_--------------------- 657
instrument correction_------------- 412, 421 modifying factors.......----------- 431
for land navigation- eds esr 669 (See also Refraction) .
Ne ee ee ne ee S 935 for sea-air temperature difference.... 424-425
altitude corrections for_------------ 437 for semidiameter. - ---------------- 433-434
(See also Sextant altitude correc- from lifeboat-.- — .-- Se: ra 657
tion(s)) A A A 441
micrometer drum, defined. --------- 936 summaryiol. ` ae A 436
described 2. sā ed st 399—401 for sun. = eee 439
principles of = A 398 tide corrections naaa cM Saa 426
vernier, defined; - 222.2 sas 952 for tilt; of se = S M 426
clamp screw type-----.-------- 401, 917 of: sextant- 5 masē ds Atis tāsi 422
endless tangent screw type------- 401 for wave height. = - so Eege 425, 953
TACIO Nn ee E Eee eee 304 work forms ford SS oe 10
reading thessi- a ros ES 405 (See also Air Almanac, The; American
rocking the se. = sa se E 402, 944 Nautical Almanac, The; Navigational
selection olen la- Se E len eee zel 415 errors)
surveying, defined- S esxs-=- esu 949 Sextant error, defined. .........-------- 946
Swinging the aro rocoso 402,949 Shade, defined-------- īss gem Sgr 946
usesof, acquiring skill... saad 407 Shade error, defined__----+---.-------- 946
for back sight: n 404 OR EE 411
fordowcalütudes- 2... naaa 442-445 Shade glass, defined. ...---.----------- 946
for moon- = E 403 Olisextāanistrzse ZV BS ee 400
personal error in A 408 Shadow, of radio waves. .------------ 295-296
for starorplanet=eses ses" WIL qe 403-404 of underwater sound- Tras 347
GE ee 608 Shadow zone of underwater sound__----- 745
er TE ee eg ee ees 402 Shchetkin, N. O.; sight reduction method
(See also Bubble sextant, Lifeboat Of. 220733 Æl umen o reU ae MER 555
navigation, Navigational practice) Shearme, F. N.; sight reduction tables of. . 534
Sextant adjustment, defined. ----------- 946 Shelf, continental (insular) - - - -------- 1, 699
Sextant altitude, defined. ........ 402, 421, 946 ice shelf mean SP ES 613
plotting of for accuracy check_-------- Shelf ices sect t ee > AA 748
(See also Altitude) Shielding factor, for compass location. - - - 182
Sextant altitude correction (s)--------- 421-448 definedz ccce ceo E 946
foraeccelerationc- "eb 428. Shingle; defined ste ss eee 108
for air temperature_.__.----------- 432, 909 Ship heading marker, defined. .......... 946
table 99m. cota. reo ponlo. ehe vet 1980 . Ship logs seta qe e ÓN 25
explanation Of -ae P 1192 Ship sheet for hydrographic survey ------ 859
by almanac, Air Almanac-------- 439 Sbip's head, defined TES pases 946
NauncalAlmande z a A 438 Ship's inertial navigation system (SINS). 608
for artificial-horizon sextant........ 436,437 “Ship-shore'” method of visual survey
for atmospheric pressure____-_-_------- 432 tontīroli ass 2—22-22224, D DB ant 858
table,;24 F cua mem eir 1281 Shoal, use of, in plotting- E 258
explanation lol eme 1109 Shooting:star=- <> 3 se: TOME MINE A 365
forradugmentation...-..-...--Ereweges 494 Shoran, defined n-a neuen PAN 946
for back 'sights MANT- -CEN salsu e 445 development. of. c TO NUS 59
computation'of,-moon= 23 ——= eee 440 principles:0f ssi vol >: sasar 90091 93 330
planetsi= meg o o aoe 441 Shoreline sheet for hydrographic survey_- 859
A n ad I. e I. 441 Short, Accurate, and Comprehensive Al-
puns E A ld AY 439 titude-Azimuth Tables; of Johnson... 570
for Coriolis. force ee 428 “Short” methods of sight reduction,
Celine ater reo o MR TA 946 historieal..:.:-2222-.-- 30 SP A 56-57
for deflection of the vertical_ --------- 427 Short ton, conversion factors____________ 958
for: dip ee os oa acierto a ae 422-426 Short-distance navigation, defined___-_-_-- 946
shortíofshorizon ss eee 9 424 Short-long flashing light, defined________ 946
table 22252-24504 Soa ic JE 1278-1279 Short-range navigation, defined_________ 946
explanation of accen T 1192 Shortrede, Robert; azimuth tables of_____ 569
for height of egenen 422-426 Side of triangle, defined- --------------- 1022
for "index. errors 22200 ANS 421 Sidelertor defined SS 946
fortinstrūnient. elfOf neie EE 421 Ofsextant e e" 413
forsirtadiationc2. mano 2 MEDIO A 433 Sidereal, defined. =a 946
in lifeboat navigation. ---------=-2--- 657 Sidereal day uc Set PO DUO 375, 483
for low-altitude sights_------------- 442-445 defined... 22. 28 Oeeososmtepbē do ` 946
foraomarincfsexstant s =e Ara 436, 437 Sidereal hour ang css 383
with artificial horizon. 200 436, 437 defined os es «ra e LE
a A A MR ME 440 Sidereal month, of moon... 362
order of application. ooo ee 437 Biderealnoon- s. s a e ON 483
for paralar cens Ee A 435-436 _ Sidereal revolution and rotation, defined. 353
fromslitepoa tae naaa A 657 Sidereal time --------------.- 375, 482, 496, 946
for personal errors. EE 422 Greenwich, defined. 22 , 928
2 local,.defined ēka < sa BEER EE 497, 934
phase DOE EE 434 reference for E 2 375
for planetss2s?s? S A 441: Sidereal year SE V S

INDEX 1511

Page

Sigeum in the Troad, early lighthouse at__ 28 Sight reduction—Continued
iene (8), Defined. es esse pens Me eks 946 graphical method, of Baker... 562
Sight reduction EEN 502-516, 946 Old bentinss s m coc E 557
imainnavigationt = ee 675 Ol CONSTAN S = 7 e OT AS e 557
altitude curve method, of Baker... —— 562 of diOcagnest: = cet load 325 555-557
DO Seegen DA 561 of Favé and Rollet de VIsle_____._.. 557
obs Br gadi L RO is dis 564 OL Jernms c ag ES NA 557
E EE ER 563 Of, Littiehs les o o. loo ete le 557
0f-Dusinberretióna £f. aa Loi sa 564 Of, Mereire edu e ao te 557
MINA ARA El MAYER 563 OL WIN Peris e dm. 1 se e 556-557
(JM EE Ea 564 (See also Sight reduction, altitude
ob Lelok AAA A epos 563 curve method)
of, Littlehalesse dls lau bøna sl hos 564 great-circle intercept method, of Pierce. 555
oli Longley set Air deuh M 9 562 high-altitude method- ------------- 513-514
of Pritchard and Lamplough ESTAT 562 defined te 322 o e to 930
of Voigt (“Orion’ ERRE CTE Ns Sh toes 564 inspection tables, of Ashton___________ 545
(et KANTON ad 564 British Air Pub. 1618. ------.------ 540
of Weems, “Polar Computer” ------- 563 Experimental Air Navigation Tables. 545
Star Altitude Curves- 562 OisHoehnet ts. 4 SE 541
(See also Sight reduction, graphical Hohentafeln nach Ke Seene Zeiss 541
method) HO $Pubš No 243 "PN 540
altitude methods "oc 302 to... Js 528-546 H.O. Pub. No. 218 E ta C 540
perpendicular from body, of Ageton__ 538 H.O. Pub. No. 230 (Goetz) --------- 542
OFA QUINO ce = eo eee e 537 H-OxDubsNoj2405e cee 542-545
of Fontoura da Costa and Pen- of Japanese Hydrographic Office... 541
teadoces- Sire. aletas n 539 of Ménéclier and Chevalier. ........ 541
ORE SÉ E aM ii 537 latitude method(s), by meridian altitude. 517-821
ofoHickerson-3--t. herido 539 byiPolāriss 25 eat ars ae 521-523
H.O. Pub. No. 209 (Pierce)....... 538 in Rebeet 658
H.O. Pub. No. 211 (Ageton)...... 538 longitude.method (s) mete Ee 523—526
of Japanese Hydrographic Office. 539 GË Te KE but 525
(e TE EE B 538 of ¿Cassini Y e o 524
GEST a ll scere 539 OfsDawvis e Ito at S PX 525
USE lee K ee 539 ofeCioOo d Win «bom wees EE 526
perpendicular from zenith, of Ageton.. 536 ofsklommeyec- d$ oec a= see 524
of Benest and Timberlake... .... 536 H.O. Pubs Nos. 203, 204 ....... 526
Ole Bertin® TE o ee EE 533 ofyLalandecm co ene 524
Oba OLN eee EE e el 536 ofiLitilehales- ss Er EE 526
OtGomrie t" vēls A 536 on Gynnes o s e 524
of Germans NEE bke===-8 536 ofi Marielli le a ke SE 524
Ot Gingrichs. ELLE 535 of Rust: 1-38 A D 525
HO Pub. No. 208 (Dreisonstok) - - 534 of Soule and Dreisonstok........... 526
of Italian Navy Hydrographic of Thomson (Lord Kelvin)......... 524
ES sees. g Mes = 537 Ae E 4 e 526
of Myerscough and Hamilton..... 536 low4alüitude-s---—---——— e ll 511—512
OnENcCwtonsand Finto n crae 534 use of H.O. Pub. No. 214 for ....... 6037
Of O PUT 8 ==... stat Ee. 534 map projection method, of Brown-
of Smart and Shearme. -_--------- 534 Nassau e eee Coa ee S 560
otesouillagouet- preto ea 57, 533 OfMHvabu-e ces coe E LS TE EM 560
of Weems, Line of Position Book... 534 of-Litilehāalesše s Fa e € 560
New Line of Position Tables___-- 536 of Pierce 3-2. 68 se ea local go 561
triangle not divided, of Ball........ 529 Ree 561
olā DIS GA E se ee 530 NET SSS DEE 560
ofi liess ah ocaso dose 531 mechanical method, of Bertin___------ 559
Ol Avis A Ë 528, 529 ofiBy ara vete 2 do E 559
Të Ke E, vibus 532 desk'computers:= = -- ada === === 560
Gelee emet SKT n TES sia 531 ota esor e m E 560
HOT Pub No: UE 530 ofiPoor mass 7 oe a eee 558
of Japanese Hydrographic Office--- 530 one-body method, of Willis--------- 551-554
OL Rose ar be ee 532 in polar regions, methods of. ......... 637
o Wallets PE are er lege GN position determination_-------------- 547
triangles other than navigational tri- preliminary computation - --------- DULCE
Bile. vob K otlarien ege 539 sphere method, of Hiltner...........- 565
azimuth difference method, of Quilter__ 546 of Japanese Navy n RO æ E queis t SE
Aziiouthmethodsde cs: cssc cer 546 pi Melen ay USN)... BE
common tangent method, of Benest e E Device Center ( )--- 565
and Timberlake 2 wee c Rz 536 d Z Dr EE tel AA Ze 566
computing sextant method, of Bedell.. 566 GI PS ieber pi C 48
a Beehler RRA o EE IA v 566 three-body method, of de Jonge------- 5
oføHagnerð F = sd eec ec = ME 566 two-body method, of Dozier.......- 548—549
cosine-haversine method, of Davis----- 528 of Por E 548
Workiform for ð cepas San mete 1056 of#Kotlarie e ete orici 550

double altitude method. ............- 546 on Uribe: Whites ss ke 7 550

1512 INDEX
Page Page
Sight reduction—Continued Slide rule—Continued
two-body method-same altitude, of description of _---------------------- 1015
Collins erre sete eee 555 nautica K Á sa ce cientes y BOSE 125
of later deet? 555 of Poor ds ii eee MOB RE 558
two-body method-same azimuth, of Sling psychrometer -------------------- 779
Colas ene ener nea = 555 Slip of ship’s screw- ----------------- 130-131
of Mc Keēstertesstkaness 288 10393 555 Slope, continental (insular) ------------- 7
unique situations:2===2=22-: EME 222 554 lush. .-i-2:2-l---2ee2c—--cece o RS 748
using pole as assumed position -------- 638 Small area plotting sheet, construction of. 89-90
work forms for (see Work form(s)) Small circle, defined. - ----------- 63, 947, 1029
zenith photograph method__---------- 566 Small craft, navigation in_-_------------ 605
(See also Altitude, Azimuth, Meridian Small scale, defined-------------------- 947
angle, Navigational triangle) Small’s light, historical significance of.... 28, 55
Sight reduction tables, defined. ........- 946 Smart, W. M.; sight reduction tables of 57, 534
FER LUT ESTO ae e 502 Smith, John; on “bittacle” .- 2-2Le22-+- 24
Sight Reduction Tables for Air Navigation description of travas-==1-29522=> 35222 29
(H.O. Pub. No. 249), description and Smog, defined 2. ———————- = e 808, 947
S Ee etc 542-545 Smooth log, origin ofS So NIIST ES 29
d KEEN 1180-1182 Snapper, bottom sampler. 2 700, 842
history and contents of--—----------- 57,98 Snell, Willebrord; law’ of.) MB gts 430
Star identification sO see ea 590 Snow blink - 3 EE 759
usel opin polar Tecions SeS ME 638. Sofardefined- += = eee 312, 947
HO ost secs SA apta 1055 principles*ofe = 22 =f Heuer TREE 347
EE 140 Soft iron, defined---====+es=s: CENNA N 947

Siehts round of, denned eee d sea 455, 944

Sin lofa mon perder se seme 1005
of zodiac) denned ee EE 374
symbols. mass ene
(See also Zodiac)
Signal systems, sources of information on- 97
Signals for survey stations, types of- - --- 854
Signals, International Code of (see Inter-
national Code of Signals)
Signal-to-noise ratio, defined_----------- 946

Signature, magnetic, of vessel_-------- 204, 946
Sicomicantciciistdecmneci Ea
Significant wave height, defined---------
Similar triangles, defined___------------
Simpleiconic projection s m ee 78-79
(See also Projection (s))
Simplified Celestial Observation Table
(Japanese H.O. Pub. No. 603).--.-----. 541
Simultaneous Altitudes and Azimuths of

Celestial Bodies (H.O. Pub. No. 201)... 530
Sines defined s e m 1032

OL RADA LM ven a 959
Single interpolation, definition and meth-

O e sn bay roe ace P. 1045-1048
Sia, Ol O. ae e < 809
SINS (ship’s inertial navigation system)... 608
Siren as fog signal, defined_-------------- 267
DITOC COM eae E 16
Skip distance of radio waves_--------- 294, 947
Skip zone of radio waves__-_-_------ ---- 294, 947
Sky, appearance of, as sign of land... 660

COPA ES TEE 809

Wale Sky E os Ge A PUN 759
Sky compass cetined === a= nR 947

explained 27 =. y+. 90107 SŪ RUN 627

Sky diagrams of Air Almanac, described. . 591

Sky maps. 92... GI NE 759
SkEyiwave(s) defined: = oS RDUM 947
of loran=. acoso Ae oa 337-338
ET EE ME 295
patosio -_--- Ree tui io 294—295
(See also Loran, Radio waves)
SEELEN 339
defined os roo ci 947
Slack of current, time computation of__-- 274
Slack water, defined mI Ata 712, 947
in, pilotingss E EE 267
slave station=etē << E O 310, 947
Slide rule ol Berüihsccee eens RN 559
OM BvetaVvel ed AO c 559

Solar (see Sun)

Solar day, astronomical significance of. . - 374
defined mees see EE E 947
Solar parallax, defined. -----. 12116022 436
Solar prominence! E „OE Us ae 380
Solar system, bodies Of_-------------- 353-365
mechanical stability of. V. vævangdab it 38
motions Of +: EE 39
motions of bodies in_—-22=s 24S Ub EE 353-356
Solar tide. 2-22 BSS 705, 947
Solar time; defined = SES Ses Sas 482, 947
Solar year ht ee DR Eee GE 370
“Solarometer”, of Beehler___-----------=- 566
Solid, defined see ss Fa E 1020
Solid geometry, defined. ele 1020
Solomon, provided pilots by Hiram. ..... 28
Solstice, December. — 24-22) E 313
defined PATA IMA Es OS ADE 947
explained? LIMITE X ue cA 371
June <= 2 iek á i AND 3/3
Summer. (4d O Dira CORA eS. 371, 949
winter. H + PE a Pon Baas 371, 953
Solstitial tide; defined ---— EE 947
ODAT. 20 eae ANTAN DAR DAS 309, 947
echo sounder, a form: of— 320008 una 133
ice detection bys se === SAS Sm EEN 760
in polar regions. SOS S SS Sake E 635
Sonic depth De = [ee =) as UR 28, 133
defined: 2. =. ts me 2 r dS BS BARAM 30 947
(See also Echo sounder, Sounding ma-
chine)
Sonic navigation, defined" = _ == 62, 947
Sonic Soundings (H.O. Pub. No. 606-b)_ - 96
Sonne. 2225-25 Me ura AS 59, 308, 317, 947
Sonobuoy ft E DA ee 742, 947
Sostratus of Omdust EE ¿DIA 4D 28

Souillagouet, F.; sight reduction tables of_ 51,

533
Soule, C. C.; sight reduction tables of... 526
Sound, speed of, air-water conversion
factors: mA 3V. ILLERA Anas HS ZIM 961
in sea water--<-2=5== <PARAM S 743
underwater Y. "MP TIS 8 AS AR 742-745
reflection oF Garn S eee 744
refraction-o0f: ` ee 745
ee E EE Weeer EC 742
speed ofta stt Aen, hu Jer AN 743
(See also Echo sounder)
Sound buoy, defined. seu ane 947
Sound signal, submarine, defined________ 949

4
E
^
+
E
Á

INDEX

Page
Sound wave, definede restra 947
Sounding(s), on charts, accuracy of______ 105
symbols. forzs sanita OE 107-108, 996
danger. defined... < BW 10 (ve 920
A A den dali TAM TO . 2
(lefinod com nere O PO 947
echo;sdefined£ 5... ð taða MIC T War! 923
By (echossounder esse. 290995 ITE 28, 133
Ērrorsjofš e ee e e e lt 134
Mistor Of ee. PAO VM J 27
Iinesofz defined -te mrt LLC TUS NAMAM 933
in piloting- 19994 oam vin ubt. 258
oceanic sU» JA SUM iam tU D OF o 868-873
deep sea sounding Ines... 869
equipment forss Hon de 869
evaluation of-e -—— 0 MUM DOR y 869
LOG Of roped = dence DS JO Æ 873
records Of RA, E E RA. 871
small-area methods................ 870
of ‘andion; defined Paz. 22104. ZI Woe ` 938
iN Oe 2-2 ua DC ] 631

published in Notice to Mariners... 99
Sonic Soundings (H.O. Pub. No. 606-b). 96

tidal effects Upon: : 0. KEE, 394. 267
units of various nations- ---- 222.2 999
Upper sir defined ae afer i es gui an 952
Lserofsin;pilobing =< 38402103. € 257-258
(See also Depth, Echo sounder, Lead,
Sounding machine)
Sounding book, for hydrographic survey. 859
Sounding lead, defined - ---------------- 947
Sounding line. defined. 222-283. C 947
in hydrographic survey_-------------- 859
Sounding machine, buoy sounder___----- 27
COR Teen ederet c e D. 947
desegiptionjioisees eese e LEE 132
carlvatypestol ADELA rH m 27
of William Thomson (Lord Kelvin)... - 28
Orlgin'OMMe A HITUIIUM HIM 27
selfsactinpgseme amos S ded t 27
(See also Echo sounding)
Sounding wire, defined” HEC Ses 947
SoutheAtlantic-current_..---_=_ "e 722
South equatorial current, in Atlantic Ocean_- 719
mnsindiane'Oceane--e-— fas et e 724
imsPacifienÜceanc- sero ee cn RJ! 723
Southeast drift current, in Atlantic Ocean. 722
Southeastutrades4 6.0." emerit 798
Southeasterlies of antaretic_------------ 799
Southerland, W. H. H.; azimuth table of. 569

Southernscerossa-<#<ke-che dE SE E 582
Soutimgsdefinede-—— eternon T
Space coordinates, defined... - ----------- 1031
Space motion, of celestial bodies... 353, 366, 370

defined 948

pacesnavigatione=====rcs=cpna SS 676
Spacing dividerssseece= = 220209 10991 847, 889
Span length-unitn sees 26
Sparihuoy: “defined == eM. uus Le 264, 948
Specific gravity of sea water..........-- 696
Specific heat of sea water--------------- 698

Specifie pulse repetition rate, of loran.. 334, 948

Spectrum cc e e «das ti 809
of electromagnetic frequencies. - ------ 290
Speed, of advance, defined......... 66, 218, 948

Conversion factors see eee S 960-961

of current, finding by table------------ 274
Altrenteffeciupon r RS 218
denned LERMA: > seso Honda Agošajā 66
inca cie Don ales, hati ahs dea e 629
of light, conversion factors----------- 961
made- good, defined eee dis 218
for measured mile, table 18____------- €

explanation) ota altere as]

1513
Page

Speed—Continued e
measurement of, in lifeboat. |... 65
metodes sot byrsa na = CØ 127-131
by, radio === een Daniel. Ti 308
of ocean waves, equation for... 29

over ground, define
in polar regions

of relative movement... ... 326
of sound (see Sound)
Units. Of erties eet eee et 25, 66, 124, 673
Of windas.5-.-....10 390 hes MONG 797
Speed error, defined... 4222/14 al. 948
of gyro compass... =. ene erh ee 146-148
computation of in polar regions. ____ 151
Speed line, defined--.- 222222 453, 948
Speed, time, distance; table 19______ 1271-1275
GE OT EE 1191
Sperry, Elmer A 221222222. Ono mo DM 24
PE armillary, description and origin
Of cce EE EE 4
celestial denned EEC ce SE mar 351, 916
center of, defined... eu Tata Ja 1029
defined — m r PS Rates ee 1029
description and properties. ....... 1029-1030
oblique, parallel, and right__________ 367-368
Sieht reduction Dy. EEE TN 565
undevelopable property of------------ 69
(See also Navigational triangle, Spher-
ical triangle)
“Sphereman Crast Positioner", of Train-
ing Device Center (USN)............ 565
Spherical coordinates, defined........... 1031
Spherical excess, of survey triangle....... 857
Spherical sailing, defined- -------------- 948
Spherical triangle, biquadrantal, defined__ 1039
defined atico fors eaotiaau 393, 948, 1029
obliques solutions for eee DP 1040
quadrantal, definition and solution of.. 1039
Solution. Of eee been a= 1039-1040
Lagrangestormula see 558
triquadrantal, definition and solutions.. 1039
(See also Navigational triangle)
Spherical Triangle Nomogram, of Wim-
perisdsion erte a ER 556-557
Spherical trigonometry, defined. ........ 1031
Spheroid(s), for charts of North America. - 62
of Clarke (see Clarke, A. R.)
defincdøkreban ri wearin 2 948, 1030
earthías3- mea cn d 357, 427
international, dimensions of......... 357, 957

(See also International nautical mile)
oblate, defined 222-2. 7 2239s" --- 62, 1030
earth.asse A ee 357
(See also Earth)
prolate, ndefired:.- 2-22 Denm aar
undevelopable property of...........- 69
Spicules ofice hanter = 2% Se aet
of marine sediment. .-------.--------
Spieghel der Zeevaerdt (The Mariner's Mir-
ror MOL Wapghenaer =" CEST 22
Spilhaus, Athelstan F.; bathythermograph

OL OF nor sat Hero Ded nocte as 696
Spillover defined Tð VN -ma H 948
in loran receiver-indicator- ----------- 336
in cradið.receiyver co REZA AA 302

Spin axis of gyroscope (see Gyroscope)
Spire, chart definition of_-------------- 114
Spitzbergen current === ase ae 722
Spline, plastic, for chart construction... 890
Splitting of loran signals.------------- 338, 948
Spot elevations on charts_-------------- 114
Springl(scason) 6 ose ss a LL 371
Spring (IEN A E 714
Spring range, defined----============-> 948
706, 948

Spnungldeeeese ce cce d

1514 INDEX
Page Page
Squall sotesse) ss Ee 802° Star trackers cie p Eee 566
Get line. 222) ee 4: Set eres ee 802 Static in radio_--------------------- 297, 948
Squareddefined. .-:.--.-.------ cabe 1094 — Statielelectrieiiy SS 289
of a number; defined - sem 99547 1010 Static pressure of water- --------------- 128
Square root of a number- -------------- 1012 Station, of survey net, defined. .......... 854
SSiloran.s& = +25. Jer os 333, 948 Station buoy, defined_--------------- 266, 948
Stability, of radio receiver _------------- 301 not shown on charts =i IR 113
Stack, chart definition of.--.------------ 115 Station error, defined- ----------------- 948
Stadia for distance measurement- ------- 842 ` Station) pointer- ss AS 245, 948
StādimeterYdefined-+-6- See 948 Station pressure, defined_-------------- 768
description and use of___----------- 125-127 Station signals, survey .---------------- 854
Stadium, length unit, origin of---------- 26 Statute mile, conversion factors. -------- 958

Standjof.tide--55:---- ies 223388
Standard, definedētls eee seters S

Standard atmosphere, structure of------- 794
Standardscompass 4.2252 e A b 135, 137
defined. Ed 2 S dm ishalri 948
(See also Compass)
Standard deviatäon. tð usa _ sesi 681
Standard loran (see Loran)
Staándaárd/meridian Vó == Nn 482
Standard parallel, defined. ............. 948
(See also Parallel(s))
Standardalime..... seem bee t 488, 948
conversion tables for_____------------ 269
Standingiwaves 2.2 MS c or ge orbes 734
Standpipe, chart definition of..---------- 115
Star(s), altitude corrections for---------- 441
(See also Sextant altitude correc-
tion (s))
features Of- ===... CE at 365-366
groups of, defined. eio h 366
heliocentric parallax of____- 352, 365, 435, 930
identification of = P 965-972
miultiple.star J: b uha k ated ad fa 366
names of, pronunciations and meanings. 973
navigational _ 33.622 5552 sp da 575
location; of tessa cepe lee 965-972
MN A O ccs c ` SC 366
TAdIOS Mees 12er. E D 365
discoveryuofto- bs coole MP Lern 39
scintilatiomoi M TEN 575
shooting staris sean _ Siseņi M a 365
SUPernova SEK 2122 e DU E OO 366
twinkling of... Sst vedi eme 1 575
variables eo a: ateo M de be rd Tu 366

(See also Constellation (s), Planet (s))
Star altitude curves (see Sight reduction,
altitude curve method)
Star Altitude Curves, of Weems_--------
Star catalog, of Brahe__________________ 50

Star charts, described________________ 576-585
Star clouds SES 4d 6 aM 366
“Star Computer", of Longley........... 562
Star finderidefined--—--- SE 948
of Rude- 2. Si Ed eebe 586
uselofjastrolabelas EE E S 40

Star Finder and Identifier (H.O. 2102-D),
projection for

use Of 2200 fe LONE 586-590
Star globes en derer ian" Mai Judea 576, 948
Star identification, by computation. ..... 591

by adi diapgram----- EES CR 586

by H.O. Puba No. 241 591

by, H CO. Pub. No. 240 esu 590

bygH.O0:12109-: De oet 586-590

pysky dlagram - > 38 omma M 591

Dygstar chart... AR 576-585

byzstanglobe < 7079? PT AA A 576
Star names, Bayer's name______________ 575

catalog number... 22 576

Flamsteed’s number. ________________ 576

Origins OLA -—2-- eee e eee 575

Systeme Lor C a ON 575

conversion to nautical mile, table 20...
explanation of ss ss

defined sce. <= = set ease 65, 948
origin and length of: m dc 26
Steam fog defined... ——--- SS 948

“Steam Lanes Across the Atlantic”, of
Maurer

Steamer lanes in North Auante

Steering COMPASS... = s-r S
(See also Compass)

Steering repeater, defined. -------------- 948

Stellar (see Star(s))

Stellar parallax, defined-=-==-=====322 435

Stereographic projection, defined. ... 70, 82, 948
(See also Projection (s))

Stooping.of mirage ss a oe 809
Storm, detection of by radar. ........... 788
eye of, defined sed ss Jete atea d 924
described 25 ct or x sm 824
mapnetic, defined ` `" = Sa ese eee 935
radio propagation in_------------ 294, 633
maneuvering to avoid "> -eA 828—832
radarin: E ^ SOS AAA 788, 828
iracksof. = == 1225 r c TN 820-823
(See also Hurricane, Tropical cyclone,
Weather)
Storm and hurricane warnings, informa-
tion on, source Of Sane i ER 96
radio broadcasts ol. e ee 100
(See also Navigational warnings, Radio
broadcasts)
Storm tide defined: E 948
described. 112: 2 7 E "SE 832
Storm tracks = S 820-823
Storm wave, defined................. 833, 948
described ss: eee CARTÓN 734
Straight angle, defined. -----222-==2===2 1021
Straight line, defned a 1020
Stranding, defined. 948
te HIE 782, 948
Stratopause 522 _- = s ana e 360
Stratosphere api ar ea 360
Stra Lg oo o ee 782, 949
Stray lines stov tetpet C. zs
Stream current, defined- ------------- 718, 949
Stream tidez--..—..----- COT 703
Strength of current, defined------------- 949
Strobe, use of in gee___________ E ene 344
Sub
-astral
-lunar
-satellīte,.)poinii ša 6 NE 393
-solar
-stellar
Submarine bell, defined________________ 949
Submarine navigation. 2 607-611
defined eege eege 62, 949
ati periscope depth e 609
submerged, daylight only----------- 607—609
day and night: eee dd A ME 610
surfaced 222201 55555. 0l fact is 607
undericesi. 30e 8M aber al te eaten 762

INDEX 1515
| Page Page
Submarine sound signal, defined_________ 949 Sun's way, defined... ... 2 002 356
Subordinate station SUteds Boe oed 5. st, 949 Super high frequency, defined.________ 949
current prediction for- --------------- 273 Superintendent of Documents, publica-
cide prediction! foris M Essa 269, 711 tions sold by Unica ion dead 94, 1002-1004
Subsurface current, dene. 718 Superior conjunction, defined______ y 375
Subtense bar for distance measurement.. 842 Superior miragesienciad birmas 33100 9 809
Subtraction, of algebraic expressions.__._ 1018 Superior plans. 357
arithmetic and algebraie 1009 GUDeRDOVAIDIG Eege ee: 366
of numbers, explained... .... 2-2 1008 Super-refraction, of radio waves... .... 292
Subtrahend, defined- _ 1008 Supersaturation, of air... ture
Sum of numbers, defined ` y Lan 1008 Supplement, defined... 949, 1021
Suma de Geographia, of Encisco__________ 32 Supplementary angles, defined__________ ' 1021
Bimimer:(86as0n)...... br hh. caia att 371 Surf, defined 731
Summer solstice, defined. ------------ 371, 949 features Of ==. COD ADORA akts an^ 738
ar MEA A IAN 482, 488 Sound of, as sign of land AS 661
Sumner, Thomas H...... E - Æ í 453 Surf zone 732
A New and Accurate Method of Finding Currents in. BRE jā is A 738
a Ship’s Position at Sea by Projection Sutface, defined 66) 270^ DES WOO DIO Tor ie 1020

on Mercator’s Chart of_-.-..________ 55

Sumner method, defined... .... <

determination of line of position by... 56,547

Sun, altitude corrections for... 439
(See also Sextant altitude correction(s))

apparent--------.--2-3e A, , 495
dehnedes west ec ck oce teh 911
Dackstays of: Jaivas Je. sor 90 812
curve of magnetic azimuth of_______ 197-199
diameter of. Sink eine mute 955
EISE reiege hito domin 955
ürawingswater- wc a 812
eclipse phenomena. _--_ 52 2222252222 379-381
features of M HAN ENTE de dero vta 356
procen vilash PERE sy CD n 811
MASON sia mA abe 955
ss ee ES 495
astbasis for timen ot SM se fenior Y 374
defines e Cc. ain mui: 374, 935
midnight. oo evene nce ES 368
LOC Kent CENA. A: dcm 811
MOONS cae ee Deua n 356
occultationtof planets. -zres M 375
rising and setting of, almanac time of. 473
INpolarregions ø EE 3 639-640
rotation of, Galileo on___------------- 50
semidiameter of, by almanac.......... 479
solar prominencestēlšasea D4 = 380
speed of, relative to center of galaxy_-- 366
relative to neighboring stars. ----.-- 955
transit of by plānet-------- O 375
im (ër et 626
forland navigation- < + eee eee ne 667
Sun'crosss eene A SS IS 811
SUMO OG Beso fees A ee PESE 811
Sunpllar- SSS AI To EA E 811
SUD a EE, 356
Sunlight, duration of, in polar regions...- 639
Sunrise and sunset, almanac time of ---- 473
InSDOlamregionsc- ee 639-640
computational formulas. ------------- 642
longitude determination by..........- 660
au moving!crakteeese O 478
In polarregions Eee SEO LODI 639-642
tables of, in tide tables_----------2--- 269
of U. S. Naval Observatory--------- 269
Work forms 38852 DEBE MEMO S 1057

Sun's True Bearing or Azimuth Table, of
Davis and, Davis. Sip IE 57

Surface tension of sea water____________ 698

Survey, bathymetric, procedure for______ 865
beach proced urer Oras A 864
checking chart accuracy, procedure for. 865
current observations__---_--------- 844, 860
electronic controlin: 222225 O V
exploratory, procedure for_____----- 862-863

geodetic idefined 3451-2200 AO
geodetic. controlues2s E es

baselinesforio. 29 ose. do CIS, Mu 853
defined BUILD Eat qv NA J 854
direction: st Eee soci 852
eccentric point, use of______________ 856
observations, by astrolabe__________ 850
astronomical AA 850
by direction theodolite___________ 851
high-latitude Monuc 10 E 852
origin o dee. S mma DEAD EN 850
records,0f ohh = AITAS MOVIDO A 856
sphericallexcess IE TN 857
station signals, types of... -_ 854
(TAVETRENĀSA Hue YE TEN HS AN 854
trangulation 2 = F 7 52272 ee epee 854
trilaterð tíð À 9 C RAE ERAS 854
geomagnetic, institution of... 31
unit of measurement in___________-_ 161
hydrographic, defned S AMIRE T TS 848, 930
(See also Hydrographic survey)
hydrographic control, defined ____----- 854
renge er Ee eem 104
Limitedatewte E 862-866
origingo AA ZE = 850
ELE 848-849
running procedúre lor 864
tideigage for = E e 843
timing equipment fors == = --2--- 839
traverse fór wc A oe AN AR 854
use of horizontal angles in-_----------- 245
SŪnveyIinpēdefinedēs sms mm S eer 848
Surveying sextant, defined__------------- 949
Surveyor s level 22-5) a ee de 842
Surveyor stransi e ae eS 840
Sweat, defined-------. E eos 778
Sweep, of cathode ray tube..---------- 302, 949
Sweeping, defined. ...............-..-- 949
Swell, appearance of, as sign of land... 660
defined qute soe Ser asilo 727, 949
direction of, defined... .........-.- 922, 949
ground swell, defined. .-------------- 928
effectrofeupon ships ee wt T € 27 781

1516 INDEX

Page Page
inging thearo. 102 tc EE 402, 949 Táboas de Alturas, of Braga.-.........- 57, 530

iie dede ER E 949 Tabuas de Altura e Azimute, of Fontoura
procedure for- = £541 Je ze 194 da Costa and Penteado.............. 539
(See also Compass adjustment) Tabulae Prutenicae, of Reinhold........ 51
Swirl error, defined ------------------- 949 Tubular iceberg_..__ 222204) II Ta 748
Sylphon cell of aneroid barometer. ------ 766 Tabulated altitude, defined. ............ 949
Symbols, of celestial bodies- ------------ 906 Tacan, air navigation system ---------- 674
general en A A ES 903-907 Tachometer, speed measurement by. .... 131
mathematical ¿24.0 5-3 asas 906, 1017 Taffrail log, defined. dum 949
miscellaneQus Se: 31. Je: (eg 907 description and use of________________ 127
on nautical charte .------==-222:42 983—998 Tailof comet______—- anar Claus 364
(See also Chart symbol(s)) Talus, continental (insular)........... 601, 700
for navigational positions____________- 906 Tangent, to circle, defned 1025
use of, in chart construction......... 894—895 common, defined- ------------------- 1025
Zodiacal O. ees 906 defined 34 ft Se AE 1032
Symonds, W. P.; azimuth tables of______ SLL Tangent aré- ` k c NMS 811
Synodical month of moon" PT 362 Tangent screw of sextant________ .----- 400, 949
Synodical revolution and rotation, defined. 353 Tank (gas, oil, water), chart definition of... 115
Synopticrchartess a aes 816, 949 Tape, distance measuring--------------- 842
Synoptic observations------------------ 790 Tape gage, tide measuring-------------- 844
Systematic error, defned. 00-22 949 Target, radar, defined_________ Ud mmu 942
discussed ot eeh 679-680 Toron, H (1 A I. Là i2 of Italian Navy re

iti z ydrographic Institute- ------------ à

t ú dab ADEN Beneo Tavole nautiche e Tavole dei Semisenoversi,
(Special Pub. No. 38), of International ofChies-. os NUR 531
Hydrographic Bureau... 976-977,1004 Taylor, A. Hoyt; development of radar. _ 58
Te Kee EE pat

= Telegraph buoy, defined________________
Table(s) 3 critical, defined. -------------- EH Telemeter, defined_____________________ 949
explanations of „0100 1s AN Telescope, invention et E:
Table d'angles horaires, of Hommey......-- 524 Telescope error, of sestant — AnA 414
Table des Azimuts du Soleil, of Labrosse. - 569 Temperate zones VA dän e Albis od 373
Ke sare Cadran Solaire Azimutal, of T Temperature, absolute, define d. M 775-776

Table 902, Azimuls; French azimuth table. 572 Of atmosphere, altitude correction for,

Tables du Point Auziliare, of Souillagouet_ 57,

538
Tables for Calculating Altitude and Azimuth

of Celestial Bodies, of Yonemura________ 530
Tables for Facilitating Sumner’s Method at

Sea, of Thomson (Kelvin) _____________ 524
Tables for Finding Azimuth at Sea, of

Mhortrode. 22. SE D as dee ee ee 569
Tables for Sea and Air Navigation, Hughes’ ;

Of Comrie res: 55 6 eee ās 536
Tables Graphiques d’ Azimut, of Constan... 572
Tables of Azimuth of the Sun, of Zhdanko__ 571
Tables of Computed Altitude and Azimuth

(H.D. 486), of British Admiralty______- 540
Tables of Computed Altitude and Azi-

muth (H.O. Pub. No. 214)_______ 57, 98, 540

Adsolutionse wee Sa 505—506
Ad and Atisolution r eet 506
Ad, At, and AL solution______________ 506
description oí Sad 503-505
extracts:from Ness SMA 1170-1176
first publication of. 57
interpolation for azimuth_____________ 507
star identification by_________________ 591
use of for altitudes less than 5%..______ 637
WOLK,fOPMS 2e ee b SE ee 1055
Tables of Logarithms, of Martelli._______. 524

of Burdwoods----. -. 5. emet 569
Tables to Facilitate the Practice of Great
Circle Sailing, of Towson and Atherton. 569
Tables to Find Altitudes and Azimuths, of
US SS aa S. Se eee M MEUM 57, 537
Tablette de Point Sphérique, of Bertin_____. 533

table EE 1280

explanation of ` PLAN 1192
measurement cf C ` ee 775
Celsius, defined" 1. TEEN 775, 916
centigrade, defined________________ 775, 916
Eet ere M 775
of dew point (see Dew point)
effectiof upon dip__ E 423
effect of upon refraction______________ 432
Fahrenheit, defined________________ 775, 924
Kelvin, defined 1 "oe 776, 932
lapse rate of. —.-... -SMAA M POR 794
measurement oficsasur -onai but 776
Rankine, defined... siet sua 776, 943
Réaumur, defined. - 2201400 X. 775, 943
Of sea water, eesepla cd da qt 695
sea-air difference correction, defined... 945
discussed sien Air tw tems 424-425
units of... via den 775-776
conyersionof-- ____<.-danel wes 776
table 15:5, coa a ee ON al 1265
explanation ofge better de 1190
Temperature difference, sea-air, effect of
on sextant altitude._______________ 424-425
Temperature error, of barometer________ 769
defined... ... S ES SM 949
Temperature inversion- -_________ 807
Temperature lapse rate, effect of on terres-
trialirefraction eg gege Sain 425

Tenting of sea ice feed Eug eee 750
Terminator of moon - hina Sante 378
Terra Australis Nondum Cognita_________ 21
Terrestrial refraction, defined_________ 430, 949

effect of upon dip Here n teva m9 423

effect of temperature upon... 425
Terrestrial triangle, defined... 950

INDEX 1517
Page Page

Thales of Miletus, on electrical phenomena 57 Tide—Continued
gnomonic projection [je PEE 18, 82 enuinoetialdefinede*- PE n 2 924
scientific contributions of... 35 establishment of the portē sess Seep „ 268, 709
Theatrum Orbis Terra, of Ortelius... 21 fainstideydefined =. EC ' 924
Mheodolite;, defined... 25:9: Tisas 950 ialüngsudesdefinede ce eec 924
CTE OE aa 785-787, 839-841 featur of 2 UU ste gd Ze 704
upper air observations by____________ 785 halitide level; 8... a e 710, 929
Thermal conductivity, re tt: Olalla 698 harmonic constants- e E 710
ATA A 698 height of, contrasted with depth... 267
Thermal expansion, coefficient of, of sea defined £e somete eee E eed 929
Gun lle tovc ta 698 effectioffland upon -t RP 268
Thermocline of sea water------------- 696, 743 effect of weather upon... 711
erter dee eet ee ke ste Ree A ee 270-273
Thermometer, defined- -gajas anien 950 OT Ee $ 704, 930
reversing, for Nansen bottle_________- 696 infpioUung.--. Aereo uo oes 207
scale conversions, table 15_------------ 1265 high water datums, defined__________ 710
explanationjof ict dzēne sz 1190 high water full and change..... 268, 709, 930
(See also Temperature) high water inequality, defined--------- 930
A 5 o eat ee 776-778 high water lunitidal interval. _ — - 268, 709, 930
Bhermometerscales2_2= a artes 775 higher high water, defined____________ 930
Thomson, Joseph J.; discovery of electron higher low water, defined.__--------_-_- 930
1, m MN 58 information on, sources of... 97
Thomson, William (Lord Kelvin) (see lesser ebb (flood), defined------------- 933
Kelvin, Lord) lowMdehned Res cn r 704, 934
¡Phreesarm protractor... 0 $=. 950 low water datums, defined_________- 709-710
for chart construction... .....-.... 889 low water inequality, defined. -------- 934
description and use of... 122, 245 low water lunitidal interval, defined... 934
for hydrographic surveying--------- 845, 857 lowywaterisprings = e eae eee 709
Three-point fix method of visual survey lower high (low) water, defined. _--.--- 934
controle Lone E foe ps 857 lunar (defined cena a se eM 934
Ee enee, 0 ant árl: 813 and lunar day month) e ecc 708
Barrett red ars A Ae los 703 lunitidaljintervale Aa 268, 709, 934
definen VARN. 15 sera lA. dtes 711, 950 maximum ebb (flood), defined--------- 935
featurestotsess Poder 11 XE judo dh 7 mean tide levels, defined__-_---.- 709—710, 935
Mire pio ting sieve ef — theta 4 267-268 measurement of, for survey_-------- 844, 860
pes Of eps 2c d des rs oe ni 713 meteorological, defined_____---_------- 936
variations ¡and ey cles:2122 === === 2 714 mixed. tido: henares u 705, 937
(See also Current(s), Tide) andinmoomecycles a < < e Es 708
¡Bidalcarrent charts. - < — X lil: 95 peapea o A E: 706, 937
decidi e 268 Observatlonjofc A E 710
Tidal current tables, contents of---- 95, 273, 716 harmonic analysis Er (Au!
dennett Ta piedā Ate, t. dl 950 in hydrographic survey----------- 844, 860
bey frome ¡AE ees 1132-1135 perigean tls. ume A ne 706, 939
fy ores E, MA 273-276 perigean spring ` SEE ee ee 706
Tidal datum (s) definede bos: Ee aures 950 in polar regions o ce E 616, 629
discussedia odon pe cepere HI. e hee 709 predietingimachine ss =) =e 11
of various areas, table of- - ------- 1000-1001 prediction gl erger eebe 267—269, 410
idalday EE 482, 709 primary station, defined_------------- 940
defined Mee oe o o r 950 range of, computation DE nl 270
Tidal difference, defined---------------- 950 ER lie 704, 943
Muda dāki: e S T lD piloting- aða 4 oras 267
sidaltwawver defined sed: at 950 relation to current speed. .......... 715
described Sæ Ð L aea ater do as 733, 833 variations in- F ee es ee 706
(See also Storm wave, Tsunami) risexol, defined EE 944
ote sl tem Cr dE See 703-717 secondary station, defined. ----------- 945
ACTO Co) Seas 2. Se EE EE 0 semüdiurhaleetie4 oe po a ee 705, 945
altitude correction for_------------- 426, 950 EE 705, 947
apogeenn eee apr dtum T 706, 911 solstitial defined. S es 947
Apogcanimeaps e «cassum des az 70 special effects_--------------------- ade We

astronomical, defined ` - ------22====== 912 springe ae aries just 06,
bored TV ol le in 706, 735 spring range, defined O 948
CausessOfer c eee CHE 70 stand of, defined. ............-- 267, 704, 948
Et re 916 storm tide, defined. ----------------- is
chartisyimbols forsee eee CS 998 described sane SSS < or E a
and'curreni see! 222 so eA 267, 703 adīt e ea ite
evoles oreet FA acre aci 708 LE Ge 108
datunileyels EE E 3 709 relation to tidal current_---------- Dr
i = tropica na AA RT ee a € ;

Rd of various areas, table of - - ares tropic higher high water-_------------- 710
SUE elias eelerer i tropic lower low water_.-------.----- 709
ne IO Y 20. 705, 922 types of at Pied! Lo (out nents. gale.» 704
doubic + .--+----=----+=---=------ 706, 923 vulgar establishment____------------- 709
eft ects obe ce V E eae 267-268 waves iO Ley eee ee b ts 735
effects OrawinG Up as 711 weather effects UPON 2 se e 711

CQUALOTIO. ASI See ye aioe E 706, 924

(See also Current(s), Tidal current)

1518 INDEX

Page Page
Tide gage defined- SS 950 Time—Continued
Send EE et 843-844 radio signals, defined_____----__------ 942
Tide level, half tide, defined- --------- 710, 929 sidereal 34.4 Seen Sh OEE 375, 482, 496, 946
mean, defined Ai ese E 709-710, 935 signals eee ou Ig dls gee) Sd We 491
Tide plāneWhārmoncsssee 42" seer see = 709 (See also Time signals) h
Tidelrip,chartssymibol forð ur === = 110 solar, defined. - ~=.-----~----------- 482, 947
defined Sisk eee ee A HS 268, 950 standard times ¿EA E E 488, 948
(See also Rip current) conversion tables for, cited___ 269, 467, 468
Tide statics ss niae UE ASE NE 844 summer time se. — ec PENA 482, 488
dE ee Le se A 950 survey eguipment_-------------L---- 839 `
primarys defined 255 SE 940 of tide==..---- ee DR RE 708
secondary, defined ae UM NNI 945 relation to tidal current__---------- 715
Tide tables defined’ To Se- TAO J 950 units Ofte E cr E DP 483-484 `
extracts rom. Ta Ce ee 1129-1131 conversion factors... Segue eee 954 `
publication and contents of__---- 95, 269, 711 universal, defined_______------- 375, 487, 952
dkidetwayēs: =< + BMS aa M 785, 950 wartime, defined - i 0044 RNS 952
Tillman, E.; sight reduction table of----- 539 wateherrorsĒsetebi nuk 419, 492—494, 952
Tilt, of sea, altitude correction for__----- 426 watch, times» AO aa EE 492, 952
of sextant, altitude correction for |... 422 Ser OÍ AM:anduPMus s AA cR 483
Tilt correction, for planimetric map-_----- 876 (See also Watch)
iltrerror defined sass o wor] 950 zone time, conversion tables for, cited-- 269,
O Sextanto aE Æt suum eo corse 422 467, 468
Timberlake, E. M.; sight reduction tables defined Late ae MAE canem 375, 953
GË Ët ee 1 eee oc ME 536, 547 time meridians fore I as 482
mee ata =: TROU GIGS xn 482—501 userOf o EE 487—490
apparent, defined... ........... 374, 482, 911 (See also Calendar, Chronometer, Hour
Andina RUDO” INTERE MUI U 495 angle, Meridian angle, Watch)
apparentisolar= sv SES O A 374,482 Time and altitude azimuth, defined... ... 950
and arc, interconversion of_________ 484-486 formulastforsaus JO. Dodot x eee 567
astrographi mean oss a = ee 002 l'Time'jazimuth; defined araen 950
‘astronomical significance of... .. 374 formulas. for... <i TM 567
SE E O 2 2m ea 370 Time Azimuth Diagram, of Godfrey------ 572
Chronometerkerrot a= EAST eee ae 490-491 Time Azimuth Diagram, of Weir... 572
chronometer times ss m 4184903916 i Time balls. shee sated LIS 47, 492
WSC EON AMAN CGP Meee ET 483 Time base, ‘defined nei- t 950
(See also Chronometer) Timeldiāģraniess c AN 383-384
avili changeror almanac tons e 52 defined. eie cL... eee ee 950
reversión to mesnitime n:n mmn nn 53 Timemeridian? 15. SZ (BM 482, 487, 950
cayo usano san 482, 488, 920 Time sight, defined_....._.2.11_1_. 2222 950
defined meer em 3 es o M 950 formulas AVO MOR e ÓN 523
determination of, in lifeboat__________ 660 for computing times of rising and
(See also Chronometer, Watch) setting of celestial bodies_________ 642 Y
catiyablnepleces. Skeem c SE 17 history ofz ¿Us eo. ans MG 5408
ephemeris time, defined___________-_ 375, 496 litte of position by TE 56 Y
equation of, by Air Almanac---------- 496 use of jin: lifeboat..—-- Hao. NEN 660 —
defined deer ate See MET 375, 924 Time signals, of Bureau of Standards
by NeuticalvAlmangca2= === eee 478 (WWV) A ik at POT 492
Usera Sima I PIOS IMA es 495 definēdsstoš el ee 950 A
geomnagnellonst cuc GET ET ES 162 discusseds Scu oon ee ts S TM A01 8
(Greenwich Str. Er A 375 first transmission. of-.- VAn AA 58
Greenwich apparent, defined.--------- 928 history Ofrece Rati 47
e Sia pat ld de 495 information on, source of_____________ 96
Greenwich civil, dehned-- ee 928 radio broadcasts: of “MLV 100
Greenwich mean, defined... — 482, 928 of U. S. Naval Observatory (NSS).... 492
fading ST pu ance ee 487 Time, speed, distance; table 19... 1271-1275
Greenwich sidereal, defined... . 497, 928 ēxplanationjofee 6s (43 ÓN 1191
andžhouanglo--=<7 T. ESA mas 497 'Timevtick22# 60 a. < NAI 491, 950
Kindstofsdefined SE S S 482 Í iTime Zone; defined MESA M 487, 950
localvdetined Sy ee eee eee 375, 482 Time zone chart, illustrated... 489
local apparent, defined_______________ 933 publicationiof tiss cr r S 101
locales e ee ON 933 Timepieces, early. 99-9 993 oe eee 17
local mean, conversion tables for______ 269 Timing equipment for hydrographic survey. 839
defined: Siu. < O ee 939 Timocharis S c M 37
Ending obf mor ^ te Ee da 494 Titanic, SSC S R ON 31, 757
local sidereal, defined n. TE EmA 934 Miles Tor Chartissa ON ' 116
finding AE a co RES ERA 497 “Tokyo Datum ass ss MA UNI 892
EE 486 et EE A Ka eb 48, 51
lunarSE st: Jes Bree Re a QE 375, 482 Ton (mass), conversion factors... . |. 958-959
mean «5c. ed at. 482, 936 Ton (volume), conversion factors-------- 962
(See also Mean time) Mopsis for.buOYS dat. ue os Ss TN Ae
mean sidereal, defin Deg ane cce ced 9
EE Va gi sa rer 374 "e E (See 2 Uode System of buoyage)
A Ir a eg , opogra n i i
of meridian transit- s- M 519-521 ` ee AE reg

of prime vertical orossing .____ 526-528 Tornado 813

INDEX

Page

Torque axis of gyroscope (see Gyroscope)

Torricelli, Evangelista; mercurial barom-
SECULAR a ENT 766

Bu O en EN Rr cts 372

Acs e rectas 379

Total pressure of water... 128

Tower (lookout, observation, water), chart
o pes es E eim 11

er of Winds’) o mb 23

A A EE OS 809

Towson, John Thomas; azimuth and great-
circlettables of. 222.6. LAOMA ar 569

PGC aha eesti rātes iisti Lente leon!) 950
of..cathode raystube- Toer menmun ada 302

Tracing table, use of in photogrammetry. 876

Track, in air navigation, defined________ 672
dead reckoning, defined... 921
efined as len Meter 66, 951
Ofidirectionaligyrow epe qo tien e naan 88
Rreatseirclezdefinēdēr= =< aa 927

discunsedē E, DT EE 66, 229
magnetic ¡defined 2. hs stammt». 935
radiofdefined.- 35 Jte e erat did due ad 307

irackaichart. defined. - _Sa.eenjold si 951
(See also Chart(s))

Jet EE EES 951
explained eee (Lk e ce et es les 327
pzocesstofe. _-_ We abran hrs 156
by radaniplotatert cio amne fe ER ale 325-329

Traction capacity of beach____________-_ 740

(Brādešwinds šiet 1-1. e es 797

pinalnofiloran signals f ieceri se 333

Training Device Center (USN), sight re-
duction method of ___€- 5. 2- < bese 565

Traité de Nomographie, of d'Ocagne...... 556

Transducer of echo sounder 4222-0452 134

Transfer, allowance for... 276-278
co e E re 951

asi da sc 951
lowerdefincd A A ET 383, 934
of meridian, defned -aaan 383, 936
osun by planeto ous 9 Sew ree 0 SeU MIS
time of, determination of__________- 519-521

longitude determination by--------- 659
byanauticallalmanac==2 2.2222 "= 478
Wpperadefined < eee IE emm 383, 952

Transit instrument, camera type-------- 840
Invention ofc e jue cde? STUNT 50
SUDVeVOR Sa ce cese reo = E PME 840

puransimissometer? <6 eM erllcic-..2. 0 785

Transmitter, radio, components of------- 301

Transparency of sea water. 2 699

Maransbpondere- Soe" See ss Š6 5 309, 951

Transposition of algebraic expressions.... 1019

Mtansyersal delinede----—— 2... e: 1021

Transverse conic projection... .......... 78

Transverse cylindrical orthomorphic pro-
jection (see Transverse Mercator pro-
jection)

Transverse Mercator projection, de-

fine eee PS en 74, 76, 951
(See also Projection(s))

Transverse rhumb direction, for auto-

matic dead reckoning eguipment_-_-- 88

rapezold edefined Sesh Seana sey Sees _ : 1023
Tratado da Sphera, of Nunes_-__ -------- 30, 32
Pravas origin obs se acc UE MBA 29
ira verse gd efmed- = 4. es oe 223, 951

of/surveys defined 4—--. essa? sar 854
Traverse method of visual survey control. 858
Traverse sailing, defined_-------------- 221, 951

examplerof ¿o Sede Hot madens 223

history oia a 7 o See 29

1519

Page

Traverse.table; defnped. Idae 951

described so... ET DEE EEN 222

ORENSE? 00 1190957 ge de Ee 29
simplified, for lifeboat navigation______

table;ð 4s -erenlere civium nýt = 1218-1235

explanationjof 8e fm MN 1186

Trench, in ocean, defined De cuca 700

usexotiimmiloting- aem CC 258

Triangle(s), astronomical, defined...... 393, 912

circumscribed circle of 2200 1022
insenibedicircleofawts Ee ans tm 1022
kinds and properties of. 1022-1023
assparalielirulers.. 2. ama Tora 122
as pOly pond. sen site Aa ene? 1023
quadrantal spherical. AA EM 1039
Tight planes. ha nee dr hs 1022
nghbsphercaldsdead ónt mas 0 ri 1039
similar, equal, and congruent; defined... 1023
Solutions LOA A UE 1037-1040
spherical defined Sa Eeer 1029
(See also Spherical triangle)
Triangulation net, defined______________ 854
(niggersienalsss septs o co A 309
Trigonometric functions, defined ________ 1032
invero- aLr Paws pl str EE 1037
INAVarious quadrants? a see ae 1034-1036
Trigonometric identities.__.____________ 1033
Trigonometry, logarithms of functions,
table 33 nso lisas fne beh deer ieee! 1376-1420
explanation of pra leer ase 1196
natural functions, defined__-__________ 1032
Galleys stat: Lal cai húkar had 1312-1356
El ee 1196
principles ofa: meta! es 1031-1040

solution, of oblique plane triangle__ 1037-1038

of oblique spherical triangle_________ 1040
of right plane triangle-..——-.----.-- 1037
of right spherical triangle----------- 1039
Trilateration net, defined__.___________- 854
¡Brimetrogonica mera c M 879
Trinity Houses water cs _gatb Re ect 28
Triple interpolation, defined- ---------- 1045
method or ennaa e E ien 1049
Triquadrantal spherical triangle, definition
and solution Of2 sese som sð eee 1039
Tropic, of Cancer, defined_____________- 372
of Capricorn, defined? — = se 373
Tropickeurrentk gest Aknee E 714
Eropicihigher Mu EE 710
Tropic lower low waters kjic ea 709
ropicsrange, defined ^ ^os 951
Tropic tides. cet abs meten e id 706, 951
Hiropienlleyclonese A 819-833
arol Se. EE eer 825
centeriotHlocatina iem 826
maneuvering to avoid________---- 828-832
coastal effects #2. sees islas datets 832
dangerous and navigable semicircles of. 828
defined Vel pa dre Erase 951
described: =: seize. dot den Rub lerri 805, 819
life'eyclesoftsxn bte rente qe Deni ze
locating, and tracking ofi- -L 824
bvēradāres o. data foc 828
Maneuvering rules ete 832
occurrence-of;sareas-Of ge E sA 819
season and frequency of_----------- 820
origin and development of_-_-------- 823-824
DEE E Lee 825
StOMMBURACK EEN 820-823
theories of formation «m een ee 824
tidesMrommeseset A uc 832
AMES ronem umm m e S ð 833
Bropicalyeare=a ral ataner esta E 370
Tropopause, defined 1.121 rcc 793
hei gto fee ce 92 360

1520 INDEX

Page
(«Lropospherel-s-5---- 2 NE 358—360, 793
Trough, of radio wave, defined---------- 290
Of water waves og M d.
True, Clarence H.; sight reduction dia-
aq RR Ent I d 561
True amplitude, defined__-__------------- 951
True azimuth, defined sss) IN 951
"rue" bearing, defined 5-9 ee 241, 951
Truexcourse, defined? 3099 mp UN 951
True heading, defined------------------ 951
Trúermotion radar -mesna N 319
Airuetnorth,tdefiiedss S SALA CN 951
True windrdefined s A 770, 951
(See also Wind)
Truncated cone, defined---------------- 1027
Truncated pyramid, defined____________ 1026
TSUNAMI dra DES. OM VA 733
defined ar rima Kung MF Jue O MP 951
epicenten of sat Sr mr NM 733
radio warnings Olja. esse EE 100
Tsushima currente MM NOD 723
Tüfa defined. Hen EE deu TOR 109
A e M 612
Lurning buoy, defined: A 951
Turning characteristics of vessel, allow-
aee Tor A JT AO 276-278
Tuve, Merle A. ` origin of pulse ranging__-. 58
Twilight, astronomical, defined... .. 368, 912
civil defined ME o. eor 368, 917
computational formulas _ 11 MAA 642
definitions) of a O. AS 368, 951
duration of- me rn M 369
inspolar/regionss-- Sonn 640
ALTO VIJ KCI LLU NESEN 32 ed: ĒKA 478
nautical .defined Pet 368, 937
timet by almanacs see ee se ERN 474
inipolar regions Senai TO 640
WOTk formas: ANAL uut 1057
Twilight compass, defined____________ IEC Sl
explained ie. mē: mesti Get ADO TREE 627
(win klirig to S8 ta EE er? 575
¡Typhoon Teei . DocPeb SPIRE 820
U-shaped.errorb.- susu aetas gen 682
Ultra high frequency, defined... 951
Ultrasonic depth finder--.............. 28, 133
defined... =2-a2 5 DM IEVADI 951
(See also Echo sounder, Sounding ma-
chine)
Ultraviolet; defined “ARA 51
Uncertainty, circle of... 20 685, 916
Uncorrecting, compass error... 168
enned- 2 2 ce L cas c NLIS AR 951
Undercurrent, defined T ER 951
Underwater navigation, defined... 62, 951
Underwater obstacle detection. |... 105
Underwater sound M 742-745
(See also Sound)
Unfavorable current, defined... 951
nidireetional, defined............ wm 952
Uniform Cardinal System of buoyage_____ 977,
981-982
Uniform Lateral System of buoyage.... 977—980
Uniform System of buoyage.______ 976, 977, 982
U. S. Air Force, Aeronautical Chart and
Information Center, publications of____ 94,
100, 1003
U. 8. Coast and Geodetic Survey, charts
and publications of... 94, 1002-1004
electronic position indicator of __ 330
founding ofr S 30
functions. of... 7.2 ES 93, 96

Hydrographic Manual (Pub. No. 20-2) . 848

Page j

U. S. Coast and Geodetic Survey— Cont. :
ISOMARNEIC charts of c EE 162
tide and tidal current predictions of__ 268-269
U. S. Coast Guard, functions of_________ 98

ice patrol'ofeseecem rc 758
Lists oj Lights opcm A A 261
maintenance of aids to navigation by__ 261
maintenance of fog signals by_________ 266

publications of... —— 94, 101, 102, 1003, 1004 `
U.S. Corps of Engineers, district offices of,

charts published by----------- 94, 1002-1004
U. S. Geological Survey, publications of. 94
U. S. Lake Survey (see U. S. Corps of En-

gineers)
U. S. Naval Observatory, establishment

ii er MAR Ri E. 51
functions of 35:5 Los nana M 93
issuance of first American Air Almanac Re

by:25-.coktecoon- EE D ee
publications of. -—------—- 94, 466, 1002-1004 .
time signals 0f 1... 722 súa MEM 492 `
U. S. Naval Observatory and Hydrograph-
ical Ofice,.history-0f = ES eee 31
U. S. Navy Fleet Weather Central____.. 815

U.S. Navy Hydrographic Office, agents of_ 94

branch:offices osse 2425 Saba TEN 94
charts and publications of... 93, 1002-1004
(See also Hydrographic Office publica-
tion (s))
functions gf a. AAA 93
history: of - = = 4283-12 PORN 31
ice forecasts of 20021 PESA AS 762
isomagnetic charts of == PUSE 162
publications of (see Hydrographic Office
publication(s))
U. S. Navy Training Device Center, sight i
reduction method Of EEE SSS 565 7
U. S. Weather Bureau, publications of... 94, |
1002-1004 `
Units of measurement, ancient__________ 26 A
of angles. 5 d abi neturtoleh Audi 1031 `
Of area --- ..- C. ner sete d AREA 954 =
centesimalsystem--------- NA 1031
chart symbols. for: crre. ERa 986 .
conversion factors. m 954-962
of density asi danes o NE 696
A A n MEER 765
of frequency s. aru. IDA so HEN 290 *
of Denk, ge =d. LSU. sud 10 VON 776
history of aere 1220504 4 IA 26
of length, conversion factors__________ 958
depths EEN 27, 124, 999
distancias Laila IE 26, 65, 124
SEELEN 351-353
(See also Distance, Mile)
of magnetic field intensity, gauss____ 203, 926
Oerpted “en = ESIA 161, 938
of magnitude (stellar) -2 AA 353
of pressuresot . o meh. erede d 696, 765
conversion of, table 14_____________ 1264
explanation ot TT 1190
sexagesimal system. Sana 1031
of specific heats croi. ccelo ASM 698
oftipecd =e Two. r c. ` 25, 66, 124, 673
of surface tension. T Ut aed 698
of temperature: Cod det NOU 715-116
conversion of, table 15_____________ 1265

INDEX 1521

k Page Page
Units of measurement—Continued Vermierpdefinedizc!.. Uses bupceteitons 952
DEUS mee eame en Sere signe en JU 483-484 reading ofse 23522. ab bite gu 406
conversion f actors. Toe eee anu 954 of sextant 120251. .... .baafeb. smt 400

of Volume cue sei Sc 11 7: La 961-962 ` Vernier sextant.......bsnüsb 23601 sia 401; 952
of wave length, radio. Ee su dd 290 Verrazano, great-circle voyage of... 30
Universal plotting sheet, defined________ 952 Versed cosine, defined... 2. 1032
(See also Plotting sheet (s)) Wersedisine, defined malo mae J 1032

Universal Polar Stereographic grid_______ 91
375, oo 952
6

Universal Transverse Mercator grid_____ , 91
Upper air, observations of... 785
Ebert fuere snnicijeam h od * 787

Upper air sounding, defined_____________ 952
Upper branch of meridian, defined.. 63, 382, 952
802

Pepper dronb eon xev dbm la due.

Iubpenlumbsifec uu mc-- ERIT 402, 952
Upper transit, defined. .:: 2: :- 1126 383, 952
Winrush ofewaves ec se ccs eni dira 738

UPS (Universal Polar Stereographic) grid. 91
Uranus; discovery of: 19 "inu 340% vibe 39

flea tures (Of asec bah. MOLI. 362
(See also Planet(s))
Uribe-White, Enrique; sight reduction
methodfofise 45.5 EI. Siero! pere ee ts ys 550
WBSRS polanistation(ofsē <. see 692
USSR Tables, sight reduction tables... 539
UTM (Universal Transverse Mercator)
FNLS S eR CR 91
Webantidefined ss 4 4 a aiaa 952

Vacuum tube, development of... 4158
Variable, defined
VEER o TTT ee ee ee
Variation, aerial geomagnetic surveys of,

establishments me ese ese 31

annual change of, on charts___________ 164
anpiicationoiam O n 168
charis'ofjdesctibed? V e 2 100, 162
(See also Chart (s))

den a m 164, 952
determination of longitude by_________ 44
dijamnalfchange:of P VF V VT Pn a 161
fu (001 D o. e T 100, 162, 618, 928
DIstoryko[ TT MEL, ea e eg 23-24
irregularities of, on Charts-------==--- 164
magneticnaenneds ss ES. 161, 935
position determination bn... 659, 660
seculanichange ofa rcm 161, 164
(See also Grid variation)

Variation of latitude (longitude)--------- 7370

Veater, altitude and azimuth by map

projeccion T Seemann wen eor E 560
Vector(s), addition and subtraction of____ 1016
AEREA ate s erc 952, 1016
ofidistance (velocity). CL 101
AAN IN E ee 1017
of£reintrvetspeed sese eee ee 327
Wectomaaeram, cdeHnede 9 us a 952
Vector quantity, defined" `` `” 222 -- 952
Ven, RUE EE 805, 952
Vehicle direction and position indicator,
inslandinavigatiQnec e ecc 665
Weloeitysdefined- y 5e mete aem. ed 952
Velocity ratio of tidal current_-------- 274, 952
Velocity vector uscrofe= eT n m 1017
Menus$featurestof 222 BUDE eT og e 360
OLD ts0f UE es ERA JE Sun 375-376
(See also Planet (s))
Wermalsequinox, defined. T 371, 952
other mames dor. ce ave vo 373
as sidereal time reference--------2---- 375

IMernier4Pierre-e-—- eee nre ELI) 48

Mersinexdefined.--:-.:.-.-z..- iin 952, 1032

Vertex, of great circle, defined__________ 229
of-parabolac. <. 1 > ll. lllo POR t 1028
ot$trianglewdefinedā-€--. -- Ē-- EN 1022

Vertical, deflection of 2.222222 2222 358, 381

EE me AA a se 921
effectiot, upon altitude: S1020 E 427
prime vertical circle, defined________ 385, 941
principal vertical circle, defined... 385, 941

Verticalbanglemdefincd ts Sastre 1021
distance by, table 9_.....69_228 w 1255-1259

explanation ofa ae Yan AE E 1188

Vertical icircle, defined Sasou samt mMm 385, 952
prime defined Mee 385, 941
prineipalWdefined -Ten ae mi 385, 941

Vertical danger angle----2-2 22222022. 257

Vertical datum, defined_.______________ 892

Vertical force instrument, deseribed____-- 188

Vertical intensity, earth's magnetic field. - 161
Vertical method, of double interpolation__ 1049
Vertical photography, procedure for... 874-879

Vertical projector, for chart construction. 888
Very high frequency, defined____________ 952
Very low frequency, defined- ----------- 952

Vespucci, Amerigo; determination of longi-
tade py Sen AN. ss ta ada MO E 45

Vibratory gyro, principles of... 11L 142
Vigia defined 40 pem. 952
Vilkitskiy, A. A.; device for reduction to
Meridian) rg EE 518
Vimeiālieonārdosdass<=ssss= <=: M 17
World:map-0fr- DIGNE ad 20
Virtual PPI reflectoscope- 20422 im 324
Viscosity: of sea, waters == cO EE 697
Visibility, charted, defined-------------- 916
circle of defined sss FOR gm 917
defined s-o nssr ea MD? ESTA PO 39 952
Of lights woe er. BO cq 261-264
computation 01. A 263-264
measurement Of = Ce 785
radiustofo-defined see EN 943
range of defined sese pum 943
Visible horizon, correction of amplitude
for tabler"28 &.0998909 00 19990. qa 1297
explanation KEE 1194
defined Hadas rtm ¿IDAS 952
discussed «s PREDIO. AA 386
Visual control, in surveying------------- 857
Visual flight, defined — — "e eer 670
Visual Wave Observations (H.O. Special
Publication 44) 22 eet e ST 732
Voigt Orion, instrument. 2 ce 564
Volume, conversion factors. ---------- 961-962
VOR range (see Omnirange)
Vortac, air navigation system. ----- 59, 317, 674
VOTtaciTan ge des I ur o HE e 308
Vucetie, Tamara; ““Toposcope” of 3 564
Vulgar establishment----------2-22-- 709, 952
EE d 22
Waghenaer, Lucas Jans Zoon; The Mari-
UCTS VIO ZONA AT AR a 22
Wainwright, Richard; azimuth table of... ta

Wakeley, Andrew; azimuth tables of_----
Walker Thomas cara 43 C7 25
Weallottheteye or storm ss ss
Waller, George W. D.; sight reduction
methodo ee enr NM uu e

1522 INDEX

Page
Walther,Bernhard_.: =- == == S 36, 49 Wave(s)—Continued
Waning of moon, defined--------------- 378 standing xc ec eee ee
Martumexdefinoed 20 eae 952 storm waves, defined..............-
Warm air mass, defined____------------ 952 described-....-- == sis sees ce SMS
Warmfront; defined SS te se ec 801, 952 tidal... os... Poe. SE A
M arm sector---.- el Meta es 802, 952 tide. ¿e bet E Ee
Watch, comparing, defined. - ----------- 918 from tropical cyclones:1 2:22 ee
described? tē Masi e 419 tsunamis Tet sida sso nee ELE. e
error Ofan de f ds 419, 492—494, 952 types OË e ees ee mE
hack defined 4202-22 "rites 929 üprush oft: sort non ee
Tatafa ne tn a aði n nn eee ni 419, 952 wind wave, defined_-_----------------
resetting of, In lifeboat. 9-353: = 660 (See also Amphibious operations, Swell)
US CIO LM EE 419, 492-494 Wave crest, defined isn inisa 222092222
Watch buoy,defined2-——-5-- 2222: e sae 952 Wave direction, defined Czene aeea
Wiatehverror.—_ ys «des 419, 492-494, 952 Wave front, of radio wave, defined_------
Wateh raterdeñnedice do doe sere 952. v WaverheéightJ. 25.011 Eege
Watchtime: "L sr. E ag 492,952 Wave height correction_-------------
Usefoffā m and PM_.... £ dal e dede 483 ¿Wave length,dēfined_ 2-2 2425535
Watch tower, chart definition of--------- 115 and frequency, interconversion of
Water, fresh, from young ice------------ 752 of radio wave, units of. 20-22
E A A A E ee 962. "Wave period, defined. dee
(See also Sea water) ` Wave train, defined ` 20 .32221 $6283
uH o e, dynamic, measurement of 15 Wave trough, defined__-.-_-.--_.--------
C2 rs E S Waxing of moon, defined $
Water sky. so lysti sl waren d tm pepe 759 a hace Aa AA
Watercote proof, define dina - sa nette Kut Sam 888 Way point, In air navigation ------------
erennere balear 813-814 Weather, air masses, types of-----------
Watson, William; development of Leyden Har SE FES
jar A IA ales, GEA A 58 in doidrums.-.. ~--------------------
Wave(s), in amphibious operations. ... 737-741 effert.of, upon DE
boundary. SE E APR et 735 | SPP ECH GE |
reakingtOftenstüsimeradeh Zeep À kei 731 elements and circulation. ...........
CAUSES Of eL MC ENERO. MM 297 forecasting =.= =~ TET D d
characteristics of e n n RT LEE 727-730 frontal surface, defined OS :
eonvergence.0f ee MR 737 in horse latitudes S T CEE
crest and trough of, defined_________ 727, 953 influencing Of => I- S ES |
MS AS NE : 727 information on, dissemination of. ...... 817
denned E IRA 727. 953 interpretationof Sok SE AA 817 $
directedelinods pita. da co EE ee 799 —
direction of, defined___________ 922, 949, 953 Navy Fleet Weather Central......... 815 @
divergence or AA O AT 737 observations of:--s._3. SRS TEE 765-792 —
Glee of, OC shiplos Sk Ranes ZE 735 in polar region TO er 614 $
effect of beach upon. ` site de. 7 in roaring: forties o 798 _
effect of currents upon... pat trade vindea TS SS S 797 3H
eed of ET e ao eT Veco ates A (see ee
eftect of wind Upon. -ene EE 774 ee also Atmosphere, Cyclone, Storm)
SITTERS Ee 731 Weather Bureau (see U. S. Weather Bu-
teal of, defined: ic dem. Magia deus 727 reau)
RL t. Pe A eet Die Weather Map... os
ground, defined III 394908 defined aa
group velocity of, defined------------- 729 Weather Observation Sheet, Shi
er GE altitude correction for_____ F nee Weather observations, SE pres- d
indirect, defined "O81. atu cedo EUN EORR (oder dM
internal cis M Wu. C ERAS 735 auto EL at TYDER Ee r 775-778
length of, defined____...__.-.-._... 727, 953 od 1 cod heitin 788
measurement of, from ship_-----.-_---- ' 732 humidity eight hoo ais d nds
IMICTOSCISINS See. = TT S PT Sire Sane REN READ Se pe CS TTT A
olor Luse orn. EE EE: poop cc n IE 788
oscillatory defined. ee eee y TAGar------.-.----------------. 59, 788
, ` eee 730 recording of sau nee 788-79
path of water particles during passage__ 730 sea state: LS SĒR Ó
period of, defined________ 27 o n 773-775
radio, defined... 7700. "042. ule nee od
frontoi šai el 2. PIRE P E B.l----1-00--L.-.-2
(See also Radio waves) = ` zuo cin inr ok hE | TT 785
refractions Olas. Ie. ee 731, 73% «Weather rev a RN 769-775
seca Ee ' 734 eather reports, broadcasts of... 96, 100
seismic sea, defined... om 833, 945 iii ike Rolie Proa donata)
epicenter EE ER enisignabsdellnede AA 953
and shallow water 19 Weather station, automatic... ... 788
significant heigbvo oe E E Weather Station Index (H
ex. (H.O. Pub
iet n 730 .O. Pub. No.
QUIC geared 0 705 A 947 119) contents of___________ 97
ee also Loran, Radio waves) 3 Weather avimbole ak EECHER
? ymbols ie Ue N ae
sound wav ess defined u nuin ou ME 947 Weather vane, defined 777 e

INDEX

Page

Weber, Wilhelm; reflecting galvanometer
GN. o DEM ET OMM PORE 58
Weems, Philip Van Horn; Air Almanac of_ 52
Eine of- Fosition Book of--..-........8
Lunar Ephemeris for Aviators of_._____- 52

IMannuseript^Tablessof-----..... 4990 Lu 536
New Line of Position Tables of_______- 536
EPolar Computer". of = .222.22<.esce! 563
SecantóTome-Sight-0f=2 22 eben. 526
sight reduction tables of--------- 57, 526, 534
Stared livtude. Curves of NE Noda 56, 562
Weir, Patrick; azimuth diagram of_______ 572
Werner, John; lunar distance___________ 45
West Australia current 22 C 725
West Greenland cürrent---------------- 122

EU EE 723, 725

Diesunptdefinēd oss s A O 953
Wet-bulb temperature (thermometer)____ 779
Whistle, as fog signal, defined___________ 267
Whistle buoy, defined_________________- 265
Whiteside, Henry; lighthouse of... 28
Wilkes, Charles; explorations of... 691
installation of transit instrument by... 51
Survey of, for frst H.O: chart----222-2 31
Wilkins, George Hubert; oceanographic
ET EE 692
Willis, Edward J.; sight reduction method
A TE ees 551-554, 565
TU ue MU costes 807
Will m = pr DC 820
Wimperis, H. E.; nomogram of. 556-557
NindYanabatica e E Le Ln 806
ancientinames ford wee e ne 23
apparent, defined SS es a. 770, 911
Beaufort scale of: = t 774, 914, 1059
GAUSESTOL MES TT im Ē a Bee oe 794
TAT o PS e OS 793, 953
direction; defined 222 2302.2022 922, 953
effect of, upon aircraft =-------------- 672
upon refraction. = E 432
upondde*-- ede ce TT c 711
UDODĒWAVES SSS EE E 774
iairiwindsdefinedē EE 924
A erre S rm 807
favorable, defined ss E 924
veneralcirculānon=s ee L ke 794-800
Peostrophic* a ee ee ea te 797
oradien Vere d a 797
information on, sources Of... 97
AI AL EE 23
Netāstreamm=s si eure ue PA 794
katabatic= sen nee < 7 806
local types and names of___-------- 806-807
Vid oe cr 769-775
mistral ee eee CiU e S 16, 807
Mmpolar/ regions VTR eaa 629, 799
pressure gradient, defined. ----------- 797
preyallingwesterlles Ness ss eee 798
EEE Aa E eae S 773-775
SIT OC CO men MES LE C. des 16
Ped e E 797
SOTO W.eLIOL Winds tas ee e 23
bradeswind SE ees ee e 797
tuerdelined EE 770, 951

direction and speed of, table 10. 1260-1261

explanation ofo -c 2 2a

EE E DEE 770-773
Wind and Current Chart of the North Atlan-

VOKONIMauryi RN AES SE 31
Wind current, defined=---==22-22222==== 953
INNOCENTI ee ee 718
Wind direction, defined- 922, 953
Wind rose, of Aristotle- ` SE 23
TEE Ee lala 23
defined». ser yes = emerat. Zasa 953
olfEHratosthēnes = oe ene te 18, 23

Portolano eae a de 20

1523

Page
Wind, Sea, and Swell: Theory of Relations
for Forecasting (H.O. Pub. No. 601)... 96

Wind shift line, defined________________ 802
Wind triangle... 2. osc ee ong c ee 672
Wind vane... Muller M. 769, 953
Wind wave; defined:..2.:. sul eos 953
Winds aloft, electronic measurement of... 787

observation ofge sudo > 785
Winds of Aristotle... L 22... ge 23
Winter (season): 2.00 M mb ne 371
Winter solstice, defined______________ 371, 953
Wiping, defined: e ais Gens AUR 953

SUKVĒVSS0 VAS o c te ee ee oe 105

use of, in hydrographic survey.________ 860
Withdrawal of chart, defined__-_________ 888
Woods Hole Oceanographic Institution... 692
Work torm(s ee 1052-1058

azimuth by H.O. Pub. No. 260________ 1057

leh Lal oO PUDA INO), Genee 1057
bysHeOSPubSNoX2]4 0 1056

EE 1053

Mercatorisa lle 1053

moonrise and moonsets ------------—- 1058

sextant altitude corrections___________ 1054

sight reduction, by cosine-haversine for-

Mula oa c ODER ANNE 1056
PARO Ei D ANO A 1055
bya OS PUb eNO SEH AA 1055
latitude EE 1056

sunrise, sunset, twilight. ------------- 1057
World Atlas of Sea Surface Temperatures

(ELO SEU NO 225) A 695
World Geographic Referencing System

(Creoref) SMF SEE Ee 91
World map(s), of Leonardo da Vinci..... 20

of Middle Ages ss sed eee 20

ofebtolemyeec O A ee ee eee 19
World Port Index (H.O. Pub. No. 150)... 101
Wreck, chart symbol for! se =e. 110
Wreck Duoy defined assess = === eee 266
Wren, Christopher; establishment of

Greenwich Royal Observatory- ------- 50
Wright$lidward BS 2 ses S 21

Certatne Errors in Navigation Detected

andsáCorrected;ot sann 22, 30, 34
“Wrinkles” in Practical Navigation, of

DECANO A C 34
W WV, radio propagation signals. ....... 633

Gg teuren Gg, ees 492
band deincd A 953
Ward, conversion factors EE 958
Year, astronomical significance of... 374

kindskof ans e ae 370

conversion factors e cce E 954—955
Yonemura, 8.; sight reduction tables of__ 57, 530
Young, Leo C.; development of radar... 58
Young ice, defined = TR 953
Yunis Ibn; observatory Of ee eee T 38
Yustchenko, Azimuty Svetil (Azimuths of

Eelere 571
Z-marker, in air navigation -----------=- 675
Zacuto, Abraham; Almanach Perpetuum of- 51

decliinationttablesiol e 32
Zenith lee 384, 953

position of, by photograph............ 566
Zenith distance, defined. ------------- 385, 953
Zenith photograph, position by---------- 566
Zenithal projection, defined........ ---.- 70, 953

(See also Projection(s))

1524 INDEX

Page
Zerbee, Louis J.; sight reduction method of. 566
Zero, absolute; on Celsius and Fahrenheit

scales-c x A E Maka 959
defined rar, 3e m S gaļā 775, 909
Zhdanko, M.; azimuth tables of---------- 571
Zodiac; constellations of; names, meanings,
positiong-esdibis neni ca task: Atis: 974n
defined sees... savia O ARA 953
described: cosita Ee 374
symbols signs) ot... eee 906
Zodiacal Uerteel 365

Zone Auroral SEL E 162, 633, 913
skip PE 294, 947
time zone, defined--- 2232-22 aÐ US 487, 950.
torrid ee ne sie Ín es ee 37%

Zone description, defined____--------- 487, 953

Zone: meridiaN 322220... Al ds Ps 482, 487

Zone time, conversion tables for_________ 269
dēfinedš sc Ll ess Lee Tee oe eee 375, 953 `
time meridian for. EV Moa 482, 487, 950
PA PAE PRI 487-490 y]

Zooplankton, defined Šers E 701

U. S. GOVERNMENT PRINTING OFFICE : 1969 O - 353-583

q
H
p
ø
—
E a
= i
e > +
- a [2
b de Ni ,
" pan. a 3
"MJ

MON oa ee

s:
RTS See

sacar
Oé.
ES